1. 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:
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.

2. Wake fraction: water particle velocity near the propeller is not the same as the ship velocity.

3. 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.

4. Wake factor of a single screw ship Averaged Wake Fraction

5. Wake factor of a twin screw ship

6. Relative Rotation Efficiency
The efficiency of a propeller in open water is called open-water
efficiency,
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,

7. The ratio of behind-hull efficiency to open-water efficiency is called the relative rotative efficiency.
The difference between Q0 and Q is due to
wake is not uniform over the disc area while in open water, the advance speed is uniform.
model and prototype propellers have different turbulent flow. (Remember then Reynolds number are not the same)
1.0~1.1 for single-screw ship
0.95~1.0 for twin-screw ship

8. 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.

10. 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.

11. Propulsive Efficiency
“Quasi-propulsion” coefficient is defined as the ratio of the effective horsepower to the delivery horsepower.

12. 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.

13. 6.7 Cavitation
A typical pressure distribution in a blade element is shown below,
Pressure (+)
Suction (-)
Back VR
face
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. ( , vapor pressure of water)

14. Cavitation on a propeller will
lower the thrust of the propeller, & thus decrease its efficiency,
cause vibration of hull & the propeller and generate uncomfortable noise, &
cause erosion of the propeller blade.
Criteria for prevention of cavitation
Mean thrust loading coefficient

15. Cavitation number
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.

16. Cavitation diagram (SNAME)

17. 6.8 Propeller Design Methods of Propeller Design
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.

18. 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

19. Given below is the dimensions (outline, thickness) of B.4 blade

22. The B series results are presented in the form of charts of diagrams, known as diagram .
At upper right corner, the diagram gives 4.40 B. (indicating B type, 4 blades & AE /A0 = 0.40, t0/D = (blade-thickness fraction), d/D = (diameter ratio of the boss to the propeller), & the Pitch, P.
At low left corner, it gives the definitions of

23. diagram
Horizontal coordinate:
Vertical coordinate: ratio of the pitch to diameter P/D
Two sets of curves , and one optimal ( ) line

24. Propeller Design Based on Charts
-The information required for making a propeller design from
charts are:
Principal dimensions, & main coefficients of a ship used to estimate wake, thrust factors, & relative rotative efficiency.
Speed of a ship
EHP (from model tests or estimated from other available data)
engine power (SHP) & rpm.
restrictions on the maximum diameter of propeller.

27. Example a, Using the B4.40 chart to design a propeller suitable for
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 , P, D)
Vs = 16 knots Taylor wake factor w =
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.

29. Example b. Give D (due to the restriction of draft) & using
B.4.40 chart to find the optimum n, P/D, and
A cargo Ship
L = 86 m Vs = 9 knots
B = 13 m EHP = 515 hp
T = 5.66 m w = 0.184
= 4500 m3 t = 0.125
= = 0.97
D = 4m = ft χ = (load factor or allowance)

30. No.
Name
Unit
Value 1 n
rpm 90 95
100
105
110 2
18.6
19.6
20.7
21.7
22.7 3
161
170
179
188
197 4 %
64.5
64.6
64.7
64.3
63.8
P/D
0.95
0.875
0.79
0.75
0.70 5
P = P/D*D m
3.8
3.5
3.16
2.8 6
0.691
0.692
0.693
0.69
0.688

31. A different problem: given the rotation velocity, n, to determine
the optimal diameter of the propeller.