**Related Resources: calculators**

### Fifth Wheel Coupling Loading Equations and Calculators

Power Transmission Design and Engineering

**Machine and Mechanics Design Equations and Calculators**

Fifth Wheel Coupling Loading Equations and Calculators.

The required fifth-wheel coupling size is determined by the D value.

D value for fifth-wheel coupling equation:

D = ( 0.6 · G · T · U ) / ( T + R - U )

**Permissible gross weight of the semi trailer equation**:

R = ( D · (T · U ) / ( ( 0.6 · G · T ) · D )

If the permissible gross weight of the semi trailer and the D value of the fifth-wheel coupling are specified, the permissible gross weight of the trailer unit can be calculated with the following formula:

**Permissible gross weight of the tractor unit equation**:

T = ( ( D · ( R - U ) ) / ( ( 0.6 · G · R ) - D )

If the fifth-wheel load is sought and all other loads are known, the following formula can be used:

**Formula for fifth-wheel load equation**:

U = T + R - ( 0.6 · G · T · R ) / D

D = D value, in kN

R = Permissible gross weight of the semi trailer unit in metric tons, including the fifth-wheel load

T = Permissible gross weight of the tractor unit in metric tons, including the fifth-wheel load

U = Fifth-wheel load, in metric tons

G = Gravity, 9.81 m/s^{2}