Page 569 



RADIO ACOUSTIC RANGING 



6232 



the increased number of reflections. Because temperature is the predominant character- 

 istic determining the velocity, it is also the principal factor in determining the amount 

 of refraction. 



Thus, if the temperature gradient from surface to bottom is linear and the tempera- 

 ture near the surface is appreciably warmer, the sound is refracted so that its path is 

 concave downward. The path marked A in figure 125 illustrates this condition. The 

 amount of curvature of the path due to refraction depends on the velocity gradient 

 in the medium — the steeper the velocity gradient the greater the curvature of the path. 

 Similarly the length of the longest unreflected path is determined by the magnitude 

 of the velocity gradient and the depth. The sound that arrives first at a point of recep- 

 tion at a greater distance than this maximum range of an unreflected sound, arrives 

 only after one or more reflections from the bottom boundary, depending on the distance. 



Wliere the temperature at the surface is appreciably lower than the temperature 

 at the bottom and the temperature gradient from surface to bottom is linear, a sound 

 will be refracted so that its path forms a circular arc which is concave upward as illus- 

 trated by the path marked B in figure 125. This is the same type of refraction that 

 results in an ideal fluid medium when the change in velocity is due to pressue alone 

 (see 6222), but in this case the range of sound before reflection from the surface is 

 reduced because the refraction due to the two causes is additive. The length of the 



Figure 125.— Transmission of sound over great distances. 



unreflected path is short where the vertical change in velocity is great and the depths 

 are shoal, and it is long where the vertical change in velocity is slight and the depths 

 are great. The first sound wave to reach a point of reception beyond therangeof the direct 

 path, will be reflected one or more times from the surface, depending on the distance. 

 In a medium having a temperature distribution from surface to bottom such that 

 the velocity is linearly reduced by an amount just sufficient to neutralize the increase 

 in velocity due to increased pressure, the velocity will be uniform throughout. Such 

 a medium would be ideal for the transmission of sound and a maximum range of the 

 direct unreflected path would be obtained. The range of the direct path would be 

 limited, then, only by the curvature of the earth, and in the same way that the distance 

 of visibility of objects at sea is limited. The maximum distance of unreflected propaga- 

 tion would be obtained where the linear path is tangent to the bottom, as illustrated 

 by the path marked C in figure 125. In this ideal case, with the source at S, the sound 

 would be propagated linearly to any point in the volume bounded by the surface and 

 the tangent plane represented by the line from c to d. The formula, 



R=1A5 {■ylD-d-\-^D-d') 



may be used to compute the maximum range R (in nautical miles) of the direct path, 



given the depths (in feet) of the water D, of the source d, and of the point of reception d' . 



The maximum range of this direct linear path may also be obtained from Table 8 



the American Practical Navigator (Bowditch) . The required distance is the sum of 



465382—44 38 



