The wing and the drag polar
drag build-upinduced draglift and drag coefficientsaspect ratioL/D ratio
Working a wing's drag: aspect ratio, the lift coefficient the flight needs, the induced drag it costs, and the lift-to-drag ratio that results.
Wing Aspect Ratio
How slender a wing is: span squared divided by planform area. For a rectangular wing it is simply span over chord, and for every other wing it is the number that decides how expensive lift will be.
Lift Equation
The lift a wing produces: dynamic pressure times reference area times the lift coefficient. Three of the four terms are things you can measure with a tape and a gauge, and the fourth is where the whole of aerodynamics lives.
Induced Drag Coefficient
The drag a wing cannot avoid paying for the lift it makes, from Prandtl's lifting-line theory: lift coefficient squared over π times aspect ratio times the span efficiency factor. It grows with the SQUARE of C_L, which is why it dominates at low speed.
Drag Polar
The whole drag of an aircraft split in two: a part that is there whatever the wing is doing, and a part that is the price of lift. Every performance calculation an aircraft ever needs starts from this sum.
Drag Equation from the Drag Coefficient
The drag on an aircraft written the way an aerodynamicist writes it: dynamic pressure times the SAME wing reference area used for lift, times the drag coefficient. Not the frontal area a car's drag is built on.
Lift-to-Drag Ratio
Lift divided by drag: how many newtons of weight an aircraft carries for every newton it has to push against. The single number that says how good a flying machine is, and the one a sailplane pilot lives by.
How they fit together
This is the tightest chain on the site: every answer is literally the next equation's input, with nothing left over. Aspect ratio from span and area, then the lift equation run backwards — you know the weight and the speed, so solve for the lift coefficient the aeroplane needs rather than for the lift, which you already know equals weight in level flight. That CL is the number the rest of the set consumes.
Induced drag is the price of that CL, and the CL² in it is the single most useful fact in low-speed aerodynamics. Fly slower and CL must rise to hold the same weight up, so induced drag rises with the square, which is why drag increases as you slow below best-glide speed and why the region behind the power curve exists at all. Aspect ratio sits in the denominator, which is why a glider has a long thin wing and an aerobatic biplane does not. The span efficiency factor e is the term to be honest about: 1.0 is a theoretical elliptical loading nobody has, and a real light aircraft is 0.75 to 0.85, so using unity understates induced drag by a fifth.
The drag polar adds the two halves — zero-lift drag, which grows with speed, and induced drag, which shrinks with it — and the crossing point where they are equal is where lift-to-drag ratio peaks. That single fact is worth more to a pilot than the equations around it: best L/D happens at the speed where parasite and induced drag are equal, and it is the speed for maximum range in a glider, best glide after an engine failure, and maximum endurance nowhere — endurance is slower. The drag equation turns the coefficient back into newtons when you need thrust required rather than a ratio. One caution on the reference area S: it appears in aspect ratio, the lift equation and the drag equation, and it must be the same S in all three. Wing reference area, not wetted area, not planform including fuselage — mixing definitions between the lift and drag steps quietly corrupts everything downstream.