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Examples

19' Ski Boat

34' Sailboat

41' Utility Boat

Technical

Blade Area
Ratio

Calculating
the Cavitation
Number

Horsepower
Losses

Hull Speed

Kt Breakdown

Propeller
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Propeller Law

Wake Factors

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References

34' Sailboat Example:

Companion Data File:

Example 34' Sailboat 16x12p 2 bladed prop.psm_data

Example 34' Sailboat 3 bladed props at Constant RPM.psm_data

Companion data files are located in the PSModel Directory.

Boat Description:

auxiliary sloop
34' length overall
29' waterline length
fin keel and spade rudder
10 degree inclined propeller shaft at centerline of boat

Reference: owner's notes and data

Engine: inboard diesel, 4 stroke, 3 cylinders

Reduction Gear Ratio: 1.79 to 1

Maximum Engine Horsepower: 24 @ 2800 RPM

Maximum Engine Torque: 45 ft-lbs @ 2800 RPM

Propeller:

Manufacturer -- Michigan Wheel
Model -- Sailor
Number of Blades -- 2
Cupping -- none  
Diameter -- 16 inches
Pitch -- 12 inches
P/D -- 0.75 (measured)
EAR -- 0.254 (measured)

Depth to center line of propeller: 2 feet

Test Course:  1/2 nautical mile in the N.W.\S.E. direction, speed determined with a stopwatch

Water Conditions:  fresh water at 55 degrees Fahrenheit, 6" chop

Wind:  10 MPH from S.E. direction

RPM: recorded with a tachometer that counted pulses of light from reflective tape on the propeller shaft.  Since the reflective tape was located aft of the reduction gear, the RPM recorded was the propeller RPM.  

Test Data:

Knots MPH** Propeller
RPM
6.8 7.83 1397
6.1 7.02 1159
5.0 5.75 950
3.9 4.49 741
3.0 3.45 570

** MPH = 1.15078 x Knots

Calculations:

This example deals with selecting a new propeller to reduce vibrations caused by the 2 bladed, 16x12p propeller, and to improve the boat's top speed under power.  (Note, that p is used in 16x12p as a reminder that 12 is the pitch value)

The blade tips of the 16 inch diameter propeller come within 2 inches of the hull bottom.  To decrease pressure variations on the bottom of the boat, hence vibrations, it is prudent to increase this gap slightly by decreasing the propeller's diameter from 16 to 15 inches. 

The 2 bladed propeller also contributes to vibrations through unsteady loading caused by cavitation and a nonuniform wake.  To decrease vibrations caused by cavitation, the EAR will be increased from 0.254 to 0.30 or 0.50.  To decrease the nonuniform wake excited vibrations, the number of propeller blades will be increased to 3.

Propeller Series used

The B Series is used for the following reasons:

1) Test data for the 2 blade propeller and parameters for the 3 blade propeller are all within the Series range.

2) The Series propeller geometry is somewhat different than the flat faced 2 and 3 bladed propellers being examined, but close enough to give useful information.

The first step in selecting a new propeller is to construct a MPH vs. Resistance curve from the test data above.  This curve is created with aid of PSModel as follows:

1) Using the B Series Dialog Box, input the various parameters for the 2 bladed propeller.  The wake factor used is 0.90 (see the section on Wake Factors).

2) For each speed and RPM shown in the table of test data above, calculate the propeller thrust (see the companion data file Example 34' Sailboat 16x12p 2 bladed prop.psm_data).  PSModel does not provide a thrust value for 7.83 MPH (6.8 kts) since the upper RPM limit shown in the B Series Dialog Box is less than the test value.  In this case, the RPM barrier indicates that cavitation exists on the propeller, and that Kt breakdown has occurred.  For more information about Kt breakdown, see the Help topic on Kt Breakdown

With the available information, however, a very good approximation of thrust at 7.83 MPH (6.8 kts) can be found using the Propeller Law.  The Propeller Law states that the propeller thrust is proportional to the boat's speed squared:

Thrust = C x MPH2

All that is needed is the proportionality constant C, and this is easily determined since we know the thrust value (369.9 lbs) at 7.02 MPH (see the companion data file Example 34' Sailboat 16x12p 2 bladed prop.psm_data).

C = Thrust/(MPH2)  = 369.9/7.022 = 7.50603

At 7.83 MPH (6.8 kts), the thrust given by the Propeller Law is:

Thrust = 7.50603 x 7.832 = 460.19 lbs

We need to extended the MPH vs. Thrust curve to a speed greater than the maximum speed expected so choose 9.0 MPH, which is slightly greater than the Hull Speed of 8.29 MPH (7.2 kts).  At 9.0 MPH, the approximate thrust given by the Propeller Law is:

Thrust = 7.50603 x 9.02 = 607.99 lbs

The MPH vs. Thrust curve is shown in the table below.  Since thrust is almost equal to the boat's resistance at any given speed, we can also call this the MPH vs. Resistance curve.
 

MPH Thrust or
Resistance
Comments
9.00 608.0 Thrust from Propeller Law
7.83 460.2 Thrust from Propeller Law
7.02 369.9 Thrust from PSModel
5.75 249.0 Thrust from PSModel
4.49 151.2 Thrust from PSModel
3.45 89.6 Thrust from PSModel

3) Plot the MPH vs. Resistance points on a piece of graph paper.  The plotted points can be connected with straight lines to form a curve.  This graph will be used below.

The next step is to determine the horsepower available at the propeller.  The diesel engine performance curves are shown below. The manufacturer rates the engine as 24 HP at 2800 RPM.

Engine performance curves

We do not know what losses are included in the manufacturer's rating, so make the following assumptions (see the section on Horsepower Losses):

1) the reduction gear loss is 3%

2) the losses for the stuffing box and shaft bearing are 1% each

3) total loss of HP at the propeller is 5%

Therefore, the maximum available horsepower at the propeller is:

22.8 HP = 24 HP x 0.95

We now have an approximate MPH vs. Resistance curve for the 34' sailboat, and an upper limit of 22.8 HP available at the propeller.  Using this information and PSModel, we can evaluate possible replacement propellers with the following procedure:

1) If it has not already been done, plot the MPH vs. Resistance curve on graph paper, see the table above.

2) In the B Series Dialog Box, enter the following:

-- P/D, blade number, BAR, and Diameter for the propeller under consideration

-- set Depth, Wake Fraction, and Gear Ratio to 2.0, 0.90, and 1.79 respectively

-- set engine RPM = 2800, since we want to use the maximum HP and RPM of the engine.

3) Guess a speed and enter the value in the Series Dialog Box, then click the Calculate button.
(See the companion data file  Example 34' Sailboat 3 bladed props at Constant RPM.psm_data)

4) Plot the point -- defined by the speed guessed and the calculated thrust -- on the graph paper prepared in Step 1.

5) Guess at a few more speeds, calculate the corresponding thrusts, and plot the points on the graph paper.

6) On the graph paper, connect the points just plotted (you can connect the points with straight lines), and record the MPH value where the constant propeller RPM thrust curve intersects the Resistance curve.  This intersection point is the operating point of the propeller.

7) Input the intersection point MPH value into the Series Dialog Box, and click Calculate.  The calculated thrust value should be nearly equal to (or equal to) the sailboats resistant value.  Record the calculated horsepower value for this intersection point.

8) If the intersection point HP is greater than 22.8, then reduce the propeller pitch and repeat Steps 2 thru 7.  If the horsepower is reasonably close to 22.8, then the propeller is a possible choice for replacing the 2 bladed prop.

The plot below shows what the graph paper looks like after four possible replacement propellers have been evaluated (See the companion data file  Example 34' Sailboat 3 bladed props at Constant RPM.psm_data).

Boat speed vs. resistance curve and propeller thrust curve for constant 2800 engine RPM

The table below shows the propeller thrust and required horsepower predicted by PSModel at the intersection point of the curves above.
 

Diameter Pitch Blades EAR Engine
RPM
Boat
MPH
Thrust HP
15.0 11.0 3 0.50 2800 8.81 586.0 26.49
15.0 10.0 3 0.50 2800 8.28 517.0 22.03
14.0 11.0 3 0.50 2800 8.20 509.0 22.50
14.0 10.0 3 0.50 2800 7.71 449.0 18.55

B Series calculations with 3 blades and EAR = 0.30 indicated that Kt breakdown was occurring so EAR = 0.30 was not considered further.  Also tried a 3 bladed, EAR = 0.50, 14x12p propeller, but this propeller also showed signs of Kt breakdown and was dropped from the list of propellers being evaluated.

The 15x11p propeller had the greatest thrust and speed, but required HP greater than 22.8.  The 14x10p is under pitched and runs out of RPM before it can absorb the available HP and produce higher thrust values.  The 14x11p and 15x10p propellers both require less than 22.8 HP and both have respectable thrust and speed values.  However, the 15x10p propeller is the final choice since it appears to be slightly more efficient. 

Replacement Propeller:  

Manufacturer -- Columbian
Model -- Hydrosonic Style 1
Number of Blades -- 3
Cupping -- none  
Diameter -- 15 inches
Pitch -- 10 inches
P/D -- 0..667
EAR -- 0.51 

The plot below shows the horsepower available at the propeller, and horsepower predicted to be absorbed for the old 2 bladed and new 3 bladed propellers.  The 2 bladed propeller is torque limited at around 1397 RPM and, as noted above, is cavitating.  The 3 bladed propeller is operating at about 1564 RPM (2800 engine RPM) and is absorbing close to the maximum available power.  The 3 bladed propeller should also be free of cavitation.  The gap between the predicted propeller HP curves and the available power curve may be due to one or more of the following:

-- The engine may not deliver the advertised horsepower because the alternator and raw water pumps may not have been included in the rating.
-- Driveline losses may be greater than assumed.
-- Propeller HP requirements may be under predicted.

Available HP at the propeller and predicted power required by 2 and 3 bladed propellers

After the new 3 bladed, 15x10p propeller was installed, the top boat speed was about 7.2 kts at 2800 engine RPM with a noticeable reduction in vibrations.

The new 3 bladed propeller has a slightly greater drag under sail than the 2 bladed propeller, but the speed reduction while sailing was not noticeable.

Caution:

1) The manufacturer of the 34' sailboat advertised a reduction gear ratio of 2.0 to 1; however, the actual reduction gear ratio was 1.79 to 1.  Always verify the reduction gear ratio. Copy the model number and serial number from the gear box and contact the manufacturer or look at the manufacturer's web pages.  If the manufacturer is out of business, a search on the Internet will probably yield the information sought.

2) Propeller diameters and pitch can be significantly different than advertised or stamped on the propeller, so always verify the diameter and pitch of the propeller by measuring.