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→Best Glide
\[ V_{BG}=(\frac{4k \omega^2}{\pi A \rho^2 C_{D0}})^{\frac{1}{4}}=(3)^{\frac{1}{4}} V_{MS}=1.3161 V_{MS} \]
Therefore, the best glide speed is always 31.6% higher than the minimum sink airspeed according to our analysis. Slight discrepancies may arise in reality due to the approximations we have made, mainly the aerodynamic ones.
From the expression for \( V_{BG} \) given above, it is evident that:
# \( V_{BG} \propto \sqrt{\omega} \), such that the best glide speed will increase as the wing loading increases, by means such as using water ballast.
# Increasing the aspect ratio can reduce the best glide speed.
# Decreasing \( C_{D0} \) can increase the best glide speed.
It is also of interest to calculate the best '''possible''' performance of the glider, which, by definition, happens at the best glide speed. The algebra proceeds as follows:
\[ V_{BG}^2 = \sqrt{\frac{4k}{\pi A C_{D0}}} \frac{\omega}{\rho} \]
This is to be substituted into:
\[ (\frac{V_S}{V})_{\text{best}} = \frac{\rho}{2 \omega} C_{D0} V_{BG}^2 + \frac{2 k \omega}{\pi A \rho V_{BG}^2} \]
To yield:
\[ (\frac{V_S}{V})_{\text{best}} = 2 \sqrt{\frac{k C_{D0}}{\pi A}} \]
Or, alternatively (to give the large number like 40 or 50 that we are familiar with):
\[ \text{Best Glide Ratio} = 0.5 \times \sqrt{\frac{\pi A}{k C_{D0}}} \]
This is a '''very important''' result, as it gives all the factors underpinning the best performance of a glider (in a particular configuration):
# '''The wing loading does not change the best performance'''. Therefore, a 50:1 glider will be 50:1 with a light pilot or a heavy pilot, or with or without water ballast. This is, however, based on our model, and in reality more factors may come into play. For example, if the wing loading is high, then the best glide speed increases accordingly and the change in Reynolds number may have some effect. Alternatively, the different structural deflections of the wings may produce subtle differences in the aerodynamic geometry. Nevertheless, this is the rationale underpinning the use of water ballast: it does not degrade aerodynamic performance.
# 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?
