Free recoil

Small arm: Mauser 1898 action, chambered in 7×57mm Mauser, rifle weighing 4.54 kilograms (10 pounds).

Projectile: of spitzer type, weighing 9.1 grams (140 grains), with a muzzle velocity of 823 meters per second (2,700 feet per second).

Powder charge: single base nitrocellulose[1], weighing 2.75 grams (42.5 grains), with a powder charge velocity of 1,585 meters per second (5,200 feet per second).

The momentum short form:

${\displaystyle E_{tgu}=0.5\cdot [{\tfrac {(m_{p}\cdot v_{p})+(m_{c}\cdot v_{c})}{1000}}]^{2}/m_{gu}}$

and with the numeric values in place;

${\displaystyle E_{tgu}=0.5\cdot [{\tfrac {(9.1\cdot 823)+(2.75\cdot 1585)}{1000}}]^{2}/4.54=}$

${\displaystyle E_{tgu}=0.5\cdot [{\tfrac {(7489.3)+(4358.75)}{1000}}]^{2}/4.54=}$

${\displaystyle E_{tgu}=0.5\cdot [{\tfrac {11848.05}{1000}}]^{2}/4.54=}$

${\displaystyle E_{tgu}=0.5\cdot 11.848^{2}/4.54=\,}$

${\displaystyle E_{tgu}=0.5\cdot 140.367/4.54=\,}$

${\displaystyle E_{tgu}=70.188/4.54=\,}$

${\displaystyle E_{tgu}=15.46J\,}$ of free recoil

• For non-SI units of measure of energy see foot-pound force. The conversion is: 1 J = 0.737 562 ft·lb_f

From the momentum long form in both Imperial units of measure and in an English Engineering format:

• Momentum long form: ${\displaystyle v_{gu}={\tfrac {(m_{p}\cdot v_{p})+(m_{c}\cdot v_{c})}{7000}}/m_{gu}}$ → ${\displaystyle E_{tgu}={\tfrac {m_{gu}\cdot v_{gu}^{2}}{2g_{c}}}\,}$

Whereas:

E_tgu is the translational kinetic energy of the small arm as expressed by the foot-pound force (ft·lb_f).

m_gu is the weight of the small arm expressed in pounds (lb).

m_p is the weight of the projectile expressed in grains (gr).

m_c is the weight of the powder charge expressed in grains (gr).

v_gu is the velocity of the small arm expressed in feet per second (ft/s).

v_p is the velocity of the projectile expressed in feet per second (ft/s).

v_c is the velocity of the powder charge expressed in feet per second (ft/s).

g_c is the dimensional constant and is the numeral coefficient of 32.1739

7000 is the conversion factor to set the equation equal to pounds.