1. 5.7 Form (Eddie-Making) Resistance
Previously, we made an assumption that the friction
resistance coefficient of a ship (or a model) is the same as that
of a smooth flat plate with the same length (Re) & wetted
surface area; namely, the friction resistance of a ship is the
same as that of a flat plate with the same length and wetted
surface area. In generally, this assumption is approximately
correct. However, a careful investigation has shown that there
are differences between the friction resistance of a ship and
that of a plate with the same length & wetted surface. Usually,
the friction resistance of a curved surface object is greater than
that of a flat plate with same length & wetted surface. Their
difference is called the form resistance or form drag.
2. The form drag consists of 3 parts.
1. Eddy-making Resistance; the curvature causes the pressure
change along the ship. Due to the viscosity, the pressure change
will cause the flow separation from the surface, & generate
eddies. Energy is fed into eddies, and the resulting resistance is
called eddy-making resistance. Main contribution to the
form resistance is made by eddy-making resistance. For a
low speed ship, it is important to avoid the abrupt change of
the hull in order to minimize the eddy-making resistance.
3. 2. The curvature of a ship (or a model) will change the local
velocity along the ship. Since the path along a streamline from
bow to stern is longer on a shaped body than on a flat plate, the
average velocity along a ship > V. Thus
3 Interaction between viscous & wave-making resistances,
which is very complicated. It is a research topic in Marine
Hydrodynamic and ship-model test. The increase or decrease
of resistance due to the interaction are classified into form
drag. Sometimes, some items may be directly classified into
wave-making resistance.
It is understood now that why the difference between the total
resistance coeff. & frictional resistance coeff. is called the
residual coefficient,
, .
FS F Plate
R R
.
Rm Tm Fm
C C C
4. 5.8 Air or Wind Resistance
2
2 2
2
Majority of the wind resistance is due to eddie-making type, & therefore
it varies roughly with ( is the relative velo. of air to a ship)
sin cos
(Hughes formula)
cos
- a
R R
L T
R
V V
A A
F k V
k
3
n empirical constant = 0.6, (0.5~0.65), - wind resistance (lb)
- density of air, 0.00238 (slug/ft ), - wind velocity relative to a ship (ft/s)
- angle of wind direction relative to the longit
R
F
V
udinal center line of a
ship measure from the bow.
- direction of the resultant force relative to the center line.
R w s
V V V
6. 2
& are
determined based
on the figures at
the right.
A special case
(head wind)
0, 0,
0.0068 T
pa
pb
F R
kV A
7. 5.9 Appendage Resistance
Usually, the model resistance test gives the resistance of the
“naked” hull (without appendages). Appendages, such as bilge
keels, rudder and bossings (open shafts and struts), will result in
additional resistance, aka appendage resistance.
It is usually added to the “naked” hull resistance, about 10 –
15% of the latter as listed in the following table.
1. Appendage resistance of a multiple-screw (propeller) ship is
larger that that of a single-screw ship.
2. The upper limit for V/(L0.5)= 0.7 seems to be higher.
Ship type Speed/length ratio
0.70 1.0 1.6
Large fast quadruple-screw ships 10-16% 10-16%
Small fast twin-screw ships 20-30% 17-15% 10-15%
Small medium V twin-screw ships 12-30% 10-23%
Large medium V twin-screw ships 8-14% 8-14%
All single-screw ships 2-5% 2-5%
8. 5.10 Computing the naked ‘hull’ resistance
according to its model test results
The model resistance test follows the Froude # similarity.
2
1
2
1. Let / , thus , & measure
2. Based on Re , computing using a friction formula
for a flat plate;
3. Computing the residual resistance coeff. ;
4.
S Tm
s m m Tm Tm
m m
m m
Fm
m
m
Rm Tm Fm
V R
m L L V R C
S V
m
V L
C
C C C
, , Based on the Froude assumption,
;
N N S m
s m
RS Rm
F F V mV
C C
9.
1.5
2
1
2
5. Based on Re ,(if = , then Re = Re ),
computing using a friction formula for a flat plate;
6. at , ;
7. The 'naked' hull resistance, ;
8.
S S
S m
S S m
S
FS
s m T f R f T f
s s m
s s m
TS S S S TS
V L
m
C
V mV C C C C C C
R S V C
'
'
Total resistance at , ;
9. Effective power, .
s m T TS wind appendix
T S
V mV R R R R
E R V
Ex. 1 Computation of Resistance & EHP
Ship Dimensions 390’ x 54’ x 23’ (LWL x B x T)
CB = 0.69, VS = 12 knots, SS = 29,621 ft2 , sail is S.W.
Its model Lm = 15’ , sail in F.W. t = 67.5˚ F, Rtm = 4.4 lb at
corresponding velocity, find Rts , & EHP.
10. Ex. 9.1 Computation of Resistance & EHP
(see textbook p160-161)
Ship Dimensions 140 x 19 x 8.5 m (LWL x B x T)
CB = 0.65, VS = 15 knots, SS = 3,300 m2 , sail is S.W.
Its model Lm = 4.9 m , measured , sail in F.W. at
corresponding velocity of VS .
Find RTS and EHP at VS = 15 knots
19 N
Tm
R
/ 140/ 4.9
s m
m L L
11. Problems of predicting the resistance of ships based on model
tests (Summary)
1. It is assumed that the frictional resistance coeff. of a ship (or
model) is equal to that of a flat plate at the same Re #. However,
there is difference between the friction resistance of a ship
(curved surface) & the friction resistance of a flat plate is form
resistance as described in section 5.7. CR = CT – CF , includes
wave-making & form resistances, not only wave resistance.
That is why CR is called residue resistance coefficient.
2. It is noted that a model test follows the Froude similarity. The
form drag depends on viscosity or Re # and does not obey the
Froude Law. Therefore CRS is not exactly equal to CRm .
These problems result in errors in determining ship resistance from
its model test.
12. 5.11 Methods of Presenting Model Resistance Results
It is desirable that there is a standard method of presenting
model resistance data. However, so far it has not been reached.
1. Users want the original data. (speed, resistance, water
temperature, method of turbulence stimulation, cross sectional
area) The user can convert them to any desired form.
2. The data in the past were not presented in non-dimensional
form.
Introduced the following are a few methods commonly used in
presenting Model Resistance data.
13. 1. CT ~ Re or CT ~ Fr
2.
3. circle K & circle C system, they are non-dimensional
.
~ or
T
R V V
gL L
~
C K
1
2
1 1
1
2 6
6
1
2
1 1 1
1
2 6 3
6
2 2
3 3
2
4
4
1
3
2 2
1
2
4 1000
,
Relation to & Fr.
4
Fr 4
1000 1000 1000
4 8
8
T
g
T
g
T T
T
R
V V
K C
g K
C
V V L L
K
gL
R R
g S S
C C
V SV
14. At a low speed, , is almost independent
of .
When increase in speed, , increases with
1.825 2
~ ~ ~
T f
R R V V C
K
3 4
or
w
R V V
C K
Dimensional Form of circle C & circle K
1 2 3
6 3 2
2 3
400
0.5834 , 2936 427.1
where - knots, - tons, and - tons.
is specially for a ship whose 400' .
T
T
WL
R
V EHP
K C
V V
V R
C L
15. 5.12 Relation between Hull Form & Resistance
• Choice of Ship Dimensions p165-169
The owner usually specifies that the new ship shall carry a
certain deadweight (How much cargo can be loaded) at a
particular speed, and the designer estimates the probable
displacement and principle dimensions.
Displacement = cargo weight (dead weight) + self weight
Length – Cost, scantling, manning, docking, navigations.
longer L reduces wave-making resistance at high speed.
Draft – increase draft will decrease resistance, reduces scantling,
but is restricted by the water depth of harbor or channel &
stability.
Breadth – important to have adequate stability. Increase in B
may decrease L (smaller Fr, smaller wetted surface) thus
reduces the cost but results in the increase in wave-making
resistance. Also is limited by the width of canals.
16. • Choice of Form Coefficients
The most important form coefficient may be the block coeff., or
prismatic coeff. A larger CB, results in larger wave-making &
form resistance.
Block or prismatic coeff. should be reduced as the speed of a ship
increases so that in designing a ship there is a limit of fullness to
be observed for a given speed. A formula of the type, called the
‘economical’ block coefficient has often been used.
where & are constant.
Alexander formula (similar to the above)
2 1.08 , is trial speed
2 1.06 , is service speed
B
B
PP
B
PP
V
C A B A B
L
V
C V
L
V
C V
L
17. Definition of trial, service, & sustained speed
Before an owner receives a newly built or renovated ship, there is a
trail sail for the ship.
•Trial speed is the required speed when the newly built ship takes a
trial sail.
•Service speed is the required speed for the ship is service.
Usually a service speed is smaller than the trial speed.
•Sustained speed lies very close to that at which the resistance
coeff. curve begins to rise steeply; i.e., to the speed at which the
power begins to increase rapidly than V3.
1.06
T S
V V
Troast formula
1.85 , is the sustained sea speed.
sus
P sus
PP
V
C V
L
18. Breadth/ draught ratio, , & ,
Longitudinal distribution of displacement: longitudunal
position of C.B, (L.C.B), usually it is slightly positive for
a slow ship & about 10% behind the
B B
R R
T T
midship for a speedy
ship.
Length of parallel middle body: easy for manufacture &
longer for a fat ship, but does not present for a slim ship.
Shape of section (Loaded.W.L., sectional-area curve)
Bulbous bows: decrease the wave-making resistance &
decrease the form resistance. But only effective for
a limited range of speed (usu. not work for warships).
(see p168)
19.
20. 5.13 Series Experiments & Model Resistance
Data Sheets
• Series Experiments
A series of models is a set of models in which the principal
characteristics are changed in a systematic manner. The
purposes of having resistance test of a series of models are:
1. A series of tests can be made to ascertain the best form of the
ship to give minimum resistance & this would involve tests
run with various alterations to some basic form.
2. The data from the tests of series models can be used to
estimate the resistance & EHP of a ship
21. • Well-known series models:
1. Taylor’s Standard Series: starting from a single “parent ship”
2. Series 64. For naval ship.
3. Series 60. Began 1948 with ATTC Cooperation and is
published in 1963, (TMP Report 1712).
2.0
L
V
2.0
L
V
3
100
a. Five parent models cover, , from 0.60 ~ 0.80.
(see the handout) & , , & also change.
b. 400' & 406.7'
B
L
PP wL
C
L B
LCB
B T
L L
22. c. Single screw ships. No bulb at bows.
(see figure 11 of the handout) = 20 ft. Turbulence
stimulators were fitted on the model.
d. Obtain the optimum location of . . .
e. Resistanc
m
L
L C B
e data of model tests are presented in two ways
i.) , in pounds, in pounds per ton as a function of
, , & .
We will study how to use this diagram to estimate
R
R
B
WL
R
R
L B V
C
B T L
R
400
400
.
ii.) as a function of , , & .
includes the model-ship correlation
allowance ( 0.0004) using 1947 ATTC line.
T
B
ft
ft
F
L B
C C K
B T
C
C
23. • Model Resistance Data Sheet, SNAME.
This valuable sheet was issued by SNAME Project 2 of
Hydrodynamics Sub-Committee of SNAME. “Model and
Expanded Resistance Data Sheets,” available from Society.
About 200 ships, their model test results were obtained in various
towing tanks and all types of ships were included, which is
different from the Series Experiment.
The sheet gives: 1.) all principal form coeff.,
2.) basic model data
3.) results are presented in
vs. or vs. R
R
V
C K
L
24. Estimation of EHP from Series Resistance Results
The series forms a very suitable basis for making estimate of
power (EHP), particularly in the early stage of a design (concept
design).
Only a limited number of variables are considered.
They are , , , , & . . . Having these data,
you may use the Series Results to estimate the resistance
& power ( ).
Series 60 results are us
B P
L B T C C L C B
EHP
ed as an example here.
It is assumed that the shape of the designed hull is similar
to that of a Series 60.
25. 1
3
2
3
Based on , , , , , & L.C.B ( ), , .
1. Based on , & , we find using the diagrams.
If 2.5 (3.0 or 3.5), using ;
2. Given velo., computing
WL pp B p pp B
B
L B
L L B T C C L BTC
T
L B S
C
B T
B
T
interpolation or extrapolation
(speed/length ratio) or vice verse;
3. Based on , , & , using the diagram to find , & then .
4. Computing Re= / , determine 0.0004, then the frictional
resistance by multiplying
WL
R
B R
WL
F
F
V
L
R
V L B
C R
B T
L
VL C
R
2
1
.
2
5. The total resistance: ;
6. EHP (effective horsepoewer) = /550, where is in lb, & in ft/s.
T r F
T T
V S
R R R
R V R V
