Two Methods for Constructing Level-Flight Envelopes for Fighter Aircraft

doi:10.3969/j.issn.1009-086x.2026.05.013

Abstract

Abstract:

To address the diverse requirements for fighter-aircraft level-flight envelopes in air combat simulation platforms， this paper examines a fighter aircraft whose geometric parameters are unknown. It proposes a shape reverse design method based on aerodynamic simulation data and two calculation methods for level-flight envelopes， and develops a flight envelope calculation program. First， the fighter aircraft was reconstructed in three dimensions using perspective theory and NURBS surface modeling. Subsequently， aerodynamic performance analysis was conducted on the reconstructed model to obtain various aerodynamic performance parameters， and the calculated data were compared with data from the literature to iteratively refine the model. Based on the aerodynamic simulation data， the aircraft’s level-flight envelopes were obtained using the flight envelope calculation program. Finally， the two calculated flight envelopes were compared with the flight envelope reported in the literature. The results show that the aerodynamic simulation data-based shape reverse design modeling method can be used to construct a relatively detailed model. The flight envelope obtained using the refined calculation method is generally consistent with the flight envelope reported in the literature， demonstrating the validity of the method. Compared with the refined calculation method， the rapid calculation method produces flight envelope data with slightly lower accuracy， but requires fewer aerodynamic data and involves a simpler computational process， saving approximately 66% of the required time.

Key words: air combat simulation, level-flight envelope, shape reverse design, CFD numerical simulation, aerodynamic performance

摘要：

针对空战仿真平台对战斗机平飞飞行包线的多方向需求，本文以外形参数未知的战斗机为研究对象，提出了一套基于气动仿真数据的外形反设计方法及两种平飞飞行包线计算方法，并开发了飞行包线计算程序。首先基于透视理论和NURBS曲面造型对战斗机进行三维重建；随后对重建模型进行气动性能分析，得出各项气动性能参数，并将计算数据与参考文献数据比对，不断修正模型；基于气动仿真数据使用飞行包线计算程序求得飞机平飞飞行包线，最后将计算所得两条飞行包线与参考文献给出的飞行包线进行对比分析，研究发现：基于气动仿真数据的外形反设计建模方法能够构建较为精细的模型；利用精细计算方法获得的飞行包线与参考文献基本一致，证明了方法有效性；与精细计算方法相比，快速计算方法获得的飞行包线数据精度略差，但所需的气动数据较少且计算过程简单，可节省约66%的时间。

关键词: 空战仿真, 平飞飞行包线, 外形反设计, CFD数值模拟, 气动性能

CLC Number:

TJ76

Jie HUANG, Yang BAI, Yu LIU, Yizhe WANG, Guoxu FENG. Two Methods for Constructing Level-Flight Envelopes for Fighter Aircraft[J]. Modern Defense Technology, 2026, 54(5): 152-167.

黄杰, 白杨, 刘宇, 王一哲, 冯国旭. 面向战斗机的两种平飞飞行包线构建方法[J]. 现代防御技术, 2026, 54(5): 152-167.

Figures/Tables 25

Fig. 1 Overall structural block diagram

Fig. 2 Definition of inverse perspective projection transformation

Fig. 3 Geometric relationship between perspective line segments

Fig. 4 Meshes generated with different mesh sizes

Table 1 CL and CD values calculated using different grid types

Grid Type	Number of grid/W	C_L	C_D
Sparse Grid	412	0.318 31	0.029 52
Fine Grid	862	0.317 72	0.028 61
Finer Grid	1250	0.317 63	0.028 57

Fig. 5 Maximum and minimum level-flight speeds of jet aircraft

Fig. 6 Reconstruction of aircraft components

Fig. 7 Wireframe and three-view drawings of complete aircraft

Fig. 8 Aerodynamic parameters versus angle of attack

Fig. 9 Q-criterion plots of aircraft at different angles of attack at Mach 0.8

Table 2 Variation of engine thrust with altitude and Mach number

	0	5	10	15
0.3	209.171	139.219	87.737	42.394
0.6	204.717	136.254	85.869	41.491
0.8	211.955	141.072	88.905	42.958
1.2	250.931	167.013	105.253	50.858
1.5	301.600	200.737	126.502	61.127
1.8	370.643	246.690	155.466	75.120

Table 3 CD0， Em， and TA values at Mach 0.8

H/km	0	5	10	15
$C D 0$	0.0124	0.0132	0.0135	0.015
E_m	11.683	11.444	11.107	10.728
T_A	211.955	141.072	88.905	42.958

Table 3 CD0， Em， and TA values at Mach 0.8

H/km	0	5	10	15
$C D 0$	0.0124	0.0132	0.0135	0.015
E_m	11.683	11.444	11.107	10.728
T_A	211.955	141.072	88.905	42.958

Table 4 Vmax Vmin values at different altitudes at Mach 0.8

H/km	0	5	10	15
V_max/Ma	1.750	1.890	2.104	2.116
V_min/Ma	0.102	0.170	0.313	0.634

Fig. 10 Level-flight envelope obtained using Method 1

Table 5 Variation of CL with Mach number at H=5 km

$M a i$	0.3	0.4	0.5	0.6
$C L m a x i$	2.156	1.323	0.776	0.539

Table 5 Variation of CL with Mach number at H=5 km

$M a i$	0.3	0.4	0.5	0.6
$C L m a x i$	2.156	1.323	0.776	0.539

Fig. 11 Left boundary of level-flight envelope

Table 6 Required lift coefficients for level flight at different altitudes at Mach 0.8

H/km	5	10	15	20
$C L, L = G$	0.151 6	0.308 6	0.674 2	1.474 5

Table 6 Required lift coefficients for level flight at different altitudes at Mach 0.8

H/km	5	10	15	20
$C L, L = G$	0.151 6	0.308 6	0.674 2	1.474 5

Fig. 12 Aircraft static ceiling at H=5 km

Table 7 Lift-to-drag ratios in level flight at different altitudes at Mach 0.8

H/km	5	10	15	20
K_L=G	7.086	11.003	5.911	1.192

Fig. 13 Aircraft static ceiling at different Mach numbers

Fig. 14 Right boundary of level-flight envelope

Fig. 15 Level-flight envelope obtained using Method 2

Fig. 16 Process block diagrams of two calculation methods

Fig. 17 Comparison of calculation time between two methods

Fig. 18 Comparison of envelopes obtained using two calculation methods

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