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→Minimum Sink Airspeed
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.
=== Best Glide ===
The best glide ratio achievable for a given glider in a particular loading and configuration can be determined from the analytical polar. Recall that the glide ratio is given by the horizontal distance covered over the vertical altitude drop. For analytical purposes, it is necessary to make a small angle approximation such that the horizontal distance is approximately given by \( V \times t \) where \( t \) is time. The accuracy of this approximation is shown in previous sections.
Using the small angle approximation, the inverse of the glide ratio is given by:
\[ \frac{V_S}{V} = \frac{\rho}{2 \omega} C_{D0} V^2 + \frac{2 k \omega}{\pi A \rho V^2} \]
This compound quantity is to be differentiated with respect to \( V \) to reveal the minimum:
\[ \frac{d}{dV}(\frac{V_S}{V}) = \frac{\rho}{\omega} C_{D0} V - \frac{4k \omega}{\pi A \rho V^3} =0\]
This yields:
\[ V_{BG}=(\frac{4k \omega^2}{\pi A \rho^2 C_{D0}})^{\frac{1}{4}}=(3)^{\frac{1}{4}} V_{MS}=1.3161 V_{MS} \]
