T&T: Propeller efficiency

[LRZeitlin at aol.com]

I read, with interest, the comments on propeller efficiency in recent posts. 
Propeller efficiency is one of those ambiguous areas in boating, like 
seaworthiness or handling, that is important but difficult to understand.

Basically propeller efficiency is defined as the percent of shaft horsepower 
that is used to propel the boat. All one must do to calculate propeller 
efficiency is determine the amount of power input to the propeller (fairly easy), 
the speed of the boat through the water (very easy) and the thrust of the 
propeller at that speed (quite difficult). The amount of slip, per se, is primarily 
a function of the design factors that determine efficiency. The effective 
horsepower (EHP) is the amount of power necessary to overcome the drag and move 
the boat through the water at the required speed. For displacement boats, very 
little EHP is necessary to move the boat at S/L ratios below 1. For 
non-technophiles, the S/L ratio is the boat speed in knots divided by the square root of 
the waterline length in feet. Above a S/L ratio of 1 the power required rises 
exponentially. The hull speed of a displacement type boat is generally held to 
be at a S/L ratio of 1.34.

Let's take an example. My Willard trawler engine is required to generate 
about 13.7 horsepower to move the boat at 6 knots. This is a S/L of 1.15. Power 
can be measured exactly with the correct instruments but in my case I just 
calculated it by measuring the fuel consumption over a long cruise at a 6 knot 
speed. The average fuel consumption was .82 gph. Using the estimate of .06 gph per 
horsepower, the developed power came out to 13.66 hp. The gearbox, long 
shaft, and several bearings probably reduced the power available at the prop to 13 
hp.

Since one horsepower equals 550 ft. lbs. per second, a 100 % efficient prop 
would develop 7150 ft. lbs./sec. of force. Since the boat, traveling at 6 
knots, is moving at 10.1 feet/second, the prop should be delivering about 708 lbs. 
of thrust.

Now here is where the efficiency calculation gets harder. I must know the 
actual drag of the boat to determine the amount of thrust necessary to move it at 
6 knots. This can only be determined by towing the boat or tank testing. I 
could get a rough estimate by measuring the bollard pull but that would only 
tell me the amount of thrust developed at zero velocity, not at speed. In the few 
instances I have tried to drag an anchor or tow another stranded boat, I am 
sure that the prop did not develop 708 lbs. of thrust. It probably developed 
about 300 lbs. of thrust at the same engine rpm that I use for cruising.

Now let us assume that the 300 lb. thrust figure is correct. The equation for 
efficiency is:      

Efficiency = (power output/power input ) x 100

The power output of the prop is 10.1 ft/sec x 300 lbs. thrust. This works out 
to 3030 ft. lbs./sec. Since the power input to the prop is equivalent to 7150 
ft. lbs./sec., the prop is working at only 42.4% efficiency. This is in the 
range of efficiency of most trawler props which rarely exceed efficiencies of 
greater than 50%.

Now let's arrive at an estimate of prop efficiency another way. Francis 
Kinney, in "Skene's Elements of Yacht Design," the holy writ of boat designers, 
provides a chart showing the resistance of displacement type hulls as a function 
of speed. At a S/L ratio of 1.15 my Willard has a drag of 35 lbs. per long ton 
(2240 lbs.) of displacement. My boat has a total displacement of 7.14 long 
tons hence the total drag is about 250 lbs at 6 knots. The formula for effective 
horsepower is:

EHP = resistance x speed x .003

For my boat this works out to:

EHP = 250 x 6 x .003 = 4.5

Thus it takes only 4.5 hp directly applied to the boat to move it at 6 knots.

Dividing the 4.5 EHP by the 13 hp applied to the prop gives me a propeller 
efficiency of only 35%. This is not too far from the previously calculated 
efficiency of 42%. This is low but in the ballpark for most recreational trawlers. 
In fact in years of consulting on small boat designs I have rarely seen a 
recreational trawler with a propeller efficiency of as much as 50%.

Greater efficiencies can be obtained by increasing the thrust of the prop at 
a given power input. Thrust is determined by the mass and velocity of the 
water accelerated backward by the prop. You can move a large amount of water 
backward at a slow speed or a small amount at a high speed (i.e. firehose). For 
propelling a boat forward, it is most effective to move a large amount of water 
backward at a speed slightly higher than the boat's forward speed. The amount 
of water moved is determined by the prop blade diameter and the prop pitch. The 
blade area should be sufficient to avoid cavitation at maximum prop rpm. 
Generally, the fewer blades the better, given sufficient blade area, because each 
blade is moving in clearer water. You can move the same amount of water by a 
smaller prop turning at a faster speed but higher rpm means greater friction 
losses and generally lower efficiency.

So we find that the most efficient props for displacement and semi planing 
boats are large diameter, low rpm, relatively a high pitch matched to boat 
speed, with just sufficient blade area to avoid cavitation. Using this approach, it 
is theoretically possible to get prop efficiencies approaching 75% but there 
may be practical limitations of clearance, draft, and unsuitability for 
certain hull designs.

There will be no exam.

Larry Z


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