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Forces in a crash

A 75 kg person wearing a belt, car into a solid obstacle. The force pressing the body into the belt is roughly the weight of a cow at 30 km/h, a car at 50 km/h and almost an elephant at 80 km/h. Without a belt the numbers are about four times as large.

When the car stops suddenly, your body keeps going at the same speed until something stops it. With a belt, the belt and the crumple zone take the load over a few tens of centimetres. Without a belt the body stops against the wheel, dashboard or windscreen within just a few centimetres, and the forces become many times larger. Because kinetic energy grows with the square of speed, double the speed gives four times the force.

Try it yourself

How heavy do you get in a crash?

W = \dfrac{m \cdot v^2}{2 \cdot d \cdot g}

rough "weight" pressing on the body, in kg

Symbols

$m$	body weight	kg
$v$	speed before the crash	m/s
$d$	distance over which the body stops, about 0.4 with a belt and 0.1 without	m
$g$	gravitational acceleration, 9.81	m/s²

Example

You weigh 75 kg and drive at 50 km/h, so $v \approx 13.9$ m/s.

With a belt: $W = 75 \cdot 13.9^2 / (2 \cdot 0.4 \cdot 9.81) \approx 1800$ kg, about a car.

Without a belt ( $d = 0.1$ m) it is about 7400 kg, more than an elephant.

A 20 kg child on a lap at 50 km/h equals almost 2 tonnes. Nobody can hold that back, which is why children must always be restrained in their own seat.

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Part of Car licence (class B): Speed, distance and stopping distance.