Can anyone explain the correlation between center of pressure and center of gravity with reguard to velocity in spin stabalized symmetric projectiles?
Read on at your own risk, this question may get fairly technical. It's unfortunate I can only ask just one. The correlation I'm more interested in is that of optimal "rate of rotation" to properly stabilize a projectile of a given shape/size. I think answering my question above will help in answering others. In external ballistics, a projectile (bullet) of greater length for a given diameter, requires a faster "rate of twist" to stabilize than does a shorter one. An often over-looked part of this relationship is velocity. A longer bullet of a given diameter (caliber) is generally heavier, thus propelled at a slower speed. The "Greenhill Formula" is the most widely used formula I know of to calculate proper rate of twist (in the riflling of a barrel) to stabilize a bullet of given length and diameter. Some variations even account for velocity on a crude level. Still, this formula relates bullet length to rotation over distance, not rotation over time. I'm not sure which is more important to proper stabilization, or at least which has a more linear relationship to bullet length. Maybe I'm overzealous in my search for a better answer, but that hasn't held me back so far. I am afterall hoping to find a ballistics expert here. Thanks in advance for any enlightment you can provide.
Not a ballistics expert, but I think I've got your answer!! Or at least I can provide you with a few formulas that relate linear velocity of rotation to the velocity of advance, and account for caliber and rifling, and get you going. The formulas are bit complex, my calculus isn't great, and the word processor I'm writing on can't handle math and scientific notation, so I'm not going to even attempt to display them with all the greek and subscripts, but you can find the formulas here:
Encyclopedia Britannica, 11th ed., vol. 14 pg. 133 sec 51.