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Hey Folks,

A very new-comer to the rifles and ballistics scene, by way of a new job. Looking for a little help with basic ballistic theory, so I'd appreciate any help I can get. Here goes.....

All the ballistic stuff I'v being trying to get my head around tells me that the bullet path is upwards as it leaves the muzzle - and that the bore-line is angled up in comparison to the line of sight, ok?? Some things i'v read say that the rifles sights are pointed downwards. Is this true and if so, why is it like this???

Or can anyone stop me babbling and give me a decent answer as to why the bullet path is upwards??

Thanks,
Longbaugh
 

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Longbaugh

This is a relatively simple question. Rather than saying that the bore points up relative to the sights it may be better to visualize this as being two lines which when projected to any distance from the muzzle will converge at a specific point which is usually referred to as zero. If the line of the bore and line of sight were parallel or divergant then the bullet would never be able to strike at the point of aim but would always be below by at least the difference between these lines. No matter what the situation, the up/down relationship applies only to thr bore/sight relationship, not actual up or down relative to our position from the target

There are actually two situations which occur. The first being a shoulder fired gun such as a rifle, and the second being a handgun. I'll try to explain the difference and the why, and in doing so will seem to contradict my statement above.

Let's approach the rifle first. Typically the bore and sight lines will converge in this scenario. A rifle will move very little in recoil except straight back aproximately along the bore line before the bullet leaves the muzzle. Due to gravity the bullet begins to fall immediately on leaving the muzzle and to hit a target at any distance the bore must be elevated relative to the line of sight to start the bullet upward at such an angle that the bore will be pointed at a place above the intended impact (zero) equal to the total drop for that range. If you refer to any of the loading manuals which have ballistic data you will see the total drop listed for a specific bullet/range/muzzle velocity, this figure is from the bore line.

The second situation is the handgun, and it makes no difference if it is a revolver, automatic or single shot. In this case the bore line usually points away from the line of sight. This is because of the dynamics involved. A handgun, being much lighter than a rifle, will start to recoil both to the rear nad at the same time the muzzle will begin to rise. There is actually quite a bit of verticle component which occurs before the bullet leaves the muzzle. Handgun sights will be adjusted so as to cause the muzzle to be pointed below the intended point of impact before discharge. As the gun recoils and the muzzle rises the bore line will rise to point somewhat above the intended point of impact by trhe time the bullet exits.

To simplify this whole thing, to account for the dynamics of the gun/cartridge combination on firing the line of bore in a rifle will converge with the sight line (rear sight higher than front relative to bore line) and with a handgun the lines of bore and sight will diverge (front sight higher than rear relative to bore).

Either case results in the bullet, called a projectile while in flight, being launched from a bore which is pointed slightly above the intended point of impact at the moment when the bullet exits the muzzle. The amount high the bullet must be directed is directly proportional to the time of flight from muzzle to target. A pistol bullet taking x-time to reach its target at 900 f.p.s. will drop exactly the same distance from the bore line as a rifle bullet will at 2700 f.p.s. will in going three times the distance in the same x-time.

I hope this helps.
 

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The Hog Whisperer (Administrator)
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Same reason the quarterback throws the ball higher, the farther he wants it to end up downfield! Bullets are subject to the same physics as any projectile.
 

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"Bad Joke Friday" Dan (moderator emeritus)
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Longbaugh,

ALK8944’s excellent explanation reminds me of when my physics instructor was explaining the effects of gravity. He said that if you held a bullet and dropped it at the same instance a bullet left the end of the barrel (regardless of velocity), both bullets would hit the ground at the same time. This example assumes the barrel is perpendicular to the ground and not pointed upward.

The graphic demonstrates what ALK8944 explained so well. Using an example where the bullet is a 44mag 240gr. JHP with a muzzle velocity of 1350 and sighted in for 100 yds., the line of sight will be a straight line from your eye to the target but the barrel will be pointed slightly upward. The bullet will cross your line of sight (upwards) and reach a high point above the line of sight of 2.53” at 55.86 yds. and then start on the downward part of the arc and cross the line of sight at 100 yds.

Since the example cartridge load is typical of what I use for the .44 mag revolvers, I use the trajectory software to determine my best "zero" distance. Since I consider 100 yds. to be my maximum range, I find that zeroing it at 100 yds. minimizes my line of sight (LOS) variation for the range inbetween 0 yds and 100 yds.

1. zero at 100 yds = +2.53" LOS
2. zero at 75 yds = +1.14" LOS and -2.75" LOS at 100 yds.
3. zero at 25 yds = minimal variation above LOS and -5.65" LOS at 100 yds.
(note: LOS variations listed ignore the 1" difference between the barrel and sights)

And even if I wouldn't be shooting at 100yds, with my limited ability to accurately judge distance, I usually zero for 100 yds. to minimize my LOS variation.
 

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Beartooth Regular
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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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"Bad Joke Friday" Dan (moderator emeritus)
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"The fired bullet will hit the ground later than the dropped bullet, due to air resistance on the bullet"

Jack, I'm sure it will not be a surpirse that my physics classmates (me included) frequently operated in a vacuum, so my guy probably assumed we'd shoot in a vacuum.

Tables/software for calculations can certainly be helpful, but would recommend they be backed up by field testing. My RCBS software calculated my load, zeroed for 100 yds. would drop an additional 27.2" at 200 yds.. This software takes temperature, humidity, wind, etc. into consideration in it's calculations. My field test showed a 31" drop from 100 yds to 200 yds.. Not a big deal, but sufficient that I prefer to field test also.
 

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Beartooth Regular
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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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