Propeller sizing

This article combines information, intuition and speculation in equal parts. I wrote it in order to straighten out some ideas that I had concerning the smoke that would issue from the exhaust as revolutions rose through the 2000’s- was my propeller too large? Or maybe too small? Or was the prop fine, but the engine just tired out? I couldn’t do experiments, since Lady Christina was over-wintering (and some!) in Europe. So I turned to a book or two and the internet. The results that are presented here may not survive contact with reality, and I hope that you will give me feedback as and when you can go sailing again.

New propeller on Tig (photo: Arjen Schipmolder)

Propeller sizing is more of a science than an art. So, to get you in the mood for some technical stuff, here’s a short quiz involving boats, Spitfires and vacuum cleaners. Choose answers (a) or (b):

(1) The job of a boat’s propeller is to:

(a) Push the boat forwards

(b) Push the water backwards

(2) To take off in a Spitfire with a variable pitch propeller, do you:

(a) Use fine pitch to take move less air per revolution
(b) Use coarse pitch to move more air per revolution

(3) If you put your hand over the nozzle of a vacuum cleaner, the motor speeds up.

This is because:

(a) The motor tries to suck harder
(b) There is less air for the motor to move up the pipe

 

Correct answers:

(1): (b) The propeller pushes water backwards. The boat moves in the opposite direction because the momentum of the water pushed back equals the forward momentum of the boat. The idea of a propeller screwing through the water is useful for explaining the concept of the pitch of the blades but does not correctly describe the forces at work.

(2): (a) The aircraft’s engine does not have enough power at maximum revolutions to push the large amount of air backwards that coarse pitch demands. The engine must be allowed to turn as fast as possible, since this is when it generates the most power. Therefore it has to use a finer pitch. Once up to cruising speed, the engine can keep going with less power; the most economical way to do this is to use lower revolutions. The reduction in air pushed backwards is compensated for by increasing the propeller pitch to a coarse setting.

(3): (b) The motor in a vacuum cleaner achieves its maximum speed when it is turning but not moving any air up the pipe. (The maximum speed is governed by the limitations of electrical motors.) In normal operation, the motor uses up energy to move the air- the more it moves, the slower it turns. You can prove this by taking the pipe off the cleaner completely; the motor moves even more air and it slows down.

The challenge of moving displacement craft through the water

The resistance to movement of a light displacement yacht is mostly the sum of skin friction and energy lost in wave-making. For a yacht with a waterline length of 21ft these two change dramatically over a small change in speed:

Speed (kn)
(V/√L in brackets)

Skin friction %

Wave-making %

Resistance (lbf

4.6 (1.0)

65

35

70

5.0 (1.1)

51

49

90

5.5 (1.2)

37

63

120

Table 1: Changes in resistance as the ratio (speed in knots)/(square root of waterline length (ft), known as V/L , increases from 1.0 to 1.2.

Source : ‘Sailing Yacht Design’ by Douglas Phillips-Birt (1976)

This means that the amount of power that the propeller is required to produce must increase by large amounts to achieve increasing speeds. At V/√L ratios of about 1.0 smaller boats need about 1.6hp per ton to move them; at V/√L = 1.34 (the hull speed limit for displacement craft) the requirement is more like 5hp per ton.)

Finesse 24

Speed (kn)

Propeller power (hp)

3

0.9

4

2.9

V/L = 1.0 (1.7hp per ton)

4.6

5.2

5

7.1

6

14.7

V/L = 1.34 (5.3hp per ton)

6.2

16.8

Table 2: Propeller power as a function of speed. LWL 21.3ft.

Finesse 21

Speed (kn)

Propeller power (hp)

3

0.7

4

2.2

V/L = 1.0 (1.7hp per ton)

4.3

2.9

5

5.4

V/L = 1.34 (5.3hp per ton)

5.7

9.1

Table 3: Propeller power as a function of speed. LWL 18.2ft.

Most of us use a boat propeller that has a fixed pitch. The choices of pitch and diameter are made to match the engine, gearing and the boat design. The prop dimensions can be chosen to prefer more economy or more power.

Reading the specifications on an old propeller can be difficult. This one is 16×10.

Matching an engine and propeller

The next step in choosing a propeller is to consider the engine performance. The power output graph for the legacy Yanmar 2GM engine is shown here from their Service Manual (the DIN 6270A curve represents continuous operation).

Yanmar 2GM power curves (Yanmar Service Manual)

The 2GM is only capable of producing its peak of 13hp if the propeller can be turned this rapidly. This brings us back to the Spitfire question. If the power required to turn a particular pitch and size of propeller at this rate is greater than 13hp, then the engine will not be able to turn at maximum revolutions and will therefore be unable to develop its maximum power.

This type of engine power graph includes a propeller power curve and, by convention, it is always shown to intersect the engine power curve at maximum revolutions. This ideal situation, when the engine can perfectly match the maximum demand of the propeller under full throttle, is often not met in practice. The propeller curve is generic, and the rpm values do not directly apply. Unlike the engine curve which is a real representation of its capability, the propeller curve merely indicates the principle which underlines propeller choice- the engine must be able to supply the demands of the propeller, not the other way around. For example:

2GM engine propeller options (Yanmar Service Manual, with additions)

Curve A represents a propeller that requires 13hp to rotate at 3400rpm as it pushes water backwards. By convention, the engine is a perfect match. As lower revolutions, the engine can provide an excess of power to the propeller and can easily accelerate the boat if required.

Curve B shows how an over-sized propeller might perform. This prop would produce 13hp of power at 3000rpm, if only the engine could turn it. However, we have seen that the engine represented here would only produce 11.6hp at these revolutions. Worse, the intersection of the engine curve with curve B shows that the maximum power that the prop will allow the engine to produce is 10.9hp (at 2800rpm). With the throttle wide open, the engine will not turn any faster. It will be unable to burn all the injected fuel and so the engine will issue black smoke. Acceleration will be poor, and the maximum output of the engine will be down by 16%.

Curve C represents an under-sized propeller. This boat will have good acceleration, but the propeller has a power output of only 8hp at 3400rpm. This prop has limited the engine’s capability by 38% and has therefore reduced the top speed of the boat. The engine will also burn an unnecessary amount of fuel to spin this fast.

 

So now we can consider the choice between economy and power. The most economical propeller to run is one that can be turned at the required power output at the lowest revolutions- it is has a relatively large diameter and pitch, but the engine should not, and indeed cannot, run near its limit.

The default Finesse engine, the 1GM, can easily provide for 4kn as this requires less than 3hp. Note, however, that 5kn in a Finesse 24 requires 7.1hp at the prop- beyond the 1GM, even flat out. Note that the lighter 21 has this speed within reach.

If you want to run a Finesse 24 at 6kn, say in strong tidal conditions, then you need a larger engine. 14.7hp is required, which is beyond the limit of a 2GM. To run at the hull speed speed of 6.2kn, a Finesse 24 requires 16.8hp and a 3GM is needed. We found that our 3GMD engine (2.36 ratio) was not capable of turning fast enough without smoking badly, and, in an effort to increase the power output, we have recently bought a smaller second-hand prop to replace the existing 16×10. It seems a curious way to deliver more power, but I hope that this article makes the reasoning clear.

A three-cylinder engine is something of a sledge-hammer to get the last ½ knot out of a Finesse 24, but that is a result of the rapidly increasing resistance with speed. The 2GM is a good compromise, capable of providing 5.5kn at 3000 rpm or slugging away economically at lower revs with a larger prop. However, Yanmar state explicitly that their installations must be able to reach the rated power engine speed under full load at all times, or smoke and/or damage may result. It is therefore prudent to try to match the propeller to the engine installation as closely as possible.

The gearbox reduces the revolutions at the propeller. For example, a 2.36:1 box will reduce 3000rpm at the engine to 1271rpm at the propeller. The power applied by the engine now twists the prop more slowly but with more leverage. It has therefore increased the turning force, or ‘torque’, of the engine. A 2.61:1 box reduces 3000rpm to 1149rpm; therefore a higher gearbox ratio creates higher torque, enabling the engine to turn a larger propeller.

Testing on the water

To learn more about your current engine & propeller combination, take to the water. Run in conditions where you can get an accurate speed over water and wait until you have a steady speed. Then compare your speed to the values here:

Finesse type

Engine

Speed (kn)

Revolutions (rpm)

Engine output (hp)

24

3GM

6.2

2800*

16.8

2GM

5.7

3000

11.6

1GM

4.8

3000

5.8

21

1GM

5.1

3000

5.8

Table 4: Test revolutions and speeds for various engines.

*3GM engine revolutions are limited to provide V/L = 1.34.

Case A: Your engine can’t reach these revolutions, and / or there is lots of black smoke at the target speed.

Diagnosis: you may have an over-sized propeller. The good news is that it will be economical at lower speeds. The bad news is that you can’t reach the engine’s peak performance and you would waste fuel trying to.

Case B: You can run at at these revolutions without significant smoke and achieve something like your target speed.
Diagnosis: Congratulations! It’s a good match.

Case C: You can run at these revolutions under load but don’t get near these speeds.

Diagnosis: You have an under-sized propeller. You won’t get the best performance from the boat and a larger propeller would run more economically.

Thinking of a replacement?

The following suggested propeller sizes were derived using the Victoria Propeller online calculator for displacement hulls (at https://vicprop.com). From the above analysis, you can see that the least desirable outcome is an under-sized propeller. Therefore the sizes in the table could be considered to be the minimum that should be fitted. However, if your engine is not in its first flush of youth it might be prudent, when using the calculator, to reduce the engine’s stated maximum power a little. The resulting calculation would then suggest a slightly smaller diameter or pitch.

Engine

1GM (6.5hp)

2GM (13hp)

Gear ratio

2.21

2.62

3.22

2.21

2.62

3.22

F24

12×8

14×9

13×8

14×9

16×11

F21

12×9

14×10

13×8

14×10

16×13

3GM (20hp) (F24)

3GMD (20hp)  (F24)

2.14

2.63

2.83

2.36

2.61

3.2

14×8

16×10

16×11

15×9

16×10

Table 5: Suggested minimum propeller sizes

 

NOTES:

  1. 3-blade propellers only shown, diameter x pitch (inches)

  2. Parameters used: F24 displacement 6720lb, LWL 21.3ft** F21 displacement 3580lb, LWL 18.2ft***

  3. Blank entries represent diameters that are less than 12” or greater than 16”

**Practical Boat Owner April 1970
*** Practical Boat Owner November 1968
(both reviews are available at
http://www.finesse-owners-association.co.uk/downloads/)

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