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While I got this question correct I simply made an educated guess and have no intuition for why. I understand that lift would have to increase relative to drag in order to make the axial force point forward but have no idea how that relates to the tangent/cotangent of the angle of attack. What is the tangent of the angle of attack really describing? The explanation of the correct answer didn't help much either.

Otto Lilienthal carried out a series of aerodynamic measurements on small model wings using first a whirling arm and later stationary models. He tested both flat plate wings and wings with a thin curved (cambered) airfoil. For the flat plate, the resultant aerodynamic force was always inclined behind the perpendicular to the plate with an axial force always oriented in the backward direction. However, his data for the cambered airfoil showed that at some angles of attack the resultant aerodynamic force was inclined ahead of the perpendicular to the chord line; for these cases, the axial force was oriented in the forward direction. Lilienthal called this forward component a “pushing component” and cited its existence as evidence of the superiority of cambered airfoils. With the above information as background, identify the aerodynamic condition that results in a forward-facing axial force. Assume α as the angle of attack.

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The above figure shows the resultant aerodynamic force, R, resolved into two sets of components: L and D, which are perpendicular and parallel, respectively, to the relative wind and N and A perpendicular and parallel, respectively, to the chord. Consider the specific case where lift and drag are just the right ratio, such that the resultant aerodynamic force, R, is precisely along the normal. This will only occur when the ratio D/L is exactly equal to the tangent of the angle of attack, α.

D/L=tan(α)or, L/D=cot(α)

If L/D is larger than cot α, then the resultant aerodynamic force will be ahead of the normal line, and the axial force will be forward-facing.

Therefore, the condition that leads to a forward-facing A is

L/D>cot(α)

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  • $\begingroup$ You don't need any physical intuition to answer this question. It's simply a matter of trigonometry and the last few paragraphs of the question constitute the complete answer. $\endgroup$
    – D. Halsey
    Commented Jul 8 at 23:46

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The chord line intersects the leading edge at a point, but that is not the stagnation point (where the airflow divides). So you cannot necessarily use the chord line for precise calculations. The stagnation point is generally on the lower side of the leading edge, and becomes more-so as the angle of attack increases. That fact is exploited to detect the onset of stall (in small aircraft).

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