1523 
Equation (91) is then the most convenient form for plotting the 
function Pe) » Which, in terms of reduced parameters, represents 
the shape imposed upon an exponential shock wave by viscous 
attenuation after propagation over various distances, X. For 
spherical waves, one would simply introduce the factor 1/R, 
where R is the distance of the point of observation from the 
origin of the wave. 
Figure 7 shows a family of curves of 203) vs A for 
various values of & , based upon equation (91). Increasing 
Oo corresponds to increasing range of propagation. 
8.5 It will be noted that all the curves in Fig. 7 can be 
considered as originating at f = -4, and that they attain maxima 
at values of fe which increase with decreasing oO¢ . We shall 
define &r as the reduced rise time, i.e. the total time in 
units of 2 for a curve to rise from essentially zero ate -4 
to its maximum in Fig. 7. Figure 8 shows a plot of the quantity 
(Pr -4) vs. & based on values obtained from Fig. 7, and it 
is found that pr can be empirically represented by:- 
[i = Fe 0.655 tr 3.90 (92) 
5 (es 
The actual rise time @, would then be given by: 
3.20 
( Pa pO 6S Saute ae (93) 
Thus, although the reduced rise time br increases with decreasing 
o (or decreasing range), the actual rise time decreases and 
ao h7 
