219 
Sec. 5 -3- Eq. 20-21 
PART II. CALCULATION Ol DETONATION VELCCITIUS 
Die Chapman *-Jouget” Condition for Detonation Velocity 
A detonation wave differs from a shock wave in that it is self-sustain- 
ing. The energy equation must include the chemical energy released by the 
explosive on decomposition. Furthermore, the velocity of the detonation, D, 
is not controlled by the velocity of the piston, nor indeed is a piston 
necessary, There are therefore four unknown quantities, D, Po, Vo and Us 
and only three conditions (mass, momentum and enerzy). A fourth condition 
is therefore necessary, No entirely satisfactory proof of this fourth con- 
dition has been given, but it is generally accepted that it is 
D=Up + Co y (20) 
where Cy is the velocity of sound in the gas behind the detonation wave and 
Up is the mass-velocity of this gas. This is equivalent to taking D as the 
minimum velocity compatible with the other conditions, as will be shown. 
Chapman merely postulated Hq. (20), but it can be partially supported 
by the following arguments: The detonation velocity D, being given by 
(Eq. (10)) 
D= Vy \ (Baie PL) / (v, 7 Vz) ’ 
is therefore also equal to 
where P is the angle between the line A Z% and the negative V axis in 
Bis, 5-1. Z is the final point Po, Vo and A is the initial point Pi, Nats 
which does not lie on the Hugoniot curve in the detonation case, The point 
J is the 
D 
Fig, 5-1 
point of tangency of lines from A and is therefore the final state Po, Vo 
which gives the minimum value of D,. 
If the final P and V correspond to a point on the Hugoniot curve higher 
than the point J, it will be shown that the velocity of sound in the burnt 
