Calculate peak shock force from weight, fall distance and stopping distance for dropped objects or rope and cable loads with rope stiffness EA.
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Shock Force Formula
The shock force calculator estimates peak force from the object’s weight, the free-fall distance, and the distance or rope stretch available to stop the fall. Inputs are converted to SI units before the calculation.
Dropped Object Formula
F = W*(1 + sqrt(1 + 2*h/d))
- F = peak shock force, in newtons (N)
- W = weight force of the object, in newtons (N)
- h = free-fall distance, in meters (m)
- d = stopping distance after impact, in meters (m)
Rope / Cable Formula
F = W*(1 + sqrt(1 + (2*h*EA)/(W*L)))
- F = peak shock force, in newtons (N)
- W = weight force hanging on the rope, in newtons (N)
- h = free-fall distance before the rope catches, in meters (m)
- EA = rope or cable axial stiffness, in newtons (N)
- L = rope length in play, in meters (m)
The dropped object mode uses stopping distance directly. A shorter stopping distance produces a larger shock force because the same fall energy must be absorbed over less distance.
The rope / cable mode estimates stopping distance from rope stiffness and rope length. A longer, stretchier rope lowers the peak force. A short, stiff cable raises it.
Typical Stopping Distances and Rope Stiffness Values
Stopping distance has a large effect on the result. Use realistic values for the surface, catch system, or rope involved.
| Stopping situation | Typical stopping distance | Effect on shock force |
|---|---|---|
| Hard impact on metal, concrete, or rigid fixture | 0.5 to 2 cm | Very high |
| Hard surface with slight deformation | 2 to 10 cm | High |
| Padding, soft catch, or flexible support | 20 to 50 cm | Moderate to lower |
| Long energy absorber or controlled deceleration | 50 cm or more | Lower, if the absorber is rated for the load |
| Rope or cable type | EA value used | General behavior |
|---|---|---|
| Dynamic climbing rope, 10 mm nylon | 25,000 N | Stretches more, lower peak force |
| Static rope, 11 mm nylon/polyester | 60,000 N | Less stretch, higher peak force |
| Polyester rigging rope, 12 mm | 120,000 N | Stiffer rope, higher shock load |
| Steel wire rope, 10 mm | 8,000,000 N | Very stiff, very high shock load |
Shock Force Examples
Example 1: Dropped Object
An 80 kg object falls 1 m and stops over 0.05 m.
W = 80*9.80665 = 784.532 N
F = 784.532*(1 + sqrt(1 + 2*1/0.05))
F = 5,886.5 N
The estimated peak shock force is about 5.89 kN.
Example 2: Rope / Cable
An 80 kg load falls 2 m onto 10 m of dynamic climbing rope with EA = 25,000 N.
W = 80*9.80665 = 784.532 N
F = 784.532*(1 + sqrt(1 + (2*2*25000)/(784.532*10)))
F = 3,729.2 N
The estimated peak shock force is about 3.73 kN.
FAQ
Why is shock force higher than the object’s normal weight?
Weight is the steady force from gravity. Shock force is the force needed to stop motion after a fall. When an object stops quickly, its kinetic energy must be absorbed over a short distance, so the peak force can be many times higher than its normal weight.
Does a longer stopping distance always reduce shock force?
Yes, for the same object and fall distance, increasing the stopping distance reduces the peak force. Padding, rope stretch, energy absorbers, and controlled deceleration all work by increasing the distance over which the object slows down.
Is this result safe to use for rigging or fall protection design?
Treat the result as an estimate. Real shock loads depend on rope condition, knots, hardware, anchor movement, load orientation, friction, damping, and dynamic behavior. For safety-critical rigging, lifting, climbing, or fall-arrest systems, use rated equipment and the required safety factors for the application.
