78 STRESSES ON VESSELS OF THE GREAT LAKES 
It will be noticed that both the magnitude and position of the maximum bending mo- 
ment depend upon whether the crest or hollow is assumed at the bow, and also upon the wave 
dimensions. If the effect of varying heights of waves of the same length is desired, it was 
found that, for moderate changes, the bending moment varies as the square root of the height. 
The results have been summarized in Figs. 5 and 6, Plates 17 and 18, in the form of bend- 
ing moment factors. 
STRESSES. 
While the foregoing may be considered as general data with regard to bending mo- 
ments on vessels, it may be of interest to add the special application in the determination 
of the strength of lake vessels. 
If we take the form proposed by the British Committee on Freeboard as representing 
the strength, viz., = = f. d. B., the following may be developed: 
If s = stress, BM = bending moment, A = displacement, C = bending moment fac- 
tor, and C» = block coefficient: 
A py AXLE 
y G 
f. d. Bxs= We IBa Gh 32 (Gs eee 
35 C 
and if we assume s = Ae) 
es iat for salt water 
35 € 
Cs 
= —~?_ y [’* for fresh water. 
The proposed values of f are shown on Fig. 7, Plate 19. It is obvious that if the waves 
on the Lakes do not exceed a certain definite length, the value of f should show a falling off 
after this length is reached. This is indicated on the curves, and it is interesting to note that 
numbers of the present vessels, especially the larger ones, show an excess of the above values; 
or, in other words, from a strength point of view, they could be loaded deeper than the pres- 
ent depth of water available allows. 
In conclusion, and in light of the above investigations, it appears that the lake freighters 
of today are, for their service, as strong as, if not stronger than, similar ocean-going types, 
and the statement that these vessels are weaker is not borne out by theoretical investigation 
or practical operation. 
