Explain this and win the prize!

[joeblogs]

If you read through all of the derivations, you see e is defined as a correction to parasitic drag (which is independent of the coefficient of lift while induced drag is not) that results when the planform is not ellipitcal - hence the reference to Munk's span adjustment. In all the subsequent derivations, span is adjusted by a factor (k) that reflects this.

At the end of the day the effect of this is a change in a scaler in an equation that is, among other things, a function of span. Hence the function is not soley deterimined by the aspect ratio.

Yes the function can be inverted to define the aspect ratio as a function of e, but that wouldn't mean that aspect ratio is a function of e alone.  

The fact that one must assume a particular planform-rectangular with a specific taper-in order to draw a graph of the function makes this clear. One could assume different planforms and draw different graphs. The graphs would look different even if the aspect ratio was the same.

Grippen asked is aspect ratio a sufficient statistic to calculate Oswald's e?  The answer is clearly no.

-blogs

Originally posted by Crumpp
Gripen is not correct.  An instructor that teachs aeronautics explained it to him.

Read the third paragraph down and it explains Oswald's e factor and it's use.

http://naca.larc.nasa.gov/reports/1933/naca-report-408/index.cgi?page0001.gif



Now check out the induced drag formula.

As Badboy explained:

 

And for using AR as part of the formula to solve for "e":



Crumpp

[Crumpp]

Yes the function can be inverted to define the aspect ratio as a function of e, but that wouldn't mean that aspect ratio is a function of e alone.

Correct.

Nobody is claiming it is either.

Crumpp

[dtango]

Boy, I've missed the fun!

Let me give it a shot at answering the question.

The answer is yes with a caveat of depending on how accurate you want to estimate e factor.

The way I understand that it works the way it does is because Prandtl's lifting line theory makes certain assumptions that ignores the differences between different planform shapes.  

"In particular, the lifting-line model ignores the effect of chordwise distribution of vorticity on the downwash distribution since all the vorticity generated at a given spanwise location has been collasped to a single point....

....While lifting line theory is useful for approximating the performance of unswept, high-aspect-ratio wings once the chord distribution is fixed, the method is unable to account for any aerodynamic difference between wings due to different planform shapes."
(NASA-CR-191274 Analysis and Design of Planar and Non-Planar Wings for Induced Drag Minimization, 1992)
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930004275_1993004275.pdf

From what it appears to me this was understood but the impact of which was largely ignored because the results are good enough.

"For studies requiring a higher degree of accuracy, lifting-surface theories have been used [as opposed to lifting line theory], but generally it has been found that the additional complexity of these methods has not sufficiently improved the predictions to warrant common use." (NACA Report 921 - Theoretical Symmetric Span Loading at Subsonic Speeds for Wings Having Arbitrary Plan Form).
http://naca.larc.nasa.gov/reports/1948/naca-report-921/naca-report-921.pdf

By the way, I've seen in from other sources but explicitly in my copy of Raymer (Aircraft Design: A Conceptual Approach) he gives as one of the methods of estimating e for straight wing aircraft as:

e = 1.78(1- .045*AR^.68) - .64

The basis for this equation comes from a report I don't have access to which appears to have derived the equation basis empirical results from actual aircraft.  ("Subsonic Drag Estimation Methods" Cavallo, B., U.S. Naval Air Development Center Rept NADC-AW-6604, 1966.)

Anway, that's my attempt at an answer to the question!

Tango, XO
412th FS Braunco Mustangs

[gripen]

dtango,
Ah, now I see from where the formula in the Zigrat's spreadsheet comes from:

e=1*1,78*(1-0,0455*AR^0,68)-0,64

Give me your e-mail.

Regarding accuracy, these AR based formulas seem to give rather high e factor. When I have moretime I'll study couple more drag polars.

gripen

[dtango]

gripen:

dytong@nstci.com

Regarding the accuracy of e prediction using the above formula, I'm certainly no expert on the matter and the thought of using navier-stokes or panel methods for estimating this stuff makes my head swim.

Whatever the case, this is what Raymer states:

"Numerous estimation methods for e have been developed over the years, such as those by Glauert and Weissinger.  These tend to produce results higher than the e values of real aircraft.  More realistic estimation equations based upon actual aircraft (Ref 45.) are presented below."

Ref 45 is the NADC document and immediately following the above text are formulas - one for e of straight wing aircraft and one for e of swept wings.

I've seen the e formulas in question listed in several other aerodynamics text as well but never really understood how the equations were derived.

I'd be very curious to get a look at the NADC document to see how they boiled it down.

Tango, XO
412th FS Braunco Mustangs

[madness]

Originally posted by gripen
Well, if we have no idea about taper ratio, there is no way we can estimate the e factor with the aspect ratio only. However Badboy's poin't is quite sensible; most rectangular winged WWII fighters had quite similar taper ratio so in many cases generalized formula do quite well.

I have calculated some e factor data from the drag polars I have. These are e factors for whole airplane as Oswald and Perkin&Hage handle it:

Bf 109G, this is from the VL (Finnish State aircraft factory) drag polar:

Cl 0,1 => 0,741658161
Cl 0,2 => 0,798708788
Cl 0,4 => 0,769126981
Cl 0,6 => 0,759747384
Cl 0,8 => 0,787352739
Cl 1,0 => 0,769126981
Cl 1,2 => 0,713350597
Cl 1,4 => 0,619327448

The average is about 0,75

I have also a polar from Messerschmitt AG (I had to approximate Cd0):

Cl 0,1 => 1,038321425 (not in average)
Cl 0,2 => 0,83065714
Cl 0,3 => 0,778741069
Cl 0,4 => 0,755142854
Cl 0,5 => 0,70156853
Cl 0,6 => 0,692214283
Cl 0,7 => 0,696955477
Cl 0,8 => 0,692214283
Cl 0,9 => 0,7067566
Cl 1,0 => 0,711179058
 
The average 0,73

Mustang, RAE wind tunnel data:

Cl 0,6 => 0,789174119
Cl 0,4 => 0,814631349
Cl 0,2 => 0,717431018

The average is about  0,77

I also tried to calculate from the NACA 916 but there is so much varition that sensible analysis seems to be quite impossible; the e factors varied from 0,5 to 1,3 or something.

Regarding prizes; well I think the answer is not possible but in certain conditions it might be possible as Badboy pointed out.

So I think I'll send the prize to Angus and Blogs and Schutt will receive the Bonus, so post your adress and I'll send the docs. If Badboy is listening I can send both documents to you too.

gripen

Am I the only one that has absolutley no idea what all that stuff is? Im lost LOL

[dtango]

madness:  hehe

Those are values of Oswald efficiency relative to a given angle of attack (lift coefficient).

Gripen's point is that looking at the drag polars the values for oswald efficiency doesn't quite square with NACA report 916 nor with the method of estimating oswald efficiency factor using an equation based primarily on aircraft wing aspect ratio.

Tango, XO
412th FS Braunco Mustangs

[joeblogs]

The impression I get from the handful of sources I looked at is that the adjustment for departures from an elliptical lift distribution doesn't vary all that much among monoplanes of the 30s and 40s, but it does vary. Now I realize I could have that wrong.

So in terms of absolute efficiency of a wing, relying soley on aspect ratio to calculate induced drag may not be too bad. Problem is that when you compare two planes, it's the relative differences that matter. It is then very hard to say whether a  difference in this parameter between two wings is going to decide whether one plane will do something better than another.

But this is largely a distraction from the main point I made at the start. The wing cross section, or profile, is the primary determinant of parasitic drag. In the total drag calculations we've been dragging around, we are treating this as a constant (and ignoring it). This parameter is going to vary across wings even with the same aspect ratio and it will affect the relationship between lift and total drag.

-Blogs

Originally posted by dtango
Boy, I've missed the fun!

Let me give it a shot at answering the question.

The answer is yes with a caveat of depending on how accurate you want to estimate e factor.

The way I understand that it works the way it does is because Prandtl's lifting line theory makes certain assumptions that ignores the differences between different planform shapes.  

"In particular, the lifting-line model ignores the effect of chordwise distribution of vorticity on the downwash distribution since all the vorticity generated at a given spanwise location has been collasped to a single point....

....While lifting line theory is useful for approximating the performance of unswept, high-aspect-ratio wings once the chord distribution is fixed, the method is unable to account for any aerodynamic difference between wings due to different planform shapes."
(NASA-CR-191274 Analysis and Design of Planar and Non-Planar Wings for Induced Drag Minimization, 1992)
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930004275_1993004275.pdf

From what it appears to me this was understood but the impact of which was largely ignored because the results are good enough.

"For studies requiring a higher degree of accuracy, lifting-surface theories have been used [as opposed to lifting line theory], but generally it has been found that the additional complexity of these methods has not sufficiently improved the predictions to warrant common use." (NACA Report 921 - Theoretical Symmetric Span Loading at Subsonic Speeds for Wings Having Arbitrary Plan Form).
http://naca.larc.nasa.gov/reports/1948/naca-report-921/naca-report-921.pdf

By the way, I've seen in from other sources but explicitly in my copy of Raymer (Aircraft Design: A Conceptual Approach) he gives as one of the methods of estimating e for straight wing aircraft as:

e = 1.78(1- .045*AR^.68) - .64

The basis for this equation comes from a report I don't have access to which appears to have derived the equation basis empirical results from actual aircraft.  ("Subsonic Drag Estimation Methods" Cavallo, B., U.S. Naval Air Development Center Rept NADC-AW-6604, 1966.)

Anway, that's my attempt at an answer to the question!

Tango, XO
412th FS Braunco Mustangs

[Crumpp]

The basis for this equation comes from a report I don't have access to which appears to have derived the equation basis empirical results from actual aircraft. ("Subsonic Drag Estimation Methods" Cavallo, B., U.S. Naval Air Development Center Rept NADC-AW-6604, 1966.)

A friend of mine is a Test pilot for the U.S. Naval Air Development Center.  He is coming to visit soon.  In fact he hooked me up with one his professor's in college who worked on the V2 program in WWII.  I will be interviewing his professor and some other contacts who worked at Rechlin for my book.

I will see if he can't dig up a copy of that report and email it to me.  

Crumpp

[Crumpp]

This parameter is going to vary across wings even with the same aspect ratio and it will affect the relationship between lift and total drag.

Exactly, if I understand it correctly it will vary with the twist of the wing, shape of the leading edge, and the taper ratio among other things.

The thought of calculating all that seems rather daunting!

Seems though that the more detailed the analysis, the more Davids Lednicer's conclusions seem correct.

Crumpp

[gripen]

Originally posted by Crumpp

Seems though that the more detailed the analysis, the more Davids Lednicer's conclusions seem correct.

Hm... I wonder what Lednicer's conclusions has to do with the subject of this thread? He calculated the span loading and concluded that the loading distribution of the Spitfire is "not elliptical, though it is probably the most optimum of the three aircraft from the induced drag standpoint". He did not determine Oswald's efficiency for the wing nor for the whole aircraft.

gripen

[Angus]

That's what's so fascinating with aerodynamics.
It's so "twisty".
Nothing is just perfect in all matters.

[Crumpp]

Hm... I wonder what Lednicer's conclusions has to do with the subject of this thread? He calculated the span loading and concluded that the loading distribution of the Spitfire is "not elliptical, though it is probably the most optimum of the three aircraft from the induced drag standpoint". He did not determine Oswald's efficiency for the wing nor for the whole aircraft.

His comparison of drag is totally different from the one you keep calculating.  The more detailed you make the calculations the more his conclusions are correct.

In other words:

When you stop assuming values and actually calculate them.  

It is not a ding on your intelligence Gripen.  It's a matter of knowing the correct values and the formulas to use.

Obviously the formulas and data can be manipulated to produce wrong conclusions and still be correct.

If we factor in history it backs up Lednicers conclusions as well.  If Merlin Power spits were capable of converting airspeed to altitude on the same efficiency level as the FW-190 then the RAF would have recommended that they do so.  The R.A.E. had plenty of FW-190A's to test.

Historical facts are:

1.  Merlin Spitfires never fought FW-190's in the vertical.  They remained in the Horizontal where they had real advantages.

2.  FW-190A's did not fight Spitfires by making clumsy attacks and extending beyond visual range.  They got close and fought in the vertical where they had some real advantages.

FW-190's could only do this if they had some aerodynamically advantages in the vertical beyond simple mass.  Look at the P47D11, a much heavier plane that the FW-190A easily out zoomed.  In fact the only option a P47D11 had in fighting an FW-190A5 was to dive away as recommended by the USAAF.  This was the same FW-190A5 used in the US Navy test's with the same problems.  Only difference between a P47D4 and a P47D11 is the D11 is fitted with a bomb rack which further reduces it's performance.  You can read the conclusions here:

http://prodocs.netfirms.com/

Crumpp

[gripen]

Crumpp,
This thread is about estmation of the Oswald's efficiency.  Why are you bringing in issues which has nothing to do with it?

gripen

[Crumpp]

This thread is about estmation of the Oswald's efficiency. Why are you bringing in issues which has nothing to do with it?

To answer this:

Hm... I wonder what Lednicer's conclusions has to do with the subject of this thread? He calculated the span loading and concluded that the loading distribution of the Spitfire is "not elliptical, though it is probably the most optimum of the three aircraft from the induced drag standpoint". He did not determine Oswald's efficiency for the wing nor for the whole aircraft.

Because you keep skirting around the issue in both threads.

Crumpp