// /

// / /

:

Yiming Lin

Yiming Lin

:

Hongtai Zhang

China Satellite Network Group

Co., Ltd., China

University of Luxembourg,

Luxembourg

Lianchong Zhang

Aerospace Information Research

Institute,

Chinese Academy of Sciences, China

Xiaopeng Xue

Central South University, China

Space: Science & Technology

( Special Issue )

CONTENTS

(1)

(3)

(17)

(33)

Editorial Entry, Descent, and Landing of China’s Tianwen-1 Mars Mission

Zezhou Sun, Wei Rao

The Tianwen-1 Guidance, Navigation, and Control for Mars Entry, Descent, and Landing

Xiangyu Huang, Maodeng Li, Xiaolei Wang, Jinchang Hu, Yu Zhao, Minwen Guo,

Chao Xu, Wangwang Liu, Yunpeng Wang, Ce Hao, and Lijia Xu

Study on Dynamic Characteristics of Mars Entry Module in Transonic and Supersonic Speeds

Qi Li, Rui Zhao, Sijun Zhang, Wei Rao, and Haogong Wei

Analysis and Verification of Aerodynamic Characteristics of Tianwen-1 Mars Parachute

Mingxing Huang, Wenqiang Wang, and Jian Li

Thermal Environment and Aeroheating Mechanism of Protuberances on Mars Entry Capsule

Wenbo Miao, Qi Li, Junhong Li, Jingyun Zhou, and Xiaoli Cheng

Numerical Simulation of Decompression Process of a Mars Rover in the Launch Phase

Weizhang Wang, Wei Rao, Qi Li, Hao Yan, and Rui Zhao

Ballistic Range Testing Data Analysis of Tianwen-1 Mars Entry Capsule

Haogong Wei, Xin Li, Jie Huang, Qi Li, and Wei Rao

Study on Effect of Aerodynamic Configuration on Aerodynamic Performance of Mars Ascent Vehicles

Qi Li, Wu Yuan, Rui Zhao, and Haogong Wei

(45)

(53)

(65)

(71)

1

MAIN TEXT

Launched into orbit on July 23, 2020, China’s first Mars

mission Tianwen-1 has implemented the key missions

of “near-Mars capture and brake,”; “entry, descent, and

landing (EDL),” and “rover leaving the landing platform”

successively in nearly one year. The three major tasks

of “orbiting around Mars,” “Mars surface landing,” and

“exploration and detection” have also been accomplished. At

present, the Zhurong Mars rover is performing exploration

and detection tasks as planned. For Tianwen-1, China’s first

probe landing on an extraterrestrial planet to carry out such

elaborate tasks, EDL is the risk point of the Mars mission

that is mostly difficult to accomplish.

This special issue focuses on various innovations in tasks

during Tianwen-1’s EDL phase and presents a collection

of original works by authors from higher education and

research institutions. Such institutions include Beijing

Institute of Spacecraft System Engineering, Beijing

Institute of Control Engineering, Beijing Institute of Space

Mechanics and Electricity, Beijing Institute of Technology,

China Academy of Aerospace Aerodynamics, and China

Aerodynamics Research and Development Center. The

total seven articles in this special issue cover a broad

spectrum of research topics concerning the first Mars

mission, including EDL control [1], analysis of the dynamic

characteristics of the entry module [2], design of the Mars

exploration parachute and its aerodynamic verification

[3], aeroheating mechanism simulation [4], simulation of

pressure equilibrium process [5], and test data processing [6].

It also involves technologies for aerodynamic characteristic

analysis of the Mars Ascent Vehicle (MAV) for future Mars

Entry, Descent, and Landing of China’s Tianwen-1 Mars Mission

Zezhou Sun, Wei Rao*

Beijing Institute of Spacecraft System Engineering, Beijing 100094, China

*Corresponding author. Email: rauwei@163.com

sample return [7].

Specifically, the team led by Xiangyu Huang and

Maodeng Li contributed a research article [1] on guidance,

navigation, and control (GNC) system for the EDL phase.

Deducing the GNC system design of Tianwen-1 inversely

from mission requirements, their article provided structure

and algorithm for a GNC system that fits those requirements.

The actual flight results of the whole EDL phase was also

presented in the article.

Considering the large blunt-nosed and short body of the

Mars entry capsule in terms of its aerodynamic shape, the

Mars aerodynamics team from China Academy of Space

Technology developed an integrated numerical simulation

method of computational fluid dynamics and rigid body

dynamics (CFD/RBD) on the basis of detached eddy

simulation (DES). this method was applied to study the

dynamic characteristics of Mars entry capsule in free flight

from transonic to supersonic release with one degree of

freedom (1-DOF) at a low angle of attack, from which the

influence of different afterbody shapes on dynamic stability

was discussed [2] .

Mingxing Huang’s team optimized and verified the

parachute design of Tianwen-1 according to the particular

open environment of the landing phase. Drawing on various

tests and data, the research team predicted and analyzed the

aerodynamic characteristic parameters of the parachute in

Mars conditions. In addition, the high-altitude flight tests

of nine parachutes were carried out in order to verify its

aerodynamic characteristics and reliability, serving as an

important reference for the Mars exploration parachute

design [3].

Wenbo Miao’s team investigated the thermal

2

environment of the interaction region on the heat shield

surface of the Mars lander. The flow characteristics of

interactions from protuberances at different parts of the

heat-shield were studied through numerical simulation.

The heating mechanism of interactions from protuberances

at different parts was also obtained by analyzing flow

velocity, pressure, Mach number, and other characteristic

parameters [4].

Rui Zhao’s team from Beijing Institute of Technology

numerically simulated the decompression processes of the

Mars rover to study the internal-external pressure differences

under a changing ambient pressure on the rocket fairing.

As for numerical calculations, PROFILE was developed

to outlet boundary conditions and to investigate the

influences of ambient pressure setting, time step, and grid

density to improve the accuracy of simulation results [5].

To further explore the transonic and supersonic dynamic

characteristics of the Tianwen-1 lander and rover and verify

the aerodynamic shape and mass property design, the team

also carried out free-flight dynamic simulations with the

free-flight ballistic range test model under test conditions.

The aerodynamic coefficients of the model were obtained

by linear regression. A dynamic derivative model was

constructed under assumed linearization with a low angle of

attack, and the static moment coefficient and the dynamic

derivative were thereby identified [6].

To meet the mission requirements of Mars surface

takeoff and ascent, researchers including Haogong Wei

and Qi Li from the Mars aerodynamics team analyzed the

aerodynamic performance requirements of the MAV. In light

of literature survey and the results of supersonic static CFD

simulation, the team analyzed the influences of the nose and

afterbody shapes of the MAV on the aerodynamic drag and

static stability. On this basis, they proposed a nose shape

with favorable aerodynamic performance and clarified the

subsequent improvement direction of the aerodynamic

layout. Their research provided necessary theoretical and

data support for the aerodynamic model selection of a

MAV [7].

To summarize, this special issue reviewed the exciting

progress in various fields during the EDL of Tianwen-1,

outlined the frontiers of related research worldwide, and

shared the thoughts and practices of Chinese scientists with

fellow researchers around the globe.

Competing interests

The authors declare that there is no conflict of interests

regarding the publication of this article.

Acknowledgments

We would like to further extend our gratitude to all the

authors for their research contribution to this special issue.

We also thank all the reviewers and the editorial team for

their support to this special issue.

References

[1] Xiangyu Huang, Maodeng Li, Xiaolei Wang, Jinchang

Hu, Yu Zhao, Minwen Guo, Chao Xu, Wangwang

Liu, Yunpeng Wang, Ce Hao, Lijia Xu, “The

Tianwen-1 Guidance, Navigation, and Control for

Mars Entry, Descent, and Landing”, Space: Science &

Technology, vol. 2021, Article ID 9846185, 13 pages, 20

21. https://doi.org/10.34133/2021/9846185

[2] Qi Li, Rui Zhao, Sijun Zhang, Wei Rao, Haogong

Wei, “Study on Dynamic Characteristics of Mars Entry

Module in Transonic and Supersonic Speeds”, Space:

Science & Technology, vol. 2022, Article ID 9753286, 1

5 pages, 2022. https://doi.org/10.34133/2022/9753286

[3] Mingxing Huang, Wenqiang Wang, Jian Li, “Analysis

and Verification of Aerodynamic Characteristics

of Tianwen-1 Mars Parachute”, Space: Science &

Technology, vol. 2022, Article ID 9805457, 11 pages, 20

22. https://doi.org/10.34133/2022/9805457

[4] Miao Wenbo, Li Qi, Li Junhong, Zhou Jingyun, Cheng

Xiaoli, “Thermal Environment and Aeroheating Mechanism

of Protuberances on Mars Entry Capsule”, Space: Science &

Technology, vol. 2021, Article ID 9754068, 8 pages, 202

1. https://doi.org/10.34133/2021/9754068

[5] Weizhang Wang, Wei Rao, Qi Li, Hao Yan, Rui

Zhao, “Numerical Simulation of Decompression Process

of a Mars Rover in the Launch Phase”, Space: Science &

Technology, vol. 2022, Article ID 9827483, 12 pages, 20

22. https://doi.org/10.34133/2022/9827483

[6] Haogong Wei, Xin Li, Jie Huang, Qi Li, Wei

Rao, “Ballistic Range Testing Data Analysis of

Tianwen-1 Mars Entry Capsule”, Space: Science &

Technology, vol. 2021, Article ID 9830415, 6 pages, 202

1. https://doi.org/10.34133/2021/9830415

[7] Qi Li, Wu Yuan, Rui Zhao, Haogong Wei, “Study on

Effect of Aerodynamic Configuration on Aerodynamic

Performance of Mars Ascent Vehicles”, Space: Science

& Technology, vol. 2022, Article ID 9790131, 11 pages,

2022. https://doi.org/10.34133/2022/9790131

Research Article

The Tianwen-1 Guidance, Navigation, and Control for Mars

Entry, Descent, and Landing

Xiangyu Huang,1 Maodeng Li ,

1 Xiaolei Wang,2 Jinchang Hu,1 Yu Zhao,2 Minwen Guo,1

Chao Xu,1 Wangwang Liu,2 Yunpeng Wang,2 Ce Hao,2 and Lijia Xu2

1

Science and Technology on Space Intelligent Control Laboratory, Beijing Institute of Control Engineering, Beijing 100091, China

2

Beijing Institute of Control Engineering, Beijing 100091, China

Correspondence should be addressed to Maodeng Li; mdeng1985@gmail.com

Received 15 July 2021; Accepted 14 September 2021; Published 16 October 2021

Copyright © 2021 Xiangyu Huang et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative

Commons Attribution License (CC BY 4.0).

Tianwen-1, the first mission of China’s planetary exploration program, accomplished its goals of orbiting, landing, and roving on

the Mars. The entry, descent, and landing (EDL) phase directly determines the success of the entire mission, of which the

guidance, navigation, and control (GNC) system is crucial. This paper outlines the Tianwen-1 EDL GNC system design by

introducing the GNC requirements followed by presenting the GNC system architecture and algorithms to meet such

requirements. The actual flight results for the whole EDL phase are also provided in this paper.

1. Introduction

Mars has atmosphere and surface environment similar to

the Earth, making it a prime target for deep space exploration. In order to investigate the Mars surface environment,

it is necessary to perform soft landing missions to place a

lander on the surface. Of the eighteen landing missions that

have been carried out, nine achieved a complete success.

They are Viking-1, Viking-2 [1], Mars Pathfinder [2], Mars

Exploration Rover [3], Phoenix [4], Mars Science Laboratory

(MSL) [5], InSight [6], Mars 2020 [7], and Tianwen-1 [8]. As

the first Chinese Mars landing mission, Tianwen-1 was

launched successfully at 12:41 p.m. Beijing Time (BJT) on

23 July 2020, and delivered its lander to the Mars surface

with a soft touchdown velocity and a stable predefined attitude

at 7:18 a.m. BJT on 15 May 2021. The successful deployment

of the rover on 22 May 2021 completed the mission’s goals

of orbiting, landing, and releasing a rover on the Mars.

The entry, descent, and landing (EDL) phase, which

began at the Mars atmosphere interface and ended with a

surface touchdown, is crucial for a Mars landing mission

and directly determines the success of the entire mission.

The success rate of mars missions is about 50%, and most

failures occur during the EDL phase [9]. The guidance, navigation, and control (GNC) system guarantees the touchdown safety and accuracy, playing an important role in the

EDL phase. Because of the time urgency of the EDL process

and large communication delay between the Mars and the

Earth, the spacecraft must perform autonomous GNC to

provide reliable key event triggers and accurate and reliable

state estimates and to implement accurate and reliable trajectory and attitude controls. Any mistake may lead to a mission failure.

The uncertainties such as Mars environments, parachute

descent motion, and initial state, the complexity of the EDL

process (multistage deceleration, many key events, etc.), and

the limited on-board computational ability bring great challenges to the design of EDL GNC system. To meet these

challenges, the GNC hardware should have a certain degree

of redundancy, and the GNC algorithms should be suitable

for on-board implementation, robust to sensor and actuator

partial failures, and adaptive to uncertainties.

This paper summarizes the Tianwen-1 EDL GNC design

by analyzing the EDL GNC requirements, presenting the

GNC modes and GNC hardware configurations, and finally

describing the EDL GNC algorithms. The flight results that

have validated the GNC design will also be provided.

2. Mission Overview

2.1. Tianwen-1 Spacecraft Configuration. To fulfill the goals

of orbiting, landing, and roving in a single mission [8, 10],

AAAS

Space: Science & Technology

Volume 2021, Article ID 9846185, 13 pages

https://doi.org/10.34133/2021/9846185

3

Research Article

The Tianwen-1 Guidance, Navigation, and Control for Mars

Entry, Descent, and Landing

Xiangyu Huang,1 Maodeng Li ,

1 Xiaolei Wang,2 Jinchang Hu,1 Yu Zhao,2 Minwen Guo,1

Chao Xu,1 Wangwang Liu,2 Yunpeng Wang,2 Ce Hao,2 and Lijia Xu2

1

Science and Technology on Space Intelligent Control Laboratory, Beijing Institute of Control Engineering, Beijing 100091, China

2

Beijing Institute of Control Engineering, Beijing 100091, China

Correspondence should be addressed to Maodeng Li; mdeng1985@gmail.com

Received 15 July 2021; Accepted 14 September 2021; Published 16 October 2021

Copyright © 2021 Xiangyu Huang et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative

Commons Attribution License (CC BY 4.0).

Tianwen-1, the first mission of China’s planetary exploration program, accomplished its goals of orbiting, landing, and roving on

the Mars. The entry, descent, and landing (EDL) phase directly determines the success of the entire mission, of which the

guidance, navigation, and control (GNC) system is crucial. This paper outlines the Tianwen-1 EDL GNC system design by

introducing the GNC requirements followed by presenting the GNC system architecture and algorithms to meet such

requirements. The actual flight results for the whole EDL phase are also provided in this paper.

1. Introduction

Mars has atmosphere and surface environment similar to

the Earth, making it a prime target for deep space exploration. In order to investigate the Mars surface environment,

it is necessary to perform soft landing missions to place a

lander on the surface. Of the eighteen landing missions that

have been carried out, nine achieved a complete success.

They are Viking-1, Viking-2 [1], Mars Pathfinder [2], Mars

Exploration Rover [3], Phoenix [4], Mars Science Laboratory

(MSL) [5], InSight [6], Mars 2020 [7], and Tianwen-1 [8]. As

the first Chinese Mars landing mission, Tianwen-1 was

launched successfully at 12:41 p.m. Beijing Time (BJT) on

23 July 2020, and delivered its lander to the Mars surface

with a soft touchdown velocity and a stable predefined attitude

at 7:18 a.m. BJT on 15 May 2021. The successful deployment

of the rover on 22 May 2021 completed the mission’s goals

of orbiting, landing, and releasing a rover on the Mars.

The entry, descent, and landing (EDL) phase, which

began at the Mars atmosphere interface and ended with a

surface touchdown, is crucial for a Mars landing mission

and directly determines the success of the entire mission.

The success rate of mars missions is about 50%, and most

failures occur during the EDL phase [9]. The guidance, navigation, and control (GNC) system guarantees the touchdown safety and accuracy, playing an important role in the

EDL phase. Because of the time urgency of the EDL process

and large communication delay between the Mars and the

Earth, the spacecraft must perform autonomous GNC to

provide reliable key event triggers and accurate and reliable

state estimates and to implement accurate and reliable trajectory and attitude controls. Any mistake may lead to a mission failure.

The uncertainties such as Mars environments, parachute

descent motion, and initial state, the complexity of the EDL

process (multistage deceleration, many key events, etc.), and

the limited on-board computational ability bring great challenges to the design of EDL GNC system. To meet these

challenges, the GNC hardware should have a certain degree

of redundancy, and the GNC algorithms should be suitable

for on-board implementation, robust to sensor and actuator

partial failures, and adaptive to uncertainties.

This paper summarizes the Tianwen-1 EDL GNC design

by analyzing the EDL GNC requirements, presenting the

GNC modes and GNC hardware configurations, and finally

describing the EDL GNC algorithms. The flight results that

have validated the GNC design will also be provided.

2. Mission Overview

2.1. Tianwen-1 Spacecraft Configuration. To fulfill the goals

of orbiting, landing, and roving in a single mission [8, 10],

AAAS

Space: Science & Technology

Volume 2021, Article ID 9846185, 13 pages

https://doi.org/10.34133/2021/9846185

The Tianwen-1 Guidance, Navigation, and Control for Mars

Entry, Descent, and Landing

Xiangyu Huang,1

Maodeng Li,1

Xiaolei Wang,2

Jinchang Hu,1

Yu Zhao,2

Minwen Guo,1

Chao Xu,1

Wangwang Liu,2

Yunpeng Wang,2

Ce Hao,2

and Lijia Xu2

1

Science and Technology on Space Intelligent Control Laboratory, Beijing Institute of Control Engineering, Beijing 100091, China

2

Beijing Institute of Control Engineering, Beijing 100091, China

Correspondence should be addressed to Maodeng Li; mdeng1985@gmail.com

Abstract: Tianwen-1, the first mission of China’s planetary exploration program, accomplished its goals of orbiting, landing, and roving

on the Mars. The entry, descent, and landing (EDL) phase directly determines the success of the entire mission, of which the guidance,

navigation, and control (GNC) system is crucial. This paper outlines the Tianwen-1 EDL GNC system design by introducing the GNC

requirements followed by presenting the GNC system architecture and algorithms to meet such requirements. The actual flight results for

the whole EDL phase are also provided in this paper.

4

the Tianwen-1 spacecraft consists of an orbiter and a descent

module, as shown in Figure 1, where the descent module is

composed of a heatshield, a backshell, and a lander that consists of a landing platform and a rover.

2.2. Mission Profile. Figure 2 illustrates the mission profile of

the Tianwen-1 [8], which is divided into five stages: EarthMars transfer stage, Mars orbit insertion stage, Mars orbit

parking stage, deorbit and landing stage, and scientific

exploration stage. In the former three stages, the orbiter

and the descent module form as a single probe. In the deorbit and landing stage, the descent module is separated from

the orbiter and then will enter the Mars atmosphere a few

hours later, starting its EDL process. With deceleration of

Mars atmosphere, parachute, and the main landing engine

(MLE), the lander lands on the Mars surface softly. And

after a few days, the rover is released from the lander for scientific exploration.

2.3. EDL Sequence Profile. The EDL sequence profile of the

Tianwen-1 consists of atmospheric entry, parachute descent,

and landing phases.

The atmospheric entry phase begins when the vehicle

reaches the atmospheric boundary of Mars (at an altitude

of approximately 125 km) and ends in parachute deployment at a specified value of navigated velocity. During this

phase, Tianwen-1 performs a guided lifting entry at a liftto-drag ratio of 0.13 with a nonzero trim angle-of-attack

(AOA) and then deploys the trim wing at a specified navigated velocity. With the effects of the trim wing, the trim

value of the total AOA is secured suitable for the parachute

deployment.

The atmospheric entry phase is followed by the parachute descent phase, during which the heatshield is first jettisoned at a specified value of navigated velocity, and then

landing radars begin to work such that the vehicle’s altitude

and velocity with respect to the Mars can be measured.

When the vehicle reaches its stable descent velocity and

the navigated altitude and velocity are deemed suitable for

terminal braking within the available propellant budget,

the descent module releases the backshell and ignites the

MLE, implying that the landing phase begins.

The landing phase is also known as the powered descent

phase. In this phase, the lander performs a velocity reduction

via the MLE, executes a backshell evasion maneuver, when

necessary, selects a safe landing site, and finally lands on

the selected landing site safely to achieve the soft landing.

3. Overview of the EDL GNC System

3.1. GNC Requirements. The GNC system requirements for

Tianwen-1 EDL process are as follows:

(1) Key events, such as trim wing deployment, parachute deployment, heatshield jettison, backshell separation, MLE ignition, and touchdown detection,

should be triggered properly

(2) After backshell separation, the lander should not be

collided with the backshell

(3) The actual landing site should be selected on-board

within the preselected landing area

(4) The lander’s touchdown attitude, angular rate, and

vertical and horizontal velocities should meet the

requirements

(5) The fuel consumption of the EDL process needs to

be within a reasonable range.

3.2. GNC Modes. According to the EDL process profile and

GNC requirements, the EDL process is divided into eight

GNC modes: the AOA-trim mode, the lift control mode,

the parachute descent control mode, the powered deceleration mode, the hover and imaging mode, the hazard avoidance maneuver mode, the slow descent mode, and ended

with the no-control mode. The transition of these eight

modes is shown in Figure 3.

In the atmospheric entry segment, the GNC system

operates with the AOA-trim mode initially, in which the

descent module’s attitude is adjusted to a predefined attitude

for guided lift entry. Once the sensed acceleration magnitude

exceeds 0.2 Earth g, the lift control mode is activated to produce proper lift to control the entry trajectory.

With the deployment of parachute, the GNC system

switches to the parachute descent control mode and uses this

mode throughout the whole parachute descent phase. In this

mode, the descent module’s velocity would descent to about

95 m/s at an altitude of about 1.2 km above the Mars surface.

In the landing phase, the GNC system operates with the

powered deceleration mode, hover and imaging mode, hazard avoidance maneuver mode, slow descent mode, and

ends at the no-control mode when the lander has softly

touched down. The powered deceleration mode begins with

the backshell separation and ends before hover. The main

task of this mode is to use the MLE to reduce the lander’s

velocity, to avoid collisions with the detached backshell,

and to image and select a wide safe landing area for coarse

hazard avoidance. In the hover and imaging mode, the

lander maintains a hover state to take 3D images of the landing area and then selects a safe landing site. Once the landing

site is selected, the GNC system switches to the hazard

avoidance maneuver mode to perform hazard avoidance

and descent such that the lander would descent to 20 m altitude above the landing site with a zero horizontal velocity

and a preset value of vertical velocity (about 1.5 m/s). Then,

the GNC system switches to the slow descent mode. In this

mode, the lander slowly descends at a preset speed, eliminates the horizontal speed, and maintains a vertical attitude.

Once the lander’s touchdown is detected, the GNC system

sends a shutdown signal to turn off the MLE and then

switches to the no-control mode, in which no further orbit

control and attitude control are performed any more.

3.3. GNC System Configuration. The EDL GNC system

scheme is illustrated in Figure 4, where sensors, actuators,

and the GNC computer will be described in this subsection,

and the GNC algorithms will be presented in the following

sections.

2 Space: Science & Technology

3.4. Sensors

3.4.1. Star Sensors. A pair of star sensors working from the 8

hours prior to orbiter/descent module separation to 10 seconds before atmospheric entry are equipped for attitude

determination.

3.4.2. Inertial Measurement Units (IMUs). A pair of IMUs

are carried out, each of which consists of three orthogonal

accelerometers and three orthogonal gyroscopes to measure

the specific force and angular rate, respectively. During the

EDL, the IMUs are used for inertial navigation and key event

triggers.

3.4.3. Landing Radars. A microwave radar and a phased

array sensor (PAS) are configured to provide Mars-related

measurements. The microwave radar contains four beams,

each of which works automatically. The PAS contains nine

beams, four of which are selected by the GNC system to provide measurements at every measurement time. Every beam

for the two radars can measure slant-range and groundrelative velocity along its axis simultaneously.

3.4.4. Hazard Avoidance Sensors. Two hazard avoidance sensors are equipped for hazard avoidance and landing site

selection. One is called the optical obstacle avoidance sensor

Tianwen-1 probe = Orbiter

Orbiter

+ Descent module

Descent module

Backshell

Rover

Landing platform

Heatshield

Figure 1: Main components of the Tianwen-1 spacecraft.

Scientific exploration stage

Mars parking stage

Mars capture stage

Earth-mars transfer stage

Deorbitand landing stage

Figure 2: Mission profile of Tianwen-1 [8].

Space: Science & Technology 3

5

the Tianwen-1 spacecraft consists of an orbiter and a descent

module, as shown in Figure 1, where the descent module is

composed of a heatshield, a backshell, and a lander that consists of a landing platform and a rover.

2.2. Mission Profile. Figure 2 illustrates the mission profile of

the Tianwen-1 [8], which is divided into five stages: EarthMars transfer stage, Mars orbit insertion stage, Mars orbit

parking stage, deorbit and landing stage, and scientific

exploration stage. In the former three stages, the orbiter

and the descent module form as a single probe. In the deorbit and landing stage, the descent module is separated from

the orbiter and then will enter the Mars atmosphere a few

hours later, starting its EDL process. With deceleration of

Mars atmosphere, parachute, and the main landing engine

(MLE), the lander lands on the Mars surface softly. And

after a few days, the rover is released from the lander for scientific exploration.

2.3. EDL Sequence Profile. The EDL sequence profile of the

Tianwen-1 consists of atmospheric entry, parachute descent,

and landing phases.

The atmospheric entry phase begins when the vehicle

reaches the atmospheric boundary of Mars (at an altitude

of approximately 125 km) and ends in parachute deployment at a specified value of navigated velocity. During this

phase, Tianwen-1 performs a guided lifting entry at a liftto-drag ratio of 0.13 with a nonzero trim angle-of-attack

(AOA) and then deploys the trim wing at a specified navigated velocity. With the effects of the trim wing, the trim

value of the total AOA is secured suitable for the parachute

deployment.

The atmospheric entry phase is followed by the parachute descent phase, during which the heatshield is first jettisoned at a specified value of navigated velocity, and then

landing radars begin to work such that the vehicle’s altitude

and velocity with respect to the Mars can be measured.

When the vehicle reaches its stable descent velocity and

the navigated altitude and velocity are deemed suitable for

terminal braking within the available propellant budget,

the descent module releases the backshell and ignites the

MLE, implying that the landing phase begins.

The landing phase is also known as the powered descent

phase. In this phase, the lander performs a velocity reduction

via the MLE, executes a backshell evasion maneuver, when

necessary, selects a safe landing site, and finally lands on

the selected landing site safely to achieve the soft landing.

3. Overview of the EDL GNC System

3.1. GNC Requirements. The GNC system requirements for

Tianwen-1 EDL process are as follows:

(1) Key events, such as trim wing deployment, parachute deployment, heatshield jettison, backshell separation, MLE ignition, and touchdown detection,

should be triggered properly

(2) After backshell separation, the lander should not be

collided with the backshell

(3) The actual landing site should be selected on-board

within the preselected landing area

(4) The lander’s touchdown attitude, angular rate, and

vertical and horizontal velocities should meet the

requirements

(5) The fuel consumption of the EDL process needs to

be within a reasonable range.

3.2. GNC Modes. According to the EDL process profile and

GNC requirements, the EDL process is divided into eight

GNC modes: the AOA-trim mode, the lift control mode,

the parachute descent control mode, the powered deceleration mode, the hover and imaging mode, the hazard avoidance maneuver mode, the slow descent mode, and ended

with the no-control mode. The transition of these eight

modes is shown in Figure 3.

In the atmospheric entry segment, the GNC system

operates with the AOA-trim mode initially, in which the

descent module’s attitude is adjusted to a predefined attitude

for guided lift entry. Once the sensed acceleration magnitude

exceeds 0.2 Earth g, the lift control mode is activated to produce proper lift to control the entry trajectory.

With the deployment of parachute, the GNC system

switches to the parachute descent control mode and uses this

mode throughout the whole parachute descent phase. In this

mode, the descent module’s velocity would descent to about

95 m/s at an altitude of about 1.2 km above the Mars surface.

In the landing phase, the GNC system operates with the

powered deceleration mode, hover and imaging mode, hazard avoidance maneuver mode, slow descent mode, and

ends at the no-control mode when the lander has softly

touched down. The powered deceleration mode begins with

the backshell separation and ends before hover. The main

task of this mode is to use the MLE to reduce the lander’s

velocity, to avoid collisions with the detached backshell,

and to image and select a wide safe landing area for coarse

hazard avoidance. In the hover and imaging mode, the

lander maintains a hover state to take 3D images of the landing area and then selects a safe landing site. Once the landing

site is selected, the GNC system switches to the hazard

avoidance maneuver mode to perform hazard avoidance

and descent such that the lander would descent to 20 m altitude above the landing site with a zero horizontal velocity

and a preset value of vertical velocity (about 1.5 m/s). Then,

the GNC system switches to the slow descent mode. In this

mode, the lander slowly descends at a preset speed, eliminates the horizontal speed, and maintains a vertical attitude.

Once the lander’s touchdown is detected, the GNC system

sends a shutdown signal to turn off the MLE and then

switches to the no-control mode, in which no further orbit

control and attitude control are performed any more.

3.3. GNC System Configuration. The EDL GNC system

scheme is illustrated in Figure 4, where sensors, actuators,

and the GNC computer will be described in this subsection,

and the GNC algorithms will be presented in the following

sections.

2 Space: Science & Technology

3.4. Sensors

3.4.1. Star Sensors. A pair of star sensors working from the 8

hours prior to orbiter/descent module separation to 10 seconds before atmospheric entry are equipped for attitude

determination.

3.4.2. Inertial Measurement Units (IMUs). A pair of IMUs

are carried out, each of which consists of three orthogonal

accelerometers and three orthogonal gyroscopes to measure

the specific force and angular rate, respectively. During the

EDL, the IMUs are used for inertial navigation and key event

triggers.

3.4.3. Landing Radars. A microwave radar and a phased

array sensor (PAS) are configured to provide Mars-related

measurements. The microwave radar contains four beams,

each of which works automatically. The PAS contains nine

beams, four of which are selected by the GNC system to provide measurements at every measurement time. Every beam

for the two radars can measure slant-range and groundrelative velocity along its axis simultaneously.

3.4.4. Hazard Avoidance Sensors. Two hazard avoidance sensors are equipped for hazard avoidance and landing site

selection. One is called the optical obstacle avoidance sensor

Tianwen-1 probe = Orbiter

Orbiter

+ Descent module

Descent module

Backshell

Rover

Landing platform

Heatshield

Figure 1: Main components of the Tianwen-1 spacecraft.

Scientific exploration stage

Mars parking stage

Mars capture stage

Earth-mars transfer stage

Deorbitand landing stage

Figure 2: Mission profile of Tianwen-1 [8].

Space: Science & Technology 3

6

(OOAS), which consists of only a single optical imaging lens.

The other is called the multifunction obstacle avoidance sensor (MOAS), consisting of an optical imaging lens and a

laser imaging lens. During the powered deceleration mode,

2D images of the landing area are taken by the OOAS and

then a safe area for coarse hazard avoidance is selected. During the hover and imaging mode, 3D images are taken and a

safe landing site for precise hazard avoidance is selected. An

Heatshield

jettison

Backshell

separation

Optical

imaging

3D

imaging

(Not in actual proportion)

Parachute

deployment

(1.8 mach)

Trim wing deployment

(2.8 mach)

0 km

AOA-trim

~740 km

~125 km

~60 km

~10 km

~100 m

Slow

descent

Parachute descent

~20 m

control Powered

decelearation

Hover and

imaging Hazard

avoidance

maneuver

No-control

Lift control

Mars surface

Figure 3: Schematic and GNC modes of Tianwen-1 EDL [11].

Navigation

algorithm

Estimated state

Attitude

command

Guidance

law

Attitude

control

IMU & landing

radars

Dynamic &

environment

models

Actuators

(MLE & thrusters)

Estimated attitude

GNC

computer

Landing site selection

Hazard avoidance sensors

Thruster

command

MLE command

Figure 4: The Tianwen-1 EDL GNC system scheme.

4 Space: Science & Technology

additional option for precise hazard avoidance is that the

OOAS can work in conjunction with the optical imaging

mode of the MOAS.

3.5. Actuators. 6 × 25 N thrusters and 20 × 250 N thrusters

are mounted for attitude control, of which 8 × 250 N

thrusters are additionally used for translation control in

the horizontal plane after the hover and imaging phase. In

addition, a MLE for translation control is carried out to produce either a constant thrust with 7500 N or a throttleable

thrust in the range from 1500 N to 5000 N.

3.6. GNC Computer. The GNC computer, referred to as

entry and descent control unit (EDCU), collects and processes data from the sensors, actuators, and On-Board Data

Handling (OBDH) system, performs real-time GNC calculation, and then sends control signals for orbit and attitude

control. During the powered descent phase, the EDCU is

also responsible for hazard recognition and landing site

selection by analyzing the images obtained from the hazard

avoidance sensors.

4. Guidance Algorithm

The Tianwen-1 performed a guided entry, an unguided parachute descent, and a guided powered descent in succession.

The entry guidance is based on the MSL [12, 13] and

ChangE-5 reentry probe [14, 15], and the powered descent

guidance is based on ChangE-3 [16, 17].

4.1. Entry Guidance. For the entry phase, early missions

adopted the unguided ballistic trajectory, leading to a large

landing error ellipse. The MSL was the first mission that flew

the guided lifting entry at Mars. Because of the displacement

of the center of mass of the entry with its axis of symmetry, a

nonzero trim angle-of-attack can be generated to produce a

lift force. By modulating the bank angle to change the direction of the lift vector, the entry trajectory can be controlled

such that the parachute deploy ellipse is minimized. To minimize size of the parachute deploy ellipse, the Tiawen-1 also

adopted active guidance during the entry phase.

Depending on the bank angle command, the entry guidance of the Tianwen-1 is divided into four phases: prebank,

range control, heading alignment, and zero-bank.

In the AOA-trim mode, the prebank guidance is executed by commanding a constant nominal bank angle.

When the AOA-trim mode is switched to the lift control

mode, the range control begins. In this mode, the descent

module flies with its trim angle-of-attack. Based on the estimated drag accelerations, altitude rate, and range errors with

respect to a reference trajectory [18] stored on-board, an

analytic predictor-corrector guidance algorithm calculates

the commanding bank angle and then sends it to the attitude

control system such that the range error can be minimized.

When the navigated Mars-related velocity drops to

1700 m/s, the range control capability is greatly reduced,

and the commanding bank angle is easy to saturate. At

this time, the range control algorithm is ceased, and the

heading alignment algorithms begin to minimize the

cross-range error until the trim wing is deployed. Then,

the zero-bank phase begins, in which the bank command

is set to 0°

.

If the error between the navigated and nominal states at

entry interface (EI) was too large, it might not be possible to

track the reference trajectory, which may saturate the guidance bank command and make it impossible to meet the

parachute deployment requirements. To cope with this case,

a range compensation algorithm is designed to implement at

the beginning of the AOA-trim mode such that the parachute deployment altitude constraint is satisfied at the

expense of parachute deployment ellipse.

The flow chart of the entry guidance algorithm is summarized in Figure 5.

4.2. Powered Descent Guidance. The main purpose of powered descent guidance is to reduce the vehicle’s velocity

and execute hazard avoidance and backshell evasion. As

mentioned in Section 3.2, the GNC operates in five modes

in the powered descent process, i.e., powered deceleration,

hover and imaging, hazard avoidance, slow descent, and

no-control. There is no trajectory guidance for the nocontrol mode. The powered descent guidance is mainly

inherited from the ChangE-3 [16, 17], except that the backshell evasion should be considered for the Tianwen-1 during

the powered deceleration phase.

Here, we only introduce the powered deceleration guidance. For the guidance algorithms of other four modes,

readers may refer to Refs. [16, 17]. The main tasks of the

powered deceleration are reducing the lander’s velocity

using the MLE, executing a backshell evasion maneuver,

and performing coarse hazard avoidance through the safe

landing zone detection by the OOAS. The powered deceleration guidance consists of two segments. In the first segment, the lander’s velocity is reduced, and a backshell

evasion maneuver may be executed, depending on the magnitude of the lander’s navigated velocity at the time of backshell separation. When the lander reaches a specified altitude

with an almost vertical attitude, the OOAS begins to work,

trying to determine a safe landing zone. Once the safe landing zone is determined, the second segment begins, of which

a hazard avoidance maneuver is executed with a throttleable

thrust explicit guidance [19] until the lander is hovered at a

100 m altitude above the Mars surface slowly.

5. Navigation

The radar-updated inertial navigation strategy is used for the

Tianwen-1 EDL phase, whereas the GNC system relies on

the inertial navigation system (INS) only before the heatshield jettison and the radar-derived states are used to correct the INS-derived states once the heatshield is separated,

such that accurate altitude and velocity estimates can be provided. In the slow descent stage, in order to avoid the

adverse effects of engine plumes on the landing radars, pure

inertial navigation is restored at this stage.

The Tianwen-1 EDL navigation framework after heatshield separation is mainly inherited from the ChangE-3

lander [16, 17, 20]. Note that at most eight beams can be used

for correction. For each measurement time, at most eight

Space: Science & Technology 5

7

(OOAS), which consists of only a single optical imaging lens.

The other is called the multifunction obstacle avoidance sensor (MOAS), consisting of an optical imaging lens and a

laser imaging lens. During the powered deceleration mode,

2D images of the landing area are taken by the OOAS and

then a safe area for coarse hazard avoidance is selected. During the hover and imaging mode, 3D images are taken and a

safe landing site for precise hazard avoidance is selected. An

Heatshield

jettison

Backshell

separation

Optical

imaging

3D

imaging

(Not in actual proportion)

Parachute

deployment

(1.8 mach)

Trim wing deployment

(2.8 mach)

0 km

AOA-trim

~740 km

~125 km

~60 km

~10 km

~100 m

Slow

descent

Parachute descent

~20 m

control Powered

decelearation

Hover and

imaging Hazard

avoidance

maneuver

No-control

Lift control

Mars surface

Figure 3: Schematic and GNC modes of Tianwen-1 EDL [11].

Navigation

algorithm

Estimated state

Attitude

command

Guidance

law

Attitude

control

IMU & landing

radars

Dynamic &

environment

models

Actuators

(MLE & thrusters)

Estimated attitude

GNC

computer

Landing site selection

Hazard avoidance sensors

Thruster

command

MLE command

Figure 4: The Tianwen-1 EDL GNC system scheme.

4 Space: Science & Technology

additional option for precise hazard avoidance is that the

OOAS can work in conjunction with the optical imaging

mode of the MOAS.

3.5. Actuators. 6 × 25 N thrusters and 20 × 250 N thrusters

are mounted for attitude control, of which 8 × 250 N

thrusters are additionally used for translation control in

the horizontal plane after the hover and imaging phase. In

addition, a MLE for translation control is carried out to produce either a constant thrust with 7500 N or a throttleable

thrust in the range from 1500 N to 5000 N.

3.6. GNC Computer. The GNC computer, referred to as

entry and descent control unit (EDCU), collects and processes data from the sensors, actuators, and On-Board Data

Handling (OBDH) system, performs real-time GNC calculation, and then sends control signals for orbit and attitude

control. During the powered descent phase, the EDCU is

also responsible for hazard recognition and landing site

selection by analyzing the images obtained from the hazard

avoidance sensors.

4. Guidance Algorithm

The Tianwen-1 performed a guided entry, an unguided parachute descent, and a guided powered descent in succession.

The entry guidance is based on the MSL [12, 13] and

ChangE-5 reentry probe [14, 15], and the powered descent

guidance is based on ChangE-3 [16, 17].

4.1. Entry Guidance. For the entry phase, early missions

adopted the unguided ballistic trajectory, leading to a large

landing error ellipse. The MSL was the first mission that flew

the guided lifting entry at Mars. Because of the displacement

of the center of mass of the entry with its axis of symmetry, a

nonzero trim angle-of-attack can be generated to produce a

lift force. By modulating the bank angle to change the direction of the lift vector, the entry trajectory can be controlled

such that the parachute deploy ellipse is minimized. To minimize size of the parachute deploy ellipse, the Tiawen-1 also

adopted active guidance during the entry phase.

Depending on the bank angle command, the entry guidance of the Tianwen-1 is divided into four phases: prebank,

range control, heading alignment, and zero-bank.

In the AOA-trim mode, the prebank guidance is executed by commanding a constant nominal bank angle.

When the AOA-trim mode is switched to the lift control

mode, the range control begins. In this mode, the descent

module flies with its trim angle-of-attack. Based on the estimated drag accelerations, altitude rate, and range errors with

respect to a reference trajectory [18] stored on-board, an

analytic predictor-corrector guidance algorithm calculates

the commanding bank angle and then sends it to the attitude

control system such that the range error can be minimized.

When the navigated Mars-related velocity drops to

1700 m/s, the range control capability is greatly reduced,

and the commanding bank angle is easy to saturate. At

this time, the range control algorithm is ceased, and the

heading alignment algorithms begin to minimize the

cross-range error until the trim wing is deployed. Then,

the zero-bank phase begins, in which the bank command

is set to 0°

.

If the error between the navigated and nominal states at

entry interface (EI) was too large, it might not be possible to

track the reference trajectory, which may saturate the guidance bank command and make it impossible to meet the

parachute deployment requirements. To cope with this case,

a range compensation algorithm is designed to implement at

the beginning of the AOA-trim mode such that the parachute deployment altitude constraint is satisfied at the

expense of parachute deployment ellipse.

The flow chart of the entry guidance algorithm is summarized in Figure 5.

4.2. Powered Descent Guidance. The main purpose of powered descent guidance is to reduce the vehicle’s velocity

and execute hazard avoidance and backshell evasion. As

mentioned in Section 3.2, the GNC operates in five modes

in the powered descent process, i.e., powered deceleration,

hover and imaging, hazard avoidance, slow descent, and

no-control. There is no trajectory guidance for the nocontrol mode. The powered descent guidance is mainly

inherited from the ChangE-3 [16, 17], except that the backshell evasion should be considered for the Tianwen-1 during

the powered deceleration phase.

Here, we only introduce the powered deceleration guidance. For the guidance algorithms of other four modes,

readers may refer to Refs. [16, 17]. The main tasks of the

powered deceleration are reducing the lander’s velocity

using the MLE, executing a backshell evasion maneuver,

and performing coarse hazard avoidance through the safe

landing zone detection by the OOAS. The powered deceleration guidance consists of two segments. In the first segment, the lander’s velocity is reduced, and a backshell

evasion maneuver may be executed, depending on the magnitude of the lander’s navigated velocity at the time of backshell separation. When the lander reaches a specified altitude

with an almost vertical attitude, the OOAS begins to work,

trying to determine a safe landing zone. Once the safe landing zone is determined, the second segment begins, of which

a hazard avoidance maneuver is executed with a throttleable

thrust explicit guidance [19] until the lander is hovered at a

100 m altitude above the Mars surface slowly.

5. Navigation

The radar-updated inertial navigation strategy is used for the

Tianwen-1 EDL phase, whereas the GNC system relies on

the inertial navigation system (INS) only before the heatshield jettison and the radar-derived states are used to correct the INS-derived states once the heatshield is separated,

such that accurate altitude and velocity estimates can be provided. In the slow descent stage, in order to avoid the

adverse effects of engine plumes on the landing radars, pure

inertial navigation is restored at this stage.

The Tianwen-1 EDL navigation framework after heatshield separation is mainly inherited from the ChangE-3

lander [16, 17, 20]. Note that at most eight beams can be used

for correction. For each measurement time, at most eight

Space: Science & Technology 5

8

beams can be available which can provide a much more

redundancy. Therefore, a multiple-beam fault detection, isolation, and recovery (FDIR) algorithm for the landing radars has

been designed. Noting that the working beams for the PAS are

not fixed, the velocity corrections in the presence of coplanarity have also designed for the Tianwen-1. In addition, high

dynamic oscillatory motion at the beginning of the parachute

descent phase may saturate the gyroscope and produce large

attitude estimation errors, thereby producing a high landing

risk. To address this problem, an online INS reinitialization

algorithm [21] is designed by combining the data from the

IMU and the radars. The flow chart of the EDL navigation

algorithm is summarized in Figure 6.

5.1. Inertial Navigation Algorithm. The descent module’s

navigated states are initialized a few minutes before the

orbiter/descent module separation, where position and

velocity are uploaded by ground tracking and attitude

knowledge is provided by star sensors. Since then, the

descent module’s attitude is propagated by the gyroscope

measurements with the aid of the star sensors, and its

position and velocity are propagated using attitude information and high-order orbit model, where the accelerometers are used to detect and compensate for

nongravitational acceleration. Because of the block of the

Mars, the star sensors are not available about 10 seconds

prior to the entry interface. After that, the descent module

relies on the INS to propagate the navigation state using

the IMU measurements.

To compensate for the high dynamical motion during

the parachute descent phase, based on ChangE-3’s algorithm

[20], a four-interval strapdown algorithm with recursive

form attitude propagation and lever arm compensation

based on least-square methods is designed.

Bank angle = 0°

Mach < 2.8 (deploy

trim-wing)

Heading alignment algorithms

Range compensation

algorithms

Analytic predictor-corrector guidance

algorithm

Output

Navigated parameters

Altitude < 125 km

Yes

No

No

Bank angle = 52°

Get reference values of

drag, altitude rate, downrange and

gains from reference trajectory

Get the reference vertical L/D at the

velocity

Calculate bank angle magnitude

command

Command a bank reversal

Bank angle filtering and limiting

Yes

Yes

Initial longitude and

latitude error >

threshold

Yes

V < 1700 m/s

Calculate bank angle

magnitude and sign

Bank angle filtering

and limiting

Drag

acceleration > 0.2 g

Figure 5: The flow chart of the Tianwen-1 entry guidance.

6 Space: Science & Technology

5.2. Altitude Correction. Because INS errors accumulate over

time, once the heat shield is jettisoned, the landing radars

can provide surface-relative measurements to correct the

INS-derived altitude and surface-relative velocity. Before

altitude correction, an FDIR algorithm for slant-range measurements is implemented to detect and remove multiplebeam outliers.

Given the selected beams for altitude correction, a distributed fusion architecture is used [20]. Firstly, the

second-order state equation for altitude and vertical velocity

is formulated, and local estimates of altitude corrections for

each beam are updated using the Kalman filter, the gain of

which is approximated as a function of altitude, which is calculated offline according to the predefined landing

INS

propagation

Altitude &

velocity

correction

IMU

Initialization before

entry

Multiple-beam

FDIR Radar

Guidance

and

control

INS online

re-initialization

Gyroscope saturation

Figure 6: Flow chart of the EDL navigation algorithm of Tianwen-1.

Rate limiter region

PID control region

Rate limiter region

Nominal

rate control

region

Parabolic

target rate

control

region

??d = d??r

??d = –d??r

–??mL ??mL

??

–??mS ??mS

Parabolic

target rate

control

region

Nominal

rate control

region

??

Figure 7: The attitude phase plane partition.

Space: Science & Technology 7

9

beams can be available which can provide a much more

redundancy. Therefore, a multiple-beam fault detection, isolation, and recovery (FDIR) algorithm for the landing radars has

been designed. Noting that the working beams for the PAS are

not fixed, the velocity corrections in the presence of coplanarity have also designed for the Tianwen-1. In addition, high

dynamic oscillatory motion at the beginning of the parachute

descent phase may saturate the gyroscope and produce large

attitude estimation errors, thereby producing a high landing

risk. To address this problem, an online INS reinitialization

algorithm [21] is designed by combining the data from the

IMU and the radars. The flow chart of the EDL navigation

algorithm is summarized in Figure 6.

5.1. Inertial Navigation Algorithm. The descent module’s

navigated states are initialized a few minutes before the

orbiter/descent module separation, where position and

velocity are uploaded by ground tracking and attitude

knowledge is provided by star sensors. Since then, the

descent module’s attitude is propagated by the gyroscope

measurements with the aid of the star sensors, and its

position and velocity are propagated using attitude information and high-order orbit model, where the accelerometers are used to detect and compensate for

nongravitational acceleration. Because of the block of the

Mars, the star sensors are not available about 10 seconds

prior to the entry interface. After that, the descent module

relies on the INS to propagate the navigation state using

the IMU measurements.

To compensate for the high dynamical motion during

the parachute descent phase, based on ChangE-3’s algorithm

[20], a four-interval strapdown algorithm with recursive

form attitude propagation and lever arm compensation

based on least-square methods is designed.

Bank angle = 0°

Mach < 2.8 (deploy

trim-wing)

Heading alignment algorithms

Range compensation

algorithms

Analytic predictor-corrector guidance

algorithm

Output

Navigated parameters

Altitude < 125 km

Yes

No

No

Bank angle = 52°

Get reference values of

drag, altitude rate, downrange and

gains from reference trajectory

Get the reference vertical L/D at the

velocity

Calculate bank angle magnitude

command

Command a bank reversal

Bank angle filtering and limiting

Yes

Yes

Initial longitude and

latitude error >

threshold

Yes

V < 1700 m/s

Calculate bank angle

magnitude and sign

Bank angle filtering

and limiting

Drag

acceleration > 0.2 g

Figure 5: The flow chart of the Tianwen-1 entry guidance.

6 Space: Science & Technology

5.2. Altitude Correction. Because INS errors accumulate over

time, once the heat shield is jettisoned, the landing radars

can provide surface-relative measurements to correct the

INS-derived altitude and surface-relative velocity. Before

altitude correction, an FDIR algorithm for slant-range measurements is implemented to detect and remove multiplebeam outliers.

Given the selected beams for altitude correction, a distributed fusion architecture is used [20]. Firstly, the

second-order state equation for altitude and vertical velocity

is formulated, and local estimates of altitude corrections for

each beam are updated using the Kalman filter, the gain of

which is approximated as a function of altitude, which is calculated offline according to the predefined landing

INS

propagation

Altitude &

velocity

correction

IMU

Initialization before

entry

Multiple-beam

FDIR Radar

Guidance

and

control

INS online

re-initialization

Gyroscope saturation

Figure 6: Flow chart of the EDL navigation algorithm of Tianwen-1.

Rate limiter region

PID control region

Rate limiter region

Nominal

rate control

region

Parabolic

target rate

control

region

??d = d??r

??d = –d??r

–??mL ??mL

??

–??mS ??mS

Parabolic

target rate

control

region

Nominal

rate control

region

??

Figure 7: The attitude phase plane partition.

Space: Science & Technology 7

10

trajectory, statistical characteristics of the IMUs and radars,

and the terrain characteristics of the Mars. Then, local estimates are fused to form a global estimate of the altitude correction, and the fusion coefficients are determined using the

information allocation principle.

5.3. Velocity Correction. Before implementing the velocity

correction, an FDIR algorithm is used for velocimeter measurement validation and outlier removal. As mentioned in

Section 5.2, at most eight beams can be available at each

update, which allows for multiple-beam FDIR. The velocimeter FDIR algorithm is based on parity equations of five

beams. For the case when eight beams are available, 56 (C5

8

) combinations should be evaluated. Because the PAS’s

working beams are not fixed, the 56 combinations should

be calculated online, exceeding the limited on-board computational capability. Therefore, an FDIR velocimeter algorithm based on hybrid fault tree and parity equations is

designed for the Tianwen-1, in which details will be presented in an additional paper.

Once the velocimeter FDIR algorithm is implemented,

the beams that used for velocity correction can be selected.

For velocity correction, the first-order equation for the

ground-relative velocity along each beam is established,

and the velocity correction for each beam is updated using

the Kalman filter, the gain of which is approximated as a

function of velocity magnitude. These corrections are then

fused to form a 3D velocity correction. Note that the number

of selected beams for correction is not fixed, and multiple

beams may be coplanar or almost coplanar. The fusion strategy depends on the number of selected beams. If only one

beam is selected, then only the velocity along the beam is

corrected. For the case when two and more beams are

selected, if these beams are coplanar or almost coplanar,

then a plane is constructed by two beams, and the velocity

along the plane is corrected using a least-square method;

otherwise, the 3D velocity correction is performed.

5.4. INS Online Reinitialization. At the beginning of the

parachute descent phase, high dynamic oscillatory

motion, such as parachute inflation and area oscillation

[22], may cause a high angular rate and saturate the

gyroscope. The saturation of the gyroscope would produce large attitude knowledge errors and thereby cause

large errors of the altimeter-derived altitude, estimated

vertical and horizontal velocities, and the landing attitude,

which may cause serious consequences such as a complete system loss. To cope with the gyroscope saturation,

an online INS reinitialization algorithm is designed. The

key for online initialization is the determination of the

nadir vector in a redefined inertial frame using the measurements from the IMU and the radars. Given the nadir

vector, the INS can be reinitialized, and the gravitational

acceleration can be modeled such that the INS navigation

equation can be propagated, and finally, crucial parameters

used for guidance and control systems can be derived. Once

the online initialization is accomplished, the radar-updated

inertial navigation algorithm presented in Sections 5.2 and

5.3 can be implemented.

0

0

20

40

60

Altitude and mach

80

100

120

140

100

Mach

Atmospheric entry

Entry interface

Switch to lift-control mode

Altitude (km)

Deploy trim-wing

Jettison heatshield

Deploy parachute

Separate backshell

Hover and imaging

Hazard avoidance

Slow descent

Parachute descent Powered descent

200 300

Time (s)

400 500 600

Figure 8: The EDL altitude, Mach number, and key events trigger time.

8 Space: Science & Technology

6. Attitude Control Algorithm

In this section, the attitude control algorithms for the

Tianwen-1 EDL phase will be summarized, details of which

will again be presented in an additional paper.

6.1. Attitude Control for Entry Phase. In the AOA-trim

mode, the controller commands the RCS thrusters on the

backshell to track the predicted bank command, the predicted trim angle-of-attack, and the zero sideslip. Here, the

3-axis attitude is decoupled into three independent channels,

and a phase plane logic controller with straight switching

lines is used for each channel.

In the lift control mode, the controller tracks the

guidance bank command using a proportional–integral–

derivative (PID) controller with a pulse-width-modulation

(PWM) technique. It is realized that the powerful capability of the 250 N thrusters may result in angular rate resonance phenomenon. To cope with this problem, an

attitude planning technique is proposed to improve the

tracking capability. For the attitude control of the angles

of attack and sideslip, rate damping controllers are

adopted to stabilize them around their trim values. It

should be noted that, for the case when the trim wing is

not deployed properly, the trim values of the angle-ofattack and sideslip angle are still not around zero, which

cannot meet the requirements of parachute deployment.

In this case, a PID controller is used for keeping the

angle-of-attack being zero. In view of its self-stabilizing

characteristics, the rate damping controller is still used

for the sideslip angle control.

6.2. Attitude Control for Parachute Descent Phase. In the

parachute descent, the attitude controller begins to work

after a few seconds of parachute deployment. The control

strategy in this phase is similar to the one in the lift control

mode. The only difference is that the commanded attitude in

the roll channel here is calculated according to the local upsouth-east frame.

0 100 200 300 400 500 600

Time (s)

0

2

4

6

8

10

12

14

Altitude (m)

×104

0 100 200 300 400 500 600

Time (s)

–0.5

0

0.5

q1

–0.5

0

0.5

q2

–0.4

–0.2

0

q1

0 100 200 300 400 500 600

0 100 200 300 400 500 600

0 100 200 300 400 500 600

Time (s)

–100

0

100

x (deg)

–100

–50

0

50

y (deg)

–100

0

100

z (deg)

0 100 200 300 400 500 600

0 100 200 300 400 500 600

0 100 200 300 400 500 600

Time (s)

–20

0

20

x (deg/s)

–20

0

20

y (deg/s)

–20

0

20

z (deg/s)

0 100 200 300 400 500 600

0 100 200 300 400 500 600

0 100 200 300 400 500 600

Time (s)

(a) (b)

(c) (d)

Figure 9: The EDL altitude, quaternion, attitude angles, and angular rate. (a) Altitude. (b) Vector parts of quaternion. (c) Three-axis attitude

angles with respect to the J2000 frame in a “xyz” rotation sequence. (d) Angular rate of the lander.

Space: Science & Technology 9

11

trajectory, statistical characteristics of the IMUs and radars,

and the terrain characteristics of the Mars. Then, local estimates are fused to form a global estimate of the altitude correction, and the fusion coefficients are determined using the

information allocation principle.

5.3. Velocity Correction. Before implementing the velocity

correction, an FDIR algorithm is used for velocimeter measurement validation and outlier removal. As mentioned in

Section 5.2, at most eight beams can be available at each

update, which allows for multiple-beam FDIR. The velocimeter FDIR algorithm is based on parity equations of five

beams. For the case when eight beams are available, 56 (C5

8

) combinations should be evaluated. Because the PAS’s

working beams are not fixed, the 56 combinations should

be calculated online, exceeding the limited on-board computational capability. Therefore, an FDIR velocimeter algorithm based on hybrid fault tree and parity equations is

designed for the Tianwen-1, in which details will be presented in an additional paper.

Once the velocimeter FDIR algorithm is implemented,

the beams that used for velocity correction can be selected.

For velocity correction, the first-order equation for the

ground-relative velocity along each beam is established,

and the velocity correction for each beam is updated using

the Kalman filter, the gain of which is approximated as a

function of velocity magnitude. These corrections are then

fused to form a 3D velocity correction. Note that the number

of selected beams for correction is not fixed, and multiple

beams may be coplanar or almost coplanar. The fusion strategy depends on the number of selected beams. If only one

beam is selected, then only the velocity along the beam is

corrected. For the case when two and more beams are

selected, if these beams are coplanar or almost coplanar,

then a plane is constructed by two beams, and the velocity

along the plane is corrected using a least-square method;

otherwise, the 3D velocity correction is performed.

5.4. INS Online Reinitialization. At the beginning of the

parachute descent phase, high dynamic oscillatory

motion, such as parachute inflation and area oscillation

[22], may cause a high angular rate and saturate the

gyroscope. The saturation of the gyroscope would produce large attitude knowledge errors and thereby cause

large errors of the altimeter-derived altitude, estimated

vertical and horizontal velocities, and the landing attitude,

which may cause serious consequences such as a complete system loss. To cope with the gyroscope saturation,

an online INS reinitialization algorithm is designed. The

key for online initialization is the determination of the

nadir vector in a redefined inertial frame using the measurements from the IMU and the radars. Given the nadir

vector, the INS can be reinitialized, and the gravitational

acceleration can be modeled such that the INS navigation

equation can be propagated, and finally, crucial parameters

used for guidance and control systems can be derived. Once

the online initialization is accomplished, the radar-updated

inertial navigation algorithm presented in Sections 5.2 and

5.3 can be implemented.

0

0

20

40

60

Altitude and mach

80

100

120

140

100

Mach

Atmospheric entry

Entry interface

Switch to lift-control mode

Altitude (km)

Deploy trim-wing

Jettison heatshield

Deploy parachute

Separate backshell

Hover and imaging

Hazard avoidance

Slow descent

Parachute descent Powered descent

200 300

Time (s)

400 500 600

Figure 8: The EDL altitude, Mach number, and key events trigger time.

8 Space: Science & Technology

6. Attitude Control Algorithm

In this section, the attitude control algorithms for the

Tianwen-1 EDL phase will be summarized, details of which

will again be presented in an additional paper.

6.1. Attitude Control for Entry Phase. In the AOA-trim

mode, the controller commands the RCS thrusters on the

backshell to track the predicted bank command, the predicted trim angle-of-attack, and the zero sideslip. Here, the

3-axis attitude is decoupled into three independent channels,

and a phase plane logic controller with straight switching

lines is used for each channel.

In the lift control mode, the controller tracks the

guidance bank command using a proportional–integral–

derivative (PID) controller with a pulse-width-modulation

(PWM) technique. It is realized that the powerful capability of the 250 N thrusters may result in angular rate resonance phenomenon. To cope with this problem, an

attitude planning technique is proposed to improve the

tracking capability. For the attitude control of the angles

of attack and sideslip, rate damping controllers are

adopted to stabilize them around their trim values. It

should be noted that, for the case when the trim wing is

not deployed properly, the trim values of the angle-ofattack and sideslip angle are still not around zero, which

cannot meet the requirements of parachute deployment.

In this case, a PID controller is used for keeping the

angle-of-attack being zero. In view of its self-stabilizing

characteristics, the rate damping controller is still used

for the sideslip angle control.

6.2. Attitude Control for Parachute Descent Phase. In the

parachute descent, the attitude controller begins to work

after a few seconds of parachute deployment. The control

strategy in this phase is similar to the one in the lift control

mode. The only difference is that the commanded attitude in

the roll channel here is calculated according to the local upsouth-east frame.

0 100 200 300 400 500 600

Time (s)

0

2

4

6

8

10

12

14

Altitude (m)

×104

0 100 200 300 400 500 600

Time (s)

–0.5

0

0.5

q1

–0.5

0

0.5

q2

–0.4

–0.2

0

q1

0 100 200 300 400 500 600

0 100 200 300 400 500 600

0 100 200 300 400 500 600

Time (s)

–100

0

100

x (deg)

–100

–50

0

50

y (deg)

–100

0

100

z (deg)

0 100 200 300 400 500 600

0 100 200 300 400 500 600

0 100 200 300 400 500 600

Time (s)

–20

0

20

x (deg/s)

–20

0

20

y (deg/s)

–20

0

20

z (deg/s)

0 100 200 300 400 500 600

0 100 200 300 400 500 600

0 100 200 300 400 500 600

Time (s)

(a) (b)

(c) (d)

Figure 9: The EDL altitude, quaternion, attitude angles, and angular rate. (a) Altitude. (b) Vector parts of quaternion. (c) Three-axis attitude

angles with respect to the J2000 frame in a “xyz” rotation sequence. (d) Angular rate of the lander.

Space: Science & Technology 9

12

6.3. Attitude Control for Powered Descent Phase. Due to the

uncertainties of the parachute descent phase, the state dispersion from the nominal values may be large at the beginning of the powered descent phase. Therefore, the attitude

controller should have a strong robust capability. For example, the controller in the powered deceleration mode should

track the guidance command with a maximum angular rate

of 15 deg/s. Meanwhile, the rapid attitude tracking may suffer from large disturbance. As shown in Figure 7, the attitude

phase plane is partitioned into four regions: a PID control

region, a nominal rate control region, a rate limiter region,

and a parabolic target rate control region. In the nominal

rate and parabolic target rate control regions, the proportional–integral (PI)+PWM controllers are used to track the

desired rate. In the rate limiter region, when the angular rate

exceeds the threshold, the available thrusters work fully on

control to drive the angular rate to the set range. In the

PID control region, the traditional PID+PWM controller is

used to track the desired attitude angle and angular rate.

Several additional strategies are also designed. Firstly,

observers are designed for disturbance online identification

and compensation. Secondly, the commanded thrust direction is decoupled from the attitude and is sent directly to

the pitch and yaw channels, which makes the tracking of

the commanded thrust direction as fast as possible. Thirdly,

an attitude controller based on multiple-level thruster

switching logic is designed based on the level of attitude

error. Finally, an FDIR algorithm is designed for the

Tianwen-1 to identify fault thrusts and rearrange the

remaining ones, which makes the controller more robust in

case that any thrust cannot be opened.

7. Flight Results

In this section, the actual flight results for the Tianwen-1

EDL process are presented. The descent module was separated from the orbiter at 04:18:54 a.m. BJT on May 15,

2021. About three hours later, the descent module entered

the Mars atmosphere at 07:08:54 a.m. BJT on May 15,

2021. Through 537-second EDL process, the lander landed

successfully on the surface of Mars. The longitude and latitude of the actual landing site are 109.925° E and 25.066°

N, respectively, and the downrange and cross-range errors

of which with respect to the predefined landing site are

–15

–10

–5

0

Angle of attack (deg)

–50

0

50

Bank angle (deg)

0 50 100 150 200 250 300

0 50 100 150 200 250 300

0 50 100 150 200 250 300

Time (s)

–4

–2

0

2

Sideslip angle (deg)

Figure 10: Angles of bank, sideslip, and attack during the atmospheric entry.

10 Space: Science & Technology

3.1 km and 0.2 km, respectively. The actual EDL trajectories

collected from telemetry are shown in Figures 8 and 9, the

angles of bank, sideslip, and attack during the atmospheric

entry are shown in Figure 10, and the telemetry Marsrelated velocity during the powered descent phase is given

in Figure 11.

It can be seen that the atmospheric entry phase lasted

279 seconds, in which the AOA-trim mode took 68 seconds.

When the descent module’s sensed acceleration magnitude

exceeded 1.96 m/s2 at a navigated altitude of about 63 km

and navigated velocity of about Mach 24, the lift control

mode began. The trim wing was deployed at a navigated

velocity of Mach 2.8, after which the trim values of the total

angle-of-attack approached to around zero.

The parachute was deployed at a navigated velocity of

Mach 1.8 when the navigated altitude is about 13 km. After

20 seconds when the descent module’s velocity reduced to

about Mach 0.5, the heatshield was jettisoned, and then the

landing legs were deployed, and the two radars began to provide Mars-related measurements to correct the INS errors.

At a navigated altitude of 1.3 km and navigated velocity

of Mach 0.25, the backshell was separated, implying the

beginning of the powered descent phase, which lasted 90

seconds. About 1 second after backshell/lander separation,

the MLE was ignited, the lander’s velocity was reduced

–60

–40

–20

0

Up (m/s)

–10

–5

0

South (m/s)

440 450 460 470 480 490 500 510 520 530 540

440 450 460 470 480 490 500 510 520 530 540

440 450 460 470 480 490 500 510 520 530 540

Time (s)

0

2

4

6

East (m/s)

Figure 11: Mars-related velocity in the up-south-east frame during the powered descent phase.

Figure 12: Image of the actual landing positions of the lander,

backshell, and heatshield taken by the Tianwen-1 orbiter.

Figure 13: Image of the actual landing site taken by the Zhurong

rover.

Space: Science & Technology 11

13

6.3. Attitude Control for Powered Descent Phase. Due to the

uncertainties of the parachute descent phase, the state dispersion from the nominal values may be large at the beginning of the powered descent phase. Therefore, the attitude

controller should have a strong robust capability. For example, the controller in the powered deceleration mode should

track the guidance command with a maximum angular rate

of 15 deg/s. Meanwhile, the rapid attitude tracking may suffer from large disturbance. As shown in Figure 7, the attitude

phase plane is partitioned into four regions: a PID control

region, a nominal rate control region, a rate limiter region,

and a parabolic target rate control region. In the nominal

rate and parabolic target rate control regions, the proportional–integral (PI)+PWM controllers are used to track the

desired rate. In the rate limiter region, when the angular rate

exceeds the threshold, the available thrusters work fully on

control to drive the angular rate to the set range. In the

PID control region, the traditional PID+PWM controller is

used to track the desired attitude angle and angular rate.

Several additional strategies are also designed. Firstly,

observers are designed for disturbance online identification

and compensation. Secondly, the commanded thrust direction is decoupled from the attitude and is sent directly to

the pitch and yaw channels, which makes the tracking of

the commanded thrust direction as fast as possible. Thirdly,

an attitude controller based on multiple-level thruster

switching logic is designed based on the level of attitude

error. Finally, an FDIR algorithm is designed for the

Tianwen-1 to identify fault thrusts and rearrange the

remaining ones, which makes the controller more robust in

case that any thrust cannot be opened.

7. Flight Results

In this section, the actual flight results for the Tianwen-1

EDL process are presented. The descent module was separated from the orbiter at 04:18:54 a.m. BJT on May 15,

2021. About three hours later, the descent module entered

the Mars atmosphere at 07:08:54 a.m. BJT on May 15,

2021. Through 537-second EDL process, the lander landed

successfully on the surface of Mars. The longitude and latitude of the actual landing site are 109.925° E and 25.066°

N, respectively, and the downrange and cross-range errors

of which with respect to the predefined landing site are

–15

–10

–5

0

Angle of attack (deg)

–50

0

50

Bank angle (deg)

0 50 100 150 200 250 300

0 50 100 150 200 250 300

0 50 100 150 200 250 300

Time (s)

–4

–2

0

2

Sideslip angle (deg)

Figure 10: Angles of bank, sideslip, and attack during the atmospheric entry.

10 Space: Science & Technology

3.1 km and 0.2 km, respectively. The actual EDL trajectories

collected from telemetry are shown in Figures 8 and 9, the

angles of bank, sideslip, and attack during the atmospheric

entry are shown in Figure 10, and the telemetry Marsrelated velocity during the powered descent phase is given

in Figure 11.

It can be seen that the atmospheric entry phase lasted

279 seconds, in which the AOA-trim mode took 68 seconds.

When the descent module’s sensed acceleration magnitude

exceeded 1.96 m/s2 at a navigated altitude of about 63 km

and navigated velocity of about Mach 24, the lift control

mode began. The trim wing was deployed at a navigated

velocity of Mach 2.8, after which the trim values of the total

angle-of-attack approached to around zero.

The parachute was deployed at a navigated velocity of

Mach 1.8 when the navigated altitude is about 13 km. After

20 seconds when the descent module’s velocity reduced to

about Mach 0.5, the heatshield was jettisoned, and then the

landing legs were deployed, and the two radars began to provide Mars-related measurements to correct the INS errors.

At a navigated altitude of 1.3 km and navigated velocity

of Mach 0.25, the backshell was separated, implying the

beginning of the powered descent phase, which lasted 90

seconds. About 1 second after backshell/lander separation,

the MLE was ignited, the lander’s velocity was reduced

–60

–40

–20

0

Up (m/s)

–10

–5

0

South (m/s)

440 450 460 470 480 490 500 510 520 530 540

440 450 460 470 480 490 500 510 520 530 540

440 450 460 470 480 490 500 510 520 530 540

Time (s)

0

2

4

6

East (m/s)

Figure 11: Mars-related velocity in the up-south-east frame during the powered descent phase.

Figure 12: Image of the actual landing positions of the lander,

backshell, and heatshield taken by the Tianwen-1 orbiter.

Figure 13: Image of the actual landing site taken by the Zhurong

rover.

Space: Science & Technology 11

14

further, and a backshell evasion maneuver was also performed. Then, the OOAS obtained images of the predefined

landing area used for coarse hazard avoidance. When the

lander’s altitude reduced to about 100 m, the GNC switched

to the hover and imaging mode. In this mode, the MOAS

obtained the 3D images of Mars surface and determined

the final landing site. Then the GNC switched to the hazard

avoidance mode. When the lander was at an altitude of 20 m

above the landing site with a 1.5 m/s vertical velocity and

0 m/s horizontal velocity, the GNC switched to the slow

descent mode. Finally, the lander landed on the Mars softly

with a stable vertical attitude. The touchdown horizontal

velocity is less than 0.16 m/s, and the attitude error is less

than 0.1 deg.

The image of the actual landing positions of the lander,

backshell, and heatshield is shown in Figure 12, and the

image of the lander taken by the Zhurong rover is shown

in Figure 13. Therefore, the effectiveness of the backshell

evasion and hazard avoidance was demonstrated.

8. Conclusions

According to the Tianwen-1 EDL GNC requirements, the

GNC modes, GNC architecture, and key GNC algorithms

have been described in this paper.

The effectiveness of the GNC system design was demonstrated by the successful landing of the Tianwen-1, which

landed on the Mars with a small landing ellipse, a soft touchdown velocity, and a stable vertical attitude.

It should be noted that the Tianwen-1 landed at a site

with a low MOLA elevation around a relative flat area. In

the future, China will target areas that have higher scientific

value, more rugged terrain, and higher MOLA elevation.

This puts forward new requirements for the EDL GNC technology, e.g., the GNC system must have high precision navigation capability and have stronger maneuverability or

deceleration capability.

Abbreviations

AOA: Angle-of-attack

BJT: Beijing time

EDCU: Entry and descent control unit

EDL: Entry, descent, and landing

EI: Entry interface

FDIR: Fault detection, isolation, and recovery

GNC: Guidance, navigation, and control

INS: Inertial navigation system

MLE: Main landing engine

MOAS: Multifunction obstacle avoidance sensor

MSL: Mars Science Laboratory

OBDH: On-Board Data Handling

OOAS: Optical obstacle avoidance sensor

PAS: Phased array sensor.

Data Availability

The data used to support the findings of this study are

included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work is supported by the Chinese National Space

Administration (CNSA). Parts of the work are supported

by the National Natural Science Foundation of China (Grant

No. 61503023, No. 61673057, No. 61803028, and No.

61903032).

References

[1] R. N. Ingoldby, “Guidance and control system design of the

Viking planetary lander,” Journal of Guidance and Control,

vol. 1, no. 3, pp. 189–196, 1978.

[2] M. P. Golombek, “The mars pathfinder mission,” Journal of

Geophysical Research: Planets, vol. 102, no. E2, pp. 3953–

3965, 1997.

[3] R. Roncoli and J. Ludwinski, “Mission design overview for the

Mars exploration rover mission,”in AIAA/AAS Astrodynamics

Specialist Conference and Exhibit, Monterey, California,

August 2002.

[4] M. R. Grover, B. D. Cichy, and P. N. Desai, “Overview of the

Phoenix entry, descent, and landing system architecture,”

Journal of Spacecraft and Rockets, vol. 48, no. 5, pp. 706–712,

2011.

[5] M. S. Martin, G. F. Mendeck, P. B. Brugarolas et al., “In-flight

experience of the Mars Science Laboratory guidance, navigation, and control system for entry, descent, and landing,”

CEAS Space Journal, vol. 7, no. 2, pp. 119–142, 2015.

[6] T. Hoffman, “InSight: mission to mars,” in 2018 IEEE Aerospace Conference, pp. 1–11, Big Sky, MT, USA, March 2018.

[7] K. A. Farley, K. H. Williford, K. M. Stack et al., “Mars 2020

mission overview,” Space Science Reviews, vol. 216, no. 8,

p. 142, 2020.

[8] P. J. Ye, Z. Z. Sun, W. Rao, and L. Z. Meng, “Mission overview

and key technologies of the first Mars probe of China,” Science

China Technological Sciences, vol. 60, no. 5, pp. 649–657, 2017.

[9] Z. Yu, P. Cui, and J. L. Crassidis, “Design and optimization of

navigation and guidance techniques for Mars pinpoint landing: Review and prospect,” Progress in Aerospace Sciences,

vol. 94, pp. 82–94, 2017.

[10] J. Dong, Z. Sun, W. Rao et al.,“Mission profile and design challenges of Mars landing exploration,” Planetary Remote Sensing

and Mapping, vol. XLII-3/W1, pp. 75–87, 2018.

[11] X. Y. Huang, C. Xu, R. H. Hu, M. D. Li, M. W. Guo, and J. C.

Hu, “Research of autonomous navigation and control scheme

based on multi-information fusion for Mars pinpoint landing,” Journal of Deep Space Exploration, vol. 6, no. 4,

pp. 348–357, 2019.

[12] G. F. Mendeck and L. Craig McGrew, “Entry guidance design

and postflight performance for 2011 Mars Science Laboratory

mission,” Journal of Spacecraft and Rockets, vol. 51, no. 4,

pp. 1094–1105, 2014.

[13] A. M. S. Martin, S. W. Lee, and E. C. Wong, “The development

of the MSL guidance, navigation, and control system for entry,

descent, and landing,” in Presented at the 23rd AAS/ AIAA

space flight mechanics meeting, AAS 13-238, Kauai, Hawaii,

2013.

12 Space: Science & Technology

[14] J. Hu, “Adaptive predictive guidance: a unified guidance

method,” Aerospace Control and Application, vol. 45, no. 4,

pp. 53–63, 2019.

[15] J. Hu and Z. Zhang, “A study on the reentry guidance for a

manned lunar return vehicle,” Control Theory & Applications,

vol. 31, no. 12, pp. 1678–1685, 2014.

[16] H. H. Zhang, Y. F. Guan, X. Y. Huang et al., “Guidance navigation and control for Chang’E-3 powered descent,” Scientia

Sinica Technologica, vol. 44, no. 4, pp. 377–384, 2014.

[17] X. Y. Huang, H. H. Zhang, D. Y. Wang, J. Li, Y. F. Guan, and

P. J. Wang, “Autonomous navigation and guidance for

Chang’e-3 soft landing,” Journal of Deep Space Exploration,

vol. 1, pp. 52–59, 2014.

[18] M. W. Guo, M. D. Li, X. Y. Huang, and D. Y. Wang, “On guidance algorithm for Martian atmospheric entry in nonconforming terminal constraints,” Journal of Deep Space Exploration,

vol. 4, no. 2, pp. 184–189, 2017.

[19] D. Y. Wang, X. Huang, and Y. Guan, “GNC system scheme for

lunar soft landing spacecraft,” Advances in Space Research,

vol. 42, no. 2, pp. 379–385, 2008.

[20] H. H. Zhang, J. Li, Y. F. Guan, and X. Y. Huang, “Autonomous

navigation for powered descent phase of Chang’E–3 lunar

lander,” Control Theory & Applications, vol. 31, no. 12,

pp. 1686–1694, 2014.

[21] M. D. Li, X. Huang, D. Wang et al., “Radar-updated inertial

landing navigation with online initialization,” IEEE Transactions on Aerospace and Electronic Systems, vol. 56, no. 5,

pp. 3360–3374, 2020.

[22] J. R. Cruz, D. Way, J. Shidner et al., “Parachute models used in

the Mars Science Laboratory entry, descent, and landing simulation,” in AIAA Aerodynamic Decelerator Systems (ADS)

Conference, p. 1276, Daytona Beach, Florida, March 2013.

Space: Science & Technology 13

15

further, and a backshell evasion maneuver was also performed. Then, the OOAS obtained images of the predefined

landing area used for coarse hazard avoidance. When the

lander’s altitude reduced to about 100 m, the GNC switched

to the hover and imaging mode. In this mode, the MOAS

obtained the 3D images of Mars surface and determined

the final landing site. Then the GNC switched to the hazard

avoidance mode. When the lander was at an altitude of 20 m

above the landing site with a 1.5 m/s vertical velocity and

0 m/s horizontal velocity, the GNC switched to the slow

descent mode. Finally, the lander landed on the Mars softly

with a stable vertical attitude. The touchdown horizontal

velocity is less than 0.16 m/s, and the attitude error is less

than 0.1 deg.

The image of the actual landing positions of the lander,

backshell, and heatshield is shown in Figure 12, and the

image of the lander taken by the Zhurong rover is shown

in Figure 13. Therefore, the effectiveness of the backshell

evasion and hazard avoidance was demonstrated.

8. Conclusions

According to the Tianwen-1 EDL GNC requirements, the

GNC modes, GNC architecture, and key GNC algorithms

have been described in this paper.

The effectiveness of the GNC system design was demonstrated by the successful landing of the Tianwen-1, which

landed on the Mars with a small landing ellipse, a soft touchdown velocity, and a stable vertical attitude.

It should be noted that the Tianwen-1 landed at a site

with a low MOLA elevation around a relative flat area. In

the future, China will target areas that have higher scientific

value, more rugged terrain, and higher MOLA elevation.

This puts forward new requirements for the EDL GNC technology, e.g., the GNC system must have high precision navigation capability and have stronger maneuverability or

deceleration capability.

Abbreviations

AOA: Angle-of-attack

BJT: Beijing time

EDCU: Entry and descent control unit

EDL: Entry, descent, and landing

EI: Entry interface

FDIR: Fault detection, isolation, and recovery

GNC: Guidance, navigation, and control

INS: Inertial navigation system

MLE: Main landing engine

MOAS: Multifunction obstacle avoidance sensor

MSL: Mars Science Laboratory

OBDH: On-Board Data Handling

OOAS: Optical obstacle avoidance sensor

PAS: Phased array sensor.

Data Availability

The data used to support the findings of this study are

included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work is supported by the Chinese National Space

Administration (CNSA). Parts of the work are supported

by the National Natural Science Foundation of China (Grant

No. 61503023, No. 61673057, No. 61803028, and No.

61903032).

References

[1] R. N. Ingoldby, “Guidance and control system design of the

Viking planetary lander,” Journal of Guidance and Control,

vol. 1, no. 3, pp. 189–196, 1978.

[2] M. P. Golombek, “The mars pathfinder mission,” Journal of

Geophysical Research: Planets, vol. 102, no. E2, pp. 3953–

3965, 1997.

[3] R. Roncoli and J. Ludwinski, “Mission design overview for the

Mars exploration rover mission,”in AIAA/AAS Astrodynamics

Specialist Conference and Exhibit, Monterey, California,

August 2002.

[4] M. R. Grover, B. D. Cichy, and P. N. Desai, “Overview of the

Phoenix entry, descent, and landing system architecture,”

Journal of Spacecraft and Rockets, vol. 48, no. 5, pp. 706–712,

2011.

[5] M. S. Martin, G. F. Mendeck, P. B. Brugarolas et al., “In-flight

experience of the Mars Science Laboratory guidance, navigation, and control system for entry, descent, and landing,”

CEAS Space Journal, vol. 7, no. 2, pp. 119–142, 2015.

[6] T. Hoffman, “InSight: mission to mars,” in 2018 IEEE Aerospace Conference, pp. 1–11, Big Sky, MT, USA, March 2018.

[7] K. A. Farley, K. H. Williford, K. M. Stack et al., “Mars 2020

mission overview,” Space Science Reviews, vol. 216, no. 8,

p. 142, 2020.

[8] P. J. Ye, Z. Z. Sun, W. Rao, and L. Z. Meng, “Mission overview

and key technologies of the first Mars probe of China,” Science

China Technological Sciences, vol. 60, no. 5, pp. 649–657, 2017.

[9] Z. Yu, P. Cui, and J. L. Crassidis, “Design and optimization of

navigation and guidance techniques for Mars pinpoint landing: Review and prospect,” Progress in Aerospace Sciences,

vol. 94, pp. 82–94, 2017.

[10] J. Dong, Z. Sun, W. Rao et al.,“Mission profile and design challenges of Mars landing exploration,” Planetary Remote Sensing

and Mapping, vol. XLII-3/W1, pp. 75–87, 2018.

[11] X. Y. Huang, C. Xu, R. H. Hu, M. D. Li, M. W. Guo, and J. C.

Hu, “Research of autonomous navigation and control scheme

based on multi-information fusion for Mars pinpoint landing,” Journal of Deep Space Exploration, vol. 6, no. 4,

pp. 348–357, 2019.

[12] G. F. Mendeck and L. Craig McGrew, “Entry guidance design

and postflight performance for 2011 Mars Science Laboratory

mission,” Journal of Spacecraft and Rockets, vol. 51, no. 4,

pp. 1094–1105, 2014.

[13] A. M. S. Martin, S. W. Lee, and E. C. Wong, “The development

of the MSL guidance, navigation, and control system for entry,

descent, and landing,” in Presented at the 23rd AAS/ AIAA

space flight mechanics meeting, AAS 13-238, Kauai, Hawaii,

2013.

12 Space: Science & Technology

[14] J. Hu, “Adaptive predictive guidance: a unified guidance

method,” Aerospace Control and Application, vol. 45, no. 4,

pp. 53–63, 2019.

[15] J. Hu and Z. Zhang, “A study on the reentry guidance for a

manned lunar return vehicle,” Control Theory & Applications,

vol. 31, no. 12, pp. 1678–1685, 2014.

[16] H. H. Zhang, Y. F. Guan, X. Y. Huang et al., “Guidance navigation and control for Chang’E-3 powered descent,” Scientia

Sinica Technologica, vol. 44, no. 4, pp. 377–384, 2014.

[17] X. Y. Huang, H. H. Zhang, D. Y. Wang, J. Li, Y. F. Guan, and

P. J. Wang, “Autonomous navigation and guidance for

Chang’e-3 soft landing,” Journal of Deep Space Exploration,

vol. 1, pp. 52–59, 2014.

[18] M. W. Guo, M. D. Li, X. Y. Huang, and D. Y. Wang, “On guidance algorithm for Martian atmospheric entry in nonconforming terminal constraints,” Journal of Deep Space Exploration,

vol. 4, no. 2, pp. 184–189, 2017.

[19] D. Y. Wang, X. Huang, and Y. Guan, “GNC system scheme for

lunar soft landing spacecraft,” Advances in Space Research,

vol. 42, no. 2, pp. 379–385, 2008.

[20] H. H. Zhang, J. Li, Y. F. Guan, and X. Y. Huang, “Autonomous

navigation for powered descent phase of Chang’E–3 lunar

lander,” Control Theory & Applications, vol. 31, no. 12,

pp. 1686–1694, 2014.

[21] M. D. Li, X. Huang, D. Wang et al., “Radar-updated inertial

landing navigation with online initialization,” IEEE Transactions on Aerospace and Electronic Systems, vol. 56, no. 5,

pp. 3360–3374, 2020.

[22] J. R. Cruz, D. Way, J. Shidner et al., “Parachute models used in

the Mars Science Laboratory entry, descent, and landing simulation,” in AIAA Aerodynamic Decelerator Systems (ADS)

Conference, p. 1276, Daytona Beach, Florida, March 2013.

Space: Science & Technology 13

&

&

16

Research Article

Study on Dynamic Characteristics of Mars Entry Module in

Transonic and Supersonic Speeds

Qi Li,1 Rui Zhao,2 Sijun Zhang,3 Wei Rao,1 and Haogong Wei 1

1

Beijing Institute of Spacecraft System Engineering, CAST, Beijing, China 100094

2

School of Aeronautics and Astronautics, Beijing Institute of Technology, Beijing, China 100081

3

Advanced Simulation and Modeling, Inc. Madison, AL 35758, USA

Correspondence should be addressed to Qi Li; qi-ge-ge@163.com

Received 10 August 2021; Accepted 27 February 2022; Published 24 March 2022

Copyright © 2022 Qi Li et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative Commons

Attribution License (CC BY 4.0).

The aerodynamic configuration of the Tianwen-1 Mars entry module that adopts a blunt-nosed and short body shape has obvious

dynamic instability from transonic to supersonic speeds, which may bring risk to parachute deployment. The unsteady detached

eddy of the entry module cannot be accurately simulated by the Reynolds-Averaged Navier-Stokes (RANS) model, while the

computational cost for direct numerical simulation (DNS) and large eddy simulation (LES) is huge. It is difficult to implement

these methods in the coupled engineering calculation of unsteady flow and motion. This paper proposes the integrated

numerical simulation method of computational fluid dynamics and rigid body dynamics (CFD/RBD) based on detached eddy

simulation (DES) and calculates and studies the dynamic characteristics of attitude oscillation of the Mars entry module in free

flight from transonic to supersonic speeds with one degree of freedom (1-DOF) at small releasing angle of attack. In addition,

the unstable range of Mach number and angle of attack are determined, and the effect of different afterbody shapes on

dynamic stability is analyzed.

1. Introduction

The Tianwen-1 probe successfully landed on the predetermined landing area of the southern Utopia Planaria on

May 15, 2021, opening a new era of China’s landing and

exploring on Mars.

Mars is the planet with the most Earth-like environment

that has ever been detected, attracting the most interest from

human race. The history of using space probes to explore

Mars almost runs through the whole aerospace history of

human beings. Since the 1960s, nearly 50 Mars exploration

missions have been launched by the Soviet Union, the

United States, Japan, Russia, India, Europe, and other countries, but more than half failed [1]. Only ten probes from the

United States and China succeeded in the exploration missions of the surface of Mars.

The atmosphere of Mars is thin and its atmospheric density on the surface is only 1%~10% of that of the Earth [2, 3].

Therefore, the process of Mars entry, descent, and landing

(EDL) requires the combined action of aerodynamic shape,

parachute, and other deceleration methods to ensure the safe

landing of a probe and carry out the next step of work.

Tianwen-1 adopts three deceleration methods, namely, the

aerodynamic shape, supersonic parachute, and thrust

reverser, which makes the probe decelerate to 0 m/s after

entering the Martian atmosphere at a speed of 4.8 km/s

and achieve a soft landing on the surface [1] of Mars. Therefore, whether the multiple deceleration methods can be

safely connected is the key to the success of the mission of

Mars EDL.

Due to the rarefied atmosphere of Mars, for the higher

efficiency of aerodynamic deceleration, the aerodynamic

configuration of a Mars entry module is generally designed

as a blunt-body with large angle for higher drag [4–7]. However, such blunt-body presents dynamic instability when it

decelerates to below Mach 3.5 and becomes more unstable

with the decrease in the Mach number. In extreme cases,

there may even be a risk that the parachute cannot be safely

opened due to the attitude oscillation caused by the dynamic

instability [8]. Therefore, accurately predicting the dynamic

characteristics of the entry module in free flight in transonic

and supersonic speeds and determining the range of Mach

AAAS

Space: Science & Technology

Volume 2022, Article ID 9753286, 15 pages

https://doi.org/10.34133/2022/9753286

17

Research Article

Study on Dynamic Characteristics of Mars Entry Module in

Transonic and Supersonic Speeds

Qi Li,1 Rui Zhao,2 Sijun Zhang,3 Wei Rao,1 and Haogong Wei 1

1

Beijing Institute of Spacecraft System Engineering, CAST, Beijing, China 100094

2

School of Aeronautics and Astronautics, Beijing Institute of Technology, Beijing, China 100081

3

Advanced Simulation and Modeling, Inc. Madison, AL 35758, USA

Correspondence should be addressed to Qi Li; qi-ge-ge@163.com

Received 10 August 2021; Accepted 27 February 2022; Published 24 March 2022

Copyright © 2022 Qi Li et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative Commons

Attribution License (CC BY 4.0).

The aerodynamic configuration of the Tianwen-1 Mars entry module that adopts a blunt-nosed and short body shape has obvious

dynamic instability from transonic to supersonic speeds, which may bring risk to parachute deployment. The unsteady detached

eddy of the entry module cannot be accurately simulated by the Reynolds-Averaged Navier-Stokes (RANS) model, while the

computational cost for direct numerical simulation (DNS) and large eddy simulation (LES) is huge. It is difficult to implement

these methods in the coupled engineering calculation of unsteady flow and motion. This paper proposes the integrated

numerical simulation method of computational fluid dynamics and rigid body dynamics (CFD/RBD) based on detached eddy

simulation (DES) and calculates and studies the dynamic characteristics of attitude oscillation of the Mars entry module in free

flight from transonic to supersonic speeds with one degree of freedom (1-DOF) at small releasing angle of attack. In addition,

the unstable range of Mach number and angle of attack are determined, and the effect of different afterbody shapes on

dynamic stability is analyzed.

1. Introduction

The Tianwen-1 probe successfully landed on the predetermined landing area of the southern Utopia Planaria on

May 15, 2021, opening a new era of China’s landing and

exploring on Mars.

Mars is the planet with the most Earth-like environment

that has ever been detected, attracting the most interest from

human race. The history of using space probes to explore

Mars almost runs through the whole aerospace history of

human beings. Since the 1960s, nearly 50 Mars exploration

missions have been launched by the Soviet Union, the

United States, Japan, Russia, India, Europe, and other countries, but more than half failed [1]. Only ten probes from the

United States and China succeeded in the exploration missions of the surface of Mars.

The atmosphere of Mars is thin and its atmospheric density on the surface is only 1%~10% of that of the Earth [2, 3].

Therefore, the process of Mars entry, descent, and landing

(EDL) requires the combined action of aerodynamic shape,

parachute, and other deceleration methods to ensure the safe

landing of a probe and carry out the next step of work.

Tianwen-1 adopts three deceleration methods, namely, the

aerodynamic shape, supersonic parachute, and thrust

reverser, which makes the probe decelerate to 0 m/s after

entering the Martian atmosphere at a speed of 4.8 km/s

and achieve a soft landing on the surface [1] of Mars. Therefore, whether the multiple deceleration methods can be

safely connected is the key to the success of the mission of

Mars EDL.

Due to the rarefied atmosphere of Mars, for the higher

efficiency of aerodynamic deceleration, the aerodynamic

configuration of a Mars entry module is generally designed

as a blunt-body with large angle for higher drag [4–7]. However, such blunt-body presents dynamic instability when it

decelerates to below Mach 3.5 and becomes more unstable

with the decrease in the Mach number. In extreme cases,

there may even be a risk that the parachute cannot be safely

opened due to the attitude oscillation caused by the dynamic

instability [8]. Therefore, accurately predicting the dynamic

characteristics of the entry module in free flight in transonic

and supersonic speeds and determining the range of Mach

AAAS

Space: Science & Technology

Volume 2022, Article ID 9753286, 15 pages

https://doi.org/10.34133/2022/9753286

Study on Dynamic Characteristics of Mars Entry Module in

Transonic and Supersonic Speeds

Qi Li,1

Rui Zhao,2

Sijun Zhang,3

Wei Rao,1

and Haogong Wei1

1

Beijing Institute of Spacecraft System Engineering, CAST, Beijing, China 100094

2

School of Aeronautics and Astronautics, Beijing Institute of Technology, Beijing, China 100081

3

Advanced Simulation and Modeling, Inc. Madison, AL 35758, USA

Correspondence should be addressed to Qi Li; qi-ge-ge@163.com

Abstract: The aerodynamic configuration of the Tianwen-1 Mars entry module that adopts a blunt-nosed and short body shape has obvious

dynamic instability from transonic to supersonic speeds, which may bring risk to parachute deployment. The unsteady detached eddy of

the entry module cannot be accurately simulated by the Reynolds-Averaged Navier-Stokes (RANS) model, while the computational cost

for direct numerical simulation (DNS) and large eddy simulation (LES) is huge. It is difficult to implement these methods in the coupled

engineering calculation of unsteady flow and motion. This paper proposes the integrated numerical simulation method of computational

fluid dynamics and rigid body dynamics (CFD/RBD) based on detached eddy simulation (DES) and calculates and studies the dynamic

characteristics of attitude oscillation of the Mars entry module in free flight from transonic to supersonic speeds with one degree of

freedom (1-DOF) at small releasing angle of attack. In addition, the unstable range of Mach number and angle of attack are determined,

and the effect of different afterbody shapes on dynamic stability is analyzed.

18

number, the angle of attack, the dynamic derivative limit,

and the limit amplitudes during dynamic instability are the

important prerequisites for determining whether the attitude

control system of the entry module can effectively restrain

the attitude oscillation in transonic and supersonic speeds

and ensure safe parachute-opening.

The large-scale unsteady detached eddy in the afterbody

flow field of the entry module with a blunt-nosed and short

body cannot be accurately simulated by the ReynoldsAveraged Navier-Stokes (RANS) model. Direct numerical

simulation (DNS) and large eddy simulation (LES) can accurately simulate the pulsation and eddy motion of various

scales in the turbulent flow field, but the computational cost

for both is huge, making it difficult to calculate the dynamic

characteristics of unsteady coupling motion. In recent years,

detached eddy simulation (DES) has adopted the RANS turbulence model in the boundary layer to save the calculation

resources. For the separation zone far away from the object

surface, the subgrid model is adopted for the small-scale

eddy, and LES is employed for the large-scale eddy, which

can accurately and efficiently simulate the separated flow of

the entry module afterbody and the corresponding flow

stability [9].

This paper proposes the integrated numerical simulation

method of computational fluid dynamics and rigid body

dynamics (CFD/RBD) based on SA-DES. It uses leastsquares method as an identification algorithm of dynamic

derivatives to calculate and study the dynamic characteristics

of attitude oscillation of the Mars entry module in 1-DOF

free flight in transonic and supersonic speeds and low release

angle of attack.

2. Calculation Method

2.1. Fluid Flow Governing Equation and Its Algorithm. The

fluid flow governing equation is a three-dimensional

unsteady compressible Navier-Stokes (N-S) equation. In

the generalized curvilinear coordinate, the conservative form

of the dimensionless equation is

∂Q̂

∂t

+

∂F̂

∂ξ +

∂Ĝ

∂η

+

∂Ĥ

∂ζ = Ma∞

Re∞

∂F̂V

∂ξ +

∂ĜV

∂η

+

∂Ĥ V

∂ζ

 ,

ð1Þ

where the characteristic length L and the parameters of freestream, including the speed of sound of freestream c∞, temperature T∞, density ρ∞, and viscosity coefficient μ∞, are

taken as dimensionless parameters.

Equation (1) adopts the FDS discretion scheme of Roe in

space and achieves the second-order accuracy by MUSCL

interpolation and the MINMOD restrictor. The unsteady

time-marching methods include the dual time-stepping

LU-SGS algorithm or dual time-stepping subiterative

approach.

2.2. Solution to Rigid-Body Dynamic Equation. The dynamic

control equation of the entry module in free flight comprises

a six degree of freedom rigid-body dynamic equation set and

the related kinematic equation set. Among them, the

dynamics equation set for the center of mass of the entry

module in the inertial system can be expressed as

m

dV

*

dt = F

*

a: ð2Þ

The dynamic equation of rotation around the center of

mass under the body-axis coordinate system is

dH

*

dt + ω

* × H

*

= M

*

, ð3Þ

where F

*

a is the aerodynamic vector acting on the entry

module and H

*

is the vector of momentum moment of the

entry module relative to the center of mass. The above

dynamic equation set and the related kinematic equation

set can be coupled as a set of the nonlinear differential equation set with time as the independent variable.

20

10

0

–10

–20

0 0.05 0.1

Time (sec.)

Angle of attack (deg)

0

–0.001 –0.0005 0 0.0005 0.001

Reduced pitch rate

Pitching moment coefficient

Slope = pitch damping

Cms

–0.5

–1

–1.5

–2

–2.5

–3

Figure 1: Least-squares method for dynamic derivative identification [11].

2 Space: Science & Technology

In this paper, the fourth-order Runge-Kutta method is

used to solve differential equations, and the attitude angle

is calculated with the dual-Euler method. Thus, the displacement and attitude angle of the entry module in three directions at the next moment can be obtained.

For the 1-DOF free motion, with the pitching motion as

an example, only static and dynamic derivatives are considered, and the high-order derivatives are ignored. The

second-order differential equation (dimensionless) of the 1-

DOF free vibration of the capsule is as follows:

Iz

€θ = Cmq + Cmα_

� �_

θ + Cmαθ, ð4Þ

where is the dimensionless rotational inertia; Cmq + Cmα_ is

the dynamic derivative; and Cmα is the static derivative.

Let

a = −

Cmq + Cmα_

Iz

,

b = − Cmα

Iz

:

ð5Þ

Equation (4) can be rewritten as

€θ + a_

θ + bθ = 0: ð6Þ

The corresponding characteristic equation is

r

2 + ar + b = 0 ð7Þ

The characteristic root is r = ð−a/2Þ ±

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ða/2Þ

2 − b

q

=

ð−a/2Þ ± ffiffiffi

Δ

p = λ ± ωi.

In general, the capsule is in a state of static stability,

namely, b > 0. Normally, the dimensionless rotational inertia

T (s)

0 0.02 0.04 0.06 0.08 0.1

–30

30

(a) Mach=1.5

(b) Mach=2.5

Present

Ref

(c) Mach=3.5

20

10

0

–10

Pitch angle (deg)

–20

T (s)

0 0.02 0.04 0.06 0.08 0.1

–30

30

20

10

0

–10

Pitch angle (deg)

–20

T (s)

0 0.02 0.04 0.06 0.08 0.1

–30

30

20

10

0

–10

Pitch angle (deg)

–20

Figure 3: Comparison between the calculated pitch angle of MER

model and the reference value.

43.4°

80.7°

20.0°

Ø 70.00

Ø 16.38

R17.53

R1.75

39.62

25.12

Figure 2: Aerodynamic configuration and dimensions of the

ballistic target test model of MER.

Space: Science & Technology 3

19

number, the angle of attack, the dynamic derivative limit,

and the limit amplitudes during dynamic instability are the

important prerequisites for determining whether the attitude

control system of the entry module can effectively restrain

the attitude oscillation in transonic and supersonic speeds

and ensure safe parachute-opening.

The large-scale unsteady detached eddy in the afterbody

flow field of the entry module with a blunt-nosed and short

body cannot be accurately simulated by the ReynoldsAveraged Navier-Stokes (RANS) model. Direct numerical

simulation (DNS) and large eddy simulation (LES) can accurately simulate the pulsation and eddy motion of various

scales in the turbulent flow field, but the computational cost

for both is huge, making it difficult to calculate the dynamic

characteristics of unsteady coupling motion. In recent years,

detached eddy simulation (DES) has adopted the RANS turbulence model in the boundary layer to save the calculation

resources. For the separation zone far away from the object

surface, the subgrid model is adopted for the small-scale

eddy, and LES is employed for the large-scale eddy, which

can accurately and efficiently simulate the separated flow of

the entry module afterbody and the corresponding flow

stability [9].

This paper proposes the integrated numerical simulation

method of computational fluid dynamics and rigid body

dynamics (CFD/RBD) based on SA-DES. It uses leastsquares method as an identification algorithm of dynamic

derivatives to calculate and study the dynamic characteristics

of attitude oscillation of the Mars entry module in 1-DOF

free flight in transonic and supersonic speeds and low release

angle of attack.

2. Calculation Method

2.1. Fluid Flow Governing Equation and Its Algorithm. The

fluid flow governing equation is a three-dimensional

unsteady compressible Navier-Stokes (N-S) equation. In

the generalized curvilinear coordinate, the conservative form

of the dimensionless equation is

∂Q̂

∂t

+

∂F̂

∂ξ +

∂Ĝ

∂η

+

∂Ĥ

∂ζ = Ma∞

Re∞

∂F̂V

∂ξ +

∂ĜV

∂η

+

∂Ĥ V

∂ζ

,

ð1Þ

where the characteristic length L and the parameters of freestream, including the speed of sound of freestream c∞, temperature T∞, density ρ∞, and viscosity coefficient μ∞, are

taken as dimensionless parameters.

Equation (1) adopts the FDS discretion scheme of Roe in

space and achieves the second-order accuracy by MUSCL

interpolation and the MINMOD restrictor. The unsteady

time-marching methods include the dual time-stepping

LU-SGS algorithm or dual time-stepping subiterative

approach.

2.2. Solution to Rigid-Body Dynamic Equation. The dynamic

control equation of the entry module in free flight comprises

a six degree of freedom rigid-body dynamic equation set and

the related kinematic equation set. Among them, the

dynamics equation set for the center of mass of the entry

module in the inertial system can be expressed as

m

dV

*

dt = F

*

a: ð2Þ

The dynamic equation of rotation around the center of

mass under the body-axis coordinate system is

dH

*

dt + ω

* × H

*

= M

*

, ð3Þ

where F

*

a is the aerodynamic vector acting on the entry

module and H

*

is the vector of momentum moment of the

entry module relative to the center of mass. The above

dynamic equation set and the related kinematic equation

set can be coupled as a set of the nonlinear differential equation set with time as the independent variable.

20

10

0

–10

–20

0 0.05 0.1

Time (sec.)

Angle of attack (deg)

0

–0.001 –0.0005 0 0.0005 0.001

Reduced pitch rate

Pitching moment coefficient

Slope = pitch damping

Cms

–0.5

–1

–1.5

–2

–2.5

–3

Figure 1: Least-squares method for dynamic derivative identification [11].

2 Space: Science & Technology

In this paper, the fourth-order Runge-Kutta method is

used to solve differential equations, and the attitude angle

is calculated with the dual-Euler method. Thus, the displacement and attitude angle of the entry module in three directions at the next moment can be obtained.

For the 1-DOF free motion, with the pitching motion as

an example, only static and dynamic derivatives are considered, and the high-order derivatives are ignored. The

second-order differential equation (dimensionless) of the 1-

DOF free vibration of the capsule is as follows:

Iz

€θ = Cmq + Cmα_

� �_

θ + Cmαθ, ð4Þ

where is the dimensionless rotational inertia; Cmq + Cmα_ is

the dynamic derivative; and Cmα is the static derivative.

Let

a = −

Cmq + Cmα_

Iz

,

b = − Cmα

Iz

:

ð5Þ

Equation (4) can be rewritten as

€θ + a_

θ + bθ = 0: ð6Þ

The corresponding characteristic equation is

r

2 + ar + b = 0 ð7Þ

The characteristic root is r = ð−a/2Þ ±

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ða/2Þ

2 − b

q

=

ð−a/2Þ ± ffiffiffi

Δ

p = λ ± ωi.

In general, the capsule is in a state of static stability,

namely, b > 0. Normally, the dimensionless rotational inertia

T (s)

0 0.02 0.04 0.06 0.08 0.1

–30

30

(a) Mach=1.5

(b) Mach=2.5

Present

Ref

(c) Mach=3.5

20

10

0

–10

Pitch angle (deg)

–20

T (s)

0 0.02 0.04 0.06 0.08 0.1

–30

30

20

10

0

–10

Pitch angle (deg)

–20

T (s)

0 0.02 0.04 0.06 0.08 0.1

–30

30

20

10

0

–10

Pitch angle (deg)

–20

Figure 3: Comparison between the calculated pitch angle of MER

model and the reference value.

43.4°

80.7°

20.0°

Ø 70.00

Ø 16.38

R17.53

R1.75

39.62

25.12

Figure 2: Aerodynamic configuration and dimensions of the

ballistic target test model of MER.

Space: Science & Technology 3

20

is Iz > >1, and Δ < 0. Therefore, the root of the characteristic

equation is a pair of conjugate complex roots, and

λ = − a

2 = Cmq + Cmα_

2Iz

,

ω =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Cmq + Cmα_

2Iz

� �2

+

Cmα

Iz

�

�

�

�

�

�

�

�

s

:

ð8Þ

Table 1: Comparison of static and dynamic derivatives of the MER model under different Mach numbers with the reference value.

Mach 1.5 Mach 2.5 Mach 3.5

Reference This study Reference This study Reference This study

Cmα 0.1031 0.0983 0.1035 0.0971 0.1045 0.0962

Cmq + Cmα_ 0.2569 0.1547 -0.3094 -0.2774 -0.4311 -0.3886

L

D

Unfolded

trimming tab

(a) Entry module with folded

trimming tab

(b) Entry module with unfolded

trimming tab

Figure 4: Aerodynamic configuration of Tianwen-1 entry module.

(a) Entry module with folded trimming tab (b) Entry module with unfolded trimming tab

Figure 5: Dynamic simulation grid of the entry module in free flight.

Table 2: Dynamic mass characteristics of the entry module.

Relative position of the center of mass Moment of

inertia (kg.m2

)

Xcg/D 0.28 Ixx 1190.8

Ycg/D 0 (folded trimming tab)

0.009 (unfolded trimming tab) Iyy 972.0

Zcg/D 0 Izz 1020.5

4 Space: Science & Technology

The special solution to Equation (6) is obtained from the

initial conditions:

θ = Aeλt cos ð Þ ωt + φ ,

A = θ0 1 +

λ2

ω2

!1/2

,

φ = tan−1 λ

ω :

ð9Þ

From Equation (9), the motion of the capsule is the

vibration with the period T = 2π/ω, but different from that

of the simple harmonic vibration, its amplitude changes

exponentially with time t. The positive or negative value of

λ determines whether the motion of the capsule near the

equilibrium angle of attack diverges or converges, which

indicates that the sign of the dynamic derivative determines

the dynamic stability of the capsule.

The time-history curves of pitch angles can be obtained

by calculation. Pitch angles θ1 and θ2 (corresponding to θ1

and t1 and t2 = t1 + T) with one period part from each other

are selected from the curves:

θ1 = Aeλt1 cos ωt ð Þ 1 + φ ,

θ2 = Aeλt2 cos ωt ð Þ 2 + φ = Aeλt2 cos ωt ð Þ 1 + φ + 2π :

ð10Þ

The following can be obtained by dividing the two equations:

Cmq + Cmα_

� �

0 = 2Iz

T

ln θ2

θ1

,

Cmα ð Þ0≈− 4π2Iz

T2 :

ð11Þ

Therefore, the static and dynamic derivatives of the capsule can be obtained.

2.3. SA-DES Method. The basic model of DES is the SpalartAllmaras (SA) model [10]. The differential equation for solving the viscosity coefficient bν of turbulent motion in this

model is as follows:

∂bν

∂t + uj

∂bν

∂xj

= Cb1 1 − f t2

h i

Ωbν

+ M∞

Re

Cb1 1 − f t2

� �

f ν2 + f t2

h i 1

κ2 − CW1

f W

� � bν

d

� �2

− M∞

Re

Cb2

σ bν ∂2bν

∂x2

j

+ M∞

Re

1

σ

∂

∂xj

ν + 1+ Cb2

� �bν � � ∂bν

∂xj

" #

:

ð12Þ

In Equation (12), d is the closest distance to the object

surface, and the function f W is defined as

f W = g

1 + C6

W3

g6 + C6

W3

" #1/6

= g−6 + C−6

W3

1 + C−6

W3

" #−1/6

,

g = r + CW2 r

6 − r � �, r = bν

̂Sð Þ Re/M∞ κ2d2 :

ð13Þ

The first item on the right side of Equation (12) is the

generation item. The second item is the dissipation item,

and the rest are diffusion items. The variables of the generation item are defined as

̂S = Ω + bνf ν2

ð Þ Re/M∞ κ2d2 , f ν2 = 1 − χ

1 + χf ν1

, ð14Þ

where Ω is vorticity.

The DES method is to replace ~d in the equation with dw,

and the expression of dw is given as follows:

~d = min dw ð Þ , CDESΔ , ð15Þ

Table 3: Calculation state of numerical simulation in 1-DOF free flight.

Oscillation direction Mach Initial α (

°

) Initial β (

°

) State of trimming tab

Pitching

1.5 and 2 -2 0 Unfolded

1.5, 2.5, and 3 -5 0 Unfolded

1.5, 2, 2.5, and 3 -2 0 Folded

2, 2.5, and 3 -5 0 Folded

Table 4: Freestream parameters of actual gas of Mars in free flight.

Mach

number

Freestream

velocity (m/s)

Density

(kg/m3

)

Temperature

(K)

Pressure

(Pa)

1.2 272.93 0.00858 209.41 344.22

1.5 338.11 0.00708 205.67 278.78

1.75 391.49 0.00595 202.59 230.99

2.0 444.31 0.00516 199.43 197.21

2.5 546.98 0.00389 193.43 144.24

3.0 649.54 0.00326 189.43 118.43

Space: Science & Technology 5

21

is Iz > >1, and Δ < 0. Therefore, the root of the characteristic

equation is a pair of conjugate complex roots, and

λ = − a

2 = Cmq + Cmα_

2Iz

,

ω =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Cmq + Cmα_

2Iz

� �2

+

Cmα

Iz

�

�

�

�

�

�

�

�

s

:

ð8Þ

Table 1: Comparison of static and dynamic derivatives of the MER model under different Mach numbers with the reference value.

Mach 1.5 Mach 2.5 Mach 3.5

Reference This study Reference This study Reference This study

Cmα 0.1031 0.0983 0.1035 0.0971 0.1045 0.0962

Cmq + Cmα_ 0.2569 0.1547 -0.3094 -0.2774 -0.4311 -0.3886

L

D

Unfolded

trimming tab

(a) Entry module with folded

trimming tab

(b) Entry module with unfolded

trimming tab

Figure 4: Aerodynamic configuration of Tianwen-1 entry module.

(a) Entry module with folded trimming tab (b) Entry module with unfolded trimming tab

Figure 5: Dynamic simulation grid of the entry module in free flight.

Table 2: Dynamic mass characteristics of the entry module.

Relative position of the center of mass Moment of

inertia (kg.m2

)

Xcg/D 0.28 Ixx 1190.8

Ycg/D 0 (folded trimming tab)

0.009 (unfolded trimming tab) Iyy 972.0

Zcg/D 0 Izz 1020.5

4 Space: Science & Technology

The special solution to Equation (6) is obtained from the

initial conditions:

θ = Aeλt cos ð Þ ωt + φ ,

A = θ0 1 +

λ2

ω2

!1/2

,

φ = tan−1 λ

ω :

ð9Þ

From Equation (9), the motion of the capsule is the

vibration with the period T = 2π/ω, but different from that

of the simple harmonic vibration, its amplitude changes

exponentially with time t. The positive or negative value of

λ determines whether the motion of the capsule near the

equilibrium angle of attack diverges or converges, which

indicates that the sign of the dynamic derivative determines

the dynamic stability of the capsule.

The time-history curves of pitch angles can be obtained

by calculation. Pitch angles θ1 and θ2 (corresponding to θ1

and t1 and t2 = t1 + T) with one period part from each other

are selected from the curves:

θ1 = Aeλt1 cos ωt ð Þ 1 + φ ,

θ2 = Aeλt2 cos ωt ð Þ 2 + φ = Aeλt2 cos ωt ð Þ 1 + φ + 2π :

ð10Þ

The following can be obtained by dividing the two equations:

Cmq + Cmα_

� �

0 = 2Iz

T

ln θ2

θ1

,

Cmα ð Þ0≈− 4π2Iz

T2 :

ð11Þ

Therefore, the static and dynamic derivatives of the capsule can be obtained.

2.3. SA-DES Method. The basic model of DES is the SpalartAllmaras (SA) model [10]. The differential equation for solving the viscosity coefficient bν of turbulent motion in this

model is as follows:

∂bν

∂t + uj

∂bν

∂xj

= Cb1 1 − f t2

h iΩbν

+ M∞

Re

Cb1 1 − f t2

� �f ν2 + f t2

h i 1

κ2 − CW1

f W

� � bν

d

� �2

− M∞

Re

Cb2

σ bν ∂2bν

∂x2

j

+ M∞

Re

1

σ

∂

∂xj

ν + 1+ Cb2

� �bν � � ∂bν

∂xj

" #:

ð12Þ

In Equation (12), d is the closest distance to the object

surface, and the function f W is defined as

f W = g

1 + C6

W3

g6 + C6

W3

" #1/6

= g−6 + C−6

W3

1 + C−6

W3

" #−1/6

,

g = r + CW2 r

6 − r � �, r = bν

̂Sð Þ Re/M∞ κ2d2 :

ð13Þ

The first item on the right side of Equation (12) is the

generation item. The second item is the dissipation item,

and the rest are diffusion items. The variables of the generation item are defined as

̂S = Ω + bνf ν2

ð Þ Re/M∞ κ2d2 , f ν2 = 1 − χ

1 + χf ν1

, ð14Þ

where Ω is vorticity.

The DES method is to replace ~d in the equation with dw,

and the expression of dw is given as follows:

~d = min dw ð Þ , CDESΔ , ð15Þ

Table 3: Calculation state of numerical simulation in 1-DOF free flight.

Oscillation direction Mach Initial α (

°

) Initial β (

°

) State of trimming tab

Pitching

1.5 and 2 -2 0 Unfolded

1.5, 2.5, and 3 -5 0 Unfolded

1.5, 2, 2.5, and 3 -2 0 Folded

2, 2.5, and 3 -5 0 Folded

Table 4: Freestream parameters of actual gas of Mars in free flight.

Mach

number

Freestream

velocity (m/s)

Density

(kg/m3

)

Temperature

(K)

Pressure

(Pa)

1.2 272.93 0.00858 209.41 344.22

1.5 338.11 0.00708 205.67 278.78

1.75 391.49 0.00595 202.59 230.99

2.0 444.31 0.00516 199.43 197.21

2.5 546.98 0.00389 193.43 144.24

3.0 649.54 0.00326 189.43 118.43

Space: Science & Technology 5

22

where CDES is a calibration constant equal to 0.65; dw is the

distance to the wall surface; and Δ is the largest grid space in

the area, defined as Δ = max ðΔx, Δy, ΔzÞ. In the near-wall

region, dw < 0:65Δ, ~d = dw, which is represented by the SA

model and can be solved by the RANS method. In the flow

separation region, dw > 0:65Δ, ~d = 0:65Δ, and the turbulent

stress is solved by the LES subgrid model:

~v ≈ Δ2

Ω ð Þ DES ,

vSGS ≈ Δ2

S ð Þ Smagorinsky , ð16Þ

where S = ffiffiffiffiffiffiffiffiffiffiffi

2SijSij p and Sij is the deformation rate tensor of

velocity.

2.4. Identification Method of Dynamic Derivatives. After the

numerical simulation of free flight is carried out to obtain

the oscillation curves of attitude and aerodynamic moment

of the entry module within several periods, dynamic derivatives are identified according to the linearized dynamic

derivative [11]. With the pitching direction as an example,

according to the definition of linearization, there is a linear

relationship between the pitching moment coefficient at

the same angle of attack and the corresponding dimensionless angular velocity at each moment during the free motion

(a) Ma=1.2, α=0° (b) Ma=1.2, α=10°

(c) Ma=1.5, α=0° (d) Ma=1.5, α=10°

P/P∝ P/P∝

P/P∝ P/P∝

Figure 6: Cloud image of pressure field on symmetry plane of Mars entry module with trim tab unfolded.

6 Space: Science & Technology

of the entry module, as shown in the following equation. The

slope is the value of the dynamic derivative, which can be

obtained by the least-squares method.

Cm − Cms − Cmq ⋅ ql

2V∞

= 0, ð17Þ

where Cm is the pitching moment coefficient at a certain

moment; Cms is the static pitching moment coefficient; Cmq

is the pitching damping derivative; and q is the dimensionless angular velocity at a certain moment.

3. Verification of Algorithm

The pitching attitude and dynamic derivative identification

results in free flight tests within the supersonic ballistic range

of Mars probe MER [11, 12], as shown in Figure 1, are used

to verify the algorithm in this paper and evaluate the ability

of the calculation method to predict the dynamic characteristics of the entry module with the blunt-nosed and short

body. MER is a Mars probe used by NASA in 2003 to implement a Mars exploration project. The main purpose is to

send the probes named “Spirit” and “Opportunity” to the

surface of Mars for detection. The aerodynamic configuration and dimensions of the ballistic target test model of

MER are shown in Figure 2.

(a) Ma=2.5, α=0° (b) Ma=2.5, α=10°

(c) Ma=3.0, α=0° (d) Ma=3.0, α=10°

P/P∝ P/P∝

P/P∝ P/P∝

Figure 7: Cloud image of pressure field on symmetry plane of Mars entry module with the trim tab unfolded.

Space: Science & Technology 7

23

where CDES is a calibration constant equal to 0.65; dw is the

distance to the wall surface; and Δ is the largest grid space in

the area, defined as Δ = max ðΔx, Δy, ΔzÞ. In the near-wall

region, dw < 0:65Δ, ~d = dw, which is represented by the SA

model and can be solved by the RANS method. In the flow

separation region, dw > 0:65Δ, ~d = 0:65Δ, and the turbulent

stress is solved by the LES subgrid model:

~v ≈ Δ2

Ω ð Þ DES ,

vSGS ≈ Δ2

S ð Þ Smagorinsky , ð16Þ

where S = ffiffiffiffiffiffiffiffiffiffiffi

2SijSij

p and Sij is the deformation rate tensor of

velocity.

2.4. Identification Method of Dynamic Derivatives. After the

numerical simulation of free flight is carried out to obtain

the oscillation curves of attitude and aerodynamic moment

of the entry module within several periods, dynamic derivatives are identified according to the linearized dynamic

derivative [11]. With the pitching direction as an example,

according to the definition of linearization, there is a linear

relationship between the pitching moment coefficient at

the same angle of attack and the corresponding dimensionless angular velocity at each moment during the free motion

(a) Ma=1.2, α=0° (b) Ma=1.2, α=10°

(c) Ma=1.5, α=0° (d) Ma=1.5, α=10°

P/P∝ P/P∝

P/P∝ P/P∝

Figure 6: Cloud image of pressure field on symmetry plane of Mars entry module with trim tab unfolded.

6 Space: Science & Technology

of the entry module, as shown in the following equation. The

slope is the value of the dynamic derivative, which can be

obtained by the least-squares method.

Cm − Cms − Cmq ⋅ ql

2V∞

= 0, ð17Þ

where Cm is the pitching moment coefficient at a certain

moment; Cms is the static pitching moment coefficient; Cmq

is the pitching damping derivative; and q is the dimensionless angular velocity at a certain moment.

3. Verification of Algorithm

The pitching attitude and dynamic derivative identification

results in free flight tests within the supersonic ballistic range

of Mars probe MER [11, 12], as shown in Figure 1, are used

to verify the algorithm in this paper and evaluate the ability

of the calculation method to predict the dynamic characteristics of the entry module with the blunt-nosed and short

body. MER is a Mars probe used by NASA in 2003 to implement a Mars exploration project. The main purpose is to

send the probes named “Spirit” and “Opportunity” to the

surface of Mars for detection. The aerodynamic configuration and dimensions of the ballistic target test model of

MER are shown in Figure 2.

(a) Ma=2.5, α=0° (b) Ma=2.5, α=10°

(c) Ma=3.0, α=0° (d) Ma=3.0, α=10°

P/P∝ P/P∝

P/P∝ P/P∝

Figure 7: Cloud image of pressure field on symmetry plane of Mars entry module with the trim tab unfolded.

Space: Science & Technology 7

24

The altitude is zero, and the Mach numbers are 1.5, 2.5,

and 3.5. The center of mass is fixed, and the initial release

angle of attack is 20°

. The model vibrates freely with only

1-DOF under the above flow conditions.

Figure 3 shows the time-history curves of pitch angles

(angle of attack) of 1-DOF vibration with three Mach

numbers. The calculated results match well with the

results from the reference [11]. From Figure 3, when the

model is at Mach 1.5, the amplitude of the angle of attack

increases gradually at the initial release angle of attack,

while the trim angle of attack is 0°

, which indicates that

the model is dynamically unstable in this state. However,

when the model is at Mach 2.5 and 3.5, the amplitude of the

angle of attack decreases gradually at the initial release angle

of attack, and the trim angle of attack converges to 0° in the

end, which indicates that the model is dynamically stable at

this time. Table 1 presents the comparison between the identified pitching static and dynamic derivatives and the values

from the reference [11]. The difference between the pitching

static derivative calculated by this paper and that from the reference is only 10%, and the dynamic derivative shows the consistent variation, with the error within 40%.

Alpha

–2 0 2 4 6 1 108 2

1.4

1.7

(a) Axial force coefficient of the module with

the trim tab unfolded

1.65

1.6

1.55

1.5

CA

1.45

Alpha

–2 0 2 4 6 1 108 2

–0.03

0.02

(b) Pitching moment coefficient of the module with

the trim tab unfolded

0.01

0

–0.01

–0.02

CMZ

Alpha

–12 –10 –8 –6 0–2–4 2

1.4

1.7

(c) Axial force coefficient of the module with

the trim tab folded

1.65

1.6

1.55

1.5

CA

1.45

Alpha

–12 –10 –8 –6 0–2–4 2

–0.02

0.01

(d) Pitching moment coefficient of the module with

the trim tab unfolded

0.005

0

–0.005

–0.01

CMZ

–0.015

Yizhankai_air_ma1.2

Yizhankai_mar_ma1.2

Yizhankai_air_ma1.5

Yizhankai_mar_ma1.5

Yizhankai_air_ma1.2

Yizhankai_mar_ma1.2

Yizhankai_air_ma1.5

Yizhankai_mar_ma1.5

Yishoulong_air_ma2.5

Yishoulong_mar_ma2.5

Yishoulong_air_ma3.0

Yishoulong_mar_ma3.0

Yishoulong_air_ma2.5

Yishoulong_mar_ma2.5

Yishoulong_air_ma3.0

Yishoulong_mar_ma3.0

Figure 8: Comparison of transonic and supersonic aerodynamic coefficients of the Mars entry module in air and Martian atmosphere.

8 Space: Science & Technology

4. Calculation Model and State

The calculation model is the shape of the Tianwen-1 entry

module, as shown in Figure 4. Figures 4(a) and 4(b), respectively, show the configuration of the entry module with

folded trimming tab and unfolded trimming tab. The maximum windward diameter D of the entry module is approximately 3.4 m, and the total height L of the entry module is

about 2.6 m. The grid diagrams of the wall surface and symmetrical plane are shown in Figure 5. The mass characteristics of the entry module are shown in Table 2, and the

calculation state of free flight is shown in Table 3. The

parameters of the freestream of the entry module in transonic and supersonic speeds are shown in Table 4. The density, temperature, and pressure in Table 4 are derived from

the Martian atmosphere model in reference [13]. According

to the calculation method of the equivalent specific heat

ratio of the Martian atmosphere [14, 15], the equivalent specific heat ratio across the transonic and supersonic speed

region is approximately 1.29.

5. Analysis of Calculation Results

5.1. Flow Field Analysis. Figures 6 and 7, respectively, show

the symmetrical plane pressure distribution nephogram of

Mars entry module with the trim wing deployed and the

trim wing retracted under typical conditions. It can be seen

from the figures that with the decrease of Mach number,

the distance of detached shock wave in front of the head of

the capsule increases and the intensity decreases gradually.

After the unfolded of the trim tab, the airflow compression

appears near the tip of the windward side of the trim wing,

Time (s)

0 5 10 15 20

–5

5

(a) Mach=1.5, folded trimming tab

Alpha

4

3

2

1

0

–1

–2

–3

–4

Time (s)

0 5 10 15 20

–5

5

(c) Mach=2.0, folded trimming tab

Alpha

4

3

2

1

0

–1

–2

–3

–4

Time (s)

0 5 10 15 20 25

–10

10

(d) Mach=2.0, unfolded trimming tab

Alpha

5

0

–5

Time (s)

0 5 10 15 20 25

–10

10

(b) Mach=1.5, unfolded trimming tab

Alpha

5

0

–5

Figure 9: Attitude oscillation in free flight of the entry module with folded trimming tab (release angle of attack: −2°

).

Space: Science & Technology 9

25

The altitude is zero, and the Mach numbers are 1.5, 2.5,

and 3.5. The center of mass is fixed, and the initial release

angle of attack is 20°

. The model vibrates freely with only

1-DOF under the above flow conditions.

Figure 3 shows the time-history curves of pitch angles

(angle of attack) of 1-DOF vibration with three Mach

numbers. The calculated results match well with the

results from the reference [11]. From Figure 3, when the

model is at Mach 1.5, the amplitude of the angle of attack

increases gradually at the initial release angle of attack,

while the trim angle of attack is 0°

, which indicates that

the model is dynamically unstable in this state. However,

when the model is at Mach 2.5 and 3.5, the amplitude of the

angle of attack decreases gradually at the initial release angle

of attack, and the trim angle of attack converges to 0° in the

end, which indicates that the model is dynamically stable at

this time. Table 1 presents the comparison between the identified pitching static and dynamic derivatives and the values

from the reference [11]. The difference between the pitching

static derivative calculated by this paper and that from the reference is only 10%, and the dynamic derivative shows the consistent variation, with the error within 40%.

Alpha

–2 0 2 4 6 1 108 2

1.4

1.7

(a) Axial force coefficient of the module with

the trim tab unfolded

1.65

1.6

1.55

1.5

CA

1.45

Alpha

–2 0 2 4 6 1 108 2

–0.03

0.02

(b) Pitching moment coefficient of the module with

the trim tab unfolded

0.01

0

–0.01

–0.02

CMZ

Alpha

–12 –10 –8 –6 0–2–4 2

1.4

1.7

(c) Axial force coefficient of the module with

the trim tab folded

1.65

1.6

1.55

1.5

CA

1.45

Alpha

–12 –10 –8 –6 0–2–4 2

–0.02

0.01

(d) Pitching moment coefficient of the module with

the trim tab unfolded

0.005

0

–0.005

–0.01

CMZ

–0.015

Yizhankai_air_ma1.2

Yizhankai_mar_ma1.2

Yizhankai_air_ma1.5

Yizhankai_mar_ma1.5

Yizhankai_air_ma1.2

Yizhankai_mar_ma1.2

Yizhankai_air_ma1.5

Yizhankai_mar_ma1.5

Yishoulong_air_ma2.5

Yishoulong_mar_ma2.5

Yishoulong_air_ma3.0

Yishoulong_mar_ma3.0

Yishoulong_air_ma2.5

Yishoulong_mar_ma2.5

Yishoulong_air_ma3.0

Yishoulong_mar_ma3.0

Figure 8: Comparison of transonic and supersonic aerodynamic coefficients of the Mars entry module in air and Martian atmosphere.

8 Space: Science & Technology

4. Calculation Model and State

The calculation model is the shape of the Tianwen-1 entry

module, as shown in Figure 4. Figures 4(a) and 4(b), respectively, show the configuration of the entry module with

folded trimming tab and unfolded trimming tab. The maximum windward diameter D of the entry module is approximately 3.4 m, and the total height L of the entry module is

about 2.6 m. The grid diagrams of the wall surface and symmetrical plane are shown in Figure 5. The mass characteristics of the entry module are shown in Table 2, and the

calculation state of free flight is shown in Table 3. The

parameters of the freestream of the entry module in transonic and supersonic speeds are shown in Table 4. The density, temperature, and pressure in Table 4 are derived from

the Martian atmosphere model in reference [13]. According

to the calculation method of the equivalent specific heat

ratio of the Martian atmosphere [14, 15], the equivalent specific heat ratio across the transonic and supersonic speed

region is approximately 1.29.

5. Analysis of Calculation Results

5.1. Flow Field Analysis. Figures 6 and 7, respectively, show

the symmetrical plane pressure distribution nephogram of

Mars entry module with the trim wing deployed and the

trim wing retracted under typical conditions. It can be seen

from the figures that with the decrease of Mach number,

the distance of detached shock wave in front of the head of

the capsule increases and the intensity decreases gradually.

After the unfolded of the trim tab, the airflow compression

appears near the tip of the windward side of the trim wing,

Time (s)

0 5 10 15 20

–5

5

(a) Mach=1.5, folded trimming tab

Alpha

4

3

2

1

0

–1

–2

–3

–4

Time (s)

0 5 10 15 20

–5

5

(c) Mach=2.0, folded trimming tab

Alpha

4

3

2

1

0

–1

–2

–3

–4

Time (s)

0 5 10 15 20 25

–10

10

(d) Mach=2.0, unfolded trimming tab

Alpha

5

0

–5

Time (s)

0 5 10 15 20 25

–10

10

(b) Mach=1.5, unfolded trimming tab

Alpha

5

0

–5

Figure 9: Attitude oscillation in free flight of the entry module with folded trimming tab (release angle of attack: −2°

).

Space: Science & Technology 9

26

while a large backflow low pressure area appears at the root

of the wing. In addition, it can be seen from the figures that

the wake region calculated based on DES model is quite

large and unstable. Therefore, even at zero angle of attack,

the pressure asymmetry caused by the unsteady effect of

the afterbody separation vortex is very obvious. For the configuration with unfolded trimming tab, the distribution of

the pressure field near the tab plate is very different Mach

numbers and angles of attack, indicating that the trimming

tab is sensitive to changes in the angle of attack and Mach

number.

5.2. Static Aerodynamic Force Calculation and Analysis.

Figure 8 shows the comparison of calculated aerodynamic

coefficients of the Mars entry module with the trim tab

unfolded in the air environment and the Martian atmosphere environment. It can be seen that at the same Mach

number, the axial force coefficient of the entry module in

Martian atmosphere is slightly larger than that in air environment. The linearity of pitching moment coefficient

changing with angle of attack is good, and the trim angle

of attack is all around 1 degree, and there is little difference

between the two environments.

5.3. Dynamic Stability Analysis before and after Unfolding

Trimming Tab. Figure 9 compares the characteristic curves

of free oscillation of the pitching attitude with 1-DOF when

the entry module is released at an initial angle of attack

of −2° in the states of Mach 1.5 and 2.0 with folded

and unfolded trimming tab. From the figure, the

(a) Mach=2.5, folded trimming tab

(c) Mach=3.0, folded trimming tab (d) Mach=3.0, unfolded trimming tab

Time (s)

0 5 10 15

–10

10

(b) Mach=2.5, unfolded trimming tab

5

0

–5

Alpha

Time (s)

0 5 10 15 20

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15 20

–10

10

5

0

–5

Alpha

Figure 10: Oscillation of supersonic pitching attitude of the entry module before and after unfolding trimming tab (release angle of

attack: −5°

).

10 Space: Science & Technology

divergence trend of attitude oscillation of the shape with

unfolded trimming tab is more obvious within the range of

Mach = 1:5 – 2:0 than that with folded trimming tab. In this

Mach range, the pitching oscillation of folded trimming tab

at a small angle of attack tends to be stable, while unfolded

trimming tab tends to oscillate and diverge, and the oscillation period is slightly less than that with folded trimming

tab. Therefore, the dynamic stability of the shape with

unfolded trimming tab is worse than that with folded trimming tab within the supersonic range of Mach = 1:5 – 2:0.

Figure 10 compares the characteristic curves of the free

oscillation of the pitching attitude with 1-DOF when the

entry module is released at an initial angle of attack of -5°

in the states of Ma2.5 and Ma3.0 with folded and unfolded

trimming tab. The convergence trend of attitude oscillation

of the shape with unfolded trimming tab is more evident

than that with folded trimming tab in the same state;

namely, the dynamic stability of the shape with unfolded

trimming tab is better than that with folded trimming tab

within the supersonic range of Mach = 2:5 – 3:0.

5.4. Attitude Oscillations at Different Release Angles of

Attack. Figure 11 shows the curves of the angle of attack

for the pitching attitude oscillation with 1-DOF when folding and unfolding the trimming tab of the entry module at

different release angles of attack under characteristic Mach

number. When the absolute value of the release angle of

attack increases, the oscillation of pitching attitude tends to

(a) Mach=1.5, unfolded trimming tab, α0

=−2°

(d) Mach=2.0, folded trimming tab, α0

=−5°

Time (s)

0 5 10 15

–10

10

(b) Mach=1.5, unfolded trimming tab, α0

=−5°

5

0

–5

Alpha

Time (s)

0 5 10 252015

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15 20

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15 20

–5

5

(c) Mach=2.0, folded trimming tab, α0

=−2°

Alpha

4

3

2

1

0

–1

–2

–3

–4

(f) Mach=2.5, folded trimming tab, α0

=−5°

Time (s)

0 5 10 15 20

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15

–5

5

(e) Mach=2.5, folded trimming tab, α0

=−2°

Alpha

4

3

2

1

0

–1

–2

–3

–4

(h) Mach=3.0, folded trimming tab, α0

=−5°

Time (s)

0 5 10 15 20

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15 20

–5

5

(g) Mach=3.0, folded trimming tab, α0

=−2°

Alpha

4

3

2

1

0

–1

–2

–3

–4

Figure 11: Oscillation of supersonic pitching attitude of entry module before and after unfolding the trimming tab.

Space: Science & Technology 11

27

while a large backflow low pressure area appears at the root

of the wing. In addition, it can be seen from the figures that

the wake region calculated based on DES model is quite

large and unstable. Therefore, even at zero angle of attack,

the pressure asymmetry caused by the unsteady effect of

the afterbody separation vortex is very obvious. For the configuration with unfolded trimming tab, the distribution of

the pressure field near the tab plate is very different Mach

numbers and angles of attack, indicating that the trimming

tab is sensitive to changes in the angle of attack and Mach

number.

5.2. Static Aerodynamic Force Calculation and Analysis.

Figure 8 shows the comparison of calculated aerodynamic

coefficients of the Mars entry module with the trim tab

unfolded in the air environment and the Martian atmosphere environment. It can be seen that at the same Mach

number, the axial force coefficient of the entry module in

Martian atmosphere is slightly larger than that in air environment. The linearity of pitching moment coefficient

changing with angle of attack is good, and the trim angle

of attack is all around 1 degree, and there is little difference

between the two environments.

5.3. Dynamic Stability Analysis before and after Unfolding

Trimming Tab. Figure 9 compares the characteristic curves

of free oscillation of the pitching attitude with 1-DOF when

the entry module is released at an initial angle of attack

of −2° in the states of Mach 1.5 and 2.0 with folded

and unfolded trimming tab. From the figure, the

(a) Mach=2.5, folded trimming tab

(c) Mach=3.0, folded trimming tab (d) Mach=3.0, unfolded trimming tab

Time (s)

0 5 10 15

–10

10

(b) Mach=2.5, unfolded trimming tab

5

0

–5

Alpha

Time (s)

0 5 10 15 20

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15 20

–10

10

5

0

–5

Alpha

Figure 10: Oscillation of supersonic pitching attitude of the entry module before and after unfolding trimming tab (release angle of

attack: −5°

).

10 Space: Science & Technology

divergence trend of attitude oscillation of the shape with

unfolded trimming tab is more obvious within the range of

Mach = 1:5 – 2:0 than that with folded trimming tab. In this

Mach range, the pitching oscillation of folded trimming tab

at a small angle of attack tends to be stable, while unfolded

trimming tab tends to oscillate and diverge, and the oscillation period is slightly less than that with folded trimming

tab. Therefore, the dynamic stability of the shape with

unfolded trimming tab is worse than that with folded trimming tab within the supersonic range of Mach = 1:5 – 2:0.

Figure 10 compares the characteristic curves of the free

oscillation of the pitching attitude with 1-DOF when the

entry module is released at an initial angle of attack of -5°

in the states of Ma2.5 and Ma3.0 with folded and unfolded

trimming tab. The convergence trend of attitude oscillation

of the shape with unfolded trimming tab is more evident

than that with folded trimming tab in the same state;

namely, the dynamic stability of the shape with unfolded

trimming tab is better than that with folded trimming tab

within the supersonic range of Mach = 2:5 – 3:0.

5.4. Attitude Oscillations at Different Release Angles of

Attack. Figure 11 shows the curves of the angle of attack

for the pitching attitude oscillation with 1-DOF when folding and unfolding the trimming tab of the entry module at

different release angles of attack under characteristic Mach

number. When the absolute value of the release angle of

attack increases, the oscillation of pitching attitude tends to

(a) Mach=1.5, unfolded trimming tab, α0

=−2°

(d) Mach=2.0, folded trimming tab, α0

=−5°

Time (s)

0 5 10 15

–10

10

(b) Mach=1.5, unfolded trimming tab, α0

=−5°

5

0

–5

Alpha

Time (s)

0 5 10 252015

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15 20

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15 20

–5

5

(c) Mach=2.0, folded trimming tab, α0

=−2°

Alpha

4

3

2

1

0

–1

–2

–3

–4

(f) Mach=2.5, folded trimming tab, α0

=−5°

Time (s)

0 5 10 15 20

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15

–5

5

(e) Mach=2.5, folded trimming tab, α0

=−2°

Alpha

4

3

2

1

0

–1

–2

–3

–4

(h) Mach=3.0, folded trimming tab, α0

=−5°

Time (s)

0 5 10 15 20

–10

10

5

0

–5

Alpha

Time (s)

0 5 10 15 20

–5

5

(g) Mach=3.0, folded trimming tab, α0

=−2°

Alpha

4

3

2

1

0

–1

–2

–3

–4

Figure 11: Oscillation of supersonic pitching attitude of entry module before and after unfolding the trimming tab.

Space: Science & Technology 11

28

converge; namely, the initial attitude will affect the oscillation characteristics of the entry module. Therefore, it can

be inferred that the angle of attack causing the dynamic

instability of the entry module should be limited to the small

angle of attack.

5.5. Dynamic Instability of the Entry Module in Transonic

and Supersonic Speeds. The dynamic derivative of the entry

module is identified by the least-squares method to obtain

the dynamic derivative at a small angle of attack for the

shape with folded and unfolded trimming tab under each

characteristic state, as shown in Tables 5 and 6, respectively.

The entry module with the folded trimming tab only shows

the dynamic instability within the angle of attack (−1°

, 1°

),

and the maximum dynamic derivative does not exceed 0.5.

However, when the trimming tab are unfolded, the entry

module is dynamically unstable within the angle of attack

(−4°

, 4°

), and the maximum dynamic derivative is close

to 1.5, as shown in Table 7. When Mach ≤ 2:0, the

dynamic instability derivative of the shape with unfolded

trimming tab is larger than that with folded trimming

tab. When Mach > 2:0, the dynamic instability of the

shape with folded trimming tab is stronger than that with

unfolded trimming tab.

5.6. Comparison of Dynamic Instability between Different

Afterbody Shapes. Afterbody shapes will affect the dynamic

instability of the entry module in transonic and supersonic

speeds by affecting the configuration of the separated vortex.

To compare the influences of different afterbody shapes on

dynamic stability, this paper calculates and compares the

pitching derivatives in free flight at a small angle of attack

and a transonic-supersonic speed between the entry module

with the tricone afterbody shape of Mars Science Laboratory

(MSL) [16] and that with the sphere-cone afterbody of

Tianwen-1. The comparison between the shapes of tricone

and sphere-cone afterbodies is shown in Figure 12. They

both have the same windward base and the first rear cone

Table 5: Dynamic derivative of the entry module with folded trimming tab at a small angle of attack and transonic-supersonic speed.

α (

°

) Cmq (α0 = −2°

) Cmq (α0 = −5°

)

M = 1:5 M = 2:0 M = 2:5 M = 3:0 M = 2:0 M = 2:5 M = 3:0

1 -0.08 -0.06 -0.07 -0.1 -0.18 -0.21 -0.22

0 0.45 0.28 0.54 0.16 0.19 0.24 0.13

-1 -0.08 -0.06 -0.07 -0.1 -0.18 -0.21 -0.22

Table 6: Dynamic derivative of the entry module with unfolded trimming tab at a small angle of attack and a transonic-supersonic speed.

α (

°

) Cmq (α0 = −2°

) Cmq (α0 = −5°

)

M = 1:2 M = 1:5 M = 1:75 M = 2:0 M = 1:5 M = 2:5 M = 3:0

5 -0.16 -0.07 -0.35 / -0.11 / /

4 0.27 0.83 0.02 -0.38 0.64 -0.27 /

3 0.57 1.27 0.26 0.04 0.68 -0.28 /

2 0.85 1.49 0.52 0.35 0.75 -0.26 -0.35

1 1.04 1.25 0.62 0.42 0.92 -0.19 -0.28

0 0.99 1.07 0.48 0.53 1.05 -0.09 -0.24

-1 0.41 0.66 0.33 -0.18 0.78 -0.15 -0.34

-2 -0.03 0.56 0.29 -0.2 0.51 -0.34 -0.38

-3 -0.38 -0.16 -0.15 -0.41 0.16 -0.45 /

-4 -0.47 -0.19 -0.44 -0.66 -0.14 -0.41 /

-5 / -0.15 / / -0.19 / /

Table 7: Dynamic derivatives of the entry module with unfolded trimming tab and different afterbody shapes at a small angle of attack and a

transonic-supersonic speed.

α (

°

) Cmq of tricone afterbody Cmq of sphere-cone afterbody

Mach 1.2 Mach 1.5 Mach 1.2 Mach 1.5

4 0.29 1.14 0.27 0.83

1 1.13 1.31 1.04 1.25

0 1.08 1.1 0.99 1.07

-1 0.45 0.9 0.41 0.66

-4 0.38 0.37 -0.47 -0.19

12 Space: Science & Technology

angle, and the maximum windward envelope, the center of

mass, and the moment of inertia are also consistent. The

shapes for calculation all have the unfolded trimming tab.

The layout and size parameters of trimming tab for the

two afterbody shapes of the entry module are the same.

The grid distribution of the wall surface and symmetry plane

is shown in Figure 13, and the grid topology of the two afterbody shapes is consistent.

The following table shows the dynamic derivative at a

small angle of attack corresponding to the entry module with

the two afterbody shapes in free flight with 1-DOF under

Mach 1.2 and 1.5, where all the release angles of attack are

2°

. With the same forebody shape and the configuration of

trimming tab, the angle of attack and the maximum

dynamic derivative of the dynamic instability of the tricone

afterbody in transonic and supersonic speeds are greater

(a) Grids of tri-cone afterbody (b) Grids of sphere-cone afterbody

Figure 13: Comparison of computational grids between unfolded trimming tab of tricone and sphere-cone afterbodies of the entry module.

Figure 12: Comparison between tricone and sphere-cone afterbodies of the entry module.

Space: Science & Technology 13

29

converge; namely, the initial attitude will affect the oscillation characteristics of the entry module. Therefore, it can

be inferred that the angle of attack causing the dynamic

instability of the entry module should be limited to the small

angle of attack.

5.5. Dynamic Instability of the Entry Module in Transonic

and Supersonic Speeds. The dynamic derivative of the entry

module is identified by the least-squares method to obtain

the dynamic derivative at a small angle of attack for the

shape with folded and unfolded trimming tab under each

characteristic state, as shown in Tables 5 and 6, respectively.

The entry module with the folded trimming tab only shows

the dynamic instability within the angle of attack (−1°

, 1°

),

and the maximum dynamic derivative does not exceed 0.5.

However, when the trimming tab are unfolded, the entry

module is dynamically unstable within the angle of attack

(−4°

, 4°

), and the maximum dynamic derivative is close

to 1.5, as shown in Table 7. When Mach ≤ 2:0, the

dynamic instability derivative of the shape with unfolded

trimming tab is larger than that with folded trimming

tab. When Mach > 2:0, the dynamic instability of the

shape with folded trimming tab is stronger than that with

unfolded trimming tab.

5.6. Comparison of Dynamic Instability between Different

Afterbody Shapes. Afterbody shapes will affect the dynamic

instability of the entry module in transonic and supersonic

speeds by affecting the configuration of the separated vortex.

To compare the influences of different afterbody shapes on

dynamic stability, this paper calculates and compares the

pitching derivatives in free flight at a small angle of attack

and a transonic-supersonic speed between the entry module

with the tricone afterbody shape of Mars Science Laboratory

(MSL) [16] and that with the sphere-cone afterbody of

Tianwen-1. The comparison between the shapes of tricone

and sphere-cone afterbodies is shown in Figure 12. They

both have the same windward base and the first rear cone

Table 5: Dynamic derivative of the entry module with folded trimming tab at a small angle of attack and transonic-supersonic speed.

α (

°

) Cmq (α0 = −2°

) Cmq (α0 = −5°

)

M = 1:5 M = 2:0 M = 2:5 M = 3:0 M = 2:0 M = 2:5 M = 3:0

1 -0.08 -0.06 -0.07 -0.1 -0.18 -0.21 -0.22

0 0.45 0.28 0.54 0.16 0.19 0.24 0.13

-1 -0.08 -0.06 -0.07 -0.1 -0.18 -0.21 -0.22

Table 6: Dynamic derivative of the entry module with unfolded trimming tab at a small angle of attack and a transonic-supersonic speed.

α (

°

) Cmq (α0 = −2°

) Cmq (α0 = −5°

)

M = 1:2 M = 1:5 M = 1:75 M = 2:0 M = 1:5 M = 2:5 M = 3:0

5 -0.16 -0.07 -0.35 / -0.11 / /

4 0.27 0.83 0.02 -0.38 0.64 -0.27 /

3 0.57 1.27 0.26 0.04 0.68 -0.28 /

2 0.85 1.49 0.52 0.35 0.75 -0.26 -0.35

1 1.04 1.25 0.62 0.42 0.92 -0.19 -0.28

0 0.99 1.07 0.48 0.53 1.05 -0.09 -0.24

-1 0.41 0.66 0.33 -0.18 0.78 -0.15 -0.34

-2 -0.03 0.56 0.29 -0.2 0.51 -0.34 -0.38

-3 -0.38 -0.16 -0.15 -0.41 0.16 -0.45 /

-4 -0.47 -0.19 -0.44 -0.66 -0.14 -0.41 /

-5 / -0.15 / / -0.19 / /

Table 7: Dynamic derivatives of the entry module with unfolded trimming tab and different afterbody shapes at a small angle of attack and a

transonic-supersonic speed.

α (

°

) Cmq of tricone afterbody Cmq of sphere-cone afterbody

Mach 1.2 Mach 1.5 Mach 1.2 Mach 1.5

4 0.29 1.14 0.27 0.83

1 1.13 1.31 1.04 1.25

0 1.08 1.1 0.99 1.07

-1 0.45 0.9 0.41 0.66

-4 0.38 0.37 -0.47 -0.19

12 Space: Science & Technology

angle, and the maximum windward envelope, the center of

mass, and the moment of inertia are also consistent. The

shapes for calculation all have the unfolded trimming tab.

The layout and size parameters of trimming tab for the

two afterbody shapes of the entry module are the same.

The grid distribution of the wall surface and symmetry plane

is shown in Figure 13, and the grid topology of the two afterbody shapes is consistent.

The following table shows the dynamic derivative at a

small angle of attack corresponding to the entry module with

the two afterbody shapes in free flight with 1-DOF under

Mach 1.2 and 1.5, where all the release angles of attack are

2°

. With the same forebody shape and the configuration of

trimming tab, the angle of attack and the maximum

dynamic derivative of the dynamic instability of the tricone

afterbody in transonic and supersonic speeds are greater

(a) Grids of tri-cone afterbody (b) Grids of sphere-cone afterbody

Figure 13: Comparison of computational grids between unfolded trimming tab of tricone and sphere-cone afterbodies of the entry module.

Figure 12: Comparison between tricone and sphere-cone afterbodies of the entry module.

Space: Science & Technology 13

30

than those of the sphere-cone afterbody. In other words, the

sphere-cone afterbody can improve the dynamic stability of

the entry module at a small angle of attack and a transonicsupersonic speed.

In order to analyze the reason why the dynamic stability

of the sphere-cone afterbody configuration is better than

that of the tricone afterbody configuration, the entry module

shape is divided into three parts, the forebody, the midpiece,

and the back-end. Figure 14 shows the subsection rules of

the two configurations of the entry module.

The 1-DOF free flight dynamic simulation under the

condition of Ma = 3:0, α = 0°

was carried out for the entry

module of the two afterbodies, respectively, and the pressure

field on the surface of the module body obtained was pieceally integrated. The method in Section 2.4 was used to complete the identification of the dynamic derivatives of the

pitch moment in each section. The piecewise contribution

of the dynamic derivatives of typical states under the two

afterbody configurations is shown in Table 8.

It can be seen from the table that the flow field of the

forebody of the entry module is dynamically stable; thus,

its contribution to the dynamic derivative is negative. Due

to unstable vortex separation, the contribution of the midpiece to the dynamic derivative is positive. The separation

vortex of the flow field in the back-end of the two configurations is obviously different, so the contributions of the two

back-end shapes to the dynamic derivative have obvious differences. In detail, the poor flow structure stability of the

tapered back-end will increase the dynamic instability of

the entry module, while the spherical back-end can reduce

the separation area of the afterbody. In other words, the

spherical back-end can reduce the instability of the separation vortex, so its contribution to the dynamic derivative of

the entry module is negative.

6. Conclusions

An integrated numerical simulation method of computational fluid dynamics and rigid body dynamics (CFD/RBD)

based on SA-DES is adopted in this paper to simulate the

dynamic characteristics of the Tianwen-1 Mars entry module before and after unfolding the trimming tab. The oscillation characteristics of pitching attitude and the identification

results of dynamic derivatives are analyzed, and the effects of

different angles of attack and afterbody shapes on dynamic

stability are compared. Conclusions can be drawn as follows:

(1) The entry module is generally dynamically unstable

at a small angle of attack within the transonicsupersonic range of Mach 1.2–3.0. The unstable

angle of attack is only (−1°

, 1°

) for the shape with

folded trimming tab, and the maximum dynamic

derivative is not greater than 0.5. The entry module

is dynamically unstable within the angle of attack

(−4°

, 4°

) after unfolding the trimming tab, and the

maximum dynamic derivative is close to 1.5

(2) The maximum dynamic instability of the shape with

the folded trimming tab is in the vicinity of Ma2.5,

and the maximum dynamic instability of the shape

with the unfolded trimming tab occurs at about

Mach 1.5. When the angle of attack for initial vibration increases, the convergence trend of attitude

oscillation grows

Table 8: The piecewise contribution of the dynamic derivatives of

typical states under the two afterbody configurations (Ma = 3:0,

α = 0°

).

Cmq Sphere-cone afterbody Tricone afterbody

Total 1.08 1.94

Forebody -0.31 -0.28

Midpiece 1.51 1.57

Back end -0.12 0.65

Forebody Midpiece

Back end Back end

Figure 14: Schematic diagram of compartmentalization of the entry module in two configurations.

14 Space: Science & Technology

(3) With the same forebody shape, the sphere-cone

afterbody can improve the dynamic stability of the

entry module in transonic and supersonic speeds

compared with the tricone afterbody, including

reducing the angle of attack of dynamic instability

and the extreme value of dynamic derivatives. It is

because the spherical back-end can reduce the separation area of the afterbody to reduce the instability

of the separation vortex. Thus, the contribution of

the spherical back-end to the dynamic derivative is

negative

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

All authors declare no possible conflicts of interests.

Authors’ Contributions

Li Qi is the main writer of this paper and has completed the

data collation and analysis related to the paper. Zhao Rui is

responsible for the research on the dynamic aerodynamic

modeling method of Mars entry module. Zhang Sijun completed the numerical simulation of dynamic characteristics.

Wei Haogong completed the identification and analysis of

dynamic derivatives. Rao Wei completed the creation of relevant research ideas of the paper.

Acknowledgments

This work came from the Tianwen-1 Mars exploration mission and was supported by the Natural Science Foundation

of China (Grant No. 11902025).

References

[1] G. E. N. G. Yan, Z. H. O. U. Jishi, L. I. Sha et al., “A brief introduction of the first Mars exploration mission in China,” Journal of Deep Space Exploration, vol. 5, no. 5, pp. 399–405, 2018.

[2] J. S. Martin, “Mars engineering model,” NASA-TM-108222,

1975.

[3] R. Wei and C. Guoliang, “The characters of deceleration and

landing technology on Mars explorer,” Spacecraft Recovery &

Remote Sensing, vol. 31, no. 4, 2010.

[4] Anon, “Entry data analysis for Viking landers l and 2 final

report,” NASA-TN-3770218, NASA-CR-159388, 1976.

[5] K. Edquist, A. Dyakonov, M. Wright, and C. Tang, “Aerothermodynamic design of the Mars science laboratory heatshield,”

in 41st AIAA Thermophysics Conference, San Antonio, Texas,

2009.

[6] W. Willcockson, “Mars pathfinder heatshield design and flight

experience,” Journal of Spacecraft and Rockets, vol. 36, no. 3,

pp. 374–379, 1999.

[7] T. Wei, X.-f. Yang, G. Ye-wei, and D. Yan-xia, “Review of

hypersonic aerodynamics and aerothermodynamics for Mars

entries,” Journal of Astronautics, vol. 38, no. 3, pp. 230–239,

2017.

[8] M. Schoenenberger and E. M. Queen, “Limit cycle analysis

applied to the oscillations of decelerating blunt-body entry

vehicles,” in NATO RTO Symposium AVT-152 on LimitCycle Oscillations and Other Amplitude-Limited, Self-Excited

Vibrations (No. RTO-MP-AVT-152), Norway, 2008.

[9] F. Deng, Y.-z. Wu, and L. Xue-qiang, “Simulation of vortex in

separated flows with DES,” Chinese Journal of Computational

Physics, vol. 25, no. 6, pp. 683–688, 2008.

[10] S. Xiao-pan, Z. Rui, R. Ji-li, and W. Yuan, “Numerical simulation of fluctuating pressure environment of Mars entry module,” Journal of Astronautics, vol. 39, 2018.

[11] S. M. Murman and M. J. Aftosmis, “Dynamic analysis of

atmospheric-entry probes and capsules,” in 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2007.

[12] M. Schoenenberger, W. Hathaway, L. Yates, and P. Desai,

“Ballistic range testing of the Mars exploration rover entry

capsule,” in 43rd AIAA Aerospace Sciences Meeting and

Exhibit, Reno, Nevada, 2005.

[13] S. R. Lewis, M. Collins, P. L. Read et al., “A climate database for

Mars,” Journal of Geophysical Research Planets, vol. 104,

no. E10, pp. 24177–24194, 1999.

[14] X.-f. Yang, T. Wei, and G. Ye-wei, “Hypersonic flow field prediction and aerodynamics analysis for MSL entry capsule,”

Journal of Astronautics, vol. 36, no. 4, pp. 383–389, 2015.

[15] E. H. Hirschel and W. Claus, Selected aerothermodynamic

design problems of hypersonic night vehicles, Springer Press,

Berlin, 2009.

[16] M. Schoenenberger, J. Van Norman, A. Dyakonov,

C. Karlgaard, D. Way, and P. Kutty, “Assessment of the reconstructed aerodynamics of the Mars science laboratory entry

vehicle,” in 23rd AAS/AIAA Space Flight Mechanics Meeting,

Kauai, HI, 2013.

Space: Science & Technology 15

31

than those of the sphere-cone afterbody. In other words, the

sphere-cone afterbody can improve the dynamic stability of

the entry module at a small angle of attack and a transonicsupersonic speed.

In order to analyze the reason why the dynamic stability

of the sphere-cone afterbody configuration is better than

that of the tricone afterbody configuration, the entry module

shape is divided into three parts, the forebody, the midpiece,

and the back-end. Figure 14 shows the subsection rules of

the two configurations of the entry module.

The 1-DOF free flight dynamic simulation under the

condition of Ma = 3:0, α = 0°

was carried out for the entry

module of the two afterbodies, respectively, and the pressure

field on the surface of the module body obtained was pieceally integrated. The method in Section 2.4 was used to complete the identification of the dynamic derivatives of the

pitch moment in each section. The piecewise contribution

of the dynamic derivatives of typical states under the two

afterbody configurations is shown in Table 8.

It can be seen from the table that the flow field of the

forebody of the entry module is dynamically stable; thus,

its contribution to the dynamic derivative is negative. Due

to unstable vortex separation, the contribution of the midpiece to the dynamic derivative is positive. The separation

vortex of the flow field in the back-end of the two configurations is obviously different, so the contributions of the two

back-end shapes to the dynamic derivative have obvious differences. In detail, the poor flow structure stability of the

tapered back-end will increase the dynamic instability of

the entry module, while the spherical back-end can reduce

the separation area of the afterbody. In other words, the

spherical back-end can reduce the instability of the separation vortex, so its contribution to the dynamic derivative of

the entry module is negative.

6. Conclusions

An integrated numerical simulation method of computational fluid dynamics and rigid body dynamics (CFD/RBD)

based on SA-DES is adopted in this paper to simulate the

dynamic characteristics of the Tianwen-1 Mars entry module before and after unfolding the trimming tab. The oscillation characteristics of pitching attitude and the identification

results of dynamic derivatives are analyzed, and the effects of

different angles of attack and afterbody shapes on dynamic

stability are compared. Conclusions can be drawn as follows:

(1) The entry module is generally dynamically unstable

at a small angle of attack within the transonicsupersonic range of Mach 1.2–3.0. The unstable

angle of attack is only (−1°

, 1°

) for the shape with

folded trimming tab, and the maximum dynamic

derivative is not greater than 0.5. The entry module

is dynamically unstable within the angle of attack

(−4°

, 4°

) after unfolding the trimming tab, and the

maximum dynamic derivative is close to 1.5

(2) The maximum dynamic instability of the shape with

the folded trimming tab is in the vicinity of Ma2.5,

and the maximum dynamic instability of the shape

with the unfolded trimming tab occurs at about

Mach 1.5. When the angle of attack for initial vibration increases, the convergence trend of attitude

oscillation grows

Table 8: The piecewise contribution of the dynamic derivatives of

typical states under the two afterbody configurations (Ma = 3:0,

α = 0°

).

Cmq Sphere-cone afterbody Tricone afterbody

Total 1.08 1.94

Forebody -0.31 -0.28

Midpiece 1.51 1.57

Back end -0.12 0.65

Forebody Midpiece

Back end Back end

Figure 14: Schematic diagram of compartmentalization of the entry module in two configurations.

14 Space: Science & Technology

(3) With the same forebody shape, the sphere-cone

afterbody can improve the dynamic stability of the

entry module in transonic and supersonic speeds

compared with the tricone afterbody, including

reducing the angle of attack of dynamic instability

and the extreme value of dynamic derivatives. It is

because the spherical back-end can reduce the separation area of the afterbody to reduce the instability

of the separation vortex. Thus, the contribution of

the spherical back-end to the dynamic derivative is

negative

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

All authors declare no possible conflicts of interests.

Authors’ Contributions

Li Qi is the main writer of this paper and has completed the

data collation and analysis related to the paper. Zhao Rui is

responsible for the research on the dynamic aerodynamic

modeling method of Mars entry module. Zhang Sijun completed the numerical simulation of dynamic characteristics.

Wei Haogong completed the identification and analysis of

dynamic derivatives. Rao Wei completed the creation of relevant research ideas of the paper.

Acknowledgments

This work came from the Tianwen-1 Mars exploration mission and was supported by the Natural Science Foundation

of China (Grant No. 11902025).

References

[1] G. E. N. G. Yan, Z. H. O. U. Jishi, L. I. Sha et al., “A brief introduction of the first Mars exploration mission in China,” Journal of Deep Space Exploration, vol. 5, no. 5, pp. 399–405, 2018.

[2] J. S. Martin, “Mars engineering model,” NASA-TM-108222,

1975.

[3] R. Wei and C. Guoliang, “The characters of deceleration and

landing technology on Mars explorer,” Spacecraft Recovery &

Remote Sensing, vol. 31, no. 4, 2010.

[4] Anon, “Entry data analysis for Viking landers l and 2 final

report,” NASA-TN-3770218, NASA-CR-159388, 1976.

[5] K. Edquist, A. Dyakonov, M. Wright, and C. Tang, “Aerothermodynamic design of the Mars science laboratory heatshield,”

in 41st AIAA Thermophysics Conference, San Antonio, Texas,

2009.

[6] W. Willcockson, “Mars pathfinder heatshield design and flight

experience,” Journal of Spacecraft and Rockets, vol. 36, no. 3,

pp. 374–379, 1999.

[7] T. Wei, X.-f. Yang, G. Ye-wei, and D. Yan-xia, “Review of

hypersonic aerodynamics and aerothermodynamics for Mars

entries,” Journal of Astronautics, vol. 38, no. 3, pp. 230–239,

2017.

[8] M. Schoenenberger and E. M. Queen, “Limit cycle analysis

applied to the oscillations of decelerating blunt-body entry

vehicles,” in NATO RTO Symposium AVT-152 on LimitCycle Oscillations and Other Amplitude-Limited, Self-Excited

Vibrations (No. RTO-MP-AVT-152), Norway, 2008.

[9] F. Deng, Y.-z. Wu, and L. Xue-qiang, “Simulation of vortex in

separated flows with DES,” Chinese Journal of Computational

Physics, vol. 25, no. 6, pp. 683–688, 2008.

[10] S. Xiao-pan, Z. Rui, R. Ji-li, and W. Yuan, “Numerical simulation of fluctuating pressure environment of Mars entry module,” Journal of Astronautics, vol. 39, 2018.

[11] S. M. Murman and M. J. Aftosmis, “Dynamic analysis of

atmospheric-entry probes and capsules,” in 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2007.

[12] M. Schoenenberger, W. Hathaway, L. Yates, and P. Desai,

“Ballistic range testing of the Mars exploration rover entry

capsule,” in 43rd AIAA Aerospace Sciences Meeting and

Exhibit, Reno, Nevada, 2005.

[13] S. R. Lewis, M. Collins, P. L. Read et al., “A climate database for

Mars,” Journal of Geophysical Research Planets, vol. 104,

no. E10, pp. 24177–24194, 1999.

[14] X.-f. Yang, T. Wei, and G. Ye-wei, “Hypersonic flow field prediction and aerodynamics analysis for MSL entry capsule,”

Journal of Astronautics, vol. 36, no. 4, pp. 383–389, 2015.

[15] E. H. Hirschel and W. Claus, Selected aerothermodynamic

design problems of hypersonic night vehicles, Springer Press,

Berlin, 2009.

[16] M. Schoenenberger, J. Van Norman, A. Dyakonov,

C. Karlgaard, D. Way, and P. Kutty, “Assessment of the reconstructed aerodynamics of the Mars science laboratory entry

vehicle,” in 23rd AAS/AIAA Space Flight Mechanics Meeting,

Kauai, HI, 2013.

Space: Science & Technology 15

&

32

Research Article

Analysis and Verification of Aerodynamic Characteristics of

Tianwen-1 Mars Parachute

Mingxing Huang , Wenqiang Wang, and Jian Li

Beijing Institute of Space Mechanics and Electricity, Beijing 100094, China

Correspondence should be addressed to Mingxing Huang; hmx1620@163.com

Received 27 July 2021; Accepted 28 February 2022; Published 20 March 2022

Copyright © 2022 Mingxing Huang et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative

Commons Attribution License (CC BY 4.0).

The Mars parachute flight environment is supersonic, low-density, and low dynamic pressures. To ensure the operating

performance and reliability, the design optimization and verification of the Tianwen-1 Mars parachute have been carried out.

Firstly, through supersonic and subsonic wind tunnel tests, the design optimization of the parachute structure is realized.

Subsequently, the high-altitude flight tests of four parachutes were conducted, the drag coefficient and the oscillation angle of

the parachute from supersonic to subsonic speed were gained, and the aerodynamic characteristics and reliable opening of the

parachutes were thoroughly tested and verified. This article presents the design, development, and qualification of the

Tianwen-1 Mars parachute, which can provide a reference for the creation of future Mars exploration parachutes.

1. Introduction

China’s Tianwen-1 Mars probe successfully landed on the

Utopia Plain at 7 : 18 a.m. Beijing Time, on 15 May 2021

[1]. The success rate of Mars missions is about 50%, and

most failures occur during the entry, descent, and landing

(EDL) phase [2]. Parachutes of low-density supersonic play

a vital role in the EDL of Mars and directly determine the

success of the entire mission.

Generally, the disk-gap-band (DGB) parachute has been

primarily employed in the Mars exploration missions to date

[3]. The DGB designs utilized for the successful missions to

Mars fall into three evolutionary phases, an initial Viking

design, modified designs for MPF (Mars Pathfinder) and

MER (Mars Exploration Rover), and a return to the Viking

geometry for the Phoenix, MSL (Mars Science Laboratory),

and Insight and Perseverance [4]. To verify the deceleration

and stability under the Mars conditions, numerous wind

tunnel tests [5, 6], low-altitude subsonic drop tests [7], and

high-altitude flight tests [8–11] have been performed for

Mars missions [12, 13].

From the 1960s, a series of supersonic flight tests, including the Planetary Entry Parachute Program (PEPP), the

Supersonic Planetary Entry Decelerator Program (SPED),

and the Supersonic High-Altitude Parachute Experiment

(SHAPE) aimed at maturing supersonic decelerators for

the Mars Viking Project, have been conducted to confirm

the inflation characteristics in low density and high Machnumber conditions [14–16].

The first DGB used at Mars, on the Viking missions,

leveraged heavily from design aspects of the preceding

PEPP, SPED, and SHAPE tests. The Viking parachute is a

DGB parachute with geometric porosities of 12.5 percent.

Wind tunnel testing was conducted to finalize the parachute

system configuration. The testing results show that the

increase in the ratio of the suspension line length to the

canopy diameter from 1.0 to 1.7 increased the parachute’s

drag coefficient.

The airbag landing system of Mars Pathfinder (MPF)

placed stability requirements on the parachute that could

not be met with a canopy of the geometry flown by Viking.

Thus, the Viking DGB parachute was modified to increase

the length of the band to improve stability, and the MPF

parachute is a DGB parachute with geometric porosities of

9.2 percent [17–19]. Qualification of the MPF parachute

was conducted through wind tunnel tests and low-altitude

flight tests.

Recently, the Low-Density Supersonic Decelerator

(LDSD) supersonic flight tests were conducted to develop

the supersonic disk-sail (SSDS) and the supersonic ring-sail

(SSRS) parachutes based on the MSL parachute [20, 21];

however, the newly developed parachutes failed in each

AAAS

Space: Science & Technology

Volume 2022, Article ID 9805457, 11 pages

https://doi.org/10.34133/2022/9805457

33

Research Article

Analysis and Verification of Aerodynamic Characteristics of

Tianwen-1 Mars Parachute

Mingxing Huang , Wenqiang Wang, and Jian Li

Beijing Institute of Space Mechanics and Electricity, Beijing 100094, China

Correspondence should be addressed to Mingxing Huang; hmx1620@163.com

Received 27 July 2021; Accepted 28 February 2022; Published 20 March 2022

Copyright © 2022 Mingxing Huang et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative

Commons Attribution License (CC BY 4.0).

The Mars parachute flight environment is supersonic, low-density, and low dynamic pressures. To ensure the operating

performance and reliability, the design optimization and verification of the Tianwen-1 Mars parachute have been carried out.

Firstly, through supersonic and subsonic wind tunnel tests, the design optimization of the parachute structure is realized.

Subsequently, the high-altitude flight tests of four parachutes were conducted, the drag coefficient and the oscillation angle of

the parachute from supersonic to subsonic speed were gained, and the aerodynamic characteristics and reliable opening of the

parachutes were thoroughly tested and verified. This article presents the design, development, and qualification of the

Tianwen-1 Mars parachute, which can provide a reference for the creation of future Mars exploration parachutes.

1. Introduction

China’s Tianwen-1 Mars probe successfully landed on the

Utopia Plain at 7 : 18 a.m. Beijing Time, on 15 May 2021

[1]. The success rate of Mars missions is about 50%, and

most failures occur during the entry, descent, and landing

(EDL) phase [2]. Parachutes of low-density supersonic play

a vital role in the EDL of Mars and directly determine the

success of the entire mission.

Generally, the disk-gap-band (DGB) parachute has been

primarily employed in the Mars exploration missions to date

[3]. The DGB designs utilized for the successful missions to

Mars fall into three evolutionary phases, an initial Viking

design, modified designs for MPF (Mars Pathfinder) and

MER (Mars Exploration Rover), and a return to the Viking

geometry for the Phoenix, MSL (Mars Science Laboratory),

and Insight and Perseverance [4]. To verify the deceleration

and stability under the Mars conditions, numerous wind

tunnel tests [5, 6], low-altitude subsonic drop tests [7], and

high-altitude flight tests [8–11] have been performed for

Mars missions [12, 13].

From the 1960s, a series of supersonic flight tests, including the Planetary Entry Parachute Program (PEPP), the

Supersonic Planetary Entry Decelerator Program (SPED),

and the Supersonic High-Altitude Parachute Experiment

(SHAPE) aimed at maturing supersonic decelerators for

the Mars Viking Project, have been conducted to confirm

the inflation characteristics in low density and high Machnumber conditions [14–16].

The first DGB used at Mars, on the Viking missions,

leveraged heavily from design aspects of the preceding

PEPP, SPED, and SHAPE tests. The Viking parachute is a

DGB parachute with geometric porosities of 12.5 percent.

Wind tunnel testing was conducted to finalize the parachute

system configuration. The testing results show that the

increase in the ratio of the suspension line length to the

canopy diameter from 1.0 to 1.7 increased the parachute’s

drag coefficient.

The airbag landing system of Mars Pathfinder (MPF)

placed stability requirements on the parachute that could

not be met with a canopy of the geometry flown by Viking.

Thus, the Viking DGB parachute was modified to increase

the length of the band to improve stability, and the MPF

parachute is a DGB parachute with geometric porosities of

9.2 percent [17–19]. Qualification of the MPF parachute

was conducted through wind tunnel tests and low-altitude

flight tests.

Recently, the Low-Density Supersonic Decelerator

(LDSD) supersonic flight tests were conducted to develop

the supersonic disk-sail (SSDS) and the supersonic ring-sail

(SSRS) parachutes based on the MSL parachute [20, 21];

however, the newly developed parachutes failed in each

AAAS

Space: Science & Technology

Volume 2022, Article ID 9805457, 11 pages

https://doi.org/10.34133/2022/9805457

Analysis and Verification of Aerodynamic Characteristics of

Tianwen-1 Mars Parachute

Mingxing Huang, Wenqiang Wang, and Jian Li

Beijing Institute of Space Mechanics and Electricity, Beijing 100094, China

Correspondence should be addressed to Mingxing Huang; hmx1620@163.com

Abstract: The Mars parachute flight environment is supersonic, low-density, and low dynamic pressures. To ensure the operating

performance and reliability, the design optimization and verification of the Tianwen-1 Mars parachute have been carried out. Firstly,

through supersonic and subsonic wind tunnel tests, the design optimization of the parachute structure is realized. Subsequently, the highaltitude flight tests of four parachutes were conducted, the drag coefficient and the oscillation angle of the parachute from supersonic

to subsonic speed were gained, and the aerodynamic characteristics and reliable opening of the parachutes were thoroughly tested and

verified. This article presents the design, development, and qualification of the Tianwen-1 Mars parachute, which can provide a reference

for the creation of future Mars exploration parachutes.

34

flight test. Subsequently, the Advanced Supersonic Parachute Inflation Research Experiments (ASPIRE) project

was conducted as a risk reduction activity for the Mars

2020 mission [22–24]. This leads to a critical need to better

understand the dynamics of the supersonic parachute inflation in a Mars-like environment [25].

Using the heritage data from the previous Mars

parachute system, a new DGB parachute was selected as

the candidate for Tianwen-1. The parachute was performed

through wind tunnel and high-altitude flight tests. This

paper describes the design and qualification of the Mars

parachute system of Tianwen-1, which can provide references for the development of parachutes for subsequent deep

space exploration missions.

2. Parachute Design

2.1. Mars Parachute Type Analysis and Selection. The Mars

parachute opening flight is characterized by supersonic

speed, low density, and low dynamic pressure [26]. In addition, atmospheric activities, such as the Martian vortex activity and dust devil, may cause harsh parachute opening

conditions [27]. Compared with the parachute working on

earth, the parachute of the Mars lander faces more problems

such as difficulty in parachute opening, unstable inflation,

and decreased drag coefficient during working. Therefore,

it is necessary to investigate various parachute opening and

working performances under supersonic conditions [28].

From the 1960s, the United States carried out various

wind tunnel tests and airdrop tests. And three types of

parachutes, such as the DGB parachutes, the cross parachutes, and the improved ringsail parachutes, worked under

supersonic, transonic, and subsonic conditions [29, 30]. The

parachutes’ inflation characteristics, drag characteristics, and

stability have been observed, compared, and verified. From

the test results, although the cross parachute has the largest

drag area as the opening speed increases, it exhibits more

excellent vibration and poor stability. In contrast, the

improved ringsail parachute and the DGB parachute work

well under a Mach number of 1.9. And the DGB parachute

is better than the improved ringsail parachute in terms of

inflatable and decedent performances. When working at

supersonic speed and low dynamic pressure, the DGB parachute has better inflatable and deceleration performance

than the ringsail parachute [31].

All the foreign landers successfully achieved soft

landing on Mars have used the DGB parachute, which

has good stability and excellent inflation performance

in the supersonic and low-density working environment.

Due to its demonstrated high-altitude performance and

lower technical risk, the DGB parachute with improved

design modifications is selected as the candidate for the

Tianwen-1 Mars probe.

The basic structure of the DGB parachute is shown in

Figure 1, where Dv, DD, and DB are the diameters of the vent,

the disk, and the band, respectively; HG and HB are the

Suspension

line

Disk

Gap

Band

Parachute

canopy

DV

HG

DD

H DB B

LS

Figure 1: Construction parameters of a DGB parachute.

2 Space: Science & Technology

height of the “gap” and the “band,” and LS is the length of

the parachute suspension [5].

According to the ratio of the band area to the entire

canopy, the DGB parachutes can be divided into the Viking

type (Viking, Phoenix, and MSL) and the MPF type (MPF

and MER). The Viking type DGB parachute has a high drag

coefficient and weak stability, whereas the MPF and its

improved DGB parachute have a smaller drag coefficient

but better stability. Before landing, the landers that can

adjust the attitude, such as “Viking,” “Phoenix,” and “Mars

Science Laboratory,” generally choose the Viking-type

DGB parachute, whereas the other landers, which cannot,

such as “Mars Pathfinder,” or can only adjust the horizontal

attitude for a little, such as “Spirit” and “Opportunity,” generally choose the MPF DGB parachute [3].

2.2. Parachute Model. Two ideas were adopted to optimize

and improve the existing DGB parachute structure. One is

to increase the drag coefficient. The disk part is thus

modified to a structure with a higher drag coefficient, such

as the hemisflo parachute structure and the triconical parachute structure. The other is to enlarge the band’s area to

increase the parachute’s stability, such as adding a tapered

band on the lower skirt of the canopy. The specific parachute

structures (Figure 2) are shown in Table 1.

For the MPF DGB parachute, the ratio of the disk area to

the band area is about 38 : 52, and the geometric porosity is

between 9% and 10%. The MPF DGB parachute’s main

performance characteristic is good stability and a low drag

coefficient of about 0.4. For the Viking DGB parachute, the

ratio of the disk area to the band area is about 52 : 35, and

the geometric porosity is about 12.5%. The main performance characteristic of the Viking parachute is the high drag

coefficient of up to about 0.6, but the stability is poor.

The hemisflo DGB parachute, the triconical DGB parachute, and the tapered DGB parachute are all the improved

and optimized types based on the Viking DGB parachute.

The drag coefficient of the conventional hemisflo parachute

is 0.62~0.77, and the stable oscillation angle is between 10°

and 15°

. The hemisflo DGB parachute is a combination of

the characteristics of the hemisflo parachute and the Viking

DGB parachute. The canopy of the disk is modified to a

spherical structure, and the central angle of the entire canopy structure is 210°

. When the top is full, it tends to be

Table 1: Structural parameters of each parachute.

Parachute type MPF DGB Viking DGB Hemisflo DGB Triconical DGB Taped DGB

Disk area ratio 0.384 0.53 0.53 0.53 0.53

Gap area ratio 0.1 0.12 0.12 0.12 0.12

Band area ratio 0.516 0.35 0.35 0.35 0.35

Number of gores 20 20 20 20 20

LS/D0 1.7 1.7 2 1.7 1.7

(a) MPF (b) Viking (c) Hemisflo (d) Triconical (e) Tapered

Figure 2: Structures of different DGB parachutes.

Space: Science & Technology 3

35

flight test. Subsequently, the Advanced Supersonic Parachute Inflation Research Experiments (ASPIRE) project

was conducted as a risk reduction activity for the Mars

2020 mission [22–24]. This leads to a critical need to better

understand the dynamics of the supersonic parachute inflation in a Mars-like environment [25].

Using the heritage data from the previous Mars

parachute system, a new DGB parachute was selected as

the candidate for Tianwen-1. The parachute was performed

through wind tunnel and high-altitude flight tests. This

paper describes the design and qualification of the Mars

parachute system of Tianwen-1, which can provide references for the development of parachutes for subsequent deep

space exploration missions.

2. Parachute Design

2.1. Mars Parachute Type Analysis and Selection. The Mars

parachute opening flight is characterized by supersonic

speed, low density, and low dynamic pressure [26]. In addition, atmospheric activities, such as the Martian vortex activity and dust devil, may cause harsh parachute opening

conditions [27]. Compared with the parachute working on

earth, the parachute of the Mars lander faces more problems

such as difficulty in parachute opening, unstable inflation,

and decreased drag coefficient during working. Therefore,

it is necessary to investigate various parachute opening and

working performances under supersonic conditions [28].

From the 1960s, the United States carried out various

wind tunnel tests and airdrop tests. And three types of

parachutes, such as the DGB parachutes, the cross parachutes, and the improved ringsail parachutes, worked under

supersonic, transonic, and subsonic conditions [29, 30]. The

parachutes’ inflation characteristics, drag characteristics, and

stability have been observed, compared, and verified. From

the test results, although the cross parachute has the largest

drag area as the opening speed increases, it exhibits more

excellent vibration and poor stability. In contrast, the

improved ringsail parachute and the DGB parachute work

well under a Mach number of 1.9. And the DGB parachute

is better than the improved ringsail parachute in terms of

inflatable and decedent performances. When working at

supersonic speed and low dynamic pressure, the DGB parachute has better inflatable and deceleration performance

than the ringsail parachute [31].

All the foreign landers successfully achieved soft

landing on Mars have used the DGB parachute, which

has good stability and excellent inflation performance

in the supersonic and low-density working environment.

Due to its demonstrated high-altitude performance and

lower technical risk, the DGB parachute with improved

design modifications is selected as the candidate for the

Tianwen-1 Mars probe.

The basic structure of the DGB parachute is shown in

Figure 1, where Dv, DD, and DB are the diameters of the vent,

the disk, and the band, respectively; HG and HB are the

Suspension

line

Disk

Gap

Band

Parachute

canopy

DV

HG

DD

H DB B

LS

Figure 1: Construction parameters of a DGB parachute.

2 Space: Science & Technology

height of the “gap” and the “band,” and LS is the length of

the parachute suspension [5].

According to the ratio of the band area to the entire

canopy, the DGB parachutes can be divided into the Viking

type (Viking, Phoenix, and MSL) and the MPF type (MPF

and MER). The Viking type DGB parachute has a high drag

coefficient and weak stability, whereas the MPF and its

improved DGB parachute have a smaller drag coefficient

but better stability. Before landing, the landers that can

adjust the attitude, such as “Viking,” “Phoenix,” and “Mars

Science Laboratory,” generally choose the Viking-type

DGB parachute, whereas the other landers, which cannot,

such as “Mars Pathfinder,” or can only adjust the horizontal

attitude for a little, such as “Spirit” and “Opportunity,” generally choose the MPF DGB parachute [3].

2.2. Parachute Model. Two ideas were adopted to optimize

and improve the existing DGB parachute structure. One is

to increase the drag coefficient. The disk part is thus

modified to a structure with a higher drag coefficient, such

as the hemisflo parachute structure and the triconical parachute structure. The other is to enlarge the band’s area to

increase the parachute’s stability, such as adding a tapered

band on the lower skirt of the canopy. The specific parachute

structures (Figure 2) are shown in Table 1.

For the MPF DGB parachute, the ratio of the disk area to

the band area is about 38 : 52, and the geometric porosity is

between 9% and 10%. The MPF DGB parachute’s main

performance characteristic is good stability and a low drag

coefficient of about 0.4. For the Viking DGB parachute, the

ratio of the disk area to the band area is about 52 : 35, and

the geometric porosity is about 12.5%. The main performance characteristic of the Viking parachute is the high drag

coefficient of up to about 0.6, but the stability is poor.

The hemisflo DGB parachute, the triconical DGB parachute, and the tapered DGB parachute are all the improved

and optimized types based on the Viking DGB parachute.

The drag coefficient of the conventional hemisflo parachute

is 0.62~0.77, and the stable oscillation angle is between 10°

and 15°

. The hemisflo DGB parachute is a combination of

the characteristics of the hemisflo parachute and the Viking

DGB parachute. The canopy of the disk is modified to a

spherical structure, and the central angle of the entire canopy structure is 210°

. When the top is full, it tends to be

Table 1: Structural parameters of each parachute.

Parachute type MPF DGB Viking DGB Hemisflo DGB Triconical DGB Taped DGB

Disk area ratio 0.384 0.53 0.53 0.53 0.53

Gap area ratio 0.1 0.12 0.12 0.12 0.12

Band area ratio 0.516 0.35 0.35 0.35 0.35

Number of gores 20 20 20 20 20

LS/D0 1.7 1.7 2 1.7 1.7

(a) MPF (b) Viking (c) Hemisflo (d) Triconical (e) Tapered

Figure 2: Structures of different DGB parachutes.

Space: Science & Technology 3

36

spherical, the bulge of the canopy material at the bottom of

the disk is smaller, and the stress distribution in each part

of the canopy is more uniform. The ratio of the disk area

to the band area of the hemisflo DGB parachute is 53 : 35,

and the geometric porosity is about 12.5% [32].

The drag coefficient of the triconical parachute is generally between 0.80 and 0.96, and the stable oscillation angle is

between 10° and 15°

. To improve the drag coefficient of the

original DGB parachute, the Viking disk part is replaced

by three conical surfaces. The ratio of the disk area to the

band area of the triconical DGB parachute is 53 : 35, and

the geometric porosity is about 12.5%.

3. Comparison of Parachute Type by Wind

Tunnel Test

3.1. Test Conditions. To optimize the structure for the Mars

parachute, the subsonic, transonic, and supersonic wind

tunnel tests were carried out for the five DGB parachutes

in this work to obtain their oscillation angle. The test conditions are listed in Table 2. The test setup for the drag coefficients is shown in Figure 3.

3.2. Drag Coefficient. Figure 4 shows the drag coefficients of

the five types of DGB parachutes at different Mach numbers.

It can be seen that the drag coefficient of each parachute type

generally decreases with the increase of the Mach number,

ranging from 0.43 to 0.59. The drag coefficients of the parachutes, except for the hemisflo DGB parachute, decrease at

Mach 0.9, which may be caused by the wake of the front

strut upstream of the model parachute that has the undesired effect of having slightly reduced the measured magnitudes of the aerodynamic coefficients.

Compared with the parachute based on the Viking DGB,

the area ratio of the disk to the band of the MPF parachute is

smaller, so the drag coefficient of the MPF-type parachute is

relatively low, about 0.4. When the Mach number is 0.21, the

maximum drag coefficient of the Viking DGB parachute is

0.59, followed by that of the tapered DGB parachute of

0.55. When the Mach number is 0.90, the hemisflo DGB

parachute has a maximum drag coefficient of 0.52, followed

by the tapered DGB parachute of 0.50. When the Mach

number is 1.98, the maximum drag coefficient of the tapered

DGB parachute is 0.47, followed by that of the triconical

DGB parachute of 0.46.

In the wind tunnel test, the optical setup of a schlieren

imaging system is used to observe and record the parachute

and the flow field. The schlieren images of each DGB parachute at Mach 1.9 are depicted in Figure 5. It can be seen

from the schlieren images that a detached shock wave is

formed upstream of each DGB parachute canopy. And a

conical shock structure is generated in the front of the bow

shock.

3.3. Oscillation Angle. To evaluate the stability of each parachute, image processing is performed on the wind tunnel test

Table 2: Wind tunnel test conditions.

Mach number Dynamic

pressure/Pa

Density of

freestream/(kg/m3

) Temperature/°

C Test parachute Wind tunnel Section

size/m×m

Parachute

drag area/m2

0.21 5880 1.1 2 23 MPF DGB

Viking DGB

Hemisflo DGB

Triconical DGB

Tapered DGB

FD-09 3×3 0.9

0.90 41076 0.63 ~0 FD-12 1:2×1:2 0.04

1.98 70482 0.22 ~0 FD-12 1:2×1:2 0.04

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ma

0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

0.6

CD

MPF

Viking

Hemisflo

Triconical

Tapered

Figure 4: Comparison of drag coefficients of different types of

DGB parachutes.

V

Rise Wind tunnel

balance

Test

fixture

Figure 3: Parachute wind tunnel test.

4 Space: Science & Technology

videos. And the oscillation angle of the parachute under different conditions is obtained. The oscillation angle shown in

Figure 6 is the angle between the parachute symmetry axis

and the freestream flow direction. Figure 7 shows the oscillation angles of the five DGB parachutes at different Mach

numbers. It can be seen that the oscillation angle of each

type of DGB parachute generally does not change significantly with the increase of the Mach number, ranging from

5° to 10°

. For different parachute types, the MPF DGB

parachute oscillation angle is the smallest, followed by the

tapered DGB parachute. The oscillation angle of the triconical DGB parachute under each Mach number is the highest.

Combined with the wind tunnel test results at different

Mach numbers to select a parachute with better deceleration

and stability performance, the tapered DGB parachute can

be the best deceleration parachute for the Tianwen-1.

(a) MPFDGB parachute (b) Viking DGB parachute

(c) Hemisflo DGB parachute (d) Triconical DGB parachute

(e) Tapered DGB parachute

Figure 5: Flow field schlieren diagram of each parachute under Ma 1.98.

Space: Science & Technology 5

37

spherical, the bulge of the canopy material at the bottom of

the disk is smaller, and the stress distribution in each part

of the canopy is more uniform. The ratio of the disk area

to the band area of the hemisflo DGB parachute is 53 : 35,

and the geometric porosity is about 12.5% [32].

The drag coefficient of the triconical parachute is generally between 0.80 and 0.96, and the stable oscillation angle is

between 10° and 15°

. To improve the drag coefficient of the

original DGB parachute, the Viking disk part is replaced

by three conical surfaces. The ratio of the disk area to the

band area of the triconical DGB parachute is 53 : 35, and

the geometric porosity is about 12.5%.

3. Comparison of Parachute Type by Wind

Tunnel Test

3.1. Test Conditions. To optimize the structure for the Mars

parachute, the subsonic, transonic, and supersonic wind

tunnel tests were carried out for the five DGB parachutes

in this work to obtain their oscillation angle. The test conditions are listed in Table 2. The test setup for the drag coefficients is shown in Figure 3.

3.2. Drag Coefficient. Figure 4 shows the drag coefficients of

the five types of DGB parachutes at different Mach numbers.

It can be seen that the drag coefficient of each parachute type

generally decreases with the increase of the Mach number,

ranging from 0.43 to 0.59. The drag coefficients of the parachutes, except for the hemisflo DGB parachute, decrease at

Mach 0.9, which may be caused by the wake of the front

strut upstream of the model parachute that has the undesired effect of having slightly reduced the measured magnitudes of the aerodynamic coefficients.

Compared with the parachute based on the Viking DGB,

the area ratio of the disk to the band of the MPF parachute is

smaller, so the drag coefficient of the MPF-type parachute is

relatively low, about 0.4. When the Mach number is 0.21, the

maximum drag coefficient of the Viking DGB parachute is

0.59, followed by that of the tapered DGB parachute of

0.55. When the Mach number is 0.90, the hemisflo DGB

parachute has a maximum drag coefficient of 0.52, followed

by the tapered DGB parachute of 0.50. When the Mach

number is 1.98, the maximum drag coefficient of the tapered

DGB parachute is 0.47, followed by that of the triconical

DGB parachute of 0.46.

In the wind tunnel test, the optical setup of a schlieren

imaging system is used to observe and record the parachute

and the flow field. The schlieren images of each DGB parachute at Mach 1.9 are depicted in Figure 5. It can be seen

from the schlieren images that a detached shock wave is

formed upstream of each DGB parachute canopy. And a

conical shock structure is generated in the front of the bow

shock.

3.3. Oscillation Angle. To evaluate the stability of each parachute, image processing is performed on the wind tunnel test

Table 2: Wind tunnel test conditions.

Mach number Dynamic

pressure/Pa

Density of

freestream/(kg/m3

) Temperature/°

C Test parachute Wind tunnel Section

size/m×m

Parachute

drag area/m2

0.21 5880 1.1 2 23 MPF DGB

Viking DGB

Hemisflo DGB

Triconical DGB

Tapered DGB

FD-09 3×3 0.9

0.90 41076 0.63 ~0 FD-12 1:2×1:2 0.04

1.98 70482 0.22 ~0 FD-12 1:2×1:2 0.04

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ma

0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

0.6

CD

MPF

Viking

Hemisflo

Triconical

Tapered

Figure 4: Comparison of drag coefficients of different types of

DGB parachutes.

V

Rise Wind tunnel

balance

Test

fixture

Figure 3: Parachute wind tunnel test.

4 Space: Science & Technology

videos. And the oscillation angle of the parachute under different conditions is obtained. The oscillation angle shown in

Figure 6 is the angle between the parachute symmetry axis

and the freestream flow direction. Figure 7 shows the oscillation angles of the five DGB parachutes at different Mach

numbers. It can be seen that the oscillation angle of each

type of DGB parachute generally does not change significantly with the increase of the Mach number, ranging from

5° to 10°

. For different parachute types, the MPF DGB

parachute oscillation angle is the smallest, followed by the

tapered DGB parachute. The oscillation angle of the triconical DGB parachute under each Mach number is the highest.

Combined with the wind tunnel test results at different

Mach numbers to select a parachute with better deceleration

and stability performance, the tapered DGB parachute can

be the best deceleration parachute for the Tianwen-1.

(a) MPFDGB parachute (b) Viking DGB parachute

(c) Hemisflo DGB parachute (d) Triconical DGB parachute

(e) Tapered DGB parachute

Figure 5: Flow field schlieren diagram of each parachute under Ma 1.98.

Space: Science & Technology 5

38

4. High-Altitude Flight Test Verification

4.1. Flight Test Scheme. To demonstrate the capability of fullscale tapered DGB parachutes in Mars flight conditions, four

high-altitude flight tests were carried out by sounding

rockets in April 2018. The sounding rocket assembly consists of a first stage and an approximately 1280 kg test vehicle. The parachute system was installed at the tail of the

test vehicle, as shown in Figure 8. The test flight process is

shown in Figure 9.

During the flight, the first stage burned out at altitudes of

approximately 17 km~20 km, respectively, the payload section reached apogee between 49 km and 64 km. When the

payload got the target dynamic pressure and Mach number,

the parachute was mortar-deployed. The deployment, inflation, and supersonic and subsonic aerodynamics of the parachute were analyzed by a suite of instruments, including a

high-speed video system trained on the parachute, a set of

load pins at the interface of the parachute bridles and the

payload, and a GPS and inertial measurement unit (IMU)

onboard the payload. After decelerating to subsonic speed,

the parachute and payload descended to the test range for

recovery.

4.2. Test Architecture. Figure 10 shows a schematic of the

parachute configuration after deployment. The relevant

dimensions of the parachute-payload system are labeled in

the schematic, and their values are also listed in Table 3.

The parachute is a 48-gore DGB with a nominal diameter (D0) of 15.96 m. The majority of the canopy is constructed using a Nylon fabric with a rated strength of

~1000 N/5 cm. The circumferential reinforcements at the

trailing edge of the disk and the band leading and trailing

edges are ~10000 N Kevlar webbing, and the reinforcements

at the vent are ~40000 N Kevlar webbing [33]. The parachute is built using a cord insertion construction where the

suspension lines continue into the radials. The suspension

lines are constructed from the 7350 N Kevlar line. The entire

packed parachute assembly has a mass of 39 kg. The parachute was tested in the wake of a slender payload whose

diameter is approximately a sixth of the 4.5 m aeroshell.

4.3. Analysis of Test Conditions. These tests targeted a specific dynamic pressure at parachute deployment to reach a

desired load on the parachute at full inflation. The parachutes were mortar-fire deployed at dynamic pressures

ranging from 100 Pa to 950 Pa and Mach numbers between

2.05 and 2.35. In comparison, the parachute of Tianwen-1

must be able to get opened reliably within the range of Ma

1.6~Ma 2.3 and dynamic pressure range of 250 Pa~850 Pa.

Under the high-altitude opening test conducted on the earth

and the actual working conditions of Mars, the Reynolds

numbers are both in the order of 2 × 106.

Table 4 shows the test condition settings of the highaltitude open parachute test. There are four test conditions.

Figure 11 shows the height and speed boxes for different

working conditions.

(1) Test condition 1 is the nominal working condition of

Mars parachute opening

(2) Test condition 2 increases the angle of attack based

on the nominal condition

(3) Test condition 3 increases the Mach number and the

angle of attack but reduces the dynamic pressure

based on the nominal condition

(4) Test condition 4 increases the Mach number, the

angle of attack, and the dynamic pressure based on

nominal conditions

4.4. Test Article Performance. The results of the four supersonic flight tests are shown in Figures 12–16. Figure 12 is

v

??

Figure 6: Oscillation angle of the parachute.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ma

4

5

6

7

8

9

10

Oscillation angle (°)

MPF

Viking

Hemisflo

Triconical

Tapered

Figure 7: Comparison of oscillation angle of different types of DGB

parachutes.

Parachute

First stage Text vehicle

Figure 8: Schematic of the parachute high-altitude flight test

launch configuration.

6 Space: Science & Technology

the time curve of the height of the parachute. After the

parachute deployed, the height of the parachute first

increases and then decreases, and the test vehicle reaches

apogee at approximately 63 km. The parachute drag

increases rapidly after deployment, and the speed of the

parachute decreases before the apogee of trajectory in

Figure 13. As the aerodynamic drag increases further, the

parachute gradually decelerates until it reaches about

15 m/s of landing speed.

The parachute drag during the opening process is shown

in Figure 14. In the fourth test, the parachute opening load is

the largest, 110 kN, and the third test has the smallest

dynamic pressure, so the parachute opening load is the

smallest, only 39 kN. In the process of a parachute opening,

it can be seen that large parachute force oscillations occur

after the first inflation peak force, indicating that under the

condition of supersonic speed, the projection area of the

tapered DGB parachute changes repeatedly, and the parachute canopy undergoes collapse and reinflation cycles. A

T = 0 Launch

T = 1.5 s Liquid engine Ignition

T ≈ 40 s Solid

engine burnout

T ≈ 58 s~68 s Rocket

separation

T ≈ 70 s~87 s

Mortar Fire

T ≈ 71 s~88 s

Parachute

deployment

The first stage

of free fall

T ≈ 1150 s

Landing

Figure 9: Concept of the rocket operations.

d

LS

LR

LB

Figure 10: Parachute system.

Table 3: Dimensions of the parachute system.

Item Symbol Design

Parachute nominal diameter (m) D0 15.96

Parachute nominal area (m2

) S0 200

Vent diameter (m) DV 1.12

Disk diameter (m) DD 11.53

Gap height (m) HG 0.69

Band height (m) HB 1.94

Geometric porosity λg 12.5%

Suspension line length (m) LS 27.15

Riser length (m) LR 4

Bridle length (m) LB 1.50

Forebody diameter (m) d 0.75

Space: Science & Technology 7

39

4. High-Altitude Flight Test Verification

4.1. Flight Test Scheme. To demonstrate the capability of fullscale tapered DGB parachutes in Mars flight conditions, four

high-altitude flight tests were carried out by sounding

rockets in April 2018. The sounding rocket assembly consists of a first stage and an approximately 1280 kg test vehicle. The parachute system was installed at the tail of the

test vehicle, as shown in Figure 8. The test flight process is

shown in Figure 9.

During the flight, the first stage burned out at altitudes of

approximately 17 km~20 km, respectively, the payload section reached apogee between 49 km and 64 km. When the

payload got the target dynamic pressure and Mach number,

the parachute was mortar-deployed. The deployment, inflation, and supersonic and subsonic aerodynamics of the parachute were analyzed by a suite of instruments, including a

high-speed video system trained on the parachute, a set of

load pins at the interface of the parachute bridles and the

payload, and a GPS and inertial measurement unit (IMU)

onboard the payload. After decelerating to subsonic speed,

the parachute and payload descended to the test range for

recovery.

4.2. Test Architecture. Figure 10 shows a schematic of the

parachute configuration after deployment. The relevant

dimensions of the parachute-payload system are labeled in

the schematic, and their values are also listed in Table 3.

The parachute is a 48-gore DGB with a nominal diameter (D0) of 15.96 m. The majority of the canopy is constructed using a Nylon fabric with a rated strength of

~1000 N/5 cm. The circumferential reinforcements at the

trailing edge of the disk and the band leading and trailing

edges are ~10000 N Kevlar webbing, and the reinforcements

at the vent are ~40000 N Kevlar webbing [33]. The parachute is built using a cord insertion construction where the

suspension lines continue into the radials. The suspension

lines are constructed from the 7350 N Kevlar line. The entire

packed parachute assembly has a mass of 39 kg. The parachute was tested in the wake of a slender payload whose

diameter is approximately a sixth of the 4.5 m aeroshell.

4.3. Analysis of Test Conditions. These tests targeted a specific dynamic pressure at parachute deployment to reach a

desired load on the parachute at full inflation. The parachutes were mortar-fire deployed at dynamic pressures

ranging from 100 Pa to 950 Pa and Mach numbers between

2.05 and 2.35. In comparison, the parachute of Tianwen-1

must be able to get opened reliably within the range of Ma

1.6~Ma 2.3 and dynamic pressure range of 250 Pa~850 Pa.

Under the high-altitude opening test conducted on the earth

and the actual working conditions of Mars, the Reynolds

numbers are both in the order of 2 × 106.

Table 4 shows the test condition settings of the highaltitude open parachute test. There are four test conditions.

Figure 11 shows the height and speed boxes for different

working conditions.

(1) Test condition 1 is the nominal working condition of

Mars parachute opening

(2) Test condition 2 increases the angle of attack based

on the nominal condition

(3) Test condition 3 increases the Mach number and the

angle of attack but reduces the dynamic pressure

based on the nominal condition

(4) Test condition 4 increases the Mach number, the

angle of attack, and the dynamic pressure based on

nominal conditions

4.4. Test Article Performance. The results of the four supersonic flight tests are shown in Figures 12–16. Figure 12 is

v

??

Figure 6: Oscillation angle of the parachute.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ma

4

5

6

7

8

9

10

Oscillation angle (°)

MPF

Viking

Hemisflo

Triconical

Tapered

Figure 7: Comparison of oscillation angle of different types of DGB

parachutes.

Parachute

First stage Text vehicle

Figure 8: Schematic of the parachute high-altitude flight test

launch configuration.

6 Space: Science & Technology

the time curve of the height of the parachute. After the

parachute deployed, the height of the parachute first

increases and then decreases, and the test vehicle reaches

apogee at approximately 63 km. The parachute drag

increases rapidly after deployment, and the speed of the

parachute decreases before the apogee of trajectory in

Figure 13. As the aerodynamic drag increases further, the

parachute gradually decelerates until it reaches about

15 m/s of landing speed.

The parachute drag during the opening process is shown

in Figure 14. In the fourth test, the parachute opening load is

the largest, 110 kN, and the third test has the smallest

dynamic pressure, so the parachute opening load is the

smallest, only 39 kN. In the process of a parachute opening,

it can be seen that large parachute force oscillations occur

after the first inflation peak force, indicating that under the

condition of supersonic speed, the projection area of the

tapered DGB parachute changes repeatedly, and the parachute canopy undergoes collapse and reinflation cycles. A

T = 0 Launch

T = 1.5 s Liquid engine Ignition

T ≈ 40 s Solid

engine burnout

T ≈ 58 s~68 s Rocket

separation

T ≈ 70 s~87 s

Mortar Fire

T ≈ 71 s~88 s

Parachute

deployment

The first stage

of free fall

T ≈ 1150 s

Landing

Figure 9: Concept of the rocket operations.

d

LS

LR

LB

Figure 10: Parachute system.

Table 3: Dimensions of the parachute system.

Item Symbol Design

Parachute nominal diameter (m) D0 15.96

Parachute nominal area (m2

) S0 200

Vent diameter (m) DV 1.12

Disk diameter (m) DD 11.53

Gap height (m) HG 0.69

Band height (m) HB 1.94

Geometric porosity λg 12.5%

Suspension line length (m) LS 27.15

Riser length (m) LR 4

Bridle length (m) LB 1.50

Forebody diameter (m) d 0.75

Space: Science & Technology 7

40

significant contributor to these area oscillations is the

interaction between the aeroshell wake and the parachute

flow fields [34].

From the parachute opening load and freestream flow

parameters, the curve of the parachute drag coefficient with

the Mach number can be obtained, as shown in Figure 15.

Table 4: Parachute deployment conditions.

Test Mach at mortar fire Dynamic pressure at mortar fire/Pa Recovery mass/kg Angle of attack/°

1 2:05 ± 0:25 550 ± 300 1285 ± 20 0±2

2 2:05 ± 0:25 550 ± 300 1285 ± 20 10 ± 2

3 2:3±0:25 100~500 1285 ± 20 10 ± 2

4 2:35 ± 0:25 250~950 1285 ± 20 13 ± 2

36 38 40 42 44 46 48 50 52 54 56 58 60 62

550

600

650

700

750

v (m/s)

800

850

h (km)

Test 1 and 2

Test 3

Test 4

Mortar Fire

Figure 11: Parachute deployment height and speed frame for different tests.

0 200 400 600 800 1000 1200

0

1

2

3

4

5

6

7

Test 01

Test 02

Test 03

Test 04

h (m)

×104

t (s)

Figure 12: Height versus time.

0

100

200

300

400

500

600

700

800

900

0 200 400 600 800 1000 1200

Test 01

Test 02

Test 03

Test 04

t (s)

v (m/s)

Figure 13: Velocity versus time.

8 Space: Science & Technology

The test results show that between Ma 0.2 and Ma 2.4, the

drag coefficient of the tapered DGB parachute increases first

and then decreases. The variation range of the drag coefficient is 0.39~0.70. At Ma 1.5, the drag coefficient reaches

the maximum value of about 0.7.

In the wind tunnel test of the drag coefficient, when the

parachute is at a Mach number of 0.21, 0.9, and 1.98, the

corresponding drag coefficients are 0.55, 0.50, and 0.47,

respectively. Except for Mach number 0.9, the drag coefficient in the wind tunnel test is consistent with the results

of the high-altitude drop parachute tests. Because parachutes

are in the wake of slender bodies in the high-altitude drop

parachute tests, its drag coefficient at Mach number 0.9 is

higher than that of the wind tunnel test. This behavior has

been observed in wind tunnel test data [35], and it is due

to the interaction between the blunt aeroshell and the parachute flow fields.

The oscillation angle of the parachute within 7 s after the

parachute inflation is shown in Figure 16. After the parachute inflation, the parachute shows repeated oscillation

within a small angle. The oscillation angle of test 03 is the

largest, about 20°

, and the maximum oscillation angle of

the other tests is 15°

. Since the dynamic pressure in the flight

tests is much smaller than that in the wind tunnel tests, the

oscillation angle of the parachute is larger than that in the

wind tunnel test results.

5. Conclusion

In this paper, the parachute of Tianwen-1 has been optimized and tested. According to the flight conditions of Mars

parachutes, five DGB parachutes with different geometries

were designed. In the wind tunnel tests, the change of drag

coefficient and oscillation angle under different Mach numbers were obtained. Based on the comprehensive performance of the parachute, the tapered DGB parachute is

selected as the priority parachute type. Then, the tapered

DGB parachute was verified by four high-altitude flight tests

using sounding rockets to reach the targeted conditions. The

test results indicate that the drag coefficient of the tapered

DGB parachute varied from 0.39 to 0.70 with the Mach

number increased from Ma 0.2-Ma 2.4 and reached the

maximum value of 0.7 at Ma 1.5; the maximum AOA after

parachute deployment is about 20°

, which have all demonstrated that the performance of the tapered DGB parachute

could meet the deceleration requirements of the Tianwen-1

Mars probe.

Data Availability

The data used to support the findings of this study are

available from the author upon request.

50 100 150 200 250 300 350 400

0

20

40

60

80

100

120

70 80 90

0

50

100

Test 01

Test 02

Test 03

Test 04

t (s)

F (kN)

Figure 14: Opening force versus time.

0 0.5 1 1.5 2 2.5

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Test 01

Test 02

Test 03

Test 04

CD

Ma

Figure 15: Drag coefficient versus Mach number.

01234567

0

5

10

15

20

25

Test 01

Test 02

Test 03

Test 04

t (s)

Oscillation angle (°)

Figure 16: Oscillation angle versus time.

Space: Science & Technology 9