Performance: The perfect aircraft (for the mission)

While I may never fly the aircraft, it’s fun to explore and marvel at the choices made in its design process. The list of specifications offers performance data such as cruise speed and stall speed that make it clear whether this aircraft was intended to be an efficient and comfortable cross-country platform or to be operated from short, unimproved strips in the mountains.

Wing loading and power loading are part of that list as well, but what they betray about the aircraft mission may not be as obvious. Let’s define these terms and see what they can tell us about the aircraft’s intended mission.

In his book Aircraft Performance and Design, John D. Anderson details the typical order of events in the design process of a propeller-driven aircraft. The process sheds light on the significance of wing loading and power loading values and the associated flying characteristics.

It starts with consideration of a set of specifications defined by the intended mission of the aircraft. For example, this set of requirements might include payload of at least 900 pounds, maximum cruise speed of 200 knots, clean stalling speed of no more than 70 knots, landing distance of no more than 1,800 feet, and takeoff distance to clear a 50-foot obstacle of no more than 2,100 feet.

Anderson explains that, after forming a rough estimate of the aircraft’s maximum gross weight, the designer chooses the airfoils from which the wing will be formed. The relationship between the coefficient of lift and the angle of attack (see p. 88), as well as the shape of the wing, contributes to the qualities of the stall. Additionally, the maximum lift coefficient that occurs at the critical angle of attack plays a key role in the formulas for stall speed, takeoff distance, and maximum cruise speed.

Wing loading is the maximum gross weight of the aircraft divided by the wing area, and this term appears in the formula for stall speed. In particular, as wing loading increases, so does the stall speed. Using the maximum lift coefficient and the maximum desired stall speed, the designer computes a maximum value for the wing loading. Similarly, landing distance increases with an increase in wing loading, so the landing distance requirement provides another bound for wing loading.

Choosing the smaller of these values for wing loading, along with the estimate of maximum gross weight, results in a minimum value for the wing area.

Thrust-to-weight ratio, along with the maximum lift coefficient and wing loading, appears in the formulas for takeoff distance, rate of climb, and maximum cruise speed. It makes sense that a higher thrust-to-weight ratio provides a shorter takeoff distance, higher rate of climb, and greater maximum cruise speed. Choosing thrust to weight as the highest of the values obtained by these constraints, we get the required value for thrust. During the takeoff roll, the required power is equal to the thrust times the speed, so we can calculate the power the engine needs to produce. Because of inefficiencies in the engine/propeller combination, the chosen rated power of the engine should be greater than the required power. The power loading of the aircraft is maximum gross weight divided by the chosen rated power. Note that a low power loading value corresponds to an aircraft with a more powerful engine and/or a lower gross weight. Low power loading means better performance.

What do wing loading and power loading say about an aircraft? We can tease this information from Anderson’s description of the design process. With other factors remaining constant, an aircraft with a higher wing loading features a higher maximum cruise speed. Wing loading is inversely related to gust sensitivity, so a higher wing loading provides a more stable platform for instrument flying. Aircraft design always involves tradeoffs and high wing loading is no exception—it comes at the expense of a higher stall speed and longer takeoff and landing distances. To curb these negative effects, high lift devices such as flaps create a more bird-like wing shape for better low-speed flight characteristics in the landing phase.

Aircraft intended for operation out of shorter strips and less forgiving terrain often have a lower wing loading, with an attendant decreased stall speed and shorter takeoff and landing distances. Here the price involves a reduced maximum cruise speed. These short takeoff and landing (STOL) aircraft operate on the slower end of the airspeed spectrum and are not optimized for long cross-country flights.

A low power loading results in better takeoff performance, better climb rates, and higher cruise speeds. At first pass, there appears to be no downside to such an increase in engine power. But that increase often comes at a price of a higher engine weight (and therefore the power loading might not actually decrease) and increased fuel consumption. Higher fuel consumption shortens endurance and, depending on cruise speeds, could reduce the range. The diagram on p. 87 offers wing loading and power loading values for a range of general aviation aircraft.

An interesting side note involves the 1903 Wright Flyer. Just one of the goals that Orville and Wilbur Wright achieved to make possible their historic flight was their invention of a powerful yet lightweight engine. They fabricated an engine that produced 12 horsepower and, assuming a roughly 775-pound gross aircraft weight (605-pound empty weight with a 170-pound pilot), the power loading comes in at 64.6 pounds per horsepower—a major feat for the day. The vast 510 square feet of wing area made the wing loading only 1.5 pounds per square foot. (To put things in perspective, a Cessna 172S has a wing loading of 14.7 pounds per square foot; a Cirrus SR22 has a wing loading of 23.5 pounds per square foot.)

With all the compromises aircraft design entails there is no such thing as a perfect aircraft. But you can be sure that each one was carefully crafted by its designer to be optimal for the intended mission. The next time you read the specifications of an aircraft perhaps the wing loading and power loading values will tell you something about the nature of that mission.

Catherine Cavagnaro is an aerobatics instructor (aceaerobaticschool.com), professor of mathematics at Sewanee: The University of the South, and speaker at AOPA fly-ins.