-HEATER ELEMENT -120 OHM KARMA 

 r TEMPERATURE ELEMENT -9500 OHM NICKEL 



PLASTIC 

 MOUNTING PLATE 



TERMINALS 



COPPER SLEEVE- 

 - WASHERS 

 -PLASTIC WASHER 

 -FOAM PLASTIC INSULATION -3" CUBE 



Fig. k. Typical electrical calorimeter. 



Calculation of Energy Spectrum Estimates by Use 

 of a Vertical Array 



Assuming that the sea surface can be approxi- 

 mated by a combination of sine waves having 5 

 different periods, one can compute (l-K) for each 

 of the 5 sensors as illustrated in Fig. 3 for 

 each of the 5 different wave periods . Each sensor 

 will respond to the 5 waves but with different 

 sensitivities due to the different depths of the 

 sensors below the buoy. The squared and inte- 

 grated output over an interval of time of each 

 sensor in the array is a linear combination of 

 such response to the 5 waves having different 

 periods . Thus one can form a set of linear equa- 

 tions describing the outputs of the 5 sensors as 

 follows : 



E 12 = +1-^6R 39 -10.03R 157 .+28.12R 352 

 -38.6lE 626 +19.20R 978 



E 8 = -2.67R 39 +7-llR 15T -12.19R 352 

 + llK28R 626 -6.79R 978 



E^ = +1.8to2 9 -1.56R 15 7+2.26R 352 



-2. 7l* 626 +l. 35R 978 - 



(6) 

 (7) 

 (8) 



The subscripts on the E's indicate period; those 

 on the R's indicate depth. 



Since a short appendage to the buoy might be 

 much more convenient in field operations than a 

 long one, an array of gages located at the 10$>- 

 response depths was also considered. The 

 inverted set of equations for the short array are: 



(9) 



E 20 = +18,271.R M -5,102.R 19 _ 8 +1,766R^ 6 



E l6 = -32,870.R^ 9+ S,814.R 19 _ 8 -2,689.R^_ 6 ^ 

 +ta).OR 79A +37.to 12 ^ 



E 12 = +lM7^.R^ 9 -3, 783. R 19- 3+1, 06^.^6 



-ill . 5R 79 _ i,.+2 . 86R 12 i,. 

 Eg = -1,721.^^4430. 5R 19 .3+109-2R^_ 6 



49 1 KlR 79# i r 2.86R 12)+ 

 E^ = + I+3.3R U>9 -75.9R 19>8+ 15.7R W _ 6 



-0.15R 79 ^-3.06R 12 ^ 



(11) 

 (12) 

 (13) 



R i = ^- K ±Ai 



(3) 



where R^ is the output energy over a given inter- 

 val from the i th sensor, K ± , is the depth attenu- 

 ation for the i" 1 sensor for the jth wave period 

 and Ej is proportional to the energy associated 

 with the j^ n wave period. These equations can 

 then be inverted to obtain the B, in terms of 

 the Rj. which is the data telemetered. 



The inverted set of equations for an array 

 with the gages located at the 95$> response depths 

 for periods of k, 8, 12, 16 and 20 seconds are: 



E 20 = 4O.393R 39 -2.80R 157 4l2.39R 352 

 -28.5R 626 +l8.56R 978 



E l6 = -1.000R 39 +7-12R 157 -29.8R 352 



+53.6R 626 -30.0R 978 



(«0 



(5) 



Obviously the coding-system resolution required 

 to use the short array would be far greater than 

 that required to use the long array. 



Once the equations for k, 8, 12, 16 and 20- 

 second periods have been solved to obtain 5 

 estimates of the energy spectrum the location of 

 any maximum might or might not be indicated. If 

 a maximum is indicated another set of equations 

 for a more narrow range of periods can be deter- 

 mined and solved to locate the energy maximum 

 in more detail. 



FIELD TRIALS 



Preliminary field trials of suspended pres- 

 sure transducer arrays were carried out during 

 September and October of 1962. Long period 

 waves were encountered in only one test when a 

 2 -unit array was in operation with sensors at a 

 depth of 88 and 2^5 feet respectively. Connec- 

 tions to the pressure transducers were by means 

 of cables to recorders mounted in a small boat. 



110 



