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→An Approximate Method of Solution: The Analytical Polar Curve
\[ V_S = \frac{1}{2W} \rho S C_{D0} V^3 + \frac{2kW}{\pi A \rho V S} \]
== Implications of the Analytical Polar Curve: Minimum Sink and Best Glide ==
The analytical form of the polar curve applies to the speed range from several knots above stall to \( V_{NE} \) (\( V_{NE} \) must be converted to its indicated value). It does not apply close to stall, which is because the aerodynamics of the glider changes considerably before the onset of stall such that the drag ceases to be a parabolic function of the lift.
The analytical polar given above can be plotted by any computer code, or a plot can be found in any gliding textbook. You can also ask an instructor to draw you one. Conventionally, the Y-axis (\( V_S \)) is turned upside-down, such that going down means higher sink rate. When plotted this way, this curve is convex and has a single global maximum. The curve is monotonic on both sides of the maximum.
=== Minimum Sink Airspeed ===
We seek an indicated airspeed that will give us the minimum sink rate. This is the indicated airspeed to fly at only if you want to stay in the air for as long as possible with a certain amount of altitude drop. Flying at this speed may not be able to get you anywhere (in extreme cases you can go backwards rather quickly), so caution and thought is needed.
To find this airspeed, the analytical polar is differentiated to reveal the maximum:
\[ \frac{d V_S}{dV} = 0\]
This gives:
\[ V_{MS} = (\frac{4kW^2}{3 \rho^2 S^2 C_{D0} \pi A})^{\frac{1}{4}} \]
