Example

Find L for T=7sec and d=8m

From the tables

x

(interpolate between adjacent values)

Using Newton-Raphson's method

 

call and d/L =x

we want to determine x for given by solving equation (78)

Then (77) becomes:

 

Call       and apply Newton-Raphson method:

First determine

Reminder:   

The recursive formulas of the previous page can be programmed very easily.

The results with for the case T=7sec and d=8m are shown next:

          L_0= 76.50420           d/L_0= 0.1045694

     N=  1           d/L=0.1482064           L=53.97879
     N=  2           d/L=0.1449496           L=55.19159
     N=  3           d/L=0.1449408           L=55.19496
     N=  4           d/L=0.1449408           L=55.19496
     N=  5           d/L=0.1449408           L=55.19496
     N=  6           d/L=0.1449408           L=55.19496
     N=  7           d/L=0.1449408           L=55.19496
     N=  8           d/L=0.1449408           L=55.19496
     N=  9           d/L=0.1449408           L=55.19496
     N= 10           d/L=0.1449408           L=55.19496

Very fast convergence!   L=55.2 after the 2nd iteration.

It can be seen that as and that the infinite depth relationships are recovered.