There are many calculations and mathematical formulas used to study the science of Shooting. Here are some of the basic ones that are handy for Muzzleloaders and modern shooters alike.
Acceleration due to gravity= 32.174 fps (feet per second)squared
Grains per pound= 7000
pi= 3.1416
Kinetic Energy = wt / (7000 x 32.174) x vel.(sq.) / 2
A projectile’s Kinetic Energy, expressed in foot-pounds, is the most commonly used unit in comparing a bullets performance. You might say it is to the Art of Shooting what Batting Average is to the game of Baseball. Kinetic Energy is found by taking the weight of the projectile and dividing it by (7000 [to convert grains into pounds] x 32.174 [acceleration due to gravity]). Then multiply by the projectile’s velocity squared, and divide by 2. If we fire our .490 round ball using 50 grs. of FFg powder from a rifle with a 32 inch barrel, the ball should have a muzzle velocity of about 1450 fps [feet per second]. To find the Kinetic Energy of the ball take;
177/(7000 x 32.174) x 1450 x 1450 / 2 = 826 ft-lb.
Momentum = wt. x vel. / 7000
Another measure of bullet performance is Momentum, expressed in pound-feet. It places less of a value on velocity which makes it a bit more appropriate for comparing black powder ballistics. If we want to kind the Momentum of our .490 round ball traveling at 1450 fps we’ll take;
177 x 1450 / 7000 = 37 lb-ft.
Lead Ball Mass (dia. cubed x 1504.5646)
To find the weight of a lead round ball take the diameter of the ball cubed times the weight of one cubic inch of lead, 1504.5646 grs. For example, to find the weight of a .490 round ball;
.490 x .490 x .490 = 0.117649 x 1504.5646= 177.0 grains.
Sectional Density (sd) = wt./(7000 x dia. squared))
Sectional Density is an indicator of how well a projectile maintains it energy in flight, and for hunters, sd also indicates the projectiles tendency to penetrate in the game. The higher the number the better. To find the Sectional Density of our .490 round ball;
177 grs. / (7000 x (.490 x .490) = .105
Recoil
Recoil Velocity = (powder wt x 1.75 + bullet wt.) x vel. / gun wt. / 7000
Recoil in Ft.-Lbs. = recoil vel.(sq.) x gun wt. / 64.4
To find out how much your gun recoils you have to do two calculations. First you must find Recoil Velocity, and then you use Recoil Velocity to find Recoil in Ft.-Lbs. If the rifle we are shooting our .490 round ball from weigh 8 pounds, we can predict what the recoil will be by;
(50 x 1.75 + 177) x 1450 / 8 / 7000 = 5.77 fps Recoil Velocity
Now we use Recoil Velocity to find our gun’s recoil;
5.77 x 5.77 x 8 / 64.4 = 4.14 ft-lb.
Required Barrel Twist
Bullet Twist In Calibers [BTC] (150 / (bullet length/bullet diameter)
Required Twist [in inches] (BTC x bore dia.)
To find the amount of twist, expressed in inches per turn, to stabilize the projectile we intend to shoot we must first determine the Bullet Twist In Calibers, and then we can find the Required Twist. So to find the twist we need in the rifle we are shooting our .490 ball from we need to find (BTC);
150 x (.490 / .490) = 150
Then we use BTC to find the required twist;
150 x .50 = 75 inches
Now if we are also going to fire a conical bullet it will require a bit more twist. If the conical bullet is .50-inches in diameter and .857-inches long we must refigure the amount of twist;
150/ (.875 / .50) = 87.5 BTC
87.5 x .50 = 44 inches
Acceleration due to gravity= 32.174 fps (feet per second)squared
Grains per pound= 7000
pi= 3.1416
Kinetic Energy = wt / (7000 x 32.174) x vel.(sq.) / 2
A projectile’s Kinetic Energy, expressed in foot-pounds, is the most commonly used unit in comparing a bullets performance. You might say it is to the Art of Shooting what Batting Average is to the game of Baseball. Kinetic Energy is found by taking the weight of the projectile and dividing it by (7000 [to convert grains into pounds] x 32.174 [acceleration due to gravity]). Then multiply by the projectile’s velocity squared, and divide by 2. If we fire our .490 round ball using 50 grs. of FFg powder from a rifle with a 32 inch barrel, the ball should have a muzzle velocity of about 1450 fps [feet per second]. To find the Kinetic Energy of the ball take;
177/(7000 x 32.174) x 1450 x 1450 / 2 = 826 ft-lb.
Momentum = wt. x vel. / 7000
Another measure of bullet performance is Momentum, expressed in pound-feet. It places less of a value on velocity which makes it a bit more appropriate for comparing black powder ballistics. If we want to kind the Momentum of our .490 round ball traveling at 1450 fps we’ll take;
177 x 1450 / 7000 = 37 lb-ft.
Lead Ball Mass (dia. cubed x 1504.5646)
To find the weight of a lead round ball take the diameter of the ball cubed times the weight of one cubic inch of lead, 1504.5646 grs. For example, to find the weight of a .490 round ball;
.490 x .490 x .490 = 0.117649 x 1504.5646= 177.0 grains.
Sectional Density (sd) = wt./(7000 x dia. squared))
Sectional Density is an indicator of how well a projectile maintains it energy in flight, and for hunters, sd also indicates the projectiles tendency to penetrate in the game. The higher the number the better. To find the Sectional Density of our .490 round ball;
177 grs. / (7000 x (.490 x .490) = .105
Recoil
Recoil Velocity = (powder wt x 1.75 + bullet wt.) x vel. / gun wt. / 7000
Recoil in Ft.-Lbs. = recoil vel.(sq.) x gun wt. / 64.4
To find out how much your gun recoils you have to do two calculations. First you must find Recoil Velocity, and then you use Recoil Velocity to find Recoil in Ft.-Lbs. If the rifle we are shooting our .490 round ball from weigh 8 pounds, we can predict what the recoil will be by;
(50 x 1.75 + 177) x 1450 / 8 / 7000 = 5.77 fps Recoil Velocity
Now we use Recoil Velocity to find our gun’s recoil;
5.77 x 5.77 x 8 / 64.4 = 4.14 ft-lb.
Required Barrel Twist
Bullet Twist In Calibers [BTC] (150 / (bullet length/bullet diameter)
Required Twist [in inches] (BTC x bore dia.)
To find the amount of twist, expressed in inches per turn, to stabilize the projectile we intend to shoot we must first determine the Bullet Twist In Calibers, and then we can find the Required Twist. So to find the twist we need in the rifle we are shooting our .490 ball from we need to find (BTC);
150 x (.490 / .490) = 150
Then we use BTC to find the required twist;
150 x .50 = 75 inches
Now if we are also going to fire a conical bullet it will require a bit more twist. If the conical bullet is .50-inches in diameter and .857-inches long we must refigure the amount of twist;
150/ (.875 / .50) = 87.5 BTC
87.5 x .50 = 44 inches
