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# Static longitudinal stability - converting airspeed to lift coefficient

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# Static longitudinal stability - converting airspeed to lift coefficient

23rd Jun 2018, 12:03

Join Date: Jan 2013
Location: Central Europe
Age: 30
Posts: 12
Static longitudinal stability - converting airspeed to lift coefficient

Hello,

as some of you probably remember from my previous threads, I am currently working on my thesis related to flight testing. While describing steps for creating stick-fixed static longitudinal stability characteristics, I have encountered one little issue which I do not understand. Maybe you will be able to help me..

According to Kimberlin's "Flight Testing of Fixed Wing Aircraft", first step is to plot elevator position vs calibrated airspeed for each flight at different CG position. Based on the points you create the curves. Until now all clear. After that there is another step in which you plot elevator position vs lift coefficient CL (which is supposed to be obtained from airspeed).

I know that CL can be calculated from the lift formula (L = (1/2) d v2 s CL). Lift itself must equal the airplane's weight.. but that is true only for straight and level flight. In case of climb or descent, to know the lift we must know the angle of attack. If that is true, I do not know why Kimberlin does not mention it while describing parameters which must be recorded during actual flight test. And apparently flights are conducted in climb, cruise and approach condition. Am I missing something?

Enclosed you can see a pdf containing two screenshots - first one show the first and second step (converting airspeed to CL), the other one describes flight test method.

Thank you!

P.
Attached Files
steps and ft method.pdf (185.3 KB, 29 views)

23rd Jun 2018, 22:16

Join Date: Feb 2000
Location: UK
Posts: 13,454
No, you don't need AoA, you need the climb/descent angle, and weight. The angle is easily calculated from (true) airspeed and rate of climb or descent.

https://www.princeton.edu/~stengel/MAE331Lecture7.pdf

You may be misled by some textbooks that use alpha, rather than the more conventional gamma (or frankly just about any other greek letter!) to describe that angle, and thought it was referring to AoA. You might find it helps taking an hour or two to derive the equations from basic principles, which helps them make a lot more sense. Plenty of good textbooks will lead you by the hand through that - my copy's in the office and I'm at home (it being Saturday evening!) but IIRC Anderson's "Introduction to Flight" does this well and is presently a very popular book in many universities.

G

Last edited by Genghis the Engineer; 23rd Jun 2018 at 22:38.

24th Jun 2018, 09:26

Join Date: Jan 2013
Location: Central Europe
Age: 30
Posts: 12
Thank you Genghis! I only wonder why they did not mention it among other parameters to record during flight test.. There is airspeed, elevator position, longitudinal control force, fuel consumed (to calculate current weight) but no angle of climb / descent.

25th Jun 2018, 13:23

Join Date: Feb 2000
Location: UK
Posts: 13,454
There is no direct readout of climb / descent angle in any aircraft.

There is a direct readout of RoC/RoD (although VSIs aren't all that precise and it's better to derive it from altimeter and stopwatch). There is a readout of IAS, which you need to route through intermediate stages of CAS, EAS, to TAS.

The angle (within the local parcel of air that the aircraft's travelling in) is then determined easily enough from RoC and TAS.

G

27th Jun 2018, 12:30

Join Date: Apr 2004
Location: England
Posts: 25
Originally Posted by Genghis the Engineer
There is no direct readout of climb / descent angle in any aircraft.

G
The velocity vector or flight path marker symbology in many aircraft shows climb/descent angle.

27th Jun 2018, 16:40

Join Date: Oct 2017
Location: UK
Posts: 689
Lift itself must equal the airplane's weight.. but that is true only for straight and level flight.
In straight and level flight lift must exceed weight in a conventional aeroplane.

28th Jun 2018, 21:04

Join Date: Feb 2000
Location: UK
Posts: 13,454
The velocity vector or flight path marker symbology in many aircraft shows climb/descent angle.
(a) I'm not sure I'd trust that for flight mechanics research.

(b) I'm guessing that's based on GPS, which is definitely NBG for flight mechanics work, which you want to be based upon an understanding of what's going on in the parcel of air you're flying in at the time - not earth axes.

G

28th Jun 2018, 21:05

Join Date: Feb 2000
Location: UK
Posts: 13,454
Originally Posted by dook
In straight and level flight lift must exceed weight in a conventional aeroplane.
Errrr ?

G

29th Jun 2018, 08:23

Join Date: Oct 1999
Location: Nigeria
Age: 52
Posts: 4,249
b) I'm guessing that's based on GPS, which is definitely NBG for flight mechanics work, which you want to be based upon an understanding of what's going on in the parcel of air you're flying in at the time - not earth axes.
AHRS/IRS, surely?

29th Jun 2018, 11:04

Join Date: Oct 2017
Location: UK
Posts: 689
Genghis,

In a conventional (non canard) aeroplane, for longitudinal stability, the tailplane produces a downforce.

This effectively adds to the weight of the aeroplane.

d

29th Jun 2018, 13:32

Join Date: Feb 2000
Location: UK
Posts: 13,454
That's a very odd interpretation. Most of us class lift as the total net lift from wings, surfaces and airframe - not just the wing.

G

13th Jul 2018, 16:09

Join Date: Apr 2014
Location: London
Posts: 134
Originally Posted by Genghis the Engineer
That's a very odd interpretation. Most of us class lift as the total net lift from wings, surfaces and airframe - not just the wing.

G
I wonder if Dook means that the elevator produces downforce (or upforce) whereas the tailplane produces lift (which is what you are saying, G, in slightly different words).

13th Jul 2018, 17:30

Join Date: Feb 2000
Location: UK
Posts: 13,454
Well of course it does, but you still take total lift on the airframe, just as you take total mass, total thrust and total drag for determination of aircraft performance.

An aerofoil's Cl is not the same as the whole aeroplane's Cl. (The reference area mind you can be slightly problematic, but so long as you use the same figure for all calculations, that generally resolves itself.).

G

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