Regarding applying accepted Oswald Efficency factors in high G turns

[drgondog]

I posted this question in another thread but it has value in this one.

The rudder/elevator combination creates some interesting (potential)theoretical holes in applying Oswald efficiency factors to the manuevering models at low speeds versus cruising conditions in perfect trim.

It is the substance of my taking opposite sides from 'well known' applications of the Induced Drag portion of the Thrust=Drag equations. Raymer for example, is a well known author of Aerodynamics texts and uses (and applies) 'e' as an extension of lifting line theory but as near as I can tell does not account for the effects of the fuselage on spanwise lift distribution, nor does he extend to high AoA and the effects of changes in AoA increasing Viscous drag due to lift.

Oswald, when he developed and published his NACA paper NACA-TR-408 on this subject in 1932, clearly states "k (1/pi*e*AR) describes the variation of parasite drag with AoA and the increase of parasite drag over the minimum case of a wing with elliptcal lift"

His paper suggests various values for 'e' to apply to high and low wing a/c without futher delving into high AoA approaching stall - or complex asymmetric .flight conditions.

Beginning with Oswald's 1932 NACA papers through various texts applying 'e' to account for increased viscous/paraite drag due to planform and Lift Coefficient (changes to AoA) through many different derivations to better model theory to wind tunnel tests - I have never seen an extension to better account for an airplane in asymmetrical flight conditions at high AoA... such as a 360 turn.

Dick Shevell in "Fundamentals of Flight" does apply empirically developed contributions to both sweep and fuselage and planform efficiency as well as fuselage interference effects - for level flight. The charts he presented from Douglas Aircraft studies on the Douglas family of commercial air liners in level flight vs flight tests are impressive.

Using the Shevell approach and values for the P-51 yields an 'e' of .87 for example - which I believe might be good assuming no propeller 'complications'

Krishnamurti, Prabahudasar and Panda presented a paper "On the Upper Limits of the Oswald Efficiency Factor for an Airplane" in the Journal of Aero Society of India, Vol 53, number 4 which extrapolated very well the importance of the ratios and contributions of the horizontal stabilizer to the wing in the calculation of 'e' - proving that e may actually exceed 1.0

I suspect that increasing contributions of lift and drag surrounding a tail at a different AoA from the wing (immersed in downwash), which must change as the required deflections increase to maintain equilibrium, and are further subjected to the increasing turbulence (beyond normal flight rotating stream tube of prop wash) as separation inevitably increases on the wing - and vortex drag increases behind the wing - must change any previously accepted value of 'e' for that wing/body combination in level flight.

Ergo - applying 'e' = .8 or .85 (or any value), so many use to start a Performance discussion, has roots in level flight dash or cruise but must be carefully re-examined starting with level flight stall and really questions in high G asymmetric flight conditions.

Probably a better approach is to first examine 'e' when Thrust is supplied by jet engine so that variations in propeller efficiency may be eliminated at the beginning of the study.

Any thoughts?

[FLS]

What do you speculate the practical consequences, in % or actual values, would be in modeling high G turns?

[drgondog]

What do you speculate the practical consequences, in % or actual values, would be in modeling high G turns?

Apparently I am limited to 8o char in the 'reply' mode.  Simply, I expect that 'e' decreases considerably as a result of the elevator deflections and parasite drag increases beyond CDo

[drgondog]

What do you speculate the practical consequences, in % or actual values, would be in modeling high G turns?
[Specifically -   CDtotal = CDparasite + CDlift related +CDcompressibility
 
CDparasite not only contains the zero lift profile drag of the wing but also friction and pressure drag of the fuselage, tail surfaces and any other component exposed to the airflow.

CDlift releated contains not only the expression for drag due to the lift of the wing but also drag due to planform and twist.

CDcompressibility is wave drag which is present only for speeds aat or above drag-divergence number (few examples in WWII but do include top speed examples of P-51, Ta 152, P-47M/N, etc where you need to be careful in calculating CDo.

So, CDp=CDo+r*CL>>2 ----> where CDo is zero lift parasite drag of the airframe and r=empirically determined constant to account for lift releated VISCOUS drag which varies with AoA and includes the change to friction and pressure drag as the AoA increases.

CDi=(CL>>2)/(e*pi*AR) which is what we frequently use in our calculations ---> where e is Oswald Efficiency factor , first estimted (.7-.9) then validated via wind tunnel and flight tests.  This 'e' and associated values of ".8" is  an Ok factor and generally accounts for the lift and drag of a horizontal stabilizer in trimmed flight.

So, now CDtotal = CDo + (r+ 1/(pi*e*AR))*CL>>2


Lets go to next post below..to finish this out./quote]

[drgondog]

What do you speculate the practical consequences, in % or actual values, would be in modeling high G turns?
[ So, to continue
 
CDi=(CL>>2)/(e*pi*AR) which is what we frequently use in our calculations ---> where e is Oswald Efficiency factor , first estimted (.7-.9) then validated via wind tunnel and flight tests.  This 'e' and associated values of ".8" is  an Ok factor and generally accounts for the lift and drag of a horizontal stabilizer in trimmed flight.

So, now CDtotal = CDo + (r+ 1/(pi*e*AR))*CL>>2 (familiar) + CDcompressibility.

Classic Aero 'redefines' e to now account for 'r' and tells us to 'assume' a value of .8 (or thereabouts).  My question is "May we assume that wind tunnel tests and the associated design value for 'e' extrapolated as a function of CL vs AoA are in fact valid for high deflection angle elevator and rudder inputs, in which the relative AoA (and associated CL for both the wing will be presumed different in a banked high G turn near Stall?


Lets go to next post below..to finish this out./quote]

[drgondog]

Finally - I just don't have a real grasp of a % change which should be made.

[drgondog]

Finally - I just don't have a real grasp of a % change which should be made.

This is an excellent reference with sound approaches to develop values of 'e' which can be extrapolated when AR, CDo are known - pay particular attention to the plots and equations under Induced Drag chapter for Lift Dependent Drag Items.

http://adg.stanford.edu/aa241/AircraftDesign.html

Short answer to my belief system -

 'e' for Mustang with extrememly low Drag wing/airframe and correspondingly low CDparasite must be significantly better than a Me 109G with similar AR for symmetrical flight conditions.. and that little research has been performed to estimate change in 'e' due to high angles of attack and asymmetrical flight conditions - while immersed in a turbulent/rotational stream tube behind the prop disk.

Next - never strive for a CDo based on high speed/high altitude speed runs for such a/c as Mustang and Ta 152 etc - which are all creeping into .65+M range at 25K+ altitude... until you have eliminated contribution due to drag rise.  Meaning go for SL data to develop CDo... then you can go back to 25K to find CDm.

[FLS]

The 80 character limit only applies to the subject line.

[dtango]

The rudder/elevator combination creates some interesting (potential)theoretical holes in applying Oswald efficiency factors to the manuevering models at low speeds versus cruising conditions in perfect trim....

Ergo - applying 'e' = .8 or .85 (or any value), so many use to start a Performance discussion, has roots in level flight dash or cruise but must be carefully re-examined starting with level flight stall and really questions in high G asymmetric flight conditions.

Probably a better approach is to first examine 'e' when Thrust is supplied by jet engine so that variations in propeller efficiency may be eliminated at the beginning of the study.

Any thoughts?

Several thoughts for you:

1) Accepted values for e between .7-.9 applies for low angle of attack flight.  At higher angles of attack viscous induced separation becomes a factor.  At higher aoa using these e values without accounting for increases in lift dependent viscous drag is not appropriate.  The result on drag is that lift dependent drag due to viscous forces increases with increasing aoa.

2) Because this lift dependent drag is a function of viscous induced separation of the boundary layer I don't know of a way to mathematically estimate this without some serious CFD analysis because details of what's happening in the boundary layer would need to be modeled.

3) Variation of e or lift dependent viscous drag can be obtained however from drag polars of wind tunnel or flight tests for specific aircraft.

4) AH models this variation of lift dependent viscous drag.  In fact for the P-51 Pyro has posted the data he has already:



5) One way to account for all of this is to vary e.  Variation of e with aoa applies for all aircraft including jets.

[drgondog]

Several thoughts for you:

1) Accepted values for e between .7-.9 applies for low angle of attack flight.  At higher angles of attack viscous induced separation becomes a factor.  At higher aoa using these e values without accounting for increases in lift dependent viscous drag is not appropriate.  The result on drag is that lift dependent drag due to viscous forces increases with increasing aoa.

We are pretty much in agreement - having said that, there is a body of literature (Raymer and others) that stipulate that the viscous lift due to drag is in fact accounted for in 'e' as I expressed it above...I have an MS in Aero but candidly this is something I never questioned either in academics or industry until I started playing with 'performance models' of WWII a/c.  It was then that I started playing with horizontal stab area/wing area and really started thinging about lift/drag due a significantly deflected elevator (and rudder) as well as started questioning a 'constant' e. 

2) Because this lift dependent drag is a function of viscous induced separation of the boundary layer I don't know of a way to mathematically estimate this without some serious CFD analysis because details of what's happening in the boundary layer would need to be modeled.

Agreed again -and the complexity of asymmetric flight immersed in a turbulent and rotational prop stream tube near stall is another model that I doubt can be set up for a Navier Stokes solution

3) Variation of e or lift dependent viscous drag can be obtained however from drag polars of wind tunnel or flight tests for specific aircraft.

I did a literature search to see if I could find papers on tests and data regarding asymmetric flight profiles in high AoA but could not find them.  Everything I did flind was 'normal AoA variations - doesn't mean the tests aren't out there, just that I was unsuccessful!

4) AH models this variation of lift dependent viscous drag.  In fact for the P-51 Pyro has posted the data he has already:

(Image removed from quote.)

5) One way to account for all of this is to vary e.  Variation of e with aoa applies for all aircraft including jets.

I absolutely buy the concept, just don't have an immediate approach at hand to apply to the WWII aircraft of interest.  Good to chat!

[drgondog]

I absolutely buy the concept, just don't have an immediate approach at hand to apply to the WWII aircraft of interest.  Good to chat!

Brain fart - I meant to say 'viscous drag due to lift' not 'viscous lift due to drag'

[Stoney]

But what amount of variation would we be looking at here, or perhaps I should say, what would be the perceptible difference in performance?  Large, small, or unknown?  Obviously, some sort of approximation has to be made for some characteristics that are beyond the scope of a flight model.  As long as the context of those approximations are always stated when presenting theoretical performance data...

[dtango]

It's significant at high aoa Stoney.  For example just look at the P-51 graph above.  AHT has CD for the P-51D at .0176 for level flight.  According to Pyro's data at Cl of 1.0 the incremental drag due to viscous separation is about .016 by itself so the viscous effects by itself nearly doubles CD.

[drgondog]

It's significant at high aoa Stoney.  For example just look at the P-51 graph above.  AHT has CD for the P-51D at .0176 for level flight.  According to Pyro's data at Cl of 1.0 the incremental drag due to viscous separation is about .016 by itself so the viscous effects by itself nearly doubles CD.

Dtango - do you have access to the written part of NA-46-130? (and thanks for posting that).

To Stoney - just a point of reference to dtango's comment about parasite drag doubling at CL=1.0, the  approximate CLmax for a 9600 pound P51D is ~ 1.7  so extension of the drag polar from 1.0 to 1.7 that he presented takes it far above 'delta' .016. 
 

[dtango]

drgondog: I'd be happy to send it to you but in this case I don't have it .  I wish I did.