I am interested in improving the in-flight behavior of an oblong projectile that is launched from something like a trebuchet (a rotating arm).* This is a hobby project and I'm not an engineer or physicist.
My problem is that the oblong projectile tends to tumble. I want it to fly straight like an arrow.**
What I want to know is simply where the center of gravity of an oblong projectile should be given my parameters.
Those parameters are:
- the launch has a rotational component that will tend to make the oblong projectile tumble
- speeds are relatively slow: max of 150 feet per second, and usually half that.
- distances are relatively short: max of 100 feet, and typically half or a quarter of that.
- the oblong projectile is very dense: it's solid steel and weighs about 250 grams, has length of 250 mm and diameter on the order of 10 mm (approx).
- the oblong projectile has very minimal spin around its longitudinal (leading to trailing) axis, and it is not possible to give it more spin (such as a rifled bullet has).
- the oblong projectile has no fins or stabilizer -- it's cylinder shaped with a point at the front. Think of a small torpedo, missile or spear without any fins. The cylinder does not have to be constant diameter nor have straight sides.
- air resistance is negligible (not worth considering); assume, fins would not help even if they could be added (which they can't).
I mention specific speeds, lengths, etc. only to give an example. The problem is a general one. The important conclusion from the above parameters is that solving this problem cannot rely on the usual methods such as center of pressure being behind the center of gravity. A different approach is required.
My question is simply: should the center of gravity to be toward the front, balanced or toward the rear? (And, if possible, why?)
UPDATE: The projectile is positioned radially on the launcher with the "front" furthest from the pivot of rotation and the back closest to the pivot. Therefore, the front of the projectile has higher velocity (compared to the rear) during the launch. It's similar to a spoke in a wheel, where in this case, the front tip of the projectile is mounted near the rim with the back end toward the hub. When the projectile is released from the rotating arm, it should fly straight without tumbling. I will work separately on engineering issues related to the release of the projectile from the rotating arm. For this general problem, I only wish to know where the center of gravity should be given that air/fluid pressure won't help stabilize the projectile.
*NOTE 1: I have tried to simplify the description to avoid a long distracting explanation of how the projectile is thrown. I'm not using a trebuchet. I'm using something with more pivots. But I want to keep the question general and simple. Engineering details of the launcher are outside the scope of this community discussion.
**NOTE 2: a lot of the tumbling will relate to the characteristics of the launch (the throw). But, again, those issues are outside the scope of this question.