Changes

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:

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:

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.