A horizontal hydraulic elevator drive transmits plunger motion through pulleys and a cable. Hiscox’s illustration includes a central-plunger pulley and a cable winding on a small pulley on a drum shaft. The calculator below is a separate ideal transmission exercise: an entered travel ratio sets the corresponding input-force multiple through work conservation.
Horizontal Hydraulic Elevator Lift Interactive Calculator
Compare entered input travel with ideal output travel and the lossless input-force multiple required by work conservation.
Equation Used
- Ideal lossless transmission with ratio defined as output travel divided by input travel.
- Static force comparison with no acceleration or stored energy.
- Output force means only the opposing load force at the ideal output coordinate.
- No rope topology, sheave efficiency, car/cylinder mass, pressure, flow, structure, controls, brakes, valves or code compliance.
If output travel is R times input travel, ideal work conservation requires input force to be R times the opposing output force. For the same unassisted lifting load, losses increase the required input work. Counterweights, other applied forces and acceleration are outside this comparison.
Abstract travel ratio
The calculator defines R as output travel divided by input travel, so soutput=Rsinput. For an ideal lossless transmission, equal input and output work require Finput sInput=Fload sOutput, hence Finput=R Fload.
The animation is an abstract coordinate comparison, not a rope path or hydraulic elevator drawing.
Use as a work-conservation check only
The identities can catch reversed travel/force relationships. They cannot select or approve an elevator, ram, rope, sheave, pump, valve or structure.
Travel ratio and work balance
Let R = soutput/sinput. Equal ideal work gives Finputsinput = Foutputsoutput, so Finput = R Foutput. Output travel greater than input travel therefore requires a larger input force in this lossless comparison.
The input/output travel fraction is 1/R. The calculator includes neither losses nor other forces, such as those from a counterweight or additional moving components.
Worked 2:1 example
With 1.5 m input travel and R=2, ideal output travel is 3.0 m. The input travels 50% as far and must exert twice the output load force in the lossless static comparison.
Scope and limitations
A real lift requires certified reeving geometry, rated load and moving masses, rope and termination design, sheaves and bearings, cylinder bore/stroke/buckling and mounting, pressure/flow/power, valve and rupture protection, brakes and safeties, guide loads, structures, controls, ride dynamics, inspection and all applicable elevator codes.
Questions
Does 2:1 reduce ram force?
No. Under the stated travel-ratio definition it doubles ideal car travel and doubles ideal input force relative to output load.
Does this calculate cylinder pressure?
No. Cylinder area, losses and loads are absent.
Can any entered ratio be built with ropes?
Not necessarily. A real reeving ratio and path must be designed and certified.
Historical source and calculation basis
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, hydraulic elevator illustrations on page 154, includes a horizontal plunger, pulley and winding-drum arrangement.
The calculator applies ideal work conservation to an entered ratio. It does not derive a ratio from that illustration or specify a realizable rope path, pressure, capacity or elevator installation.
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