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Hi, Gents:
We've got some excellent answers here and a couple of obscure technical errors.

Since the sights are above the barrel, we're throwing our bullets underhand. If we toss a ball underhand at something close and at eye level, the ball rises until it hits the target. If we back up some and don't throw any harder, the ball will rise above eye level and then start dropping back to eye level. If we don't back up far enough, the ball will hit above the target. It hits the target at the right distance and hits low at a longer distance.

Now to get technical. DOK's physics instructor made the same mistake our high school science teacher made. The fired bullet will hit the ground later than the dropped bullet, due to air resistance on the bullet. To quote from Hatcher's Notebook, page 626, "it is very much as if the value of g were to fall off from 32 at the muzzle to 28 at 500 yards and 24 at 1000 yards". This example is from the British Textbook of Small Arms, so it likely refers to a .303 British load.

To add to the fun, this apparent reduction in g is dependent on velocity, so Alk's statement that the rifle and pistol bullet drop the same distance in the same time isn't exactly right. There's a 2.5" difference at the 1 second mark. This is a minor difference compared to the drop the formula for the acceleration of gravity in a vacuum gives us. The drop in a vacuum is 193", but the rifle bullet drops 159.1" and the pistol bullet drops 161.6". However both of these bullets operate outside the ballistic fun zone, the transonic region. If we use DOK's muzzle velocity of 1350 fps, the drop in one second is 167.0".

I used the late Bob McCoy's McTraj program for these calculations. Mccoy was a ballistics genius. It's a bearcat to use but it allows a barrel elevation of zero. Most ballistic programs assume you're sighting in a gun and also use a one size fits all drop correction formula.

Luckily, we all can check these numbers by using the external ballistics calculator in Ballisticians' Corner, available though the link on the left side of this page. It's a link to Brad Millard's JBM site and it uses Bob McCoy's equations. Goto http://internet.cybermesa.com/~jbm/ballistics/ballistics.html if you want an overdose.

Alk put one constraint on this example. The distance travelled in x time is proportional to the muzzle velocity. Since the JBM calculator doesn't allow a zero barrel elevation, I took a flight time of 1 second, adjusted the ballistic coefficient so the range came out to an even number, zeroed at midrange, then reported the drop at the 1 second range. If you run this, set barometric pressure to 29.52". So starting with a .30-06 at 2700 fps and a ballistic coefficient of .410, typical of a 180 gr. spitzer, we get a range of 660 yards at 1 second. Since subsonic drag is very low, we have to use a very low ballistic coefficient of .0495 to get a 1 second range of 220 yards, which is 1/3 the .30-06 range. This is typical of .38 wadcutters, so we aren't completely off scale. For DOK's .44 Magnum 1350 fps velocity, use a ballistic coefficient of .1485 for a 1 second flight time of 330 yards. The drop below the line of sight is 96.0" for the .30-06, 96.9" for the .38 and 99.0" for the .44.

Bye
Jack
 

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7,768 Posts
Hi, DOK:
Agreed. It's a prime case for "Shoot It And See". There's a number of factors involved, but a big one is that some manufacturer's ballistic coefficients are, to put it politely, hopelessly optimistic.

Bye
Jack
 
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