Misleading Advertisements

Sir,

Recent advertisements issued by the authorities who advocate the wearing of seat belts contain the following statement:

"Crashing at 25 m.p.h. head on into a similar car travelling at 25 m.p.h. is equivalent to crashing into an (immovable) brick wall at 50 m.p.h."

This is simply untrue! Such a statement belongs in a book of "Schoolboy Howlers" not in an official advertisement by those professing to be qualified to offer advice. Mathematically inclined readers may confirm the error as follows:

Consider a pair of similar cars of mass "m" travelling at speed "v". Each car has kinetic energy of 1/2 mv.

After a head-on crash, no movement remains energy is zero. Hence the energy dissipated in deformation of the cars and their occupants is 1/2mv per car.

Now consider one car of mass "m" travelling at Speed "2v". Kinetic energy is 1/2m(2v)2 = 2mv2 4 times the previous figure, for doubled speed.

When this car hits an immovable wall, energy to the extent of 2MVR will cause very considerably more damage than in the first case. Readers who distrust mathematics may prefer the following entirely logical confirmation:

Consider two identical, symmetrical ears travelling at equal speeds, colliding head on. By the definition of total symmetry, both cars will come to rest, crushed equally and symmetrically. Hence no part of either car will project beyond the point of impact being directly in line with another identical part of the other car, which would resist such projection. Hence the noses of each car will be crushed, at the point of impact, to a vertical plane, co-incident with the nose of the other. Thus an infinitely thin, but infinitely strong, infinitely immovable wall could have existed at the impact point without affecting in any way the damage to either car! Thus clearly crashing a car at 25 m.p.h. head-on into an identical car at 25 m.p.h. is the same as crashing the same car into an immovable wall at 25 m.p.h., NOT at 50 m.p.h.

The offending advertisement continues, that a 25 m.p.h. crash head-on, being equivalent to 50 m.p.h. into a wall is equivalent to a vertical free fall front some quoted considerable height. The true figure for a 25 m.p.h. crash into car or wall is a height of 21 feet. The true figure for 50 m.p.h. is 84 feet.

Hanwort h I. R. FRANCIS