3. 
963 
It is to be noted that the shock wave photograph in tliis case probably does not 
show the intersection of the shock wave and the grid plane, but rather the intersection 
of the grid plane and a cone which has its apex at the camera lens and is tangent to 
the shock weve sphere, Thus, in determining the shock wave radius from the photograph, 
a@ corresponding correction should be applied to the apparent radius. 
Cric_in same plane with charge; charge directly in front of camera; non-spherical 
shock wave 
If the experimental conditions mcet the above requirements, the peak pressure of 
the shock wave may be calculated as follows: Referring to Fig. 137, ¢ is the position 
of the camera; S is the shock wave; 0 is the charge; 0G is the grid (perpendicular 
to the plane of the paper); R is the point at which the given light ray passes through 
the shock front; r and r' are the true and apparent points of intersection of a pair 
of grid lines, respectively; RQ is the normal to the shock wave surface at R. As in 
section 1 of this Appendix, the assumption is made that the pressure from R to x is 
constant. is the ratio of the index of refraction over this range to the index of 
refraction outside the shock wave. Although the shock wave is not assumed spherical, 
it is assumed that the shock wave surface can be represented by some equation 
f(x,y,z) = 0, the exact form being determined from the photograph of the shock wave. 
The solution proceeds according to the methods of analytic geometry. The charge 
is taken as the origin of the coordinate axes, x, y, Z, and the various points in the 
experimental arrangement are assigned the coordinates given in Fig. 137. 
The equation of ling CR is 
220 y¥- 33 Z-@ 
= = 3 = 
to 0) O-y Oveueaee (11-41) 
4 3 3 
which simplifies to 
x y- y. Z= 
— = 3! se 23 (II 
-41') 
=) ¥3 23 
These equations are combined with f(x,y,z) = 0 to obtain Xl) Yi» 21- The direction 
components of QR are 
ar of de 
—— 
t) ° 
ay Ory ts “oar 
The direction components of CR are 
X,2 “Yg2 “2, - 
my Ueeee Oe ee ot 
cos @ = - 5S%t FOV 3 “ol (II-42) 
The equation of line Rr is 
ae PND og: eee aL ee (11-43) 
ea ee eo ae | 
The direction components of this line are 
rte 18085 Ar 
15516 
