Regarding applying accepted Oswald Efficency factors in high G turns

[gripen]

Go look at the charts (Oswald's Report 408, charts 24) on page 25 which are flight test results for various German a/c.  Note the rapid change in CDp with respect to CL @ ~ 1.0 with no further extrapolation (other than a huge gradient) past CL=1 .

For the turning CL's experienced in high G manuevers, the CL's approach CLmax, which for most WWII fighters is between 1.4 and 1.7 for zero flap manuever.  

It is clear from the charts that CDp is changing far more rapidly than CDi above CL=1.0

I suggest that you actually read the text of your source before forming an argument; the CDi in these charts is an ideal case value ie lift distribution is assumed to be elliptical and all the additional drag from what ever source (induduced or parasitic) is lumped to CDp. In other words the term CDp contains also all the induced drag beyond perfect elliptical lift distribution.

[drgondog]

I suggest that you actually read the text of your source before forming an argument; the CDi in these charts is an ideal case value ie lift distribution is assumed to be elliptical and all the additional drag from what ever source (induduced or parasitic) is lumped to CDp. In other words the term CDp contains also all the induced drag beyond perfect elliptical lift distribution.

I agree that CDi (not corrected by e as denoted by solid line) is a calculated value assuming an eliptical lift distribution - and that the CDp is derived by CD-CDi, where CD total is flight test data in each of the 8 plots represented.  What I see is a sharp gradient of CDp as f(CL) and no further data points to help us understand data at say 1.3 to 1.6.  This is the substance of my comment that you chose to interpret as a 'failure to read'

So, repeating the argument in more detail.  1.) CDp as presented by Oswald does include drag terms above and beyond induced drag.  2.) CDi in the solid line is in fact CDi calculated based on 'span efficiency' as a correction to a pure elliptical planform. 3.)His arguement, elegant for CL at or below 1.0, is that the CDp represented by the dotted line plot does include 'other drag terms due to Induced drag... and therein lies the 'theory of e'.

In other words, Oswald has no thesis for 'e' for high AoA/High CL and does not present data or conclusions to account for a 'correction factor e'prime' to further account for increases to viscous drag on the fuselage and other components immersed in an increasing wake influenced by boundary layer separation, adverse pressure gradients and increased friction drag.

My thesis is threefold. 1.) there is a departure point where a constant 'e' is no longer valid, and 2.) that that the increased 'drag due to lift'  such as all the viscous and friction drag associated with increases to AoA beyond CL~1.0  is neither linear nor predictible by the methods suggested by Oswald, and 3.) that the use of 'e' in CDi calcs for high G manuevers for WWII fighters in 'games' is - simply - inaccurate .

You and I may agree to disagree but I will keep it civil.

[dtango]

@gripen You bring up a good point regarding Pyro's NAA data on the linearity.  I assumed that was additional drag beyond e assumed in the induced drag already.  It could be that the chart is representation of linear e as you suggest.  As drgondog says, it might be some schmeud methodology for accounting for it.

@stoney drgondog answered your question already.  The point is boundary layer separation occurs not only along the wing but other parts of the aircraft too.  It's possible that the wing dominates with the lift dependent viscous drags, but it's also probable that fuselage & other parts can play significant enough of a factor as well.  That's the tricky thing about the boundary layer.

[gripen]

@gripen You bring up a good point regarding Pyro's NAA data on the linearity.  I assumed that was additional drag beyond e assumed in the induced drag already.  It could be that the chart is representation of linear e as you suggest.

My point was that we can't explain the additional drag as function of parasitic drag using the Pyro's chart, firstly because it gives almost linear response and secondly because the scale of the effect is far too small; even at Cl 1.0 it's below 15% of total drag.

However you have allready posted a chart which contains the needed information for changing the polars (Cd0, Clmax and e) according to mach number:



Oswald's system is basicly a stochastic model of drag where entire additional drag caused by increased lift coefficient (complex phenomena) is lumped together to a simple term of e. It's not a perfect model but it has been proven to work well at low speeds. Obviously it does not work well when the mach number increases but we can extend it by adding some additional factors like mach number etc.

The reasons for the increased drag are, of course, even more complicated than at low speeds and we can argue about the explanations until the end of the day. However, based on the flight and wind tunnel tests we have some idea how the polar behaves when the mach number increases. And based on this knowledge we can form a relatively simple model to simulate an extremely complicated phenomena. In other words, we have limited knowledge why all this happens but we know the outcome, so we can model the phenomena in some degree.

[drgondog]

My point was that we can't explain the additional drag as function of parasitic drag using the Pyro's chart, firstly because it gives almost linear response and secondly because the scale of the effect is far too small; even at Cl 1.0 it's below 15% of total drag.

The reasons for the increased drag are, of course, even more complicated than at low speeds and we can argue about the explanations until the end of the day. However, based on the flight and wind tunnel tests we have some idea how the polar behaves when the mach number increases. And based on this knowledge we can form a relatively simple model to simulate an extremely complicated phenomena. In other words, we have limited knowledge why all this happens but we know the outcome, so we can model the phenomena in some degree.

My points and debate have focused not on high mach numbers where compressibility (and drag divergence) occur, it has always been about lower range speeds in high G, asymmetric flight conditions.

Revisit what I posed in the first post -

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 questioned in high G asymmetric flight conditions. I debate that an Oswald factor derived and explained and correlated with level flight, 1 G, symmetric flight conditions is equally valid for the turn manuever models applied to so many game simulations.

Period. The end.