In bore yaw effects on

In-bore yaw effects on lateral throw-off and aerodynamic jump for small caliber projectiles were also studied by Gkritzapis and Panagiotopoulos [6] for firing sidewise from air vehicles. They used a modified linear 6-DOF flight simulation code to predict the bullet trajectory. The coupled epicyclic pitching and yawing motion of the first 100 m of the trajectories studied are used for their analysis.
Analytical model Using the linear dhpg manufacturer of ballistics, an analytical model was developed in order to predict the projectile deflection at the target given a chamber misalignment or projectile in-bore tilt. The relationship was developed based on the work of Murphy [7] on the linearized swerving motion of rotationally symmetric projectiles. In developing the model, the total incidence of the projectile was assumed to be small (i.e. ). The projectile is assumed to be rotationally symmetric both in shape and mass distribution. As the projectile exits the misaligned chamber to enter the gun barrel, it gets tilted. The tilt is assumed to persist as the projectile gets engraved into the rifling of the barrel. Further assuming no bouncing or balloting of the projectile, its axis of symmetry follows a precession motion around the axis of the gun. The tilted bullet is illustrated in Fig. 1. The in-bore yaw is labeled . The initial complex yaw at the muzzle is given bywhere . The initial roll angle at the muzzle, , is the angle between the vertically upward plane and the plane containing both the in-bore yaw and the bore axis. The initial yaw rate or angular velocity of the tilted projectile at the muzzle is caused by its spin. The initial yaw rate is the product of the spin rate and the sine of the in-bore yaw The independent variable in Eq. (2) can be changed from the time to the dimensionless distance, s, using the following relationship Substituting Eq. (3) into Eq. (2), the initial rate becomeswhere n is the rifle barrel twist rate in calibers/turn. The generalized aerodynamic jump equation was derived by Murphy [7] and only the final result is reproduced here for brevitywhere and . is the lift force coefficient and is the pitching moment coefficient. Substituting the equations for the initial yaw and initial yaw rate in the generalized aerodynamic jump equation, one obtains the relationship for the aerodynamic jump of a projectile with in-bore yaw The aerodynamic jump can easily be determined provided the in-bore yaw, , is known. The in-bore yaw can be approximated geometrically by considering a projectile exiting a misaligned chamber and engaging in the rifling of a barrel. However, the method was found to yield non-satisfactory results and was not used for the present study. Alternatively, the in-bore yaw could have been estimated using orthogonal cameras at the muzzle during the firing. This option was not retained for the trial. In planning for this trial, Transvection was decided to locate to high-speed orthogonal camera in the vicinity of the expected first maximum yaw for the 5.56 mm projectile. More details on the experimental setup will be given in the following section. Having the first maximum yaw associated with each projectile, it is possible to compute the in-bore yaw angle using Kent\'s equation. Kent\'s equation derivation was first published by McShane et al. [9]. It relates the first maximum yaw angle to the in-bore yaw angle as follows Solving Eq. (7) for the in-bore yaw angle yields Substituting Eq. (8) into Eq. (6) yields a mean of predicting the in-bore yaw angle resulting from CT ammunition chamber misalignment based on the mean impact point observed at the target In addition to the aerodynamic jump component, there is a lateral throw-off component that arises because of the in-bore yaw angle of the projectile. Referring to Fig. 1, and assuming that the projectile tilt occurs at the mid-point of the cylindrical portion of the projectile, then there will be a static unbalance if the center of mass is located either ahead of or aft of the mid-point.