According to Sir Issac Newton, for every action there is an equal and opposite reaction. If our action is firing a bullet, then the reaction is the recoil.
Let:
mb = mass of bullet
mg = mass of gun
Vb = velocity of bullet
Vg = velocity of gun
The starting equation would then seem to be: mg*Vg = mb*Vb
But, wait, there's more.
The mass and velocity of the powder (mp and Vp respectively) has some effect. Since the velocity of the powder gases can be approximated as 1 1/2 times the velocity of the bullet, our equation applied to a non-auto becomes...
mg*Vg = (mg + 1.5mp)*Vb
With an auto, recoil is not a simple relationship. An auto acts as two or more separate masses with time delays during the recoil process.
First consider:
mbbl = mass of barrel
ms = mass of slide
mf = mass of frame
Vs = Vbbl = velocity of slide equals velocity of barrel while they are together
Vf = velocity of frame
For example a 1911 converts what would be one big "whump" in a revolver into two smaller whumps; the barrel hitting the frame and the slide hitting the frame. Some energy also goes to compressing the recoil spring but we can neglect it for now. Applying this to auto's gives us something like this:
(mbbl+ms)*Vs = (mg + 1.5mp)*Vb
Of course the slide ends up whacking the frame like two billiard balls in an almost perfectly elastic collision. For the larger of the two "whacks" this gives us:
ms*Vs = mf*Vf
Vf plays a big role on what our hand feels.
Vf = ms*Vs / mf
or...
Vf = [((mg+1.5mp)*Vb/Vs) - mbbl]*Vs/mf
Vs = [(mg + 1.5mp)*Vb] / (mbbl+ms)
While this all seems simple enough it doesn't tell us the whole story. To reach greater velocities requires greater peak pressures. Even if these pressures show no sign of gun failure, they may be propagating cracks throughout high stress areas of the gun. Even if the pressures are plenty safe, high slide velocities (Vs) can pound the slide against the frame, battering the gun.
Wear is a usually a function of force or pressure cubed. Double the pressure and you increase the wear on the gun eightfold! In other words, hot loads can wear out a nice gun a lot quicker than normal loads.
Hope this helps...GB
Let:
mb = mass of bullet
mg = mass of gun
Vb = velocity of bullet
Vg = velocity of gun
The starting equation would then seem to be: mg*Vg = mb*Vb
But, wait, there's more.
The mass and velocity of the powder (mp and Vp respectively) has some effect. Since the velocity of the powder gases can be approximated as 1 1/2 times the velocity of the bullet, our equation applied to a non-auto becomes...
mg*Vg = (mg + 1.5mp)*Vb
With an auto, recoil is not a simple relationship. An auto acts as two or more separate masses with time delays during the recoil process.
First consider:
mbbl = mass of barrel
ms = mass of slide
mf = mass of frame
Vs = Vbbl = velocity of slide equals velocity of barrel while they are together
Vf = velocity of frame
For example a 1911 converts what would be one big "whump" in a revolver into two smaller whumps; the barrel hitting the frame and the slide hitting the frame. Some energy also goes to compressing the recoil spring but we can neglect it for now. Applying this to auto's gives us something like this:
(mbbl+ms)*Vs = (mg + 1.5mp)*Vb
Of course the slide ends up whacking the frame like two billiard balls in an almost perfectly elastic collision. For the larger of the two "whacks" this gives us:
ms*Vs = mf*Vf
Vf plays a big role on what our hand feels.
Vf = ms*Vs / mf
or...
Vf = [((mg+1.5mp)*Vb/Vs) - mbbl]*Vs/mf
Vs = [(mg + 1.5mp)*Vb] / (mbbl+ms)
While this all seems simple enough it doesn't tell us the whole story. To reach greater velocities requires greater peak pressures. Even if these pressures show no sign of gun failure, they may be propagating cracks throughout high stress areas of the gun. Even if the pressures are plenty safe, high slide velocities (Vs) can pound the slide against the frame, battering the gun.
Wear is a usually a function of force or pressure cubed. Double the pressure and you increase the wear on the gun eightfold! In other words, hot loads can wear out a nice gun a lot quicker than normal loads.
Hope this helps...GB