Ochi 



Suppose that the distribution is not truncated and that the double amplitude 

 is considered instead of the single amplitude; then, r* = and r! = 4E. (where 

 E. = area under the spectrum for the relative velocity). In this case, we have 

 from Eqs. (A. 15) and (A. 16) 



ri/3 = 2.83V^ 



(A. 18) 



^1/10 = 3.60 /eT . 



These are well known formulae for the averages of the one-third highest 

 and one-tenth highest double amplitudes of the ordinary Rayleigh distribution. 



(B) TRUNCATED EXPONENTIAL PROBABILITY DENSITY 

 FUNCTION 



As was given by Eq. (15) in the text, the truncated exponential probability 

 density function may be expressed as 



1 ~ i^^P-P*> 



Hp) = -— 7 e ' , p > p, 



2cr: 



(A. 19) 



where 



P = pressure - 2Cf2, 



p* = truncated pressure = 2Cf/, 



R! = 2a.\ 



r r 



C = constant. 



Then, the lower limit of the one-third highest values, P1/3, can be obtained 

 from the following relation: 



Prob p > Pj^ 



f(P) dp = 1 . (A.20) 



Hence 



P,, = P. -2CR: flogl) . (A.21) 



Next, let the average of the one-third highest pressures be P1/3, and take 

 the moment about the origin of the density function. That is. 



588 



