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References: unpublished test report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
(ftlbs) 
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 noncupped 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 (ftlbs) 
Engine RPM =
Col. 3 x 1.23 
Wake Factors
(1w) 
Prop Torque
from
PSModel (ftlbs) 
Prop HP from
PSModel 
required Engine
Torque
(ftlbs) 
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.
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 (ftlbs) 
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.
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.
