This calculator estimates signed constant-speed tangential force for a wheeled load on a straight incline using an entered rolling-resistance coefficient. It does not design or rate an overhead tramway, trolley, beam or drive.
I-bar Travelling Tramway Interactive Calculator
Explore rolling-resistance and gravity components along a straight track under a quasistatic constant-speed assumption.
Equation Used
- Straight rigid track. Positive slope rises along the intended direction of travel; negative slope descends along that direction.
- Constant-speed quasistatic motion with no acceleration.
- Entered coefficient multiplies normal force and represents all rolling resistance in this simple model.
- No wheel/bearing geometry, flange contact, curvature, starts/stops, wind, cable/chain, drive efficiency, beam/trolley strength, deflection, fatigue, derailment, braking, load swing, supports or safety model.
A positive result requires applied force along the intended travel direction. A negative result requires force opposing that travel to keep speed constant. Track length affects ideal work, not this constant-force balance; it appears in the readout only.
Ideal force balance along an incline
Normal force is mg cosθ, so modeled rolling resistance is μmg cosθ. The grade term mg sinθ is positive for climbing and negative for descending. Their sum is the applied force along the intended travel direction needed to maintain constant speed.
The animation is a qualitative trolley path and does not model an I-beam, wheels or drive.
Use as a preliminary force decomposition
The calculation can check sign, units and order of magnitude for an entered coefficient and slope. It cannot size a beam, trolley, motor, cable, brake, support or safety system.
Rolling resistance and grade
Frolling = μN = μmg cosθ and Fgrade = mg sinθ. A positive sum calls for force along travel; a negative sum calls for opposing restraint. The sign convention assumes motion along the direction used to define the slope.
For constant force along path length L, ideal signed work would be FL, but no work output is presented.
Worked downhill-force example
For 320 kg, mu=0.008 and slope −0.5 degrees, rolling resistance is about 25.10 N, gravity grade term is about −27.39 N and signed constant-speed force is about −2.29 N. The negative sign indicates a small restraining force in the modeled direction.
Scope and limitations
A real travelling tramway requires verified dead/live/dynamic loads, trolley wheel and bearing data, flange and rail contact, beam bending/shear/lateral-torsional buckling and fatigue, supports and connections, curves and switches, acceleration and load swing, traction/cable/chain geometry, motor and gearbox, service/emergency brakes, end stops and anti-drop/derailment devices, controls, inspection and applicable hoisting/conveyor standards.
Questions
What does a negative result mean?
Gravity exceeds modeled rolling resistance, so restraint is needed for constant speed.
Why does track length not change force?
For a uniform straight slope it changes distance and work, not the constant force balance.
Does this rate an I-beam?
No. No structural or wheel-load analysis is included.
Calculation basis
For the stated straight-track model, the normal load is mg cosθ and rolling resistance is the user-entered coefficient times that load. Adding the grade term mg sinθ gives the applied tangential force for constant speed. Standard gravity is 9.80665 m/s².
A negative slope describes travel downhill. If gravity exceeds rolling resistance, the signed result is negative: restraint must oppose motion. This ideal force balance does not determine brake capacity, beam strength or a rated trolley load.
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