# Solving the Moment Amplification Factor of a Lateral Jet by the Unsteady Motion Experimental Method
###### Abstract
In summary, the changes in the flow field at the nozzle, the aerodynamic forces on the air vehicle, and the air vehicle motion occur simultaneously. The actual jet process is coupled with various unsteady factors. Past research on jets has been mainly limited to unsteady flow field and unsteady aerodynamics research, while research on the motion caused by the jet is scarce. Using this traditional research approach, in which only the unsteady characteristics of a specific parameter can be studied, must result in differences between the lateral jet influence factors obtained and the actual air vehicle, leading to inaccuracies in the interference factors measured in the pressure test. In the published literature, there is no relevant research on the unsteady flow field coupling characteristics, aerodynamic forces, and unsteady motion caused by the jet, and test methods using unsteady coupling to measure the interference factor are rare. This existing approach produces inadequate research results, and there are knowledge gaps regarding the unsteady coupling effect on actual air vehicle jets. The wind tunnel free flight test technique is a common research approach to understanding the unsteady characteristics of an air vehicle and differs from other steady (force measurement after model support) and capture trajectory simulation (CTS) methods. It has the unique advantage of no support interference. The test uses high-speed photography and the curves of the six-degrees-of-freedom parameters of the air vehicle model with time can be acquired. Later, the dynamic aerodynamic parameters of the air vehicle can be obtained through data processing. In recent years, [PERSON] et al. [23; 24; 25; 26] have greatly improved the former wind tunnel free-flight test technique and test theory, expanding the research scope and ensuring its accuracy. Meanwhile, [PERSON] et al. [27; 28] also conducted exploratory research on jet characteristics. Figure 1: The relationship between the jet, flow field, aerodynamic force, and motion of an actual air vehicle when jet control is activated. Model free-flight wind tunnel and traditional jet control test methods each have certain advantages. If these two approaches could be combined and the wind tunnel free-flight test method used to study the \(K_{M}\), the jet's action could be better understood, resulting in more accurate \(K_{M}\) values. For the study of the jet's influence on the air vehicle, the wind tunnel free-flight test technology is different from previous methods. For example, in Refs. [9; 10; 17], the air vehicle's tail is equipped with support rods during the wind tunnel test, preventing the motion of the air vehicle model by the jet force. Each test can only calculate the jet force in a single state or obtain the jet flow field diagram of a single test and is inadequate to produce coupling results and the data shown in Figure 1.  
By contrast, the approach explored in this paper uses a wind tunnel and an unsupported free-flight test model with a jet, and the jet force can act on the air vehicle model in real time. Through later data processing, the aerodynamic forces on the air vehicle at different angles of attack can be obtained. The wind tunnel test also uses high-speed photography to capture the interaction between the jet and the external flow field at different angles of attack to fully realize the effects shown in Figure 1. This method ensures that the wind tunnel test is consistent with actual flight conditions. The results of more than a dozen wind tunnel tests in the past are obtained using one test. The research content of this paper is as follows. For the lateral jet attitude control, \(K_{M}\) is obtained. The specific method uses a more realistic six-degrees-of-freedom unsteady test research method employing a wind tunnel free-flight test technique. The air vehicle's corresponding angular displacement time history is obtained in a completely free state.