## 5 Experimental Results Analysis  
The equation of motion of the armature is given by  
\[\left\{ \begin{array}{l}v=\frac{F_{v}-\mu_{v}(F_{0}+F_{N}+F_{P})-f_{p}}{m} \cdot t\\ l=\int_{0}^{t}vd\,\text{i}\
u\end{array} \right.t \tag{27}\]  
where \(\mu_{v}\) is the Poisson's ratio, F\({}_{0}\) is the armature and rail initial contact pressure, \(F_{N}=\frac{\mu S_{c}}{2(1-\mu)S}F_{a}\) is the electromagnetic pressure of the armature, \(F_{P}=\frac{\mu S_{c}}{2(1-\mu)S}f_{p}\) is the air pressure, \(f_{p}=\frac{\gamma+1}{2}\rho_{0}(Sv^{2}+Sla+\frac{c_{f}\lambda v^{2}l}{2})\) is the air resistance, m is the mass of the armature, S\({}_{c}\) is the armature and the rail contact area, S is the cross-sectional area of the armature, \(\lambda\) is the specific heat ratio, \(c_{f}\) is the coefficient of friction of air-adhesive tape, and \(\rho_{0}\) is the air density. Passing the pulse current in Figure 4 and combining Equations (13) and (25), the relationship between the inductance gradient and the armature electromagnetic thrust with time, as well as the armature velocity and the armature displacement with time, can be obtained, as shown in the Figures 14 and 15. Figure 13: The variation law of L\({}_{c}\), M\({}^{\prime}\), and L\({}^{\prime}\) with the skin depth. In Figure 14, since the dynamic skin depth is considered, the obtained inductance gradient is time-varying, which is completely different from the results in the literature [7; 8; 9]. In the early stage of launch, the skin depth is deeper, so the calculated inductance gradient is about 0.8549 \(\upmu\)H/m. Then, the inductance gradient decreases slowly with speed during the firing process. In the late stage of launch, because the speed of the armature is around 2 km/s, the skin depth is less than 0.3 mm, according to Equation (13), which can is noticed as the current tends to cover the surface of the rail completely, so the calculation result is about 0.7556 \(\upmu\)H/m. In the initial stage, since the skin depth can be approximated as constant, the inductance gradient is also kept constant. The electromagnetic thrust of the armature changes with the same general trend of current change; its peak value is approximately 31 kN. In Figure 15, the armature has been in the acceleration state; after 1.3 ms, the armature speed curve becomes slower, and the discharge speed is about 2.216 km/s. After 1.3 ms, the armature does exhibit approximately uniform linear motion; the movement time of the armature in the rail is about 1.542 ms. The block diagram of the whole system is shown in Figure 16. The test signals of the whole system are divided into three categories: voltage and current of the pulse power supply; magnetic field, voltage, and thermal energy of the launcher; and external ballistic launch velocity. Figure 14: Theoretical inductance gradient and electromagnetic thrust of the armature curves. Figure 15: Theoretical speed of the armature and displacement of the armature curves. In the experimental device, the three speed acquisition signals are located in two station light curtain targets. Passing through the signal processing unit, the speed acquisition signals are output to the oscilloscope corresponding channel. The signal acquisition rate is 1 MHz. The armature discharge velocity measured by the light curtain target is approximately 2.296 km/s. Figure 17 shows the experimental device of the electromagnetic launcher; the length of the rail is 2.18 m, and the mass of the armature in this experiment is about 7 g.  
The power supply mainly includes voltage and current sensors, which are distributed inside seven power supplies. Sensors such as the B-point coil and bore pressure test signal are located in the transmitter. There are a total of seven voltage sensors that monitor the actual charging voltage of the power module during the charging process. This signal is transmitted to the seven voltage acquisition channels of the measurement system, with a sampling rate of 100 kHz.