e i df a of 
+ - 7: 2 
cos @ = “a G5 - 7) es (I-44) 
2 ( 2 2 2 i/2 
xy“ + Moeschlp| + (25 - 2) 
: oxy “Tj aT 
Having values now for ® and @5, by Snell's law, 
aes gia ae a (1-45) 
sin 85 
he 
The corresponding pressure is then obtained from Table VII. 
After calculations have been made for several grid line intersections, the peak 
pressure is determined by the method described in Section 1; namely, by plotting the 
calculated pressures against corresponding distances of the mid-point of Rr from the 
shock front, and extrapolating to zero distance from the shock front. Since the shock 
wave is not spherically symmetric, the other grid line intersections must be chosen 
in the same general region behind the shock wave to obtain the peak pressure for that 
region. 
Attention is called also to the last paragraph in Section 2 of this Appendix, 
which is applicable here. 
Grid _ beh: hock wave: c e direc in front o era; sphe: W 
If the experimental set-up meets the above requirements, the peak pressure of 
the shock wave may be calculated as follows: Referring to Fig. 138, C is the position 
of the camera; S is the shock wave; OQ is the charge; GH is the grid (perpendicular to 
the plane of the paper); R and Q are the points 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; OR and OQ are the normals to the shock wave 
surface at R and Q respectively. As in Section 1 of this Appendix, the assumption 
is made that the pressure from R to Q is constant. ) is the ratio of the index of 
refraction over this range to the index of refraction outside 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 and y, and the various points in the 
experimental arrangements are assigned the coordinates given in Fig. 138. Due to the 
symmetry of the shock wave, the problem becomes planar for any single grid line inter- 
section. x3 and x, are obtained before the shot; and the radius of the shock wave OR, 
¥3 and % are determined from the photograph. 
The two equations 
x," + y,? = (ck)? (11-46) 
and 
y 
ee (I-47) 
pore) oa ea 
are solved simultaneously for x and yp the roots 2 and ¥2 being discarded. Due to 
the circular symmetry of the shock wave in the x,y plane, 
tan ZrQO = tan Z ORC (II-48) 
If, now, the slope of any line AB is designated oe from Eq. (II-48), 
ae Am. Acr 
Ac ie = = (II-49) 
1+ A, 2 1+ A- A 
Q 0Q QR CR 
&% 15518 
