6.6 Interaction between a hull & a propeller
So far in the study of the resistance of a ship & its propeller the
two have been considered separately. However, in reality the
propeller has to work behind the ship & in consequence one has an
interaction upon the other. How does the hull affects the water
in which the propeller is working? (later we will also study the
effects of a propeller on the hull)
A ship affects the water near its stern in 3 aspects:
1) pressure increase at the stern;
2) boundary layer (a propeller is in the boundary layer or way
of the ship);
3) Water particle velocity induced by ship generated waves.
Wake fraction: water particle velocity near the propeller is
not the same as the ship velocity.
w  Vs  VA (Vs : ship velocity & VA flow velocity at its stern)
Vs  VA
Froude wake factor: wF 
,
VA
Vs
thus VA 
1  wF 
Vs  VA
Taylor wake factor: wT 
, thus VA  Vs (1  wT )
Vs
The relationship between Froude & Taylor wake factor:
wF
wT 
1  wF
or
wT
wF 
1  wT
When VA  Vs positive wake (most cases, a single screw)
When VA  Vs , nagative wake (only for high speed ship)
wT & wF, (wake factors) are determined by the measurements
made in a model test (near a hull’s stern) or in a real ship test.
Nominal wake: wake measured near the stern of a hull in the
absence of the propeller (using pilot tubes).
Effective wake: wake measured in the presence of propeller.
The measurements show that a propeller at a rotating speed n
behind a hull advancing at velocity, Vs, delivers thrust T. By
comparing it to the results of the same propeller in the open-water
tests, we will find that at the same revolutions n, the propeller will
develop the thrust T but at a different speed (usually lower),
known as effective speed of advance, VA. The difference between
Vs & VA is considered as the effective wake.
•Relation between nominal wake & effective wake.
Since propellers induce an inflow velocity which reduces the
positive wake to some extent, the effective wake factor usually is
0.03~0.04 lower than the corresponding nominal wake.
Wake factor of a
single screw ship
Averaged Wake Fraction
Wake factor of a
twin screw ship
• Relative Rotation Efficiency
The efficiency of a propeller in open water is called open-water
efficiency,
T  VA
0 
2 nQ0
where VA is the advance speed, T the thrust, n the rotation speed
(# of rotations per unit time), & Q0 is the torque measured in the
open water test when the propeller is delivering thrust T at the
rotation speed n.
In the case the same propeller behind a hull, at the same advance
speed it delivers the same thrust T at the same revolution n but
needs torque Q. In general, Q is difference from Q0. Then, the
efficiency of the propeller behind the hull,
T VA
B 
2 nQ
•
The ratio of behind-hull efficiency to open-water efficiency is
called the relative rotative efficiency.
Q

R  B  0 , thus B  R0
0 Q
The difference between Q0 and Q is due to
1. wake is not uniform over the disc area while in open water, the
advance speed is uniform.
2. model and prototype propellers have different turbulent flow.
(Remember then Reynolds number are not the same)
R
1.0~1.1
0.95~1.0
for single-screw ship
for twin-screw ship
• The influence of the propeller on the hull
Thrust-deduction factor (fraction)
When a hull is towed, there is an area of high pressure over the
stern, which has a resultant forward component to reduce the total
resistance. With a self-propelled hull (in the presence of the
propeller), the pressure at the stern is decreased due to the
propeller action. Therefore, there is a resistance augment due to
the presence of the propeller. If T is the trust of the propeller & RT
is the towing resistance of a hull at a given speed Vs , then in order
that the propeller propel the hull at this speed, T must be greater
than RT because of the resistant augment. The normalized
difference between T and RT, is called the thrust-deduction
Fraction, and denoted by t.
T  RT
RT
t
 1
, thus RT  1  t  T
T
T
RT - is the "naked" hull resistance
T - the thrust after subtracting the resistance of the rudder & other
stern appendages.
t measured in experiments depends, not only on the shape of the hull
& the characteristics of the propeller, but also the type of the rudder.
•
Hull Efficiency
Hull Efficiency is defined as the ratio of the effective power for
a hull with appendages to the thrust power developed by
propellers.
H 
PE RT Vs 1  t


PT T VA 1  w
where
PE - effective horsepower EHP  RT Vs
RT - "naked" hull resistance
Vs - speed of the ship
PT - the work done by the propeller in delivering a thrust T
VA - the speed of the propeller w.r.t. the ambient water.
•
Propulsive Efficiency
“Quasi-propulsion” coefficient is defined as the ratio of the
effective horsepower to the delivery horsepower.
RT Vs
TVA RT Vs
PE
  B   H  0   R   H



D 
PD 2 nQ 2 nQ TVA
PE  RT  Vs
PD - delivered horsepower  2 nQ
 D  0  R  H
0 - efficiency of a propeller in open water,
 R - relative rotative efficiency,
 H - hull efficiency.
The division of the quasi-propulsive coefficient into three parts is
helpful in 1) understanding the propulsive problem & 2) in
making estimates of propulsive efficiency for design purposes.
PD ( DHP ) 
EHP
 H Ro

RT V
 H Ro
In the design, usually we let
PD ( DHP ) 
(1   ) EHP
D
,
 D   H Ro
where  is a correlation allowance, (or load factor). It depends
principally on the hull roughness of the newly painted ship,
foaling, weather condition & the length and type of a ship.
DHP
Finally, the main engine horsepower, SHP 
s
where s is the shaft efficiency.
6.7 Cavitation
A typical pressure distribution in a blade element is shown below,
Suction (-)
Back
VR
face
Pressure (+)
As the pressure on the back of a propeller falls lower and lower
with the increase in a propeller’s n, the absolute pressure at the
back of the propeller will eventually become low enough for the
water to vaporize and local cavities form. This phenomenon is
known as cavitation. ( Pv , vapor pressure of water)
• Cavitation on a propeller will
1. lower the thrust of the propeller, & thus decrease its
efficiency,
2. cause vibration of hull & the propeller and generate
uncomfortable noise, &
3. cause erosion of the propeller blade.
• Criteria for prevention of cavitation
Mean thrust loading coefficient
T
c  1 2
2 VR Ap
 - density of water, T - Thrust,
Ap
P
Ap - project blade area,
 1.067  0.229 ,
AD
D
VR - the relative velocity at 0.7 R of a propeller
V  V   2  0.7 R  n 
2
R
2
A
2
• Cavitation number
p0  pv
 1 2
2 VR
p0 - presuure at some point of a blade
pv - vapor presuure of water
The cavitation is most likely to occur at the tips of blades where
the relative velocity is the largest and the hydro-static pressure is
the lowest when blades rotate to the highest position. It can also
occur near the roots where blades join the boss of a propeller
because the attack angle is the largest.
Cavitation diagram (SNAME)
6.8 Propeller Design
Methods of Propeller Design
a. Design based upon charts (diagrams). These charts are obtained
form the results of open-water test on a series of model
propellers. (also upon software, such as NavCad).
b. Design using circulation theory and CFD (not studied here).
Methodical Series
A model propeller series is a set of propellers in which the principal
characteristics such as pitch ratio etc are changed in a systematic
manner. There are many series tested, and their results are
summarized and presented in the form of charts which can be used
in design. The most extensive model propeller series is Netherland
Ship Model Basin (NSMB) at Wageningen. This series test was run
from 1937 to 1964.
NSMB Series include
Series A: narrow blade tips, airfoil sections, high efficiency
only for light loaded propellers (not widely used)
Series B: wider tips, airfoil section from blade root to 0.7
radius, and circular back from 0.8 radius to tip.
Scope of series B is shown
Given below is the dimensions (outline, thickness) of
B.4 blade
The B series results are presented in the form of charts of
diagrams, known as B   diagram .
P
At upper right corner, the diagram gives 4.40 B. (indicating B
type, 4 blades & AE /A0 = 0.40, t0/D = 0.0045 (blade-thickness
fraction), d/D = 0.167 (diameter ratio of the boss to the
propeller), & the Pitch, P.
At low left corner, it gives the definitions of BP and 
n  PD 
Bp 
VA2.5
0.5
nD
, and  
VA
VA
(notice that J 
)
nD
n - revolutions per min, D - propeller diameter (ft)
PD - delivered horsepower at propeller
VA  Vs (1- w) - speed of advance (knots)
B p and  are dimensional!
BP  
diagram
Horizontal coordinate: BP
Vertical coordinate: ratio of the pitch to diameter P/D
Two sets of curves  &  , and one optimal ( 0) line
0
• Propeller Design Based on Charts
-The information required for making a propeller design from
charts are:
1. Principal dimensions, & main coefficients of a ship used to
estimate wake, thrust factors, & relative rotative efficiency.
2. Speed of a ship
3. EHP (from model tests or estimated from other available data)
4. engine power (SHP) & rpm.
5. restrictions on the maximum diameter of propeller.
-Design Procedures
n( PD )0.5
PE
1. Calculating B p 
, (assuming  D , for computing PD  )
0.5
VA
D
From the chart to find  , pitch ratio that give the best efficiency.
(From   D, & pitch ratio  P)
2. This will give a best propeller in open water. Since the
propeller works behind the hull, it is usually to reduce D by
5%~8%, for single-screw ship, 4% for twin screw ship.
nD
3.With the same value B p a smaller value  ( 
), use
VA
the chart again to find efficiency 0 and pitch ratio (P / D).
4. In the same way, we may use different chart & different n
to see the effects (no. of blades, blade area ratio) on 0 .
5. After determining 0 , we calculate  D (propulsive coeff).
PE
1 t
 D  0 R H where  H 
. Then we re-calculate PD (  ) .
1 w
D
6. If the newly computed, PD , is very close to the previous
assumed one, then we continue to examining the cavitation
of the propeller. If not, we use the newly computed PD to
repeat the above 1-5 steps again.
7. Examining the condition of cavitation for the propellers.
If the condition is not satisfied, choose a propeller with larger
AE , or make other adjustments (such as reducing n, & using
multiple screws).
Examples
Example a, Using the B4.40 chart to design a propeller suitable for
the following conditions. Also determine SHP. (knowing EHP, Vs to
determine 0 , P, D)
Vs = 16 knots
Taylor wake factor w = 0.3075
EHP = 5000 Hp
thrust deduction t = 0.186
Allowance for appendage 6%
Shaft loss = 3%
Allowance for weather 15%
reduction in δ = 7%
n = 120 r/min
relative rotative effi.  R  1.0
Solution: EHP(1   )  EHP(1  0.06  0.15)  6050 hp
Assuming D  0.65, PD (DHP)  EHP / D  9308 hp
Advance velocity VA  1  w  Vs  11.08 knots
n  PD 
Taylor propeller coeff., B p 
VA2.5
0.5

120   9308 
11.08
2.5
0.5
 28.33
Checking B4.40 chart,  opt  213,   213(1  0.07)  198,
1 t
0.814
o  0.597, D   H  R 0 
 0.597 
 0.597  0.705.
1 w
0.6925
The previous  D is assumed to low. New iteration starts.
Let  D  0.71, PD  EHP /  D  8521 hp, B p  27.1,
From B4.40 chart,  opt  209,   209(1  0.07)  194.4,
0.814
o  0.602,  D   H  R 0 
 0.602  0.708  0.71
0.6925
This time the assumed  D is very close to the comupted one.
 VA 194.4 11.08
nD
P

, D

 17.9 ft ,
 0.85,
VA
n
120
D
P  0.85 17.9  15.2 ft, SHP 
DHP
s
8521

 8784 hp
1  0.03
Example b. Give D (due to the restriction of draft) & using
B.4.40 chart to find the optimum n, P/D, and  D
A cargo Ship
L = 86 m
Vs = 9 knots
B = 13 m
EHP = 515 hp
T = 5.66 m
w = 0.184
t = 0.125
 = 4500 m3
 R = 1.0
s = 0.97
D = 4m = 13.14 ft
χ = 0.218 (load factor or allowance)
Solution :
1. VA  Vs 1  w   9  1  0.184   7.34 knots,
2. Assuming D  0.69,
3.
1    EHP

P (DHP) 
 909
D
D
hp,
4. Try a range of rotation velocities, n
No.
Name
Unit
1
n
rpm
2
3
4
Value
90
95
100
105
110
N ( PD )0.5
Bp 
VA2.5
18.6
19.6
20.7
21.7
22.7
ND
VA
161
170
179
188
197
64.5
64.6
64.7
64.3
63.8
0.95 0.875 0.79
0.75
0.70
3
2.8

From the chart 0
%
P/D
5
P = P/D*D
6
1 t
 D  o R
1 w
m
3.8
3.5
3.16
0.691 0.692 0.693 0.69 0.688
Based on the results shown in the table, it is found that
the highest  D value is 0.693 when n  100,
and it is also closest to the assumed  D .
Thus, n  100 is the optimal rotation speed.
Pitch. P = 3.16 m = 10.37',
PD (DHP) 909
SHP 

 937 hp.
s
0.97
A different problem: given the rotation velocity, n, to determine
the optimal diameter of the propeller.