Calculator Inputs
Angles are measured from the horizontal support line.
Plotly Graph
The chart compares actual rope tensions against safety-adjusted design tensions.
Example Data Table
| Case | Input Type | Load | Weight Force (N) | Left Angle (°) | Right Angle (°) | Left Tension (N) | Right Tension (N) | Safety Factor |
|---|---|---|---|---|---|---|---|---|
| Lighting Rig | Force | 500 N | 500.00 | 35.00 | 55.00 | 286.79 | 409.58 | 1.25 |
| Instrument Pack | Mass | 80 kg | 784.80 | 45.00 | 45.00 | 554.94 | 554.94 | 1.50 |
| Beam Support | Force | 1200 N | 1,200.00 | 25.00 | 40.00 | 1,014.28 | 1,200.00 | 1.80 |
| Motor Lift | Force | 950 N | 950.00 | 30.00 | 60.00 | 475.00 | 822.72 | 1.40 |
Formula Used
Assumption: The load hangs in static equilibrium, and both rope angles are measured from the horizontal.
Force balance equations
Horizontal equilibrium: T₁ cos(θ₁) = T₂ cos(θ₂)
Vertical equilibrium: T₁ sin(θ₁) + T₂ sin(θ₂) = W
Load force from mass: W = m × g
Left rope tension: T₁ = W cos(θ₂) / sin(θ₁ + θ₂)
Right rope tension: T₂ = W cos(θ₁) / sin(θ₁ + θ₂)
The calculator also multiplies each tension by the safety factor to estimate design tension. When rope limits are entered, it compares design tension against each limit and reports utilization percentage.
How to Use This Calculator
- Select whether the known load is a force or a mass.
- Enter the load value and keep gravity at 9.81 if appropriate.
- Enter the left and right rope angles from the horizontal.
- Add a safety factor for design planning.
- Optionally enter left and right rope working limits.
- Choose decimal precision and press the calculate button.
- Review tensions, component checks, utilization, and the graph.
- Download the result summary as CSV or PDF if needed.
Frequently Asked Questions
1. What do the left and right angles represent?
They are the rope angles measured upward from the horizontal support line. Smaller angles create larger tensions because the ropes provide less vertical lift.
2. Why are the two tensions sometimes different?
Different angles produce different force components. The flatter rope usually carries more tension because it contributes less vertical support per unit of rope force.
3. What happens when both angles are equal?
The load becomes symmetric. In that case, both rope tensions match exactly, assuming the same angle definition and a centered load.
4. Can I enter mass instead of force?
Yes. Choose the mass option, enter kilograms, and the calculator converts mass into force using gravity before solving the tension equations.
5. Why is the safety factor useful?
It raises the calculated tension into a more conservative design value. That helps when comparing against rope ratings, support limits, or planning margins.
6. Why do tensions rise sharply at low angles?
A shallow rope contributes only a small vertical component. To support the same load, the actual rope force must increase significantly.
7. What are the rope limit fields for?
They let you compare safety-adjusted tensions against allowable rope values. The calculator shows utilization percentage and flags conditions above the entered limits.
8. Is this suitable for dynamic lifting analysis?
No. This page estimates static equilibrium only. Dynamic motion, shock loading, sling angles in 3D, and hardware behavior need more detailed engineering review.