OCEN 402
Homework #6
1. If the Froude numbers of two geometrically similar ships are the same, then we
say they are running at corresponding speed. A ship is 500 ft long and its model
is 20 ft long. If this ship advances at speed 20 knots, what is the corresponding
 Rr s
speed in ft/s of the model? What is the ratio
? where  Rr s and  Rr m are
 Rr m
the residue resistance (wave-making resistance) of the ship and its model,
respectively.
2. Ship A and Ship B are geometrically similar, their length and velocity are
LA , LB ,VA and VB respectively. If ship A and ship B move at corresponding
V
velocity, what is the ratio A ? If LA  LB , then whose total resistance coefficient
VB
CT will be larger? Why?
3. A ship has the following dimensions:
LWL  383 ft , B  40.4 ft , d  13.2 ft ,   3100 tons in saltwater, S  17000 ft 2 .
When it is moving at Vs  35 knots its effective horsepower EHP  29900 HP.
Use 1957 ITTC line ( C  0 ) to find:
a.) Ratio of
Rf
Rt
Rf
for ship.
for a 20’ model.
Rt
c.) Rt in pounds for the 20’ model.
b.) Ratio of
(Hint: 1 knot = 1.689 ft/s,
For ship, ρ = 1.9903 slugs/ft3, υ = 1.2615 x 10-5 ft2/s
For model, ρ = 1.9383 slugs/ft3, υ = 1.2083 x 10-5 ft2/s)
4. From the following data and using the 1957 ITTC friction line, estimate the total
resistance and effective horsepower (EHP) for the ship.
Length (ft)
Wetted Surface Area (ft2)
Speed (knots)
Total Resistance (lb)
Model
25
106
4
16.5
Ship
400
---Corresponding
-----
Fresh
Water
2
1.2466 x 10-5
Kinematic Viscosity (ft /s)
1.94
Density (slug/ft3)
(Hint: take ΔC = 0, EHP = resistance x velocity)
Salt
1.5053 x 10-5
1.99
5. Repeat problem 4, but using 1947 ATTC friction line with ΔC = 0.0004.
6.* The following data refer to similar vessels
Vessel
Length (ft)
Wetted Surface area (ft2)
Speed (knots)
EHP
f (sea water)
A
500
42,600
13
8,600
0.008814
B
460
------0.008824
Determine the EHP required for vessel B at the corresponding velocity.
Hint: The frictional resistance of Ship A and B may be computed by Froude’s Flat
Plate Formula.
R f  fsvn
where R f (lb) – frictional resistance of ships
f – is known as Froude’s Skin-Friction Coefficient, which is based on flat
plate experiments
s (ft2) – wetted surface area of a ship
n – index, in this problem n = 1.825.
V (knots) – velocity of ships.