In order to move forward through the air, a propeller driven aircraft must produce a force to overcome the drag force opposing its forward motion. Thrust is this force. The basic concepts of work and power are key in the discussion of propeller thrust.
Recall that work is the resultant of the force required, multiplied by the distance of movement required, or desired. On the other hand, we have the concept of power, which is the resultant of work divided by time.
In the case of the propeller, we’ll refer to this force as thrust, and we can substitute velocity in feet per second for distance. A few algebraic manipulations later and we have work/secs = thrust x velocity. Since horsepower is 500 ft/lbs per second, one additional step yields the equation of thrust horsepower = (thrust x velocity)/550.
The thrust horsepower (THP) is what the propeller produces as it utilizes the brake horsepower (BHP) from the engine. Designers try to maximize the efficiency of the conversion of engine BHP to propeller THP. Therefore, the ratio of the THP to BHP is in fact propeller efficiency in terms of a percent.
What is lost in the conversion is represented through the actions of the propeller as it moves through the air; mainly friction and slippage.
Propeller efficiency varies widely (50- 87% on average) depending both on the design of the propeller and the conditions under which aircraft manoeuvring takes place. Herein lies one obvious reason for desiring a constant speed propeller system that adjusts blade angle as the aircraft is manoeuvred.
Anyway, in a theoretical world the propeller would advance a given distance through the air during one complete revolution. This theoretical world is not a fluid (air) but rather a solid medium of some sort.
The distance of advance for one revolution of the propeller is referred to as geometric pitch (or sometimes just pitch, but not to be confused with the actual blade angle). In the real world, the propeller just doesn’t "bite" the air as efficiently as in the theoretical solid, so in reality it does not advance as far after one revolution.
This "reality" distance is called effective pitch and the difference between it and the geometric pitch is called "slip." Another way of looking at it is that geometric pitch assumes no slippage while effective pitch accounts for the actual slippage through the air.
So how does this relate to propeller efficiency? If we use an example the relationship becomes clear. Suppose we could measure both the geometric and effective pitch of one revolution of the propeller. If in theory the propeller would advance 60 inches in one revolution, but it actually only advances 45 inches, the effective pitch is 45 inches and the propeller slippage is 15 inches. A 15-inch loss due to slippage means a 25% loss of theoretical efficiency (15 divided by 60). As a result, the realized propeller efficiency is 75%.
I mentioned before that a constant speed propeller system is desirable for maintaining a high level of propeller efficiency. In this kind of prop system, blade angle is continually adjusted by the prop governor to maintain the most efficient angle of attack at most engine and aircraft speeds.
With the typical propeller, the most efficient angle of attack is usually pretty low (some sources cite around 1 to 4 degrees). The blade angle required to maintain the optimum angle of attack varies with aircraft speed. Aircraft that have a wide range of speeds, as well as those that can operate at high altitudes must have a wide range of blade angles available to achieve the optimum blade angle of attack and thereby maximize propeller efficiency.
What is the trade off between blade angle and efficiency? Take a fixed-pitch propeller for instance. Since this type of propeller is fixed at a given blade angle, efficiency cannot be maximized for all phases of flight. The performance desired determines the blade angle chosen for these types of aircraft.
If climb performance is the most important, then a prop with the appropriate angle for climb is chosen. In this case, the disadvantage is that cruise performance will suffer if a climb pitch prop is installed. If a cruise pitch prop is used, then climb performance suffers. There are of course intermediate blade angles that result in sort of a middle of the road improvement in climb performance without too much loss during cruise.
One last topic deals with speed vs. propeller efficiency. As aircraft speed increases, the propeller angle of attack decreases and the propeller becomes less efficient, and hence, less THP.
Every aircraft reaches a point where THP is no longer sufficient to overcome drag and the aircraft no longer accelerates. One solution to this problem would seem to be an increase in propeller RPM. However, as blade tip speed increases above ~800 ft/sec, propeller efficiency also drops off rapidly. Shorter blade length and/or more blades help this problem to some extent.
Also, early experiments with increased engine power, in order to increase the transfer of BHP to the prop, generally failed to provide significant performance benefits due to propeller limitations. Modern turboprops have seen dramatic changes in prop design and, as such, have increased performance relative to their traditional counterparts in general aviation.
Light aircraft have seen little or no advancements in propeller design in the last few decades and there does not appear to be any significant move away from those proven designs. Of course the future may bring changes but for now it looks like we’ve reached the practical limits of propeller efficiency.
This month’s Pilot Primer is written by Donald Anders Talleur, an Assistant Chief Flight Instructor at the University of Illinois, Institute of Aviation. He holds a joint appointment with the Professional Pilot Division and Human Factors Division. He has been flying since 1984 and in addition to flight instructing since 1990, has worked on numerous research contracts for the FAA, Air Force, Navy, NASA, and Army. He has authored or co-authored over 160 aviation related papers and articles and has an M.S. degree in Engineering Psychology, specializing in Aviation Human Factors.