[Unclenick]

Fly Fish,

Right. Higher. My next sentence had it right. I changed the sentence from one speaking of the flat base and did an incomplete edit. I've fixed it now.

Last night I finished Bryan Litz's book, Applied Ballistics for Long Range Shooting. Near the end it he covers this very topic, flat base verses boattail. Litz includes what I said about greater muzzle blast deflection on the base of a boattail contributing to pitch and yaw. This is why Harry Pope said over a century ago that the base steers the bullet. The more perfect it is, the better. Litz adds that a flat base is easier to manufacture precisely than a boattail, so it also less prone to having axial mass symmetry errors. Axial mass symmetry error causes bullet jump at muzzle exit and contributes to pitch and yaw and wobble that cause an epicyclic (helical) trajectory. It takes distance to recover from that. It is obvious that even for a flawed bullet, the slower you spin it, the less of that kind of trouble it can cause. Because a shorter bullet requires less spin to stabilize, you can use a slower twist barrel with it, and that contributes even less effect from that kind of error. This is why shorter range benchrest is all shot with short shape, flat base bullets in minimum twist barrels.

Litz divides sources of error into determinate and indeterminate ones. The determinate ones are your range and sight elevation, spin drift, windage zero at a known side winds, the range of the target and elevation adjustment for that range, shooter position and control over rifle cant, and so on. Basically, these are things that the shooter can and should measure and control by determining them and making appropriate adjustments. The indeterminate influences include individual bullet imprecision or muzzle velocity variation in any particular round, the target moving unexpectedly (in hunting) and, of course, all the stuff with the wind that might change direction or temperature and density part way downrange.

The indeterminate atmospheric influences are all proportional to the time air drag adds to the flight of the bullet from the muzzle to the target. In other words, if there were no air, moa of error would be in straight lines and proportional to distance. But because the bullet is going slower and slower down range, it takes longer to cover the last hundred yards than the first. Though a constant side-wind's influence on moa tends to be less further down range because there is less total time for the bullet to drift before impact, that longer total time per unit distance increases the absolute number of inches drift over that unit distance.

The result of the above is shot dispersion tends to be shaped like a horn, flaring wider as the targets are further away. Litz has a simple formula to account for this in constant wind. Use a ballistic program to determine the time to the target. Divide that by the time for the bullet to go the first 100 yards. Multiply your group size at 100 yards by the resulting ratio to get expected group size at long range.

Example:

150 grain flat base with a BC of 0.350 and a 150 grain boattail version with a BC of 0.400. 15% is about the kind of difference a boattail can make if the nose is the same shape for both.

For a muzzle velocity of

Flat Base Times of Flight
100 yards 0.1126 s
1000 yards 1.9187 s

Ratio 17.0:1

Boattail Times of Flight
100 yards 0.1118 s
1000 yards 1.7822 s

Ratio 15.9 : 1

Thus, if both loads group 1.0" at 100 yards in steady wind or still air, you can expect them to group 17" and 15.9" at 1000 yards in still air, respectively. An advantage, but not a huge one. Once you introduce variable wind, though, it is proportional to the difference in the transit time above that in a vacuum. At 2800 fps, vacuum transit time would be .1071 s at 100 yards and 1.071 s at 1000 yards. The differences for the flat base are 0.055 s at 100 yards and 0.8473 s at 1000 yards. For the boattail they are .0047 s and 0.7108 for 1000 yards. So, at 100 yards the flat base is blown 0.0055/0.0047, or 17% more, and at 1000 yards it is blow 0.8473/0.7108, or 19% more. In a 10 MPH cross wind that works out to be only 0.13" of wind drift difference at 100 yards, but 24" of drift difference (149" vs. 125") at 1000 yards.

So, yes, it's mainly wind drift that gets the boattail the nod for long range.


Win_94,

If you push a bullet slowly through a bore with a ram, you are correct that the added bearing surface length adds friction. If a bullet needed, say, 600 lbs of force to push through a bore, then, yes the flat base version might add, say 150 lbs. However, that friction is small compared to the friction that results from the pressure difference between the bullet base and the nose and due to the base pressure acting against the bullet's inertia during firing. The pressure difference and mass inertia acting in reaction to the accelerating force swells the bullet radially outward enough to amounts to several thousand pounds of frictional reaction against forward motion, the amount varying with the pressure at the base at the moment. You can see this because, in a smooth. uniform bore (and even in many that aren't so perfect, the copper fouling builds up thickest in the first couple of inches beyond the throat, which is where the bullet was during the pressure peak. Friction there was also highest.

Though the simple friction of a few hundred pounds due to bullet elasticity pressing against the bore varies with surface area, the higher pressure-induced friction does not. In a longer bullet that swelling is spread out over the longer contact surface, so it is less per square inch of contact surface, and the total friction remains about the same. The other way to look at it is that pressure-induced friction is due to net reaction forces to the pressure so it is determined by the pressure alone.

So, as a percent of total friction in firing the greater length is a pretty small effect. The one thing you may get, though, with the pressure-induced friction being spread over a longer area in the flat base bullet, is less copper fouling per shot.