Why doesn't aircraft weight affect descent angle in a gliding flight

[Leo Liu]

It's a homework question, but I feel like it fits better in this forum. The solution fails to convince me because C_D and C_L can be both written in terms of weight:
$$C_L=\frac{2W}{\rho v^2 S}$$
$$C_D=C_{D0}+k_1 C_L(W)+K_2 C_L(W)^2$$

Question:

Solution:

Any insight will be appreciated.

 

[Lnewqban]

Please, see:
https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/lift-to-drag-ratio/

https://www.av8n.com/how/htm/aoa.html#sec-weight-drag-speed

https://en.m.wikipedia.org/wiki/Lift-to-drag_ratio

 

[Lnewqban]

The thing is that lift and lift-induced-drag are two faces of the same coin.
Within certain limits of angles and speeds, useful lift can’t exist without the useless drag induced by the wings.

If more lift is needed to keep a heavier load flying at the same speed, proportionally more lift-induced-drag will result (increased angle of attack).
If speed is instead increased to achieve more lift, more parasitic drag will be induced (increased skin friction and shape drag).

A jumbo jet has a gliding ratio as good as a very light airplane.
Both have an optimal speed/AOA for which both drags reach a minimum value, resulting in more economic horizontal flight (less fuel is used for same covered distance).

Please, also see:
https://en.m.wikipedia.org/wiki/Lift-induced_drag

https://en.m.wikipedia.org/wiki/Parasitic_drag

 

[Flyboy]

There's another, more simplified answer to the question: a stabilized approach usually has a set angle for a given runway, called glideslope. Pilots will usually have external visual references, like VASI lights or the "sight picture" out the windshield, to help them line up on glideslope, and larger airports have radio beacons to help pilots alight with that slope in poor visibility. ILS systems are more expensive, though, and generally only appear at airports with frequent high-performance and turbine powered aircraft operations.

 

[russ_watters]

There's another, more simplified answer to the question: a stabilized approach usually has a set angle for a given runway, called glideslope. Pilots will usually have external visual references, like VASI lights or the "sight picture" out the windshield, to help them line up on glideslope, and larger airports have radio beacons to help pilots alight with that slope in poor visibility. ILS systems are more expensive, though, and generally only appear at airports with frequent high-performance and turbine powered aircraft operations.

That answer is not correct. The "glideslope" is perhaps incorrectly named as aircraft are not truly gliding but are using controlled power and flaps to achieve the desired descent angle. The OP was talking about actual gliding.

The glideslope varies by airport, although it is usually close to the clean glide ratio/angle for many planes. However during actual approach and landing with the plane in a dirty configuration with flaps in landing gear down the glide ratio of the plane is much worse or steeper than when clean. So if a plane loses its engine(s) on final approach it will not be able to glide to the runway.