﻿ 火星探测器进入飞行气动测量方法研究
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 力学学报  2015, Vol. 47 Issue (1): 8-14  DOI: 10.6052/0459-1879-14-331 0

### 引用本文 [复制中英文]

[复制中文]
Yang Lei, Hou Yanze, Zuo Guang, Liu Yan, Guo Bin. AERODYNAMIC CHARACTERISTICS MEASSUREMENT OF MARS VEHICLES DURING ENTRY FLIGHT[J]. Chinese Journal of Ship Research, 2015, 47(1): 8-14. DOI: 10.6052/0459-1879-14-331.
[复制英文]

### 文章历史

2014-10-23收稿
2014-11-26录用
2014-12-12网络版发表

1 气动测量系统模型 1.1 进入飞行任务

 图 1 火星探测器进入飞行任务示意图 Fig. 1 Entry flight profile of Mars exploration vehicle
1.2 气动测量系统组成

 图 2 气动测量系统测量方案示意图 Fig. 2 Measurement scheme of aerodynamic characteristics

(2)加速度计：测量进入过程中的气动过载，结合探测器质量，用于获取气动力；

(3)陀螺，测量进入探测器的姿态角速率，用于弹道重建，获取攻角和侧滑角数据.

(4)外测系统：提供探测器的弹道外测位置数据，作为弹道重建的数据基准. 该项数据可通过环火轨道卫星的UHF设备实现.

 图 3 引压孔布局示意图 Fig. 3 Location of pressure measurement points
2 攻角和侧滑角测量方法

 $\dot{\pmb x}_e = f\left({\pmb x}_e ,{\pmb a}_e , {\pmb\omega} _e ,t \right)$ (1)

 ${\pmb Y}_e = {\pmb Y}_m + {\pmb \delta} _d$ (2)

 ${\pmb a } _e = {\pmb a } _m + {\pmb a } _d$ (3)

 ${\pmb \omega }_e = {\pmb \omega }_m + {\pmb \omega}_d$ (4)

 ${\pmb \varTheta} = \left({\pmb Y}_e \left( 0 \right), {\pmb V}_e \left( 0 \right), {\pmb \phi }_e \left( 0 \right), {\pmb a}_d ,{\pmb \omega }_d \right)$ (5)

 ${\pmb\varTheta} _i = {\pmb\varTheta} _{i - 1} + \Delta {\pmb\varTheta} _i$ (6)

 $\Delta {\pmb\varTheta} _i = - \left( {\dfrac{\partial ^2J}{\partial \varTheta _p \varTheta _q }} \right)_{\varTheta _p ,\varTheta _q \in {\pmb\varTheta} }^{ - 1} \left( {\dfrac{\partial J}{\partial \varTheta _p }} \right)_{\varTheta _p \in {\pmb\varTheta} }$ (7)

 $J\left( {\pmb\varTheta} \right) = {\pmb v } {\pmb W }^{ - 1}{\pmb v }^{\rm T} ,\ {\pmb v } = {\pmb Y } _e - {\pmb Y } _m$ (8)

 $\left. \alpha = \arctan \left( {{ - V_y } /{V_x }} \right) \\ \beta = \arcsin \left( {{V_z } / {\left( {V_x^2 + V_y^2 + V_z^2 } \right)^{1 / 2}}} \right) \right\}$ (9)
3 动压测量方法

 $P_i = f_i \left( {\pmb X} \right) + \varepsilon _i = q_c \cos ^2\theta _i + p_\infty + \varepsilon _i$ (10)

 $\cos \left( {{\theta _i}} \right) = \cos \left( \alpha \right)\cos \left( \beta \right)\cos \left( {{\lambda _i}} \right) +\\ \qquad \sin \left( \beta \right)\sin \left( {{\varphi _i}} \right)\sin \left( {{\lambda _i}} \right) + \\ \qquad \sin \left( \alpha \right)\cos \left( \beta \right)\cos \left( {{\varphi _i}} \right)\sin \left( {{\lambda _i}} \right)n$ (11)

 图 4 引压孔位置关系示意图[12] Fig. 4 Location relationship of pressure measurement points

t时刻，n个传感器的测量输出形成下述矢量，
 $\left. \begin{array}{l} P = {\left( {{P_1}\;{P_2}\; \cdots \;{P_n}} \right)^{\rm{T}}}\\ f = {\left( {{f_1}\left( X \right){f_2}\left( X \right)\; \cdots {f_n}\left( X \right)} \right)^{\rm{T}}}\\ \varepsilon = {\left( {{\varepsilon _1}{\rm{ }}{\varepsilon _2}\; \cdots \;{\varepsilon _n}} \right)^{\rm{T}}} \end{array} \right\}$ (12)

 ${\pmb P} = {\pmb f}\left( {\pmb X} \right) + {\pmb \varepsilon }$ (13)

 ${\pmb P} = {\pmb f}\left( {{\pmb X}_0 } \right) + \left( {\dfrac{\partial {\pmb f}}{\partial {\pmb X}}} \right)_{{ X} = { X}_0 } \cdot \Delta {\pmb X} + {\pmb \varepsilon }$ (14)

 ${\pmb H} = \left( {\dfrac{\partial {\pmb f}}{\partial {X}}} \right)_{{X} = {X}_0 }$ (15)

 ${\pmb y} = {\pmb P} - {\pmb f}\left( {{\pmb X}_0 } \right)$ (16)

 ${\pmb y} ={\pmb H} \cdot \Delta {\pmb X} + {\pmb \varepsilon }$ (17)

 $\Delta {\pmb X} = \left( {{\pmb H}^{\rm T}{\pmb S}^{ - 1}{\pmb H}} \right)^{ - 1}{\pmb H}^{\rm T}{\pmb S}^{ - 1} {\pmb y}$ (18)

 ${\pmb S}_E = \left(\!\!\begin{array}{ccccc} {\sigma _1^2 } & 0 & \cdots & \cdots & 0 \\ 0 & {\sigma _2^2 } & 0 & \cdots & \vdots \\ \vdots & 0 & \ddots & 0 & \vdots \\ \vdots & \vdots & 0 & {\sigma _{n - 1}^2 } & 0 \\ 0 & 0 & \cdots & 0 & {\sigma _n^2 } \end{array}\!\! \right)$ (19)

 $\begin{array}{l} R = \frac{{{p_\infty }}}{{{q_c} + {p_\infty }}} = {\left[ {\frac{2}{{\left( {\gamma + 1} \right)M{a^2}}}} \right]^{{\textstyle{\gamma \over {\gamma - 1}}}}} \cdot \\ \qquad {\left[ {\frac{{2\gamma M{a^2} - \left( {\gamma - 1} \right)}}{{\left( {\gamma + 1} \right)}}} \right]^{{\textstyle{1 \over {\gamma - 1}}}}},\\ \gamma = 1.335,\;Ma > 1 \end{array}$ (20)

 $q_\infty = \dfrac{\gamma }{2}\left( {q_c + p_\infty } \right) R Ma^2$ (21)

4 仿真分析

 图 5 基于弹道重建的攻角测量精度 Fig. 5 Angle of attack error based on trajectory reconstruction
 图 6 基于弹道重建的侧滑角测量精度 Fig. 6 Angle of sideslip error based on trajectory reconstruction
 图 7 基于FADS测量的攻角测量精度 Fig. 7 Angle of attack error based on FADS
 图 8 基于FADS测量的侧滑角测量精度 Fig. 8 Angle of sideslip error based on FADS
 图 9 动压精度水平 Fig. 9 Dynamic pressure error
 图 10 不同外测精度下的攻角和侧滑角测量精度 Fig. 10 Angle of attack and angle of sideslip error on different trajectory measurement error

5 结 论

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AERODYNAMIC CHARACTERISTICS MEASSUREMENT OF MARS VEHICLES DURING ENTRY FLIGHT
Yang Lei, Hou Yanze, Zuo Guang, Liu Yan, Guo Bin
Institute of Manned Space System Engineering, Beijing 100094, China
Fund: The project was supported by the National Natural Science Foundation of China (61403028)
Abstract: Performing aerodynamic measurement can acquire a mounts of data during Mars entry exploration. This work benefits for aerodynamic characteristics confirmation and improves key flight performance, such as landing accuracy. In this study, an aerodynamic measurement system scheme is proposed based on trajectory reconstruction and flush air data system. Angle of attack and angle of side slip are measured by output error method with measured trajectory; dynamical pressure is measured via Flush air data system and least square optimal estimation. By simulation, it shows that the proposed measurement scheme has high measure accuracy, and dynamical pressure accuracy is 1%, and angle of attack and angle of side slip accuracy are improved more than one time. This study is helpful for aerodynamic measurement of deep-space exploration entry flight, such as Mars exploration entry flight.
Key words: Mars exploration    entry    flush air data system    aerodynamic characteristics measurement