# Increasing the aspect ratio of the wing is an effective (and, in fact, easiest) way to improve the best performance, as the best glide ratio scales with \( \sqrt{A} \). This is the reason why high performance gliders have slender wings.
# Improving aerodynamic design, such that \( C_{D0} \) or \( k \) is reduced, can improve the best glide ratio as we would intuitively expect. However, modern advancement in aerodynamics has been agonisingly slow and you realise that there is not much potential to be released by comparing a fibre glass glider built in the 1980s with a modern one. What differences do you spot?
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.
From a geometric 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 view, the above solution process polar is equivalent dictated only by the '''best glide speed''' and the '''sink rate at best glide''', but, as shown previously, both quantities are proportional to finding a ray from \( \sqrt(\omega) \). Therefore, as the wing loading changes, the polar curve '''scales''' around the origin that with \( \sqrt(\omega) \) but keeps its shape. Because the best glide is a tangent to the polar curve, 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. You should ask an instructor This is difficult to demonstrate 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 you 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 reinforce the understandingbest glide line in stationary air, such that the degradation of performance is less. This geometric method Conversely, it can be demonstrated graphically that water ballast is useful detrimental to performance (in terms of covering ground distance) when more factors there is tailwind or rising air. However, gliders are taken into accountnot usually flown downwind for meaningful distances, and when rising air is present, such 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 an analytical solution carrying water ballast improves thermalling performance. A mathematical establishment cannot be obtained easilymade 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 ==
