Notes on Engine Propeller Matching

Department of Marine Engineering

Faculty of Marine Technology

Campus of ITS, Keputih

Surabaya 60111

Indonesia

Notes on engine Propeller Matching

Dwi Priyanta

Senior Lecturer of Dept. of Marine Engineering - ITS

1. Review on Powering
There are some points that must be considered in determining the main engine of the ship. Besides mechanical aspects where power delivered from main engine to propeller, the interaction between propeller and hull must also be considered. Fig. 1 shows a schematic diagram of power definitions.

Fig. 1 Schematic diagram of power definitions

2. Effective Horse Power (EHP)
Effective horsepower (EHP) is the power required to tow a hull without a propeller. Mathematically it is expressed in the following equation.
EHP = RV (1)
where,
R = resistance of ship in Newton
V = design speed of ship in m/s
EHP = effective horsepower in Watts

We may write equation (1) in Imperial units.
EHP=(RV)/550 (2)
where,
R = resistance of ship in lb
V = design speed of ship in ft/s
EHP = effective horse power in horsepower
Note that, the denominator of equation (2) is a conversion factor. Remember that
1 hp = 33 000 ft-lb/min = 550 ft-lb/sec

Example 1

A ship is designed to sail at 20 knots. From the towing tank test data, it is known that the resistance of this ship is 75,000 lbs. Determine the EHP of this ship at its design speed.

20 knots = 20 x 1.689 ft/s = 33.78 ft/s

EHP = (RV)/550 = (75000 lb x 33.78 ft/s)/(550 ft.lb/s/HP) = 4606 HP

3. Thrust Horsepower
When a ship is moving ahead, the propeller will accelerates water sternward. The acceleration will increase the momentum of water. Considering Newton’s second law, the force equivalent to the increasing accelerated water momentum is called thrust. The product of thrust and speed of water relative to the propeller – it is called speed of advance, Va – is called thrust horsepower (THP). Thus, thrust horsepower is power delivered by the propeller to the water and it is expressed by
THP = T Va (3)
Where,
T = Thrust of propeller in Newtons
Va = Speed of advance in m/s
THP = Thrust horsepower in Watts

We may write equation (3) in Imperial units.
THP = (T Va)/550 (4)
Where,
T = Thrust of propeller in lbs.
Va = Speed of advance in ft/s
THP = Thrust horsepower in horsepower

4. Propeller Operation Behind The Hull

Thrust deduction

The presence of the propeller operating behind the hull changes the pressure distribution on the hull and so is the resistance. Therefore, there is a difference between total resistance of the ship (R) and thrust of the propeller (T). Thrust of propeller will be greater than resistance of the ship. The quantity T minus R is called thrust deduction and is normally expressed as a fraction of the thrust.

t = (T – R)/T
R = (1 – t)T (5)

where t denotes thrust deduction.

Wake fraction

The presence of the hull ahead the propeller changes the average local velocity of the propeller. If a ship moves at speed V then the accelerated water sternward by its propeller will have move at the speed less than the speed of the speed. The accelerated water will move at the speed of Va, known as speed of advance. The term wake speed is usually used to quantify the difference between V and Va. It is customarily defined as a fraction of ship’s speed, V.

w = (V – Va)/V
Va = (1 – w)V (6)

where w denotes wake fraction.

Combining equation (1), (3), (5), and (6) we will have a new equation that relates between EHP and THP. The relation is expressed by

THP = (RV(1 – w))/(1 – t) = EHP / Effhull

Where Effhull represents the hull efficiency of the ship

Effhull = (1 – t)/(1 – w)

Example 2
Recall example 1. Assume that thrust deduction and wake fraction are 0.19 and 0.29 respectively. Determine the THP of this ship at its design speed.

20 knots = 20 x 1.689 ft/s = 33.78 ft/s
We already have the effective horsepower of this ship, that is 4606 HP.
The hull efficiency of this ship is

Effhull = (1 – 0.19)/(1 – 0.29) = 1.14

THP = EHP / Effhull = 4606 / 1.14 = 4040 hp

Open Water Test
Propeller characteristics can be described graphically in several ways. Most appropriate for the discussion to follow are plots of torque coefficient (Kq) and thrust coefficient (Kt) plotted as functions of the advance coefficient (J). They are defined by

KQ = Q/(rD^5n^2) (10)
KT = T / (rD^5n^2) (11)
J = Va/(nD) (12)

where Q is torque, T is thrust, D is propeller diameter, n is rotational speed, and r is water density. Units are chosen so that each of the coefficients is non-dimensional. Open water efficiency (EffOp), is usually shown on plots of these parameters. It is expressed by

EffOp = (J.KT/2.Pi.KQ) (13)

Fig. 2 KQ, KT and Open water efficiency of typical propeller

A plot of typical KT, KQ, and ho characteristics as functions of J is shown by Fig. 2. A set of these three curves is given for each of five different pitch ratios over the range 0.6 to 1.4 (pitch ratio = pitch/diameter). These curves represent either a family of fixed-pitch propellers, or a single propeller whose pitch can be varied in service.

Example 3 (Selecting Propeller and Determining its rpm - typical example of engine propeller matching)
Suppose that the ship discussed in previous example have a fixed pitch propeller with the diameter of 11 ft. Use Fig. 2 to estimate the open water efficiency of the propeller and determine the rpm of propeller.

From previous example we have
R = 75,000 lb V = 33.78 ft/s
t = 0.19 w = 0.29
r = 1.9903 lb-sec2/ft^4
We may calculate thrust of the propeller by employing equation (5).

T = R/(1 - t) = 75000 / (1 – 0.19) = 92592 lbs

Speed of advance of water flowing through the propeller is

Va = (1 – w) V = ( 1 – 0.29) (33.78 ft/s) = 23.98 ft/s

Although we have designed the speed of ship at 20 knots, but we know that the ship may not sail at full speed all time. To obtain the open water efficiency of the propeller we have to try several operating condition of the propeller including the operation when the ship sails at full speed.

Since the operational condition of the propeller is not constant (n is not fixed), then we can not obtain thrust coefficient (Kt) directly and so can the speed of advance coefficient J. We will construct Kt vs J curve for several propeller operating conditions, and plot it in Fig. 2. Since n is not fixed, then we will find the values of Kt by using (Kt/J^2)xJ^2.

KT/J^2 = (T/(r.D^4.n^2))x((n^2D^2)/Va^2) = T / (r.D^2.Va^2) = 0.6687

The following table shows the value of (Kt/J^2)xJ^2 for several values of J.

We will plot the values listed in the table above in Kt vs J curve as shown in Fig. 3.

From Fig. 3 we see that Kt - J line crossed several curves at several points. As an example, if we choose propeller having pitch ratio 1.0, the line crossed Kt curve at point a. If we draw a line parallel to the vertical axis, the line crossed J-axis at point a’ and giving value of J = 0.58. The line also crossed propeller open water efficiency curve for pitch ratio 1.0 at point a” and giving value of EffOp = 0.59. The following table summarizes the propeller open water efficiency for several pitch ratio.

Note that, we should check whether there are some cavitations problem occurred in propeller operation of the selected propeller.