How it works
A load that falls before the line comes tight has kinetic energy the rope and the anchor must absorb. If the rope behaves like a spring, energy balance gives a peak force well above the static weight.
The stretch you enter sets the rope's stiffness (force per foot of stretch). A short, stiff rope is harsh; a long, stretchy one softens the impact. Friction over a limb or through a rigging block absorbs additional energy that this simple model does not credit.
Worked example
A 200 lb limb piece falling 2 feet before a 30 ft rope with 3% stretch at 1,000 lb catches it:
- Rope stiffness k = 1,000 lb ÷ (30 ft × 3%) = 1,111 lb/ft
- Peak = W + √(W² + 2 W h k) = 200 + √(200² + 2 × 200 × 2 × 1,111) = 1,164 lb
- Impact factor = 1,164 ÷ 200 = 5.82×; rope stretch at peak = 1,164 ÷ 1,111 = 1.05 ft
| Input | Value |
|---|---|
| Weight of the piece | 200 lbf |
| Free-fall distance before the line loads | 2 ft |
| Rope length in the system | 30 ft |
| Reference load for stretch rating | 1000 lbf |
| Rope stretch at the reference load | 3 % |
| Result | Value |
|---|---|
| Peak dynamic force | 1,164 lbf |
| Impact factor (peak ÷ weight) | 5.82 × |
| Rope stretch at peak | 1.05 ft |
Assumptions and limits
- Idealized linear-elastic rope; real ropes stiffen under shock and are affected by age, wet, knots, and construction.
- No friction, no block or limb absorption, and no anchor flexibility, so this leans conservative.
- Rated working loads for the rope, hardware, and the anchor limb or stem must exceed the peak force with an appropriate safety factor.
- This is a planning aid. It does not replace a qualified arborist's judgment or the ANSI Z133 safety standard.
Common questions
What is shock loading?
The sudden increase in force when a moving or falling load is arrested by a rope, sling, or anchor. It can multiply the static load several times.
How do I reduce shock load?
Shorten free-fall by keeping the line snug, use a longer and more elastic rope, add friction (a rigging block with a friction device or wrapped stem), or cut smaller pieces.
Is this the rope's rated capacity?
No. Compare the peak force to the rated working load of each component: rope, slings, hardware, and the anchor.
Sources
- Energy method for a falling mass arrested by a linear spring: F = W + √(W² + 2 W h k).
- For tree work safety see ANSI Z133 and manufacturer working load limits.
Updated 2026-09-30