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Understanding Trajectory... Rifles

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The law of gravity dictates that a bullet will begin to drop toward the earth from the moment it leaves the rifle barrel. The reason that some rifles shoot ďflatterĒ than others is simply because their bullets travel faster and are able to cover more distance in a given amount of time. The bullets still drop to the earth at a rate of acceleration of 32 fps, but they simply cover more ground than slower bullets before dropping a given distance. It is necessary to elevate the rifleís bore slightly above the line of sight so that, when firing, the bulletís path rises on a curve that has it crossing the line of sight twice. Because the bullet begins dropping as soon as it is free from the constraints of the rifle, if it were simply fired with the bore of the rifle pointed at the target, it would hit below the target every time. The line of sight is a straight line from the sights to the target. Vision is not subject to gravity, so your eye and the bullet take different paths to the target. While your eyeís path is as straight as a laser, the bulletís path will be an arch to compensate for the effects of gravity.
The Bulletís Path
The first time the bullet crosses your line of sight will be close to the rifle. The exact distance will depend on several factors, such as the height of the sights or scope above the bore, the distance to your zeroed point of impact and the relative flatness of the bulletís trajectory. However, this distance is usually somewhere around 25 to 50 yards. The next time the bullet crosses your line of sight will be at the distance you have selected to zero your rifle for. At any point in the bulletís path other than these two, the bullet will be above or below your line of sight. Because a slower bullet takes longer to get to a given distant point, it must arch higher above the line of sight than a bullet that is traveling much faster. Letís take an extreme example and compare the .45-70 Gov. and the .300 Rem. Ultra Mag., both sighted for 200-yard zero (see graphs).
The mid-range trajectory is the apex of the bulletís arch, or the highest point that the bullet will be above the line of sight during its flight. With the .300 Rem. Ultra Mag. and a 200-yard zero, the mid-range trajectory of the bullet occurs at about 120 yards and is only 1.17 inches. The mid-range trajectory for the .45-70 Gov. with a 400-grain bullet and a 200-yard zero is 13.37 inches and occurs at 110 yards. Total bullet drop at 200 yards for the .300 Rem. Ultra Mag. is 6.99 inches. That is, if the bullet were fired perfectly level, it would have dropped 6.99 inches by the time it reached the 200-yard mark.
Total 200-yard drop for the .45-70 Gov. is 51.23 inches. The difference is that the .300 Rem. Ultra Mag. has a muzzle velocity of 3,300 fps and uses a streamlined bullet. It takes the bullet only .19467 seconds in flight to reach 200 yards and the bullet is still traveling at 2,881 fps at that distance. The .45-70 Gov. uses a bullet that is much less streamlined, so it loses velocity much quicker and starts out at a much slower 1,300 fps. The .45-70 Gov. bullet crosses the 200-yard mark with a time in flight of .53846 seconds and with 991 fps of velocity remaining.
Simply put, any bullet must arch in its path to the target relative to the line of sight. The faster the bullet gets to the target, the flatter that arch or trajectory will be.
Types Of Ballistics
The three common types of ballistics often referred to by shooters can be a little confusing. But itís really very simple.
Internal Ballistics. This is what happens inside the gun. It refers to the powder burning, pressure, the bulletís path down the barrel, etc.
External Ballistics. This is what happens during the bulletís flight through the air. It deals with trajectory, velocity, energy, etc.
Terminal Ballistics. This is what happens after the bullet has hit the target. Itís the study of things such as expansion, weight retention, penetration, etc.
Look Out Below
Remember that your line of sight is different from the bulletís path. The bullet is traveling along a line thatís somewhat lower than what you are seeing for the first several yards. The higher the scope is above the bore, the more pronounced this difference between the line of sight and bullet path becomes. Make sure you have plenty of clearance for the bullet. Itís easy to overlook a close obstacle, because you are concentrating on the distant target and not whatís up close. Also, things that are close are usually blurry in the scope, or not even in the field of view.
The best illustration of this was when I was hunting groundhogs in Dayton Ohio with some buddies who I suppose should remain nameless. I was sitting in a Jeep, spotting with binoculars for a shooter who had a sandbag on the hood of another vehicle. He shot five times, but I never saw a bullet strike. I do remember remarking to a friend sitting in the driverís seat of my Jeep that the rifle sounded funny. The ricochet sound was coming too soon after the shot.
The shooter finally gave up and in frustration said, ďBring your rifle over here and see if you can hit anything.Ē

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  1. Ken's Avatar

    This is probably the best and most concise explanation on this topic that I have ever heard or read.