Lea and Feldman 
where S(x) is the cross sectional area of the ship hull immersed in 
the water. 
IV. RESULTS AND DISCUSSION 
The resulting nonlinear problem, for the first approximation, 
can be solved numerically or solved approximately using methods of 
local linearization developed in transonic aerodynamic literature(5 
(©) | We have taken the latter approach due to limitations on compu- 
ter time and the details of which are given by Feldman\? ?, Here, we 
shall present some results for the sinkage and trim of a semi-submer- 
ged spheroidal hull. The cross sectional area of the hull is 
Pelmde (ker Ee Oe, 
where B,, 1s the maximum beam. The trim and sinkage are compu- 
ted at the bow with units of trim measured in terms of ship length and 
slenderness ratio of 1:10. The results are presented in figure 1 where 
the Froude number is based on the undisturbed depth. In figure 2, we 
have presented the same curves but using a different scale so that the 
linear results computed from Tuck's (2) solution can be viewed si- 
multaneously for comparison. 
The apparent discontinuity in slope at F, = 1.0 and F = 1.09 
is due to the method of solution and not the model equation. We note 
that these solutions do indicate the overshoot as well as undershoot 
of sinkage and trim respectively through the transcritical region 
which have been measured in experiments such as the works of Graff, 
Kracht and Weinblum as well as the more recent work of Graff 
and Binek(9), Sinkage as well as trim data have been computed for 
more realistic hulls and these will be reported else-where. However, 
one particular case with experimental results of Graft(8) et al is 
given here for comparison. The hull chosen is Model A3 of D.W. 
Taylor's Standard Series and the flow condition is exactly critical 
(Fe = 1). For computational purposes, the cylindrical hull is approxi- 
mated by a fourth degree polynomial-arc, we have 
Experiment (Graff et al) 
Trim, =a 200; Sinkage/Length, = -,015 
Theory 
Trim. = 2009; Sinkage/Length, |= -. 0123 
f=" 5. 
at ‘df 0 
* 
Paper to appear in the proceedings of the 13th ITTC Conference by 
Feldman and Lea, 
1536 
