Occasionally we are called upon to use our Cowboy Action Shooting(TM) rifle and pet loads to participate in a long-range rifle side match. The questions that now face us are; how much do I need to adjust my sight, or how much “Kentucky windage” do I need to hit a target at 100+ yards when my rifle is sighted-in at only 30 yards? Because most of us don’t have ready access to a range, this article will show you how to create a range card to estimate the answers to those questions.
The tools you will need to perform these calculations are available on your PC. The ballistics program I use is BALISTIC v4.13, copyright 1988-1995 William R. Frenchu. This program is available as shareware from http://www.simtel.com/product.php?id=49924&SiteID=simtel.net . The scientific view of the calculator that comes with your PC has the trigonometric functions needed.
First, a little theory. If a rifle’s barrel were exactly level and parallel with the ground, the instant a bullet left the barrel gravity would cause the bullet to start falling. In order to hit a target at some distance, the rifle barrel must be inclined at a small angle. Therefore, the bullet rises some amount above the line of sight before gravity pulls it down. When you sight-in a rifle by adjusting the sights you are actually adjusting the angle of the barrel so the bullet will impact the center of the target at some point along its trajectory. The two angles we need to know to calculate the adjustments are; 1 - the angle formed by the line of sight, bullet path, and front sight height above the bore (angle of departure), and 2 - the angle formed by the barrel, line of sight, and the rear sight height above the front sight.
For this exercise you will need a ballistics program for your PC capable of calculating trajectory. The program I use, BALISTIC, also gives you the angle of departure, which is the angle of the barrel, but I’ll show you how to calculate that as well. You will also need to know the ballistic coefficient and velocity of the load you are using. My .45LC LRNFP 250 grain bullet chronographs at 800 FPS with a ballistic coefficient of 0.248.
First we need to find the angle of departure, then the sight height above the front sight. The angle formed by the front sight height above the bore, the line of sight, and the bullet path from the muzzle to where it crosses the line of sight makes up a right triangle. If we measure the front sight height above the bore, and know the distance the bullet travels before it crosses the line of sight we can calculate the angle of departure as follows: Angle of departure = arctangent (sight height above bore / bullet distance to cross line of sight). (To perform the arctangent function on your PC calculator, check the ‘Inv’ box, then click the ‘tan’ button. Be sure the calculator is working in degrees.)
Example: My ballistics program says when my rifle is sighted-in at 30 yards, the bullet crosses the line of sight at 7.62 yards. 7.62 yds x 36 in. = 274.32 inches. The sight height above the bore is 0.63 inches, so arctangent (0.63 / 274.32) = 0.132 degrees angle of departure. This agrees with the angle of departure figure provided by the ballistics program.
The angle formed by the line of sight, the barrel, and the rear sight height above the front sight is also a right triangle, where the distance from the rear sight to the front sight makes up the hypotenuse. If we know the angle of departure and measure the distance between the front and rear sight, we can calculate the rear sight height above the front sight as follows: Rear sight height = tangent (angle of departure) x sight distance.
Example: I mounted a tang sight on my Marlin 1894 CB LTD, which made the distance between the front and rear sights 31 inches. At 30 yards the angle of departure is 0.132 degrees (see above). Rear sight height = tangent (0.132) x 31” = 0.0714”. This is the baseline for adjusting your rear sight for longer-range targets. Using this baseline we can calculate how much to adjust the rear sight for longer distances.
My ballistic program says that if I leave my rifle sighted-in at 30 yards, the bullet will be 18 inches low at 100 yards. To hit the target at that distance, I would have to hold 18 inches over the center of the target. But, let’s calculate how much I would have to adjust my rear sight to be dead on at 100 yards. This time, at 100 yards the bullet crosses the line of sight at 2.178 yards, so the angle of departure is:
Arctangent (0.63 / (2.178 x 36)) = 0.460 degrees (agrees with the ballistic program)
The rear sight height is tangent (0.460) x 31 = 0.249”. The difference between this new height and the baseline is 0.249” – 0.0714” = 0.178”. So, I have to move my rear sight up 0.178 inches to be on at 100 yards.
My tang sight uses a 28 threads per inch (TPI) screw to adjust the elevation. Therefore, one turn = 1/28 or 0.0357 inches. So now, divide 0.178 (sight height difference) by 0.0357 (distance of one turn) and you get 0.178 / 0.0357 = 4.985 or 5 turns. This is close enough for “minute-of-cowboy” shooting. By the way, I tested this theory at the range, and was able to hit steel by aiming dead center at 100 yards every time. This sure beats the “Kentucky windage” method!
The last step is to get your rifle sighted-in at your normal cowboy distance and note the number of turns/notches. By knowing the amount the sight is raised with each turn/notch, you can make your own range card for different distances.
Let’s try the same exercise with a standard ladder rear sight. For my other rifle, the rear sight to front sight distance is 20 inches, and each notch on the ladder raises the rear sight 0.038 inches.
Tangent (0.132) x 20 = 0.046 (sighted-in at 30 yards)
Tangent (0.460) x 20 = 0.160 (sighted-in at 100 yards)
0.160 - 0.046 = 0.114 (sight height difference)
0.114 / 0.038 = 3 notches
Hopefully, this exercise will help you win your next long-range side match. If you would like a copy of this article, please visit my web site at http://eightbits.home.att.net. If you have questions about this article you can drop me a line at eightbits@att.net. Shoot fast, shoot straight, be safe, but most of all, have fun.
References
BALISTIC v4.13, copyright 1988-1995 William R. Frenchu – This program is available as shareware from http://www.simtel.com/product.php?id=49924&SiteID=simtel.net .
“Right Triangles”- http://aleph0.clarku.edu/~djoyce/java/trig/right.html copyright 1996, 1997, 1999 David E. Joyce, Department of Mathematics and Computer Science, Clark University, Worcester, MA 01610
“Precision Ballistic Coefficient Estimator” - http://www.uslink.net/~tom1/calcbc/calcbc.htm copyright TMT Enterprises
Pact Model 1 chronograph
.45LC LRNFP 250gr., ballistic coefficient = 0.248