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 ftlbs @ 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 MPH^{2}
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/(MPH^{2}) = 369.9/7.02^{2}
= 7.50603
At 7.83 MPH (6.8 kts), the thrust given by the Propeller
Law is:
Thrust = 7.50603 x 7.83^{2} = 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 9.0^{2} = 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.
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).
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.
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.
