Although the diameter of the piston and the force exerted by a cylinder are related, they are not directly proportional to one another. Additionally, the typical mathematical relationship between the two assumes that the air supply does not become saturated. Due to the effective cross sectional area reduced by the area of the piston rod, the instroke force is less than the outstroke force when both are powered pneumatically and by same supply of compressed gas.
The relationship between the force, radius, and pressure can derived from simple distributed load equation:
Where:
: is the resultant force
: is the pressure or distributed load on the surface
: is the effective cross sectional area the load is acting on