w = B*Vo, therefore B = 1.5748
Free Recoil Velocity(自由后座速度): Vre = (((Wp/g)+B*(Wc/g))/(Wr/g))*Vo = 37.236 fps
Recoil Energy (后座能量)= ((Wr/g)/2)*Vre^2 = 5.387*10^6 ft-lb
The rotational energy of the projectile is small by comparison and can be neglected.
弹丸的旋转能量极小可以忽视。
The overall mechanical energy is only a part (40 to 50%) of the chemical energy of the propellant, since a considerable portion of the energy is carried off as heat by the propellant gases, or transmitted to the gun barrel.
总机械能只是发射药化学能的40%-50%,其余部分作为热能被燃气带走,或传递给炮管。
Ref. Rheinmetall Handbook on Weaponry, 1982, chapter 9.
Now, with these factors in mind, here are some additional calculations.
The momentum of a single projectile can be calculated as follows:
单一弹丸的动量
Projectile momentum (弹丸动量)= (Weight of projectile/g) * Muzzle velocity of projectile (弹丸重量/重力)×炮口初速
= (2,700 / 32.174) * 2,500
= 209.80 x 10^3
Momentum of the propellant gasses can be calculated from Leo's numbers as follows:
Propellant gas momentum (燃气动量)= (Wc/g) * w
= (650 / 32.174) * 3,937
= 79.54 x 10^3
Summing these:
两者的和:
Projectile momentum + Propellant gas momentum = 209.80 x 10^3 + 79.54 x 10^3
= 289.34 x 10^3
The Free Recoil momentum calculation can be used as a check, as it should be about equal to the sum of the momentums of the projectile and propellant gasses.
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