Is the maximum lift-drag ratio found at minimum drag?

  • Is the maximum lift-drag ratio found at minimum drag? user2168

    Figure 10-5 of the FAA's Pilot's Handbook of Aeronautical Knowledge shows:

    I didn't think $L/D_{MAX}$ coincided with $D_{MIN}$. Is this Figure accurate?

  • Well, for all L/D curves and D curves, the assumption is that the weight of the aircraft is constant and that there is no acceleration. Therefore the lift equals the weight (neglecting the small vertical component of thrust). So lift is a constant in these curves.

    The rest is simple mathematics; the maximum of $\frac{1}{f(x)}$ occurs at the minimum of $f(x)$ (when $f(x) > 0$), so the maximum of $\frac{L}{D}$ coincides with the minimum of $D$.

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  • Well, your lift equals weight, or the airplane drops out of the sky or climbs into orbit. Therefore, lift is constant. Then the point with minimum drag must be the one where L/D reaches it's maximum.

  • It doesn't have to, and almost certainly doesn't coincide. There is not data here on how lift varies with speed. A NASA chart I foundchart I found shows it rising quadratically with airspeed. Similarly, the drag is probably a quadratic minimum, so $D \propto a+b(v-v_m)^2$, where $v_m$ is the speed of minimum drag. Then $\frac LD =\frac {C_Lv^2}{a+b(v-v_m)^2}$. The fact that the numerator is rising will move the max $\frac LD$ point above $v_m$, but not by much.

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