# High-Speed Virtual Flight Testing Platform for Performance Evaluation of Pitch Maneuvers

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Virtual Flight Testing Platform

#### 2.1. Three-Degrees-of-Freedom Model Support

_{N}and pitch moment coefficient C

_{m}are shown in Figure 5. The red lines are the results without model support, and the blue lines are the results with model support.

#### 2.2. Measuring Devices of Aerodynamic and Motion Parameters

#### 2.3. Virtual Flight Control System

#### 2.4. Test Model

## 3. Results and Discussion

#### 3.1. One-Degree-of-Freedom Pitch Motion

#### 3.1.1. Open-Loop Control

_{z}(green line), pitch angle θ (red line), pitch rate q (pink line), and normal force coefficient C

_{N}(blue line) are shown in Figure 7. The control surfaces were successively increased in a stepwise manner from 0° to −10°, and decreased to 0° again. The test model experienced several free pitch oscillations from a trimmed equilibrium to another driven by pitch moment. Thus, the trim characteristics of the test model can be easily obtained for an arbitrary deflection of control surfaces.

#### 3.1.2. Closed-Loop Control

- 1.
- Closed-loop control of pitch angle

_{z}is the pitch control surface deflection angle, in deg. K

_{θ}

_{1}, K

_{θ}

_{2}, and K

_{θ}

_{3}are the control parameters for the closed-loop control of the pitch angle. θ

_{c}is the command of the pitch angle, and θ is the response of the pitch angle, in deg. q is the pitch rate, in deg/s.

_{c}(orange line) is given by the virtual flight control system, and the control surfaces δ

_{z}(green line) deflect following the flight control law to drive the pitch motion of the test model as expected and achieve the desired pitch angle θ (red line). The aerodynamic forces and moments, such as C

_{N}(blue line), can also be measured and used to evaluate and optimize the flight control law in the wind tunnel.

- 2.
- Closed-Loop Control of Acceleration

_{n}

_{1}, K

_{n}

_{2}, and K

_{n}

_{3}are the control parameters for the closed-loop control of normal acceleration. n

_{zc}is the command of normal acceleration, and n

_{z}is the response of normal acceleration, in m/s

^{2}. Y is the normal force, in N. m is the mass of the test model, in kg.

_{zc}(orange line) is given. The flight control law receives the data of the normal force measured by the balance and gives the command for control surface deflection δ

_{z}(green line). The test model is driven by the control surface to an expected normal acceleration n

_{z}(blue line) and pitch angle θ (red line). This is similar to a real maneuver, which uses acceleration as a command.

#### 3.2. Two-Degrees-of-Freedom Pitch and Roll Motion

#### 3.2.1. Characteristics of Pitch and Roll Coupled Motion

_{l}as the function of the pitch angle θ and roll angle ϕ, which indicates the existence of coupled motion of the test model during a pitch maneuver, as shown in Figure 12.

_{lϕ}are illustrated in Figure 13. From the result of the roll moment coefficient C

_{l}as the function of the roll angle ϕ, the test model was stable at ϕ = 0°, −90° and 90° due to C

_{lϕ}< 0, but unstable at ϕ = −45° and 45° due to C

_{lϕ}> 0.

_{l}increases abruptly as the pitch angle θ beyond 15°. This indicates that there is a significant asymmetrical flow field normally induced by vortices, which affects the control surfaces and induces a significant roll moment. With an increase in the pitch angle, the shed vortices generated from the left and right sides of the slender body gradually moved away from the body and evolved from left-right symmetry to asymmetry. The asymmetrical shed vortices of the slender body affected its downstream control surfaces and formed an asymmetric flow at a different control surface. The asymmetric flow generated a rolling moment and induced a self-excited rolling motion. As the pitch angle continued to increase above 20°, the asymmetric shed vortices moved farther away from the body and control surfaces, causing the rolling moment to decrease.

_{z}(red line) was in chaos. The roll oscillation proves the prediction based on the static test shown in Figure 12. The significant increase in the side force coefficient in Figure 15 appears as the pitch angle increases, which also indicates the existence of an asymmetric vortex flow. When the test model pitched down, the roll angle changed to oscillate around ϕ = −90°, which is a stable point, as shown in Figure 13.

#### 3.2.2. Decoupled Control of Pitch and Roll Motion

_{x}is the roll control surface deflection angle, in deg. K

_{ϕ}

_{1}, K

_{ϕ}

_{2}, and K

_{ϕ}

_{3}are the control parameters for closed-loop control of the roll angle. ϕ

_{c}is the command for the roll angle, and ϕ is the response of the roll angle, in deg. p is the roll rate, in deg/s.

#### 3.3. Comparison with Flight Data

_{g}x

_{g}z

_{g}, which includes translational motion and rotational motion, as illustrated in Figure 19.

^{2}; I

_{y}is the moment of inertia in pitch, in kg/m

^{2}; and g is the gravity acceleration, in m/s

^{2}. A is the angle of attack, in rad, θ is the pitch angle, in rad and q is the pitch rate, in rad/s. C

_{A}is the axis force coefficient, C

_{N}is the normal force coefficient, and C

_{m}is the pitch moment coefficient. C

_{T}is the thrust force coefficient. When the engine of the missile is not started or turned off, C

_{T}is equal to zero. x

_{g}is the longitudinal coordinate in the earth-fixed system, in m, and z

_{g}is the normal coordinate in the earth-fixed system, in m.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**Results of one-degree-of-freedom pitch motion with closed-loop control of pitch angle at M = 0.80.

**Figure 11.**Results of one-degree-of-freedom pitch motion with closed-loop control of acceleration at M = 0.80.

**Figure 14.**Pressure cloud maps and streamline plots of the typical cross-sections under different pitch angles.

**Figure 18.**Results of decoupled control of two-degrees-of-freedom pitch and roll motion at M = 0.80.

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## Share and Cite

**MDPI and ACS Style**

Li, H.; Li, Y.; Zhao, Z.; Wang, X.; Yang, H.; Ma, S.
High-Speed Virtual Flight Testing Platform for Performance Evaluation of Pitch Maneuvers. *Aerospace* **2023**, *10*, 962.
https://doi.org/10.3390/aerospace10110962

**AMA Style**

Li H, Li Y, Zhao Z, Wang X, Yang H, Ma S.
High-Speed Virtual Flight Testing Platform for Performance Evaluation of Pitch Maneuvers. *Aerospace*. 2023; 10(11):962.
https://doi.org/10.3390/aerospace10110962

**Chicago/Turabian Style**

Li, Hao, Yuping Li, Zhongliang Zhao, Xiaobing Wang, Haiyong Yang, and Shang Ma.
2023. "High-Speed Virtual Flight Testing Platform for Performance Evaluation of Pitch Maneuvers" *Aerospace* 10, no. 11: 962.
https://doi.org/10.3390/aerospace10110962