Location: The rifle range, or archery range or behind the computer in Alaska
Re: Angled shots
5 degrees: Normal bullet drop x .004
10 degrees: Normal bullet drop x .015
15 degrees: Normal bullet drop x .034
20 degrees: Normal bullet drop x .060
25 degrees: Normal bullet drop x .094
30 degrees: Normal bullet drop x .134
35 degrees: Normal bullet drop x .181
40 degrees: Normal bullet drop x .235
45 degrees: Normal bullet drop x .293
50 degrees: Normal bullet drop x .357
55 degrees: Normal bullet drop x .426
60 degrees: Normal bullet drop x .500
To use this chart, first find your bullet’s drop when fired perfectly level with the earth. Then find the angle of fire. Then multiply your bullet drop with the multiplier for the angle of fire you are planning to shoot. Let’s say we are shooting at a 45 degree angle at 300 yards with a .243 Winchester which is zeroed @ 300 yards. This bullet gives us an actual drop of 20.6” @ 300 yards when fired level with the earth, 20.6 x .293 = 6.03” Now you must aim 6” low to hit dead on. You should set up for a shot by aiming 6” under the target instead of 0”. Take the distance you are going to shoot and look and see what the drop is for that yardage and then multiply it by the figure for the degree of angle you are going to shoot taken from this page. Note: the drop figures are not the same drop figures for your rifle with a down range zero but they are what you need for this calculation. If the distance is further than your zero, simply deduct the number you calculate from your bullet drop chart.
Long range shooting is a process that ends with a result. Once you start to focus on the result (how bad your last shot was, how big the group is going to be, what your buck will score, what your match score is, what place you are in...) then you loose the capacity to focus on the process.
What you are calling the "ACTUAL" range is called "slope distance" in rangefinder jargon. Since gravity acts on bullets only at an angle perpendicular to a line drawn through the center of the earth, (or I suppose a line tangent to the surface of the earth, help me here Dave King, you patient, silver-tongued devil) one must figure bullet drop based on the "horizontal" distance to target.
The horizontal distance will be less than the slope distance in all cases where the line to the target is not parallel with the lines mentioned in the preceding sentence. In other words, when you aren't pointing the RF parallel with the ground.
To understand the gravity "vectors" at work on a bullet in flight, picture yourself with your right arm outstretched parallel with the ground. If I pull on your arm straight down, perpendicular to the ground, and you resist there is a certain amount of force you need to employ in order for your arm to not be pulled downward.
Now, if you move your arm upward and point it straight at the target on the hillside I will again pull on your arm, straight down toward the ground. This time you can resist more easily because (though I am still pulling perpendicular to the ground) your arm is at an angle to my direction of pull.
In this way gravity doesn't pull as hard down toward the ground on a bullet in flight at an angle, whether upward or downward.
Gravity acts by pulling objects toward the center of the earth (for our purposes). If we fire a projectile horizontal to the earth's surface and that projectile trys to fall to the center of the earth at a rate of oh... let's say 2.5 inches in a tenth of a second. A shooters we need to compensate by angling the barrel of the rifle upward (zeroing the rifle is how we do this) by this 2.5 inches for a shot taking one-tenth of a second, about 100 yards. Now let's see what happens when we use a worst case example... leave the rifle zeroed so there is a 2.5 inch up angle on the sights (horizontal 100 yard zero) and shoot straight down for a 100 yard shot. When we shoot straight down the effect of gravity is in the same direction as the projetile is traveling so the extra 2.5 inches of "drop" caused by gravity is changed from movement away from the line-of-flight to with the line of flight... and in effect there is no angular departure for the projectile BUT the rifle has 2.5 inches of "zero" (angular correction) built in and we'll shoot "high" by those 2.5 inches for a 100 yard shot.
To correct this 2.5 inch "high" miss we recalculate the line-of-sight distance by using the cosine of the angle to the target... cosine of 90 degrees is 0 (zero) and the one-tenth of a second flight time is about a 100 yard shot distance. 100 x 0 = 0 so we figure the distance at zero and set the scope for that distance. For a 60 degree shot the cosine is .5 so our distances will be 1/2 of the line-of-sight (laser) distance and for a 300 yard shot we'll set the scope as if it were a 150 yard shot. The concept once understood is simple...the solution(s) are several and it depends of how nit-picky you are as to how you fix the problem... I like to make it as difficult as possible and play with all kinds of numbers (and Excedrin) in an attempt to make an exact answer... the Angle Cosine Indicator and tools of it's like are functionally adequate and correct.
P. S. Don't try the above 90 degree example by shooting straight up in the air... you'll put your eye out [img]images/icons/wink.gif[/img].
How is this for a simplistic way of approaching this subject. Imagine that the shot is a right triangle, you are at the top, the critter is at the point away from you. Gravity is only effecting the bullet over the distance of the bottom of the right triangle, that is the horizontal distance . Imagine a line drawn straight down from where you are shooting and then measure the distance from that line to the critter. Gravity sucks the bullet down for that distance, not the hypotenuse that the bullet has to travel.
Given that, I believe that unless the angle is very steep, aiming in the center of the chest on an elk out at 300 will result in a dead elk (if you have the correct hold-off or elevation setting for 300 yards). Bullet drop is not that big of a deal and you have a BIG freaking target - 18-20 inches or so.
We shot out to 300 from a tower one time, three stories high, bullets hit close enough to point of aim that a hit would be lethal on most four-legged big-game type critters. Ten inch balloons were easy. Seems to me that this angle stuff is way blown out of proportion, just hold a smidge low and send-it.
Gentlemen: First and foremost, IF you are a throw up the rifle snap shot kind of guy/gal, never shoot beyond 100-300 yards and not a pro, then forget about ever using the ACI. You do not need it. However, if being on target matters more then guessing (hold and hope – there’s plenty of room for error) then you do. No Offense meant to anyone, it is just a fact. For the police Marksmen it is an imperative piece of kit. Why? Because their job depends on it, those near the bad guy depend on it and the simple fact of liability depends on it. For the Military Sniper, it is an imperative piece of kit because just the chance of missing puts their lives in danger or should I say increases the probability of their own death. The Federal Government teaches angle shooting because it is imperative to them. Our military teaches angle shooting because it is imperative to them. The foreign militaries teach angle shooting, because it is also imperative to them. “You cannot argue with fact unless your mind is made up of fiction”. The way that angle shooting and the ACI works is this; when you site your rifle in at 100 yards, you have adjusted the site height above the bore so that the bullet leaves the barrel, arcs up and then drops onto the X. You also have the full effect of gravity on that bullet because you are shooting flat. Although, when you shoot up or down on an angle the effects of gravity is less, but your site height above the bore is the same. This means that the bullet will try to arch up just as high, but will travel a flatter trajectory, hitting higher. Check out the web site, you will most probably at least enjoy the reading.