Handwritten calculation notes: establishment of the force formula F = 0.394 V²P/e

In this document

Page 18 — comparison of speeds and distances

The page opens with a schematic sketch comparing two vehicles travelling at 100 km/h and 110 km/h, with distance dimensions ("20", "5m", "50 metres") p. 18.

This is followed by two calculations of time and distance travelled:

The page ends with an annotation "distance d'aréri in cm" p. 18, a mention repeated and corrected to "distance d'amort" on page 19.

Page 19 — establishment of the force formula

Paul Magès sets out the basic physical relationships: e = V²/2γ (with e in m, V in m/sec, γ in m/sec²), then K = F/P = Mγ/Mg = γ/g p. 19.

He then converts the unit of speed (km/h) and distance (cm) to obtain:

e = 100 (V/3.6)² / 19.6 K, then K = 100V² / 254 e.

He arrives at the boxed formula: F = KP = 100V²P/254e = 0.394 V²P/e p. 19.

A numerical example is then calculated: V = 50 km/h, e = 20 cm, P = 75 kg, giving a result circled as "3690 kg" (partially illegible in the calculation detail) p. 19.

The page is dated "25.4.73" at the bottom right p. 19, and concludes with the reformulated formula F = 0.394 V²/e · P, with an arrow pointing to "e", annotated "distance d'amort... in cm" p. 19.

Context

This formula relates the force (F) experienced by a body during deceleration to its speed (V), its weight (P), and the damping distance (e) available to cushion the impact — a classic piece of applied mechanics reasoning, at the time, for automotive safety issues at Citroën.

The historical context (1970s) is one of growing awareness of passive safety in the automotive industry, a period during which Paul Magès, engineer and inventor of the hydropneumatic suspension, devoted part of his work to these questions.

Archivist's perspective

This document is likely the calculation draft preparatory to a more polished educational demonstration: the formula F = 0.394 V²P/e, established and dated 25 April 1973 p. 19, appears as is, almost word for word, in "Passive safety — The motorist and the technician", dated the same day.

It seems that Magès first set down here, in draft form, the algebraic steps and a numerical verification example, before integrating them into a text intended for a wider audience.

This approach — moving from raw physical reasoning to educational popularisation — also recalls that of the notes on kinetic energy entitled "Method for not breaking eggs", written a month earlier and relating to the same didactic concern for safety.