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water ballast
# Analytical form of the glide polar.
# Implications of the polar: minimum sink speed, and best glide.
# Implications of the polar: water ballast
# Adjustments to the polar: headwind and sinking air.
# Adjustments to the The non-dimensional polar: change of glider weight, first purpose of water ballast.# More effects of water ballast and recommended readings. This article is a major project which will take me at least a month to complete. I cannot save a draft on WiKi, so if you accidentally come here and see this page in its very much incomplete form, please bear with me and come back after some time.
== Glider in Unaccelerated Flight in Still Air ==
== Lift and Drag Coefficients ==
In the discussions that follow, only the incompressible flow regime is considered. This is justified by the low speed that gliders fly at.
=== Definitions ===
From a geometric point of view, the above solution process is equivalent to finding a ray from the origin that is tangent to the polar curve. You should ask an instructor to demonstrate this to you to reinforce the understanding. This geometric method is useful when more factors are taken into account, such that an analytical solution cannot be obtained easily.
=== Water Ballast ===
Water ballast has no effect on the glider best performance, but it makes the best glide speed faster, so the pilot can cover a certain amount of cross-country distance faster. This is the first reason for using water ballast.
In fact, the use of water ballast '''does not change the shape of the polar at all''', not only for the best performance point. To see this, please read the next section on non-dimensional polar. The shape of the polar is dictated only by the '''best glide speed''' and the '''sink rate at best glide''', but, as shown previously, both quantities are proportional to \( \sqrt(\omega) \). Therefore, as the wing loading changes, the polar curve '''scales''' around the origin with \( \sqrt(\omega) \) but keeps its shape. Because the best glide is a tangent to the polar, and that the polar is scaled around the origin of the ray, the slope of the ray (best performance) is invariant.
The second reason for using water ballast is to improve the performance in headwind and sinking air. This is difficult to prove mathematically as the workings in the next section will show, but geometrically this can easily be demonstrated. Because the polar curve is scaled to be larger, any shift in origin due to headwind and sinking air is '''comparatively smaller'''. This makes the new tangent to the polar closer to the best glide line in stationary air, such that the degradation of performance is less.
Conversely, it can be demonstrated graphically that water ballast is detrimental to performance (in terms of covering ground distance) when there is tailwind or rising air. However, gliders are not usually flown downwind for meaningful distances, and when rising air is present, a pilot will attempt to stay in it and soar, rather than moving to another place, so these effects are unimportant.
Experienced pilots sometimes argue that carrying water ballast improves thermalling performance. A mathematical establishment cannot be made unless a model exists to characterise the behaviour of a thermal (which indeed exists, but the validity is questionable in the author's opinion). It is worth pointing out that, very hand-wavingly we can say, if there is any benefit in carrying water ballast when thermalling, it will come from thermalling at a larger radius, rather than at a higher speed.
== Adjustments to the Analytical Polar: Headwind and Sinking Air ==
