582 T. H. Havelock. 
For small velocities the appropriate expansion is 
204800 gpblf 1, 611 a We fF il. 7 
R~ FIRES eb ye sentence se ue aE 
Me es ete (=) 39 sin (p q 
71 (»-7)} | 39 
Oo D7 » (39) 
A study of the numerical coefficients in these various formule gives some 
indication of the manner in which the resistance varies with the form, and 
this is confirmed by actual calculations which have been made in each case 
asin Table I for Model A. The general variation of the resistance is the 
same, but the differences noted between Models A and B become more 
pronounced for C and D; the resistances are less at low velocities and 
greater at high velocities as we progress from A to D. The results may 
now be collected and examined graphically. 
10. Fig. 1 shows the lines of models A and D, the curves being one- 
quarter of the water-plane section in each case. In the comparison we 
have in view with ship models the ratio of beam to length is of the order 
of 1 to 10. In order to make the diagram show the difference on a small 
seale, the ratio of beam to length in fig. 1 is 1 to 5. Further, only the 
extreme models A and D are shown; the lines for B and C would fall 
between those of A and D. 
D 
ee FIG.1 
The variations in form are summarised in Table II. 
Table II1.—Models of Constant Length and Displacement. 
Model. Beam. Water-plane coefficient. Bow and stern lines. 
A 1:0 0-667 Straight. 
B 1-042 0-64 Straight. 
Cc 1-076 0-62 Hollow. 
D 1°136 0-587 Hollow. 
For comparison with ship resistance, it is convenient to use the same 
co-ordinates as are used in experimental results. In graphing the resistance 
210 
