inches, and the diameters of the mating apertures fe: the pistons were chosen to be 12 
inches. The annular gap between each pisten and its mating aperture is sealed with a 
rolling rubber seal (fig 3). The front of the seal advances just half as far as its piston. Thus 
if the piston advances a distance s (in cm), the volume change produced in the projector (in 
cubic centimetres) is 
a) 4 D) 
(/4)D,-s + (n/4)(D,~ -D,~)(s/2). (2) 
whiere 
Do = piston diameter in cm 
D., = aperture diameter incm. 
The term on the left is the volume change prcduced by the piston’s advance. and the term 
on the right is the volume change produced by the advance of the seal. The volume change 
expressed by equation (2) can be equated to that produced by a tight-fitting piston of 
“effective” diameter De, hence the equation 
(x/4)Dg"s = (n/4)D 7s + (1/4) D,7 - Dy”) (5/2). (3) 
Solving this equation for D,, 
a 2 2 Ne A 
Dera (Dng Dr )/2 : (4) 
Inserting the values for Ds and D,, yields an effective diameter of 11.631 inches for this 
projector. 
The formula for the average acoustic power. P, from a source with small circular 
pistons operating at low frequency in the sinusoidal breathing mode is as follows:* 
P = 2n3(p/c)f4 (A-s)-, (5) 
where 
= average radiated acoustic power in ergs per second 
= water density in g/cm3 
velocity of sound in the water in cm/s 
= operating frequency in Hz 
Dee AS as) 
I 
= total piston area in em- 
s = amplitude (half the peak-to-peak excursion) of each piston’s motion in cm. 
Inserting the values for the present two-piston NRAP operating in fresh water (corresponding 
to the case at the Transdec or Lake Pend Oreille facilities) yields s = 0.197 inch for P = 4 
watt (= 10/ ergs/s), 9 = 1.00 gjem>, c= 147 950 cm/s, f = 15 Hz, and, for total piston 
area, A = 1371 cm2 (= 2(a/4) (11.631 X 2.54)2). 
*See, for example, Acoustics, by JL Hunter; Prentice Hall, 1957, p 147. 
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