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Testing:

Test Sheet

Examples

19' Ski Boat

34' Sailboat

41' Utility Boat

Technical

Blade Area
Ratio

Calculating
the Cavitation
Number

Horsepower
Losses

Hull Speed

Kt Breakdown

Propeller
Geometry

Propeller Law

Wake Factors

Glossary

References

19' Ski Boat Example:

Companion Data File: Example 19 Foot Ski Boat.psm_data.  The file is  located in the PSModel Directory

Boat Description: 19 foot V bottom ski boat

References: unpublished test report

Engine: inboard gasoline

Reduction Gear Ratio: 1.23 to 1.0

Maximum Engine Horsepower: 236 @ 4200 RPM

Maximum Engine Torque: 343 ft.-lbs. @ 2900 RPM

Propeller: 

Manufacturer -- Federal 
Number of Blades -- 3
Cup -- yes 
Diameter -- 14 inches nominal (measured: 13.875 inches)
Pitch -- 16 inches nominal (measured : 15.9 inches)
P/D -- 1.14  (15.9/13.875)
Effective Pitch** -- 17.4 inches (15.9 + 1.5)
Effective P/D = 1.25 = 17.4/13.875  (Effective P/D was used as input to PSModel)
DAR -- 0.55 measured

** The manufacturer's literature indicates that the effective pitch of the cupped prop is approximately 1 inch greater than the advertised pitch for diameters up to 14 inches, and 2 inches greater for diameters of 15 inches and greater.  So increase the effective pitch by 1.5 inches since a 14 inch diameter is near the transition to a 2 inch pitch increase.  

Depth to center line of propeller: 1 foot

Test Course:  speed recorded by averaging radar gun readings over an 850 foot course; speed also verified with a stopwatch

Water Conditions:  fresh water at 60.0 Degrees Fahrenheit, no waves

Wind:  less than 5 MPH

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

Shaft Torque: Lebow torque meter was installed aft of the reduction gear.

Test Data:

On small craft, minor changes in boat weight and trim angle can cause significant changes in test results.  Therefore, during tests, the gas tank was topped off periodically and test personnel remained in the same locations.

Col. 1 Col. 2 Col. 3
Boat
MPH
Torque
Meter
(ft-lbs)
Prop.
RPM
10.0 112 1210
15.0 145 1491
20.1 151 1678
25.0 170 1937
30.0 205 2267
34.9 246 2704
41.0 308 3419

Calculations:

Propeller Series used

Two non-cupped Propeller Series were used to predict propeller performance with the Effective Pitch value since neither Series covered the entire range of test values:

Series GBL for 10, 15, and 20.1 MPH
Series GBR for 25, 30, 34.9, and 41 MPH

The following table shows results of PSModel calculations:

Col. 5 -- torque meter values minus stuffing box and bearing losses; values in this column should be very close to the actual torque absorbed by the propeller

Col. 6 -- Col. 3 x the reduction gear ratio 1.23

Col. 7 --  wake factors used in PSModel calculations from the graph for Flat and V Bottom Boats in the Wake Factor Section

Col. 8 -- propeller torque predicted by PSModel, see the companion data file

Col. 9 -- propeller horsepower predicted by PSModel, also called Delivered Horsepower (DHP), see the companion data file

Col. 10 -- required or predicted engine torque, [(Col. 8 x 1.02) / 1.23] x 1.03; 1.03 accounts for reduction gear loss and 1.02 accounts for the packing box and bearing losses

Col. 11 -- required or predicted engine HP, Col. 9 x 1.03 x 1.02

 

Col. 4 Col. 5 Col. 6 Col. 7 Col. 8 Col. 9 Col. 10 Col. 11
Boat
MPH
Torque
Meter
x 0.98
(ft-lbs)
Engine
RPM =
Col. 3
x 1.23
Wake
Factors
(1-w)
Prop
Torque
from
PSModel
(ft-lbs)
Prop
HP
from
PSModel
required
Engine
Torque
(ft-lbs)
required
Engine HP
Col. 9 x 1.02
x 1.03
10.0 109.8 1488 0.940 106.5 24.54 91.0 25.78
15.0 142.1 1834 0.950 138.6 39.35 118.4 41.34
20.1 148.0 2064 0.962 142.3 45.46 121.5 47.76
25.0 166.6 2383 0.970 157.5 58.09 134.5 61.03
30.0 200.9 2788 0.977 196.4 84.77 167.8 89.06
34.9 241.1 3326 0.982 240.3 123.70 205.3 129.96
41.0 301.8 4205 0.990 294.3 191.60 251.4 201.29

Comparing Cols. 5 and 8 one sees that the measured and predicted values of torque absorbed by the propeller are in good agreement.  Surprisingly, the agreement is good at 41 MPH where the propeller blade on the downward swing on the inclined shaft had a full cavity over its back. 

The torque and horsepower required at the engine by the propeller, Cols. 10 and 11 above, are plotted over the engine performance curves below.  Note that the rated horsepower of 236 has not been reached.  Possible reasons for this are:

1) The engine performance curves are generated under ideal conditions, but the test boat engine was run under conditions of high humidity and heat with a water exhaust and possibly small parasitic loads such as a charging alternator and raw water pump.  The non ideal conditions could explain the approximate 8.5% reduction in available torque and horsepower 

2) The engine performance curves may have been generated with carburetor secondary's connected, however, the secondary's were not connected on the test boat.

In any case, the engine appears to be torque limited at 4205 engine RPM.

Engine performance Curves and propeller requirements

An average skier adds about 70 pounds of drag to the boat when being pulled in a straight line.  The easiest way to find the maximum boat speed when towing a skier is to guess at a reduced boat speed then calculate the required engine torque and RPM for the new speed.  The following ratio -- calculated from the companion data file's RPM and MPH columns at 34.9 and 41.0 MPH -- helps to estimate the prop RPM at the reduced boat speed:

ΔRPM/ΔMPH = (3419 - 2704) / (41.0 - 34.9) = 117.2  

The following table organizes the required calculations:

Col. 1 -- guess at a new boat speed

Col. 2 -- estimated propeller RPM for Col. 1 speed without  a towed skier = 3419 - 117.2 x (41.0 - Col. 1), where 117.2 is ratio derived above

Col. 3 -- required thrust = (PSModel predicted thrust for Col. 1 speed and Col. 2 prop RPM) + 70 pounds for towed skier

Col. 4 -- prop RPM which obtains Col. 3 required thrust, use PSModel to home in on the correct RPM value

Col. 5 -- required prop torque for Col. 4 prop RPM from PSModel

Col. 6 -- Col. 4 x reduction gear ratio 1.23

Col. 7 -- engine torque = [(Col. 5 x 1.02) / 1.23] x 1.03, where 1.03 represents reduction gear losses and 1.02 represents packing box and bearing losses

Col. 8 -- torque limit of engine at Col. 6 engine RPM

If Col. 7 is greater than Col. 8, reduce the boat speed and try again.

If Col. 7 is less than Col. 8, increase the boat speed and try again.

If Col. 7 is nearly equal to (or equal to) Col. 8, then Col. 1 is the reduced maximum boat speed while towing a skier.

Col. 1 Col. 2 Col. 3 Col. 4 Col. 5 Col. 6 Col. 7 Col. 8
New
Boat
MPH
Estimated
Prop RPM
at Col. 1
speed w\o
skier
 
Req'd
Thrust
with
skier
 
Prop
RPM
for Req'd
Thrust
Req'd
Prop
Torque
Eng.
RPM
Eng.
Torque
(ft-lbs)
Eng.
Torque
Limit at
Col. 6
RPM
40.0 3302 1115 3441 309 4232 264 251
39.0 3185 1102 3307 300 4068 256 259

Col. 7 is shown plotted on the Engine Performance Curves below.  The dotted line in this plot represents an estimate of the actual engine output from the initial testing, see comments above.

Exploded view of upper engine performance curves

At 39 MPH the engine torque required for towing a skier is nearly equal to the maximum available, so towing a skier results in about a 2.0 MPH drop in the top speed of the ski boat. 

The maximum boat speed while towing a skier is approximate for the following reasons:

1) The attachment of the skier's towline to the boat will likely cause a change in the boat trim angle resulting in increased boat resistance or drag.  This in turn will slow the boat even more.

2) The shaft angle relative to the direction of travel was ignored in calculations.  If accounted for, thrust requirements would have risen slightly.