(November 2011) It is a bracing feeling to stand up and deny accepted knowledge. So bracing, in fact, that I try to do it as often as possible. I have argued (countless times) that downwind turns are no different from upwind ones, dismissed as a wives’ tale the common notion that the horizontal tail of an airplane always provides a downward force, and attributed P factor to several things but not to the supposedly increased angle of attack of the downgoing blade. I have denounced countless physics textbooks for their stupid explanations of wing lift, but defended Bernoulli against the assaults of revisionist Newtonians.
I am always on the lookout for some piece of accepted wisdom to deny, and so I was immediately interested when a friend sent me a copy of an article with the title “Questioning the Overbanking Tendency.” I did not have to read far to discover the author’s answer: “For all practical purposes,” he states, “there is no such thing as an overbanking tendency.”
My fellow antinomian has the sublime satisfaction of contradicting the FAA’s Airplane Flying Handbook, which he quotes: “As the radius of the turn becomes smaller, a significant difference develops between the speed of the inside wing and the speed of the outside wing. ... This creates an overbanking tendency that must be controlled by the use of the ailerons.” He prefers the view of Charles Zweng in his 1946 classic Flight Instructor: “Overbanking tendencies approach their minimum in steep turns. The steeper the turn, the less they are present.”
So here we have two apparently authoritative sources taking diametrically opposite views of the question. Does it matter? Not really. We use our ailerons to create and maintain a bank angle without troubling ourselves about their absolute positions. The overbanking tendency, if it exists, must be quite weak, at least at normal bank angles; no one complains of tired arms after making a two-minute turn. But still, the question is an interesting one. Why is there disagreement about it?
To be sure, my author is hedging his bets. Notice the weasel words, “for all practical purposes,” by which he situates himself in neutral territory somewhere between Zweng and the FAA. Zweng, after all, allows that there are overbanking tendencies, but claims that they have the mysterious property of existing only at moderate bank angles. The FAA merely asserts that overbanking tendencies must be controlled with aileron, but does not say how much; so it’s not really sticking its neck out either. None of our commentators on this important topic seems to be willing to make a definite, quantitative statement.
But I am.
The argument for the existence of the overbanking tendency, as the FAA handbook says, is that since the outer wing in a turn is slightly farther from the center of the circle than the inner wing is, it moves a little faster, and so it has more lift. The argument against it is — I assume — that as the bank steepens the radii of turn of the two wings get closer and closer together, and so the difference in speed and lift must shrink. In a 90-degree bank, after all, the difference is zero; where is the overbanking tendency now? Of course, in a coordinated 90-degree bank the turn radius is zero and the G-loading is infinite, so ordinary arithmetic fails us.