119
edits
Changes
From CUGC Wiki
glide ratio and L/D
=== Governing equations from an energy perspective ===
An alternative way to think about this is from an energy perspective. Because the drag force wants to slow down the glider and take its kinetic energy away, the glider must keep descending, so that it releases its gravitational potential to make up for the loss, otherwise it cannot remain at the same speed. Consider riding a bicycle: if you stop pedalling on level ground, you will gradually slow down and eventually stop, this is because drag force steals your kinetic energy away and you have no means of replenishing it. However, if you cycle downhill, you will not stop even if you do not pedal.
Therefore, we conclude that a glider flies downhill. This is in agreement with the conclusion of the previous section. We can borrow the notation and call the slope angle of this imaginary hill \( \theta \). Geometrically, if we travel for a unit distance on the face of the hill, then in the horizontal direction the distance travelled will be \( \cos(\theta) \) and in the vertical direction the height drop will be \( \sin(\theta) \).
From an energy conservation point of view, the following expression holds (it means the energy that the drag force uses up equals to the energy the gravity must provide):
\[ D \times 1 = W \times \sin(\theta) \]
This is the same result as in the last section.
=== Glide ratio ===
The glide ratio is a measurement of the efficiency of the glider. It means 'how many feet can the glider travel forward for every foot of altitude drop?' If a glider has a glide ratio of 50:1 (fifty-to-one), it means the glider is capable of travelling 50 feet forward for every foot of altitude drop, the same thing applies in meters, etc. We want the glider to travel as far as possible while losing minimum altitude, therefore, a larger glide ratio is favourable over a smaller one.
This measurement we can vaguely call ''''performance'''', although strictly speaking this is only one aspect of it. We can say glider A (50:1) has a higher performance than glider B (30:1), for example.
In the last section, we concluded that, for each unit distance travelled on the hill, the horizontal distance covered is \( \cos(\theta) \) and the vertical distance covered is \( \sin(\theta) \). Therefore, the glide ratio is:
\[ \textrm{Glide ratio} = \frac{\cos(\theta)}{\sin(\theta)} = \frac{1}{\tan(\theta)} = \frac{L}{D}\]
This is a '''very important''' result. It is also worth noting that, up until now, we have made no approximations.
