The Induced Drag Coefficient (CDi ) — Page 125, Lesson 147

Right, let's get into the induced drag coefficient — CDi. This is the heart of why drag behaves so counter-intuitively as you change speed. First, the big picture. We have the induced drag equation: Di = ½ ρ V² CDi S. Let me unpack that. Di is induced drag, the drag that comes from generating lift. ρ is air density, V is true airspeed, S is wing area, and CDi is the induced drag coefficient — a dimensionless number that captures how efficiently the wing shape produces that drag. The ½ ρ V² part is what we call dynamic pressure, the pressure from the air's motion. Now, here's the trap. Looking at that equation, you'd think "more speed means more induced drag, because V² is in there." But that's wrong, and the reason is that CDi is not a constant. CDi is proportional to CL² — the square of the lift coefficient — and inversely proportional to wing aspect ratio, AR. Aspect ratio is the span of the wing compared to its chord, how long and slender the wing is. So the real relationship is: CDi = CL² / AR. That's the key formula. As speed increases, to keep the lift force constant — which you must in level flight — you have to reduce CL. So CL drops, CL² drops even faster, and CDi decreases. The drag coefficient shrinks as you go faster. Let me walk you through the worked example, because it makes this concrete. Take an aircraft whose speed is increased from 80 knots, which is 41 metres per second, to 160 knots, which is 82 metres per second. Double the speed. Now, dynamic pressure Q = ½ ρ V². If you double V, you quadruple Q, because of that square. The example uses sea-level ISA density, 1.225 kilograms per cubic metre, but any constant density gives the same result. Let's do the numbers. At 41 m/s: Q = 0.5 × 1.225 × 41 × 41 = 1029.6. At 82 m/s: Q = 0.5 × 1.225 × 82 × 82 = 4118.4. And 4118.4 is exactly four times 1029.6. So dynamic pressure is four times greater. Now look at the lift formula: L = Q CL S. Lift equals dynamic pressure times lift coefficient times wing area. If Q has quadrupled, and we need L to stay the same, then CL must drop to a quarter of its previous value. That's the only way to keep the product constant. Now feed that quarter into the CDi formula. CDi = CL² / AR. If CL becomes ¼ of what it was, then CL² becomes (¼)², which is 1/16. Since AR is constant — the wing doesn't change shape — CDi becomes 1/16 of its previous value. Finally, put that back into the induced drag equation. Di = Q × CDi × S. Q went up by a factor of 4, CDi went down by a factor of 1/16. Multiply those: 4 × 1/16 = ¼. So Di is reduced to a quarter of its previous value. So here's the conclusion, and I want you to remember this sequence because it's exam gold. If speed is doubled in level flight: dynamic pressure becomes four times greater, CL must be decreased to ¼ of its previous value, CDi becomes 1/16 of its previous value, and Di is reduced to ¼ of its previous value. And the reverse, which is just as important. If speed is halved in level flight: dynamic pressure becomes ¼ of its previous value, CL needs to be four times greater, CDi becomes 16 times greater, and that gives you four times more induced drag. That's why slow flight is so draggy — you're flying at high CL, and the induced drag penalty is severe. The takeaway for you as a pilot: induced drag dominates at low speed, and it falls off rapidly as you accelerate. The coefficient CDi is the piece that makes the whole thing work — it's not a constant, it's tied to CL² and to your aspect ratio. Higher aspect ratio, lower CDi at any given CL. That's the relationship you're carrying forward.