Ballistic Clock

The ballistic clock , developped at the point in 1742 by Benjamin Robins, is a device making it possible to measure the speed of a projectile starting from its impact. In other words, it is an measuring instrument of the percussions (measured in Descartes; 1 descartes: = 1 Newton.seconde)

For the origin, it was intended to measure speed for bullets, one makes use of it still sometimes of this manner, but for the measurement of the other movements, the Chronophotographie replaced this intrument.

Presentation

Simplified case: use of the simple Pendulum

That is to say a projectile of mass m, animated a speed V. This projectile is sent in a block of mass M beaucoup more grande that Mr. the block M is suspended by two of the same stems length L and of negligible mass. After the shock the block M starts to oscillate. When it reaches its maximum amplitude, its speed is cancelled and the variation height of the center of mass of the block is H.

One can show, to use of it the conservation of energy and that of the momentum, that V = \ frac {M \ sqrt {2gH}} {m} \,

More realistic case: use of the heavy Pendulum

That is to say a made up heavy Pendulum oscillating around O, G its center of gravity, L the length of simple sound Pendulum synchronous. On line OG (OG = a), vertical at rest, let us place O', such as OO'= L = has + \ frac {J} {my} \,

This O' point is called the center of percussion (relative to O).

That is to say a horizontal percussion, EP, applied in O': the moment of this percussion out of O is A =l \, P_e \,

So the pendulum takes an initial speed such as J \ dowry {\ theta_0} = A.

That is to say an initial kinetic energy has ² /2J, which will be converted into potential energy, when the pendulum stops with the height H: = has (1 - cos \ theta_ {max} ), such as

With ² /2J = mgH

from where the value of EP.

The choice of the O' point comes owing to the fact that there does not exist any reaction of percussion out of O, which can be very well the peak of the knife of suspension of the pendulum: the pendulum will absolutely not slip on its plan of rest out of agate.

Application: the balls of mousquet were drawn in a sand pocket, placed in a notch made in O'; the pendulum was sufficiently heavy to neglect the mass of the ball (if not, it is easy to adapt the correction). One deducted the momentum from it of the ball, therefore his speed. These instruments made it possible to measure of 1000 to 100000 descartes.

Notice

The movement of the pendulum is possibly of great amplitude; one recorded during time the displacement of the pendulum; and obviously one ran up against the problem of the inversion of Sn (T) of Jacobi. This problem was solved only about 1830.

Note historical

The Mersenne father put the question of the centers of percussion to the Huygens young person, not for this problem, but for a problem of handling of weapon: when a sword receives a percussion EP in the center of O' percussion of the handle O, then one feels no percussion of reaction out of O. It is thus important to locate O' on the blade of the sword.

See too

External bond

  • an animation and a demonstration of the formula

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