Practical Ship Hydrodynamics

146 Practical Ship Hydrodynamics
4.6 Exercises: seakeeping
Solutions to the exercises will be posted on the internet (www.bh.com/companions/0750648511)
1. Solve the following two problems for seakeeping:
(a) A surfboard travels with Froude number Fn D 0.4 onadeepwater
wave of 4 m length. How long must the surfboard be to ‘ride’ on the
wave, i.e. have the same speed as the wave?
(b) Wavebreaking occurs theoretically when the particle velocity in the x
direction is larger than the celerity c of the wave. In practice, wavebreaking
occurs for wave steepness h/ exceeding 1
14 .Whatarethe
theoretical and practical limits for h concerning wavebreaking in a
deep water wave of D 100 m?
The potential of a regular wave on shallow water is given by:
�
�
ich
kx⊳
D Re cosh⊲k⊲z H⊳⊳ei⊲ωt
sinh⊲kH⊳
The following parameters are given:
wave length D 100 m
wave amplitude h D 3m
water depth H D 30 m
Determine velocity and acceleration field at a depth of z D 20 m below
the water surface!
2. A ship travels at 28.28 knots in deep sea in regular sea waves. The ship
travels east, the waves come from the southwest. The wave length is
estimated to be between 50 m and 300 m. The encounter period Te is
measured at 31.42 seconds.
(a) What is the wave length of the seaway?
(b) There has been a storm for one day in an area 1500 km southwest
of the ship’s position. Can the waves have their origin in this storm
area?
seaway
V = 28.28 kn
N
W E
S
3. The position of two buoys is given by their (x, y) coordinates in metres as
sketched below. The buoys are excited by a regular wave of D 62.8m,
amplitude h D 1 m, and angle D 30° to the x-axis.
(a) What is the maximum vertical relative motion between the two buoys
if they follow the waves exactly?
(b) What is the largest wave length to achieve maximum vertical relative
motion of twice the wave amplitude?
y
P 1 (0,0)
•P 2 (30,10)
x
x wave propagation