Calculation note: forces experienced by bus passengers during sudden braking

In this document

Initial hypotheses

The note sets the case study: a bus travelling at 36 km/h (10 m/s) undergoes a "very sudden and exceptional braking" resulting in a deceleration of 8 m/s². The stop occurs over approximately 6 metres, in 1.25 seconds. The reference passenger weighs 70 kg p. 20.

The seated passenger, facing backwards

They directly experience the vehicle's deceleration: a force of 52 kg distributed over the seat, and 4 kg on the head p. 20.

The passenger holding the strap

Moving approximately 30 cm further than the bus, they experience a force of 53 kg, "taken almost entirely by their arm" if they do not move their feet — a force barely higher (5%) than that of the seated passenger p. 20.

The driver

Holding the steering wheel and bracing against the brake, they experience: 4 kg on the head, 30 kg on the arms and 19 kg on the legs p. 21.

The standing passenger who is not holding on

Most detailed hypothesis: before hitting a wall, they move 1 metre in 0.6 seconds using their legs (force of 14 kg), acquiring a relative speed of 3.6 km/h at the moment of impact.

Ink sketches accompany these calculations, representing the postures (seated, standing, driver) with arrows indicating, according to the handwritten legend, "the direction of the forces felt by the passengers" p. 20.

Context

This type of calculation falls under automotive passive safety, a field in which Paul Magès, inventor of the hydropneumatic suspension at Citroën, was particularly interested beyond his core profession.

The 1970s saw the rise of reflections on braking distances, seat belts, and kinetic energy in the French automotive industry, in a context where road safety regulations were tightening.

Archivist's perspective

This note is likely part of a series of personal works by Magès on the physical effects of shocks and braking, as evidenced by other documents in the same file devoted to the force formula as a function of speed and distance.

The choice of the bus as a case study — rather than a private car — is notable: it broadens the reflection to situations where passengers are standing or poorly restrained, which explains the wealth of detail on the user "who is not holding on" p. 21.

This pedagogical approach using annotated sketches recalls the method used in "Method for not breaking eggs", where Magès popularises kinetic energy through example. We also find the same calculation logic (force according to speed and distance) as in the Handwritten calculation notes: safety distances, dated 25 April 1973, which suggests a possible dating of this note to the same period, without documentary certainty.