MarMas,
The thing that struck me about your initial post is the specific set of constraints. Backing up a little from that, for general purposes, there are four areas of ballistics. In the order in which they are involved in taking a shot, they are:
- Interior ballistics
- Transitional ballistics
- Exterior ballistics
- Terminal ballistics
Interior is about what is happening while the bullet is still in the barrel of the gun. Transitional ballistics is about the brief period when the bullet has cleared the muzzle but is still being influenced by the gases from the muzzle blast that comes from behind it, and is greatest for the first six to twelve calibers of bullet travel beyond the muzzle. Exterior ballistics is about the way the bullet coasts to the target after the transitional ballistic influence is no longer present, so it covers most of the bullet's trajectory to the target. Terminal ballistics is about how the bullet's impact affects the target.
For the interior ballistics of your hypothetical situation, you have to keep in mind what is called expansion. Expansion refers to the fact that while the bullet is still in the barrel, the volume behind the bullet grows as the bullet moves forward. The volume behind the bullet at the muzzle divided by the volume behind the bullet when it is still in the chamber is called the expansion ratio of the gun. If you pick a powder like Bullseye, because it burns quickly, the pressure peak will be reached before the bullet has moved very far, and thus the pressure peak occurs in a small volume behind the bullet and often before the bullet has completely left the cartridge case. Reaching a given pressure in a small volume does not require very much gas, so a small charge of fast powder can make enough gas to reach the peak pressure. But with a slow-burning powder, the bullet has time to move further down the barrel and have more expansion of the volume behind it more before the pressure peak is reached. This means the peak pressure occurs in a larger volume and requires more gas to be reached which requires a larger charge of the slow powder. When there is more gas, pressure does not drop off as fast as the bullet goes beyond its peak pressure position, and thus there is more post-peak acceleration with the larger load of slow powder than there is with the smaller load of fast powder. As a result, the larger charge of slow powder produces higher velocity. The downside to the slow powder is the greater gas mass produces more recoil in addition to the greater acceleration of the bullet producing more recoil.
Transitional ballistics generally results in around 3-4% gain in velocity of the bullet after it clears the muzzle, but this varies with expansion ratio. This is from the muzzle blast blowing against the bottom of it. Since the bullet is outside the rifling for that, no additional increase in spin occurs; just forward velocity increases. The deflection of the gases off the bullet base can also exaggerate the initial yaw of the bullet, making it tip a bit more as it spins. That increases drag a bit at first, but far enough downrange it should settle. With soft lead hollow-base wadcutters, if the muzzle blast is too great it can cause expansion of the hollow base which reduces the bullet BC all the way to the target and introduces odd drag.
Exterior ballistics is all about how drag on a bullet affects its flight and how precession from spinning like a gyroscope causes it to correct its alignment into the wind. It is also about where the critical values for the effect of these factors lie in order to know what spin is minimally required. Starting in the late 1860s, when early electromechanical chronographs became available, standard practice was established in which thousands of standard shape projectiles were fired at different velocities to see how fast they slowed down at those velocities to determine the overall effect of drag on the projectile. Then, all other projectiles were compared to the standard shape by how fast they slowed down in comparison. That became the basis for the ballistic coefficient you commonly see now. Today you can select different standard projectile shapes to compare to, each having its own unique BC for your bullet and each producing a different degree of accuracy in matching your bullet's shape and therefore accuracy in matching its drag behavior at different velocities. But the default BC you see generally published is for the G1 standard projectile. The comparison and your bullet's velocity near the muzzle (but after transitional ballistics are done) is used to determine trajectory tables by comparing to how the standard projectile was measured to behave at the same velocities.
You don't have to use BC's to determine a trajectory if you have the drag function for an individual bullet. Doppler RADAR is making those easier to determine than they have been in the past, so more and more bullet drag functions are being published. Lapua has published them for about twenty years. Hornady now has a lot you can select from for their 4 DOF ballistic calculator. For the cylinder like you propose to shoot, the U.S. Army Ballistic Research Laboratory (BRL) determined the drag function long ago. It is called the RA4 drag function. If you find
an exterior ballistics calculator that lets you select that drag function and you enter the measured velocity of your cylindrical bullet, you will get the most accurate prediction of the trajectory by using RA4 instead of the G1 drag function. (In the calculator I linked to, the first entry window at the top left has a drop-down menu that has RA4 at the bottom of its list.)
It is not true that a cylinder will necessarily become unstable at long range. That observation is an artifact of over a century of using hollow-base wadcutters with inadequate rifling twist rates, as commonly occurs due to many standard-for-caliber twist rates having been chosen originally for lighter, shorter bullets around the end of the 19th century, but subsequently used with the longer, lower velocity wadcutters anyway. This has caused issues with both 32 Long and 38 Special wadcutters at times. I saw the report of an experiment done with the 32 Long HB commercial wadcutter ammunition published in an article twenty years ago in which the author started, IIRC, with a standard 18.75" twist in a gun, then went to 16", then to 14", then to 12" then to 10". The groups at pistol range kept getting tighter and tighter down to the 12" twist, then opened a little with the 10" (again, IIRC). But the point is the 18.75" twist is not optimal for subsonic HB wadcutter shooting, where extra high stability factors seem to pay dividends with that particular bullet shape. 18.75" (476.3 mm) remains the SAAMI standard, and 476.00 mm (18.74") is the CIP standard.
Terminal ballistics will get you into the realm of bullet penetration, bullet shape, expanding bullet performance, kinetic energy, momentum, bullet tumbling, and other factors in target damage for hunting or personal defense purposes. It will more simply also get you to using sharp edges for cutting clean holes in target paper. Except for clean holes in paper, terminal ballistics is the least predictable area of ballistics, with the same loads often producing a significant variation in results from one shot to the next on living targets. This has resulted in lots of arguments about the relative roles of bullet shape, kinetic energy, momentum, sectional density, and other factors, and no universal predictive formula has yet been successfully devised that provides a sure prediction of what load under what bullet will produce the best results every time.
Welcome to a hobby that lets you get as involved as you please with the details, but that also can be as simple as following a recipe and just practicing your shooting skills. Immersion in the details of ballistics can cause you to forget that your marksmanship skills outweigh all else in getting a gun to do the job you intend it to do.
