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I'm making a school project where I intend to design and calculate an rc airplane. Reading some books I found something I can't understand, it says that CL/Cd is equal to L/d, but the only possible way to make that true is to use the same surface on Drag and Lift equations. Isn't drag equation supposed to use frontal surface and Lift equation to use wing surface?

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The frontal surface is indeed used for the drag coefficient of cars.

For airplanes, however, almost* all coefficients use the wing area as their reference. This makes sense exactly because it allows to express L/D as c$_L$/c$_D$.

* For the nitpickers: Control surface hinge moment coefficients use the area of their respective control surface, not the wing surface.

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  • $\begingroup$ Thank you Peter, I was really struggling with that one, because the Cl/Cd made sense but using the frontal area would make the L/d absurd. $\endgroup$ – Lucas Delgado Jul 6 at 20:56
  • $\begingroup$ Your answer makes me wonder something, If the area is constant at any AoA (wing Area), wouldn't the parasite drag coefficient need to change at different AoAs? because I'm "showing" more or less area to the relative wing which should increase drag $\endgroup$ – Lucas Delgado Jul 6 at 20:59
  • $\begingroup$ @LucasDelgado The area you "show" to the flow is only relevant in super- and hypersonic flow. Since subsonic flow bends around the plane, it is the length of the flow path that matters, not the area facing the flow. $\endgroup$ – Peter Kämpf Jul 7 at 8:44
  • $\begingroup$ Ok that makes sense, I have only one more question, I'm sorry if it sounds stupid, why resistance goes up when slipping in a plane of frontal area doesn't matter? $\endgroup$ – Lucas Delgado Jul 7 at 21:58
  • $\begingroup$ @LucasDelgado: Haha, good point. Now we are leaving linear aerodynamics and the blunt fuselage at an angle doesn't behave like a wing but more like a barn door. Similar to cars, now the frontal area does have some bearing on drag. $\endgroup$ – Peter Kämpf Jul 8 at 5:00

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