Force Calculation: F = P x A

Hydraulic cylinder force is determined by Pascal's Law. The force output equals the system pressure multiplied by the effective piston area:

F = P x A x eta

• F = Force output (N, kN, or lbf)
• P = System pressure (bar, MPa, or psi)
• A = Effective piston area (mm2 or in2)
• eta = Mechanical efficiency (typically 0.92-0.98)

Extend vs Retract Force Difference

The critical difference between extend and retract forces comes from the rod area:

• Extend (Push): Uses full bore area: A_bore = pi x D^2 / 4
• Retract (Pull): Uses annular area: A_annular = pi x (D^2 - d^2) / 4

The rod displaces fluid on the rod side, reducing the effective area. This means:

• Retract force is always less than extend force (typically 60-80%)
• Retract speed is always faster than extend speed (same flow, smaller volume)
• Area ratio determines the force/speed differential

Flow Requirements: Q = A x v

The flow rate required to achieve a desired speed is:

Q = A x v

• Q = Flow rate (L/min or GPM)
• A = Piston area being pressurized
• v = Desired cylinder velocity

Conversely, cylinder speed from a known flow rate: v = Q / A

Rod Buckling Considerations

For long-stroke cylinders in compression (pushing), rod buckling becomes a critical factor. Using Euler's formula:

F_critical = pi^2 x E x I / (K x L)^2

• E = Modulus of elasticity (steel: 200 GPa / 29,000 ksi)
• I = Moment of inertia of rod: pi x d^4 / 64
• K = End fixity factor (0.5 to 2.0 depending on mounting)
• L = Extended rod length (stroke + exposed rod)

Cylinder Types

• Single-Acting: Hydraulic pressure in one direction only; return by gravity, spring, or external force
• Double-Acting: Hydraulic pressure in both directions; most common industrial type
• Telescopic: Multiple nested stages for long stroke in compact retracted length

Area Ratio and Speed Ratio

The ratio between bore area and annular area determines performance characteristics:

Area Ratio = A_bore / A_annular = D^2 / (D^2 - d^2)

• Typical area ratios: 1.25:1 to 2:1 (depending on rod/bore ratio)
• Speed ratio equals area ratio: retract is faster by the same factor
• Force ratio is inverse: extend force is greater by the same factor