# Does lift coefficient for maximum range change for a glider experiencing headwind?

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?). 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?

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: