# Solving the Moment Amplification Factor of a Lateral Jet by the Unsteady Motion Experimental Method
###### Abstract  
In this paper, unsteady motion tests of a lateral jet adjusting an air vehicle's attitude are carried out. Curves of pitch moment amplification factors (\(K_{M}\)) for a lateral jet versus angle of attack (\(\alpha\)) are obtained using a wind tunnel free-flight test technique with a jet and data processing method. This new method overcomes the disadvantage of previous experiments that can study only one unsteady characteristic. The free-flight test technique in the proposed method ensures that the test model can be coupled in real-time with multiple parameters (unsteady flow caused by the jet, unsteady air vehicle aerodynamic force, and unsteady air vehicle motion). This approach simulates an actual air vehicle's complete jet test process and ensures more authentic and reliable test results. In the new data processing method, continuous data curves are fitted to discrete data points, making it easier to convert the angular displacement versus time curve into the pitch moment versus a curve to obtain \(K_{M}\). The results show that when the pressure of the micro high-pressure gas cylinder is 2.0 MPa, \(K_{M}\) is below 1, indicating that the lateral jet does not significantly promote the pitching moment. When the gas cylinder pressure is 4.0 MPa and the angle of attack is \(5^{\circ}<\left|\alpha\right|<16^{\circ}\), \(K_{M}\) is greater than 1, and the lateral jet promotes the pitching moment. When \(16^{\circ}<\left|\alpha\right|<20^{\circ}\), \(K_{M}\) is less than 1, and the lateral jet does not significantly contribute to the pitching moment. It was further found that \(K_{M}\) decreases slowly with increasing \(\alpha\). When \(\left|\alpha\right|>30^{\circ}\), the influence of the jet on the pitching moment nearly disappears. m m  
flow around a laterally jet-controlled missile. The case studies covered various jet flow conditions, including jet Mach numbers, jet pressures, and circumferential jet positions. They also compared the normal force and moment distribution in each region. [PERSON] et al. [9] performed wind tunnel testing for a novel supersonic fluidic oscillator to study its characteristics and the conditions for jet oscillation. The experimental results showed that periodic asymmetrical flipping of the supersonic jet appears at certain nozzle pressure ratios. [PERSON] et al. [10] demonstrated code rationality using experimental results. Comprehensive analyses were conducted on the influences of heat reduction performance and the lateral jet pressure ratio, spike length ratio, and lateral jet location on the drag. [PERSON] [11] compared the numerical results of a flat plate and a missile with four turbulence models. [PERSON] [12] used nine turbulence models derived from standard one- and two-equation models to compare the jet interactions of cold air, hot air, and hot gas jet cases. The jet interactions of a generic missile at several jet conditions were investigated, and the effects of flux functions were compared in a previous numerical study [13]. [PERSON] and [PERSON] [14] investigated jet interaction on configurations with lifting surfaces. Under certain circumstances, the presence of the surfaces resulted in large force or moment amplification because of the interaction of the jet-induced flow field with the planar surfaces. The interaction between a lateral jet and the external flow for various missile body geometries was investigated by [PERSON] et al. [15]. In several circumstances, lifting surfaces led to force or moment amplification of the jet interaction with the missile surfaces. [PERSON] and [PERSON] [16] studied the dynamic stall control of a pitching NACA 0012 airfoil. A synthetic jet in a low Reynolds number compressible flow was used to improve its aerodynamic performance. In a particularly relevant study, [PERSON] et al. [17] numerically studied motion-induced unsteady effects on transverse jet interaction. The potential effects were evaluated by choosing forced oscillation and free-response motion.