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Fluid mechanics · Hydraulics

Hydraulic cylinder extension and retraction force

Extension uses the full piston area; retraction uses the annular area.

Created v1.0

By Thibaut Grzelak, Mechanical Analysis Engineer

Hydraulics
01Calculation inputsF = P · A
ExtensionDdptank returnFextRetractionptank returnFret
Input identificationThe same pressure p is applied to the cap end for extension and to the rod end for retraction; the forces act in opposite directions.
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02

Results

Extension force
—

Cap-end force.

Retraction force
—

Rod-end force.

Piston area
—

Full area.

Annular area
—

Rod-end area.

Relation and numerical substitutionFsortie = p·πD²/4·η ; Frentrée = p·π(D²−d²)/4·η

—

Uniform pressure. d < D. Back pressure, buckling and dynamics not checked.

01Formulas and symbols

Formulas used

ApπD²/4Piston area
Aaπ(D²−d²)/4Annular area
Fp·A·ηCorrected theoretical force
02Assumptions and limits

Scope of validity

  • Uniform pressure.
  • d < D.
  • Back pressure, buckling and dynamics not checked.
03Validation example

Reference numerical case

  1. 100 bar, D = 50 mm, d = 25 mm, η = 90%.
  2. Fextension = 17.671 kN; Fretraction = 13.254 kN.
04References

Technical references

  1. Circular and annular areas.
  2. Relation F = P·A.

Calculation path and sources

Pressure determines force, flow rate determines speed, and their product determines hydraulic power.

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External technical sources

Hydraulic preliminary sizing

Size a hydraulic cylinder: force, bore, flow and speed

Pressure and force determine required area. Area sets bore, then flow determines speed and stroke time.

Cap-end bore

Minimum bore depends on required force, available pressure and efficiency.

D = √[4F / (πPη)]

Rod-end area

During retraction, the rod reduces active area.

Aa = π(D² − d²) / 4

Complete calculation

The dedicated calculator connects force, bore, rod, stroke, time and flow.

Size the cylinder