The flying equation

September 1, 2011

Albert Einstein gave us E=MC2, one of the most venerable of physics equations. It’s an equation that allows us to understand the relationship between mass and energy. Aviation also has its venerable equations, and one of my favorites involves no math at all. This equation expresses the relationship between attitude, power, and performance. It’s to be taken seriously, but not literally. It reads: Attitude + Power = Performance (A+P=P).

This is the equation I use on every flight. Every one! When the two variables of attitude and power are exchanged for specifics, I can estimate my airplane’s performance with a high degree of precision. Pushing the throttle fully forward at sea level on a cool day and raising the nose to climb attitude allows me to anticipate good climb performance (good for that specific airplane, of course). Turning base, reducing power to flight idle, and selecting a specific nose-down attitude allows me to predict the airspeed I’ll achieve during the descent. The equation doesn’t lie, as long as long as you are aware of two traps that can alter one or more of its variables.

For instance, some pilots misinterpret A+P=P to read: Attitude + Throttle Position = Performance. Unfortunately, the only thing that this equation predicts is that some pilot might have a reason to use the word deductible at some future time. That’s because for normally aspirated engines, as density altitude increases, the position of the throttle (full forward, half forward, et cetera) becomes a less accurate indicator of power production.

Move the throttle to its full forward position while flying at 5,000 feet msl on a standard day, and your engine might produce 75 percent of its maximum rated power. Do the same thing at a higher altitude and/or warmer conditions and you’ll get less power even with the throttle pushed to its full forward position. That’s why Attitude + Power = Performance is only useful when you consider how environmental conditions influence power production. At high density altitudes, you can raise the nose to climb attitude and move the throttle fully forward, but don’t anticipate sea-level climb performance. If you understand that, you will successfully avoid trap number one.

Trap number two involves mistaking attitude for angle of attack. Attitude is not angle of attack, though it can be a good approximation as long as you can compare it to the airplane’s direction of motion (i.e., the movement directly opposite the relative wind). Most pilots make this comparison by looking directly over the airplane’s nose. Others do it by looking out their left window to observe the airplane’s motion relative to the wing’s chord line. The airplane’s attitude can provide a practical estimate of the angle of attack, but only when you’re aware of the direction your airplane is moving. Understanding this concept allows you to avoid selecting an attitude that might cause the wings to exceed their critical angle of attack. Using attitude to estimate your angle of attack becomes less reliable when it’s harder to identify the airplane’s actual motion through the air. This is most likely to happen during steep descending turns to landing.

Steep descending turns involve increasing elevator back-pressure, which produces a relatively quick increase in angle of attack and an increase in load factor. Since the airplane is turning, the background scenery constantly changes instead of moving steadily toward you. This makes it more difficult to assess the airplane’s motion through the air, so an accurate estimate of the angle of attack is more difficult to make. Complicating matters, the nose is pointed below the horizon in these turns. Unfortunately, many pilots have difficulty understanding how the wings can exceed their critical angle of attack when the airplane is in a nose-low attitude. High G loading in a descending turn is where this is likely to happen.

Avoiding trap number two means recognizing that a sudden increase in apparent weight (load factor) implies that you’re closer to a stall than the nose-low attitude might suggest.

AOPA Aviation Summit

Rod Machado will entertain and educate pilots at AOPA Aviation Summit, September 22 through 24, in Hartford, Connecticut.

Given those caveats, is A+P=P still useful? You bet it is. Abraham Lincoln once said that nearly every major decision he made was influenced by the Declaration of Independence. In a structurally similar way, every maneuver I make in an airplane is guided by the equation A+P=P. Every single one.

No, I’m not sitting there manipulating the controls while mumbling, “A plus P equals P.” In the back of my mind A+P=P is simply the strategy used for flying my airplane.

Fortunately, this equation involves no math, which is good because five out of four people have trouble with math. It does, however, involve two generalizations—without the ability to generalize, there can be no wisdom. Simply be aware that the throttle position doesn’t necessarily represent engine power—and that attitude becomes a less reliable indicator of angle of attack when accompanied by an increase in load factor. Given these caveats, A+P=P becomes a useful tool for anyone who flies.