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Old 23rd October 2006 | 22:53
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john_tullamarine
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From: various places .....
Va and weight ..

The FlightLab notes look OK but I wouldn't spend too much time with the other two links. Nor would I spend too much time trying to tie Va and momentum.. apart from anything else, speed and momentum are different animals

It may help to look at the basics of where the equations come from .. for an aircraft in accelerated flight, there will be a load factor (n = L/W or think g-loading as being close enough) other than 1.0. The normal pilot lift equation can be put

L = nW = CL . 1/2 . rho . V2 . S

ignoring the L term and rearranging the other two terms for our consideration of interest

nW = CL 1/2 rho V2 S

V2 = (2 nW) / (CL rho S)

Vstall2 = (2W)/(CLmax rho S) . n

Vstall = constant . SQRT(n)

or, looking at the W term for constant load factor

Vstall = constant . SQRT(W)

End result is that the stall curve on the V-n diagram (g-load on the vertical axis and speed on the horizontal) is a curve as shown in the FlightLab notes (and any garden variety engineering text book on the subject).

The secret is to look at the various (similar) curves for different weights and then plot the limit load factor (which doesn't vary as it is locked into the design basis for the Type). The lower weight curves are to the left and the intersection of individual curves and the limit load factor occur at progressively lower speeds for lower weights. Hence we can say that the real world Va will reduce at lower weights.

Be wary of confusing wing bending strength margins at lower weights and maximum attachment load capability for isolated lumps of stuff in the aircraft .. the published limit load factor is the limit the pilot can use for routine operations, regardless of weight. In any case you shouldn't be going there too often as the (unmonitored) effect on fatigue life is going to bite someone further down the track ..

Other considerations ..

Be wary of playing fighter pilot (and I'm sure that most of us have been in the back seat of a 172 or similar with some idiot doing stupid things in the front seat .. my first fixed wing flight was just such an experience ..) regarding the degree of grunt put into pulling the control column back .. there is a phenomenon, often referred to as accelerated stall (but different to the usual term referring to increased stall speed with load factor) where the wing can go considerably above the "normal" stall incidence due to the formation of a vortex on the upper surface. This is only a problem with very high pitch rates (>70 deg/sec as I recall from a paper I read quite a while ago on the subject) but can bite you if your aircraft is so capable.

Be careful with rolling pullups .. the notes refer to the need to unload before rolling .. you can see this in practice at every airshow where a high performance fighter puts on a good display .. the pilot unloads in pitch very positively prior to rolling into the next part of the manoeuvre sequence .. if it's good enough for the aces, then it's good enough for us plodders ..

The AA accident shows very clearly the problem associated with a little knowledge .. if one wants to be other than reasonably gentle with a civil design then one needs to know a fair bit about just how the thing was certificated in the first place. Another area which can bite is the stall departure .. over the years the details of just how the stall was looked at in the certification for light aircraft has varied and some aircraft can be a little vicious if "held" into the stall rather than unload at the indication of stall .. I recall an instructor TP who related the tale of one particular higher performance light twin Type which, when held into the stall, had a desire to flick into an inverted spin .. hadn't be a certification consideration.
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