by James W. Hebert
This analysis will compare two modern 90-HP outboard motors to see how their rated power, rated speed, and various combination of gear ratio and propeller selection can affect the boat speed that might be produced. We will rely on the published data from the manufacturer for all measured values. To these values we will apply in a completely consistent manner a set of assumptions that is perfectly reasonable to predict a boat speed that might result. There is no claim made that our method will produce accurate results, however the results it does produce ought to be useful for making comparisons among the motors being analyzed inasmuch as the method was applied equally and consistently.
The Mercury 90-HP FOURSTROKE is a modern four-stroke outboard motor. ("FOURSTROKE" is the model name used by Mercury, not to be confused with the four-cycle design of the motor.) Its published specifications are:
Cylinders = 4 Displacement = 1.732 liter Weight = 399-lbs (for 20-inch shaft model) Power rating = 90-HP at 5,500-RPM midpoint of rated 5,000 to 6,000-RPM Gear ratio = 2.33:1 Source: Mercury website
The E-TEC 90-HP is a modern two-stroke outboard motor. Its published specifications are:
Cylinders = 3 Displacement = 1.295 liter Weight = 320-lbs Power rating = 90-HP at 5,000-RPM midpoint of rated 4,500 to 5,500-RPM Gear ratio = 2.0:1 or 2.25:1 Source: Evinrude website
It can be shown that horsepower is related to torque by the rotational speed of the engine's output shaft. The relationship is
Power = torque * rotation rate / 5252
The factor 5252 is a scalar which accounts for the various units, which in this case are
Power = horsepower Torque = foot-lbs Rotation Rate = revolutions per minute
And thus we find that horsepower and foot-pounds are related by
HP = (FT-LBS * RPM) / 5252 Cf.: http://www.nsxprime.com/FAQ/Miscellaneous/TorqueHPSpeed.htm
From this we can also solve for torque if horsepower and rotational speed are known.
FT-LBS = HP X 5252 / RPM
Using this relationship we will compute the engine torque at the rated speed and horsepower for the two 90-HP motors.
FOURSTROKE = 90 X 5252/5500 = 85.94 FT-LBS E-TEC = 90 X 5252/5000 = 94.53 FT-LBS
This may be a surprise, but the E-TEC produces more torque at its output crankshaft than the FOURSTROKE. However, we now apply this torque to the gear case of the motor, and it is this output which will turn the propeller shaft.
Both motors have a gear reduction. Here we will assume there is no loss in the gear reduction to simplify our comparison. Since the gear reduction decreases the rotational speed, it must therefore amplify the torque at the output. We can scale the torque upward by the gear ratio. Thus
FOURSTROKE = 85.94 * 2.33 = 200.25 FT-LBS E-TEC = 94.53 X 2.0 2.00:1 gear case; = 189.06 FT-LBS 5.56 percent less than Mercury = 94.53 X 2.25 2.25:1 gear case; = 212.69 FT-LBS 6.21 percent more than Mercury
We see that the actual torque available at the propeller shaft to turn the propeller is quite close in all three cases, varying roughly by about five to six percent depending on which gear ratio is used for the E-TEC. If we select the 2.25:1 gear ratio for the E-TEC so that it is more comparable to the FOURSTROKE, we see the E-TEC develops more torque. And, correspondingly, if we select the 2.00:1 gears for the E-TEC, it develops less torque.
Torque is the force that will actually allow the propeller shaft to turn a propeller. In general about a propeller we can say that the larger its pitch, the harder it is to turn. So torque is thus a measure of propeller pitch that an engine can turn. From some test data we know that the FOURSTROKE has sufficient torque to turn a 20-inch-pitch propeller, so we can infer that the E-TEC with 2.25:1 gears and more torque can certainly turn at least a 20-inch-pitch propeller, and possibly one 6-percent larger, or about 21-inch-pitch. We can also infer that the E-TEC with 2.00:1 gears can turn a propeller about 5-percent smaller in pitch, or about a 19-inch-pitch propeller. Therefore we will use these pitch values to predict performance.
We have not consider the propeller shaft speed. The speeds are different, and must be accounted for in our comparison. Assuming as we have that the engines reach the mid point of their rated speed range for their horsepower, we use that as the input speed to the gear reduction. The output or propeller shaft speeds are thus:
FOURSTROKE = 5500 / 2.33 = 2360.5 RPM E-TEC = 5000 / 2.0 = 2500 RPM 2.0:1 gear case; 11.76 percent faster than Mercury = 5000 / 2.25 = 2222 RPM 2.25:1 gear case; 5.86 percent slower than Mercury
If we assume we have propellers which are of equal efficiency and differ only in pitch we can project a certain boat speed by using the propeller shaft speed for each engine and applying it to the pitch of the propeller which we assume would be used. In actual practice, there is some SLIP factor, so we here arbitrarily assign the same SLIP factor of 10-percent to all cases. Now we can estimate the boat speed:
FOURSTROKE = 20 * (2360.5/1056) * (1-(SLIP/100)) = 40.23 MPH E-TEC = 19 * (2500/1056) * (1-(SLIP/100)) = 40.48 MPH 2.0:1 gear case = 21 * (2222/1056) * (1-(SLIP/100)) = 39.77 MPH 2.33:1 gear case
The results are quite interesting. They show the predicted performance of the various combinations of engine design, gear reduction, and propeller pitch all produce about the same result for potential speed. The FOURSTROKE and E-TEC differ by no more than 0.25 to 0.46 MPH. This is a variation in speed of one-percent or less. Considering that the two engines are rated to have the same power, this is not particularly surprising. A boat's speed is proportional to the power of its engine.
This outcome is based on a consistent analysis, and it uses as its basis the manufacturers' published data for power and rotational speed. From that we have deduced torque, fitted appropriate propellers, and spun them via the associated gear reduction, ultimately discovering a predicted speed. Of all the assumptions made in this analysis, the only one which is perhaps somewhat controversial is the relationship of propeller pitch to torque needed to turn it. I am quite certain that these are proportional, although here I have assumed a linear relationship which may not be entirely accurate. However, like all the other assumptions, it has been consistently applied.
Other factors which could influence these results which have not been considered include differences in the gear case and engine weight. Transmission of power through a gear case will cause some loss due to the energy needed to turn the gears. In general, a gear case with a larger reduction ratio may have higher losses. This has not been accounted for in this analysis, but may lead to reduced power output as the gear ratio become larger. Boat speed is generally inversely proportional to weight, and thus a heavier engine will tend to slow a boat. The difference in the weight is approximately 80-lbs. This influence has not been accounted for in this analysis.
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Author:James W. Hebert
This article first appeared December 28, 2007.