5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 53
© C.G. Daley
Which gives;
L BP
R = ,
2π
r
R
=
π
20
L BP r =
40
To construct a plot of the wave, we start with a coordinate system at the crest of the
wave.
x = Rθ
− r sin θ
z = r ( 1 − cos θ)
This is a parametric equation ( θ is a parameter). We can write;
L L
x = θ − sin θ
2π
40
= ( 1 − cos θ)
40
L
z
To plot the wave, it is a simple matter to calculate x and z as a function of θ and
then plot z vs x. This is done in the spreadsheet below.
L 100
H 5
}
θ x z
0 0 0
10 2.343657 -0.03798
20 4.700505 -0.15077
30 7.083333 -0.33494
40 9.504142 -0.58489
50 11.97378 -0.89303
60 14.5016 -1.25
70 17.09521 -1.64495
80 19.7602 -2.06588
90 22.5 -2.5
100 25.31576 -2.93412
110 28.20632 -3.35505
120 31.16827 -3.75
θ = rolling angle
z
2
0
-2
-4
-6
0 50 100 150 200
x