Re: Aircraft speed and weight at cruise.

Date:         24 Oct 97 04:33:15 
From:         Brian Bishop <bish@stanford.edu>
References:   1
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> -A wing generates a lift value which is proportional to the air speed.

Lift (and drag) is proportional to velocity squared.
L=(1/2)(density)(velocity)^2(lift coefficient)(wing area)

> -The weight of an aircraft changes as fuel is exhausted during cruise.

Yes, quite a bit. For example, single-stage-to-orbit craft are roughly
85% by mass fuel. Not sure about planes.

> QUESTION:
>
> Assuming a LAX-SYD flight with no winds. Towards the end of the flights
> when the plane is much lighter, doesn't the lift provided by the wings
> exceed by quite a bit the lighter weight of the aircraft ?
>
> Is this change so trivial that it is not an issue, or do pilots take
> this into consideration (reducing speed to reduce lift or what ?) ????

It is a simple matter of trimming the plane. In essence, you lower the
coefficient of lift in the above equation. Note that it's not linear.

> Would a fully loaded plane not travel faster then a same plane but
> lightly loaded ?

In fact, a fully loaded plane would max out a slower speed. Passenger
aircraft usually fly close to the speed of sound (.8-.9 Mach) and are
bounded on the upper speed not by a shock wave forming off the nose, but
instead by a shock wave that forms over the wing. Shocks are killers of
efficiency, so you don't want them. Besides, you get nasty vibrations
out of them that aluminum structures (without an endurance limit) don't
like (crack propagation). To make lift, you must create circulation
around the wing which creates lower pressure (lift!) from increased air
velocity. Somewhere near the top of the wing, the air is moving fastest
and may be faster than the speed of sound. Here you get a shock. You
also get a shock in the adverse pressure gradient further back. The
result is a roughly triangular shape between sub- to supersonic shock
and the super- to subsonic shock and the wing skin. (You can sometimes
see this since the shocks the divider between discontinuous indices of
refraction.) So, back to your original question. To create more lift for
the heavier plane, you need a lower pressure on top of the wing. That
means faster air velocity. That means the shock comes sooner.