SECT. 5] 



WIND WAVES 



689 



Here g is balanced out, z is the term required and {x + y)l2g represents the 

 error due to the method of mounting. 



If the wave spectrum is known, the spectrum of the error term can be calcu- 

 lated (Tucker, 1959). Its total energy over the range of wave frequencies is of 

 the order of 2 or 3% of the wave energy, but (in terms of wave height) it rises 

 steeply at low frequencies and presents a problem if the acceleration is in- 

 tegrated (Fig. 12). 



10^ 



0.3 0.4 0.5 0.6 0.8 



0.15 0.2 0.3 0.4 0.5 0.6 



Angular frequency (rodians/sec) 



30 20 15 12 10 



Wove period (sec) 



Fig. 12. Wave spectra computed from Neumann's formula for an equilibrium wave system, 

 and the spectrum of the errors introduced by measuring the waves using a buoy 

 containing an unstabilized accelerometer whose output is integrated twice. (After 

 Tucker, 1959. By courtesy of the Journal.) 



Tucker has described an instrument which combines measurement of the 

 vertical acceleration of a ship with the pressure on its hull (a full description is 

 given in Tucker, 1956, and a shorter description in Tucker, 1956a). In principle, 

 the pressure at a point on the ship's hull gives the height of the water surface 

 above this point, and this is added to the vertical displacement measured by 

 an accelerometer and double-integrator system (Fig. 13). 



The pressure gauge is mounted as close to the water line as is possible without 

 its emerging as the shijD rolls (typically 10 ft below the water line), and the 

 accelerometer is mounted close to the pressure unit. A single measuring head 



23— s. I 



