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When a glider or unpropelled aircraft experiences headwind, I understand that the flight velocity and sink velocity for the "new" maximum possible range both increase (see velocity polar from How does wind affect the airspeed that I should fly for maximum range in an airplane?).

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Intuitively I would think this means that $C_{L}$ needs to decrease so that the now higher $\frac{1}{2}\rho v^2$ can be compensated (small glide slope assumption $L \approx G$ i.e. $L >> D$).

For the theoretical $C_{L_{R_{max}}}$ equation for a symmetric $C_{L}-C_{D}$ polar, I don't see this playing a role:

$C_{L_{R_{max}}}=\sqrt{C_{D_0}\pi\Lambda e} $

...as $C_{D_0}$ to my knowledge doesn't change with velocity.

Does lift coefficient $C_{L_{R_{max}}}$ for maximum range change for a glider experiencing headwind?

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Your first statement is correct, look at the lift vs AOA chart. You go faster by pitching down (reducing lift and drag) and speeding up above Vbg(lift recovered now more drag), which effectively changes your trim and lowers AOA. Why? Because best gliding "Vbg" is all about covering the most distance per unit altitude, NOT time in the air.

In the most extreme case: headwind = gliding airspeed you can see that no forward progress is made unless you glide faster. Forward progress per unit altitude is:

(airspeed - headwind)/altitude

Your new Vbg now factors in ground gain vs increase in parasitic drag. The result is (obviously) you can't glide as far into a headwind, but (more importantly) you can help making your landing zone in a headwind by increasing your airspeed above published Vbg.

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  • $\begingroup$ A very experienced glider pilot once told my non believing ears that not only going above Vbg to "get home", but also giving up altitude and "getting low" worked well in a headwind (wind gradient makes gliding lower more efficient). Technique will vary from plane to plane. $\endgroup$
    – Robert DiGiovanni
    Sep 1, 2019 at 13:03
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    $\begingroup$ This is what glider pilot mean when they talk about "penetration", $\endgroup$
    – John K
    Sep 1, 2019 at 13:09
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    $\begingroup$ @HotDogCannon CA? You get same lift with lower Clift when you fly faster, but parasite drag increases, so total drag increases above Vbg. You weigh this against headwind effects on gliding distance to get your new headwind condition Vbg. $\endgroup$
    – Robert DiGiovanni
    Sep 3, 2019 at 13:05
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    $\begingroup$ @RobertDiGiovanni I meant CL... it's CA in the german speaking world ;) I think I understand it a bit better now. CL is simply no longer the CL given by the equation for CL( (CL/CD)max ) in "still air" and must be calculated from the optimal velocity that is calculated by taking into account the reference frame shift between ground / TAS, etc, which gets more complicated, or done graphically using the method in the figure above. In any case, given a headwind, the optimal velocity for max range is higher, meaning my CL is lower for constant lift. $\endgroup$
    – HotDogCannon
    Sep 6, 2019 at 12:24
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    $\begingroup$ Yes, in a glider with a ground point reference you would pitch down until that point rises in your windscreen the least (or even starts falling) to get headwind Vbg. Not an exact science as wind will vary. But even without headwind the concept holds for max distance, which is why maximum time in air (minimum thrust to maintain flight/rate of descent) speed is lower still, right at the top of the curve. You just don't go as far. $\endgroup$
    – Robert DiGiovanni
    Sep 6, 2019 at 13:39

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