sensing and telemetering some estimates of the 

 energy spectrum. A vertical array of pressure 

 sensors suspended at various depths below a buoy 

 on an effectively rigid cable would follow the 

 vertical motion of the buoy provided the weight 

 of the array is sufficient to insure that (a) 

 the array remains essentially vertical in the 

 presence of current shear and (b) the weight is 

 greater than the hydrodynamical drag so as to 

 force the sensors to descend as rapidly as the 

 buoy. 



Consider the suspended vertical array of pres- 

 sure sensors indicated in Fig. 3- A 5 unit array 

 is shown with the buoy at the trough (a) and at 

 the crest (b) of a surface wave. A sinusoidal 

 wave is used for simplicity. The constant- 

 pressure surfaces shown at the various depths in 

 the figure were computed by using the exponen- 

 tial decay in wave activity derived from tro- 

 choidal wave theory and also by using the hyper- 

 bolic cosine ratio resulting from the concept of 

 a sinusoidal wave on the surface which is infin- 

 ite in extent. Both methods resulted in essen- 

 tially the same configuration of constant- 

 pressure surfaces . 



The following equations were used: 

 K = e^ Z / L 



Fig. 3- Wave sensor configuration schematically 

 displayed relative to constant pressure 

 contours for a wave period of 9- 3^ 

 seconds. 



K = cosh [ard/L(l-Z/d)] 



(1) 



(2) 



where d is the water depth, Z is the mean depth of 

 the pressure surface, L is the wave length and K 

 is the factor by which the amplitude of the con- 

 stant-pressure surface at depth Z is reduced com- 

 pared to the constant-pressure surface at the 

 water surface. 



One can see from Fig. 3 that the shallow 

 sensors cross fewer constant-pressure surfaces as 

 the wave passes than do the deeper sensors. The 

 pressure change to which each sensor in the array 

 is exposed is proportional to the difference in 

 amplitude between the constant -pressure surface 

 at the water surface and the constant-pressure 

 surface at the depth of the sensor. Therefore, 

 the response of each sensor is proportional to 

 1-K. 



Integration of Wave Measurements 



To obtain an integration of the output of a 

 wave sensor over a period of time (for example, 

 20 minutes) the concept of an electrical calo- 

 rimeter is used. 1 If a voltage which is at all 

 times proportional to the deviation of the pres- 

 sure from a mean value as measured by any one 

 of the pressure transducers in the vertical array 

 (Fig. 3) is applied across an appropriate resis- 

 tance, whose heat capacity is known and which is 

 highly insulated, the rise in temperature of the 

 resistance over a given period of time is a 

 measure of the energy introduced into the resis- 

 tance during that time. This temperature change 

 can be telemetered as a measure of the mean 

 square of the amplitudes (also the total energy) 

 of the pressure variations to which the wave 

 sensor responds. 



Such an "electrical calorimeter" has been con- 

 structed and is illustrated in Fig. h. The unit 

 consists of a copper bobbin on which are wound 

 a heater winding and a resistance-thermometer 

 winding. The calorimeter is insulated from its 

 surroundings by foam plastic. A 30-gram copper 

 bobbin in the center of a 3-inch cube of foam 

 plastic has a thermal time constant of about 

 20 minutes and averages over a 20-minute period 

 with good accuracy. With the full scale output 

 of the wave sensor described above, the calorim- 

 eter would show a temperature rise, above ambient, 

 of 70°F. The coding system of the weather buoy 

 has a resolution that corresponds to about 0.^°F 

 so that overall system accuracy should be adequate. 



Superior numbers refer to similarly numbered references at the end of this paper. 



109 



