Sustained Turn Performance Of Piston Engine Aircraft

Timppa said:

Since you brought this in public:
In one post...and he is gone. First HoHun and now badger45. I can tell when somebody knows his stuff, and badger45 was one. So thanks a lot for ruining a good conversation.

Click to expand...

A good conversation is one that does not involve insults and childish name calling. We do not tolerate that on this forum.

Everyone has a bad day, and we mods like to give everyone the benefit of the doubt. When you ignore a mods warnings and refuse to remain civil, that is when action is taken.

If you consider conversations poluted with insults and childish behavior to be good conversations, well...

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?

Aircraft Design, Synthesis and Analysis

This is an EXCELLENT course on aircraft design from Stanford..

Last - but not least on the in depth research front. dtango on AcesHigh posted this 1946 drag polar 'delta' as a function of CL
Questions regarding applying accepted Oswald Efficency factors in high G turns

What is very obvious is that as AoA increases and CL ---> 1.0 the corresponding CDp increases by .016 or roughly double CDo value of .0176.

This is why accepted values of 'e' for low to middle ranges of AoA should fail miserably in accounting for increased parasite drag due to lift as aircraft approach CLmax in high G turns.

So, for a summary:
1. for high speed a/c like P-51B/D/H and Ta 152 and P-47D/M/N and Me 109K you may NOT extract a valid CDo by the classic gamer approach of picking the high speed velocity/altitude and rated Bhp to solve T=D=Parasite Drag + Induced Drag and assume that Compressibility Drag = zero. If you do, you will overstate CDo. You must get the low altitude high speed runs to 'eliminate' compressibility drag factor.

2. when contemplating turn performance, 'e' should NOT be that same as for low AoA symmetrical flight.

3. Last but definitely not least. As presented in the post immediately above, it is clear that the CDo calculated for Parasite Drag in the T=DRAGparasite+DRAGinduced+DRAGcomp will depart rapidly when high AoA increases viscous drag due to lift (i.e form drag due to separation, etc.). You can see for a CL approximately 60% of CLmax for a Mustang, that Parasite Drag increased .016 ---> from .0176 to a new 'CDo" of .033 or almost double normal flight conditions.