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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?

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  • $\begingroup$ Closely related, but couched in terms of gliding flight-- could be adapted to address your question-- the answer is "yes", whether we are flying horizontally or gliding -- aviation.stackexchange.com/a/81790/34686 $\endgroup$
    – quiet flyer
    Oct 20, 2020 at 15:04
  • $\begingroup$ Also related -- aviation.stackexchange.com/a/87933/34686 . The answer is "yes"-- and note that we need not assume that Lift is constant, i.e. exactly equal to Weight. $\endgroup$
    – quiet flyer
    Jun 25, 2021 at 16:47

2 Answers 2

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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 $D$.

enter image description here

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  • $\begingroup$ @user2168: As long as your trajectory through the air is reasonably horizontal, the component of gravity perpendicular to it (which will have to be canceled out by lift) does not change much. On the other hand, the component of gravity in the direction of your motion (which is what must outbalance drag) can change by much more as you climb or descend. $\endgroup$
    – hmakholm left over Monica
    May 1, 2014 at 14:33
  • $\begingroup$ @user2168 As Henning Makholm says, during glide lift $\approx$ weight as long as the glide is fairly horizontal and the vertical acceleration is zero. The chart that you pulled from the book is in the section 'Straight and level flight'. It mentions 'steady flight condition' and 'condition of equilibrium' and 'a lift equal to the aircraft weight' when the chart is discussed. How much more explicit would you like it to be? $\endgroup$
    – DeltaLima ♦
    May 1, 2014 at 15:03
  • $\begingroup$ @user2168 From your comments on this answer and the other answer, it seems to me that you think that during glide the lift is unequal to the weight. Make sure you have a good understanding of the balance of all four forces (lift, drag, weight, thrust) acting on an aircraft in steady symmetric flight. The equilibrium of these forces holds also during steady glide and steady climb. I'll be happy to assist if needed. $\endgroup$
    – DeltaLima ♦
    May 1, 2014 at 15:12
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    $\begingroup$ Assuming a spherical aircraft in a vacuum... $\endgroup$
    – Vikki
    May 21, 2018 at 17:22
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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.

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    $\begingroup$ This is a very simple, intuitive answer which most pilots should understand easily once they read it. +100 if I could! $\endgroup$
    – Lnafziger
    May 1, 2014 at 16:01
  • $\begingroup$ Is it correct for both propeller and jet aircraft? $\endgroup$
    – Nikita
    Sep 18, 2019 at 6:28
  • $\begingroup$ I heard that in a propeller-driven aircraft speed for (L/D)max is a little bit greater than speed for minimum drag, because of the thrust being not directly produced by the engine. $\endgroup$
    – Nikita
    Sep 18, 2019 at 6:37
  • $\begingroup$ @Nikita: What you probably mean is that maximum endurance speed for propeller aircraft is lower than the speed of optimum L/D. Since thrust is inverse to speed, flying at higher drag but lower speed reduces power for sustained flight to its minimum at a point where drag is not minimal. At maximum L/D range has its maximum for propeller aircraft and endurance for pure jets. Turbofans are in between. $\endgroup$
    – Peter Kämpf
    Sep 18, 2019 at 8:09
  • $\begingroup$ Lift equal weight, or there will be a vertical acceleration, i.e., your vertical velocity will be changing! Many assume, (incorrectly), that weight greater than lift causes a descent, and weight less than lift causes climb. NO! these conditions do not cause vertical velocity, they cause vertical acceleration! $\endgroup$
    – Charles Bretana
    Oct 31, 2020 at 2:15

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