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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 ==
=== Governing equations from a force perspective ===
Hopefully you already understand how a glider can remain airborne, but just in case you are in confusion, consider an unpowered glider in unaccelerated flight in still air: three forces act on the glider, namely:
# Gravity (weight), pointing vertically downwards.
# Lift, pointing upwards and perpendicular to the flight path.
# Drag, pointing backwards and along the flight path.
By Newton's first law, in order for the glider to stay unaccelerated, these three forces must balance. Imagine the glider is flying horizontally. If this is the case, then the lift force must point vertically upwards. We then have a drag force pointing horizontally backwards with no force balancing it, because the other two are both in the vertical direction.
Therefore, the only way for the forces to balance is that, the glider cannot be flying in the horizontal direction. The flight path must be at an angle to horizontal. We shall denote this angle as \( \theta \). By experience, a glider in unaccelerated flight in still air keeps descending, rather than climbing. Therefore, we know the flight path is inclined downwards. We shall define this direction as positive \( \theta \).
With this made clear, the gravity (\( W \)) can be decomposed into two components, one to balance the lift (\( L \)), and one to balance the drag(\( D \)). The following relationship holds:
\[ W \sin(\theta) = D \]
\[ W \cos(\theta) = L \]
Dividing these two expressions, \(W\) can be eliminated, giving:
\[ \frac{L}{D} = \frac{1}{\tan(\theta)}\]
The quantity \( \frac{L}{D}\) is referred to as the '''Lift-to-Drag Ratio'''.
=== Governing equations from an energy perspective ===
