483 
The asymptotic forms of Eqs. 9.13 and 9.14 are 
AD _ a Habe sky 
aR ~Ni2nt/ B 4 
dp, of ln (ee) Rp” : (9.15) 
dR 2R 12°77 Dre 
with the integrals 
= ~-Y2, 
Rp, = RLYR- te] 
(9.16) 
D =[(n+ wort?) RMR p, : 
where F and ng are constants. 
To obtain the propagation equations for the two-dimensional 
wave, we let r and Z be the cylindrical coordinates rela- 
tive to an origin in the detonation front with the Z -axis coincident 
with the axis of the cylinder. The velocity of the detonation wave rela- 
tive to a stationary origin in the negative 2Z -direction is U, e The 
profile of the shock wave is a surface of revolution cor Zl R y) with 
the differential equation 
a = tan® . (9.17) 
Since the distance traveled by the shock front in time d¢ in the direction 
of its normal is U At and in the same time, the origin of the coordinate 
system travels a distance U, At in the negative Z -direction, 
Cos B= U/Up : 
(9.18) 
93 
