Airgun Mathematics

---------- Table Of Measurement Units ----------

Quantity	Unit	Remark
Gravity Constant		many people beleave it was 450240,but the correct one is 450436.68.
Length	millimetre ( mm ) Centimetre ( cm ) metre ( m ) kilometre ( km ) inch ( " )	1 mm = 0.03937 inch 1cm = 10 mm 1 inch = 2.54 cm 1 m = 100 cm 1 km = 1000 m
Weight	milligram ( mg ) gram ( g ) kilogram ( kg ) tonne grain ( g ) pound ( lb )	1 g = 1000 mg 1 kg = 1000 g 1 tonne = 1000 kg 1 grain = 0.00006479891 Kg 1 Kg = 2.2046 lbs (pounds) 1 lbs (pounds) = 0.4536 Kg
Speed	metre per second ( m / s , mps ) feet per second ( f / s , fps ) kilometre per hour ( km / h  , kmph )	1 kmph = 5 / 18 mps
Temperature	degree Celsius ( 'C ) degree Fahrenheit ( 'F )	1'C = ( 9 / 5 + 32 ) 'F 1'F = [ 5 ( -32 ) ] / 9 'C
Caliber	inch ( " ) gauge ( ga )	.177 " = 4.4958 mm .20 " = 5.08 mm .22 " = 5.588 mm .25 " = 6.35 mm .30 " = 7.62 mm .32 " = 8.128 mm .357 " = 9.1749 mm .36 " = 9.144 mm .38 " = 9.652 mm .40 " = 10.16 mm .44 " = 11.176 mm .45 " = 11.43 mm .50 " = 12.7 mm .58 " = 14.732 mm .60 " = 15.24 mm .70 " = 17.78 mm 28 ga = 13.97 mm 12 ga = 18.5166 mm 10 ga = 19.685 mm
Pressure	pounds per inch squared ( psi ) bar	1 bar = 14.5 psi

Airgun Energy ( Airgun Power )

Energy in Foot Per Pound :
( velocity ( fps ) x velocity ( fps )  x projectile weight ( grains ) ) / 450240 = ft/lbs

Energy in Joule :
( velocity ( mps ) x velocity ( mps ) x projectile weight ( grams ) ) / 2000 = J

To convert ft/lbs to Joules = ft/lbs x 1.355817 = Joules

To convert Joules to ft/lbs = Joules / 1.355817 = ft/lbs

Velocity Via Air Pressure

 Formula : V = P A t (g/m)

V = final velocity in feet/second
P = average pressure in pounds/inch squared (  psi )
A = cross-sectional area of tube in inches squared
t = time during which pressure acts
g = gravitational constant ( g = 32 feet/second )
m = mass of accelerated body in pounds

Twist Rates Of Bullet

When a bullet leave the barrel , the gravity start to pull the bullet downward . We need a spin to bring the bullet upward , rifling will do the work . Different rifling , rifle groove numbers effect the upward rate , it was called Twist rates .
The most famous Twist Rates calculating fomula was the Greenhill Formula .
There are two formula .

Formula 1 is for bullet velocity less than 2800 fps .
Formula 1 : ( 150 x Bullet Diameter Squared ) / Bullet Length = Required Spin
Example 1: .50 inch , Bullet length = .75 inch
Formula : ( 150 x .50 x .50 ) / .75 = 50 Spin

Formula 2 is for bullet velocity greater than 2800 fps .
Formula 2 : ( 180 x Bullet Diameter Squared ) / Bullet Length = Required Spin
Example 2 : .50 inch , Bullet Length = .75 inch
Formula : ( 180 x .50 x .50 ) / .75 = 60 Spin

Why larger caliber can hunt larger games?

This is true . People only use large caliber to hunt large animals , have you seen anyone use a .177 to hunt deer or bull ? At least , i havn't . Larger caliber have larger power transfer to the animal . This is called the Bullet Potential ( Knock Out Power , K.O.P. ) .

The most well known formula of calculating bullet potential is K.O. .
K.O. ( Knock Out ) method of evaluating the potential of big game rifles, is probably the easiest and best way to tell the raw knock out power of any given airgun and projectile.
This formula can be applied to any bullet or caliber.
Let's prove LARGER CALIBER REMAINS LARGER POWER ...................

We suppose the temperature , the humidity , the air density , the altitude , bullet weight and velocity remains unchange . Then we can see which caliber have more Knock Out Power .

K.O.P. Formula = ( Bullet Weight X Muzzle Velocity X Bullet Diameter ) divided by 7000

Example 1 : .45 caliber ( inch ) , bullet weight = 370 grain , velocity = 1000 ( FPS ) .
Formula : ( 370 X 1000 X 0.45 ) / 7000 = 23.78

Example 2 : .50 caliber ( inch ) , bullet weight = 370 grain , velocity = 1000 ( FPS ) .
Formula : ( 370 X 1000 X 0.50 ) / 7000 = 26.42

Example 3 : .60 caliber ( inch ) , bullet weight = 370 grain , velocity = 1000 ( FPS ) .
Formula : ( 370 X 1000 X 0.60 ) / 7000 = 31.71

The result above have tell us that larger caliber punch more power at the animal . And in real airgun , the bullet length is fixed , too long will be diffcult to stablize . When we have to  raise the Knock Out Power , we have to raise another factor , Bullet Weight . We have to use a larger caliber , and the Knock Out power will raise at a standard ratio . That's why people use large caliber to hunt deers , bulls and elephants .

What Twist Rates do i need?

Many people ask me this question . All i can say is : larger caliber , heavier , longer bullet need a higher twist rate .

---------- Recommended Twist Rates ----------

What Is Gauge?

Gauge is the number of spherical lead balls , with the diameter of the bore , that make 1 pound ( 453.6 Grams ) .

Volume Of Spherical = 4/3 * pi * r^3
So the radius of a 12 gauge ( # balls = 12 ) :

        ( 39.96 / 12 * ( 4/3 ) * pi ) ^ ( 1 / 3 ) = 0.9264 cm

        The diameter is twice the radius
        D = 1.853 cm and 2.54 cm = 1 inch

        so your bore diameter :
        1.853 / 2.54 = 0.729 inch

This is the table of gauge vs diameter

Speed Of Sound?

What Is MOA?

MOA - Minute Of Angle . This is a mathematical term that by chance happens to be very useful for measuring accuracy of rifles / ammo . It represents 1 " at 100 yards , 2 " at 200 yards , 3 " at 300 yards , etc etc. In reality it is actually 1 . 047197551 " at 100 yards , but its close enough to 1 " ( 1 . 145226878 " at 100 meters , a little bit more then 1 " ) . So if you have a rifle that will shoot 1 MOA , it should shoot ( barring any wind or other funky atmosphereic effects ) 1 " groups at 100 yards , 2 " groups at 200 yards , etc etc .