9.2: How to Calculate the Force Output of an Hydraulic Cylinder in Retraction (Pulling)

When a cylinder is retracting, the piston rod takes up some of the area inside the bore. This means that the effective surface area the fluid can push against is reduced. This annular area (sometimes called the "ring area") is what we use to calculate retraction force.

To find the retraction force, we use:

F = P × A annular = P × (A piston − A rod)

Or, combining both into a single formula:

F = P × 0.7854 × (D² − d²)

Where:

• D = piston (bore) diameter
• d = rod diameter

Example: Calculating the Retraction Force of a Cylinder Given its Size and Pressure

Let’s use the same cylinder from the previous example, but now account for a 1.0-inch diameter rod and the same 1000 psi system pressure.

A annular = 0.7854 × (2.0² −1.0² )

= 0.7854 × (4−1) = 0.7854 × 3

= 2.356 in²

F = 1000 × 2.356 = 2,356 lbs

Result

The retracting force of this cylinder is 2,356 lbs, which is less than the extending force (3,142 lbs) because of the reduced surface area.

---