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→Minimum Sink Airspeed
=== 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. It is useful when thermalling. 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:
\[ V_{MS} = (\frac{4kW^2}{3 \rho^2 S^2 C_{D0} \pi A})^{\frac{1}{4}} \]
It is common practice to define a quantity called wing loading as \( \omega = \frac{W}{S} \) which quantifies how much weight each meter squared wing area is carrying. With this definition in place, notice that \( V_{MS} \) is proportional to the square root of wing loading. The implication is, the minimum sink airspeed is not fixed: with the glider loaded heavier it will become higher.
It is worth noting that, by flying at this airspeed, the sink rate scales at the 3/2 power of the wing loading. Therefore, by loading the glider heavier, the minimum sink rate '''possible''' is also higher. This implies that gliders with low wing loading can make use of weaker thermals with a limited rising speed.
If a glider thermals at the minimum sink airspeed, carrying water ballast will enable the glider to fly faster and likely at a larger radius. This can prove to be beneficial as some experienced pilots will say, but a mathematical proof is not possible in the absence of a model to characterise the behaviour of the thermal. Water ballast is usually carried on good thermal days but not on days with marginal conditions. You will sometimes hear pilots say that the water doesn't work, the author's interpretation to which is that, because the thermals are not strong and big enough, the increased minimum sink by carrying water ballast outweighs the possible benefits if any.
