# br Theoretical model and numerical method

Theoretical model and numerical method

Results and discussion
A 3D transient analysis of a solid-armature railgun was examined. The mesh of coupled multi-field model including armature and rails is shown in Fig. 1. The unit of geometric size in Fig. 1 is millimeter. The initial conductor temperature was set to 25 °C.
Table 1 lists the material properties used in calculation. The symbols σ, ρ, E, ν, c and κ represent electrical conductivity, density, modulus of elasticity, Poisson\'s ratio, heat capacity and thermal conductivity, respectively.
Pulsed current was applied on the breech segment of railgun model. The armature was accelerated by the Lorentz force, which is generated by the action of current and magnetic fields. The profiles of the imposed current and armature velocity are shown in Fig. 2. The armature velocity reached 2623 m/s.

Summary

Introduction
In-bore yaw of a projectile in a gun tube has been shown to result in range loss if the yaw is significant [1]. Kent [2,3] and later, Sterne [4], developed the following equations that related in-bore yaw to First Maximum Yaw (FMY).
In this equation, IT and IP are the projectile\'s transverse and polar moments of inertia, respectively, Sg is the gyroscopic stability factor, and δtm is the (small) angle of the projectile in the bore of the weapon at the instant of muzzle exit. We can write this in terms of bore clearance. If we assume that the wheel Sephin 1 of the projectile is determined by the longest distance between the largest diameters of the forward and aft bourrelets (lbb) and assuming small angles, we can writewhere dbore is the diameter of the bore, d is the projectile bourrelet diameter and δtm is the in-bore yaw in radians. These equations were later implemented and plotted against test results in the experimental firings of Kent and Hitchcock [5].
In 2012, experiments were conducted at Yuma Proving Ground during an effort to determine the effect that severely worn lands at the muzzle of a 155 mm howitzer would have on the range of a projectile [6].
The FMY described in Eq. (1) is physically generated by the spinning of a yawed projectile, irrespective of the gas dynamics about that projectile. If the weapon has a muzzle brake or other muzzle device, the gas dynamics will likely have more of an effect on the yaw because the projectile is not constrained by the bore during the initial stages of gas ejection.
Measuring the pressure distribution in the muzzle brake is problematic due to the weapon geometry. Pressure gages can easily be placed on the baffle surfaces but determination of the pressure in the flow channels is problematic. Placement of a gage in the flow channels of a muzzle brake has to meet two diametrically opposed criteria: The gage has to remain stationary while hot, high pressure gases blow by it and yet has to be so non-invasive as to not affect the flow. Non-invasive mounting techniques will not survive the gas flow and mounts that are sturdy enough to survive invariably affect the gas flow. Because of this, it was decided to mount twelve pressure transducers, in three sets of four, at a position somewhat up-bore of the muzzle brake. A picture of the mounted gages is shown in Fig. 1.

Test description

Pressure data collection
Blow-by pressure was recorded at 10, 15, and 20 inches from the muzzle of the gun tube forming cross sectional planes B, C, and D respectively, each plane containing four pressure transducers 90° apart. The convention used for plane/sensor designation and for the blow-by analysis is as shown below, as viewed toward the muzzle and rotating clockwise starting at 12 o\'clock as 0° as shown in Fig. 2. This sensor orientation was configured to determine the blow-by pressure distribution along the side of the projectile in terms of time and was used to calculate the net overturning moment acting on the projectile.