Explain this and win the prize!

[dtango]

Starbird:

Here are three of my favorite sites that explain a lot of the fundamentals:

Aerodynamics Index

US Centennial of Flight: Theory of Flight

NASA Beginner's Guide to Aerodynamics

There are a lot of books out there.  I did come across one that was really helpful in terms of explaining the concepts at fundamental and intermediate levels without getting heavy into the math but I can't remember the name of it.  I borrowed it from my uncle awhile back and it was a short digestable book geared for pilots.  I'll see if I can dig it up.

Hope that is helpful!

Tango, XO
412th FS Braunco Mustangs

[joeblogs]

From the first reference we have:

"From our earlier discussions, we know that up wash increases and therefore induced drag increases when CL2 increases. We also predicted that induced drag would be inversely proportional to the aspect ratio (AR).

A full development of the equation for Cdi (coefficient of induced drag) is beyond the scope of this course, however the equation is:

Cdi =   CL²/ (pi*e*AR)
     
In the equation e is a number known as the Oswald efficiency factor. It is a number less than or equal to one. The Oswald efficiency number would equal 1 only for an elliptical wing with no fuselage or other appendages to affect the up wash. In the real world of course, most aircraft do not have elliptical wings and other factors such as the fuselage may also contribute to up wash. Therefore, e is always less than 1, even on a Spitfire. Usually e’s value is between .7 and .9. Low values will be for aircraft with boxy square wings and large fuselages. Aircraft with long tapered wings (like gliders and most airliners) will have high values for e."

Nuff said

-blogs

Originally posted by dtango
Starbird:

Here are three of my favorite sites that explain a lot of the fundamentals:

Aerodynamics Index

US Centennial of Flight: Theory of Flight

NASA Beginner's Guide to Aerodynamics

...

Tango, XO
412th FS Braunco Mustangs

[gripen]

Here is the e factor estimate for the Spitfire, this is based on the RAE wind tunnel data:

Cl 0,1 0,565121862
Cl 0,2 0,869418249
Cl 0,3 0,847682793
Cl 0,4 0,904194979
Cl 0,5 0,94186977
Cl 0,6 0,847682793

The average is 0,88

I had no wind tunnel data to calculate e factor of the Fw 190. But Lednicer calculated span loadings and here is estimated e factors calculated by taking 8 samples (semispan fractions 0,2-0,9) and measuring distance to the elliptical span loading:

Spitfire: 0,8684
Fw 190: 0,7857
P-51: 0,7965

The values of the Spitfire and P-51 are suprisingly close to the values which are calculated from the drag data above. So it is quite safe to say that the value for the Fw 190 is in the right ballpark.

Below is an example of the drag polar. It is the drag polar of the Bf 109G from the Messerschmitt AG.

Blogs, could you give your e-mail address.

gripen

[Crumpp]

Here is the e factor estimate for the Spitfire, this is based on the RAE wind tunnel data:

Interesting, because Zigrats spread sheet calculates the "e" factor for the Spitfire to be:

Spitfire = 0.88552405

Which is EXACTLY what you say the average should be!

The average is 0,88

It calculates the FW-190 "e" factor to be:

FW-190 = 0.865317063


Which is nothing like:

Fw 190: 0,7857

And therefore probably nothing like:

So it is quite safe to say that the value for the Fw 190 is in the right ballpark.

What is going on?

Either the math only works for the Spitfire by some fluke of GOD.

or

Something is not right with your calculations.

Crumpp

[Crumpp]

Woods formula for the Spitfire lends:

Spitfire = 0.873125707

Again within your ballpark.


FW-190A8 = 0.857305852

Again NOTHING close to your calculations.

It backs up David Lednicers analysis though.

Crumpp

[dtango]

Woods formula for the Spitfire lends:
Spitfire = 0.873125707

Again within your ballpark.

FW-190A8 = 0.857305852

Again NOTHING close to your calculations.

It backs up David Lednicers analysis though.

Firstly Wood's and the NADC formula's for e are all approximations based mainly on AR.  If you're expecting values to match up perfectly with everything you're expecting a bit much.  

2ndly I'm not sure how any of this has anything to do with Dave Lednicer's analysis since (1) the flat plat drag values he quotes aren't things he calculated using VSAERO, the CFD s/w he used that I'm aware of and (2) he doesn't mention any specific analysis of oswald efficiency factor which is a specific component of lift dependent drag breakdown.

Seriously crumpp, where are you going with all this?  I had enough of the last thread because of the "I'm right no matter what" routine.  I hope we're not going down that path.

Tango, XO
412th FS Braunco Mustangs

[gripen]

Crumpp,
Seems that you don't fully understand the issue here. All my values are based on the documentation on the discused planes and the calculated e factors are following:

Bf 109G: 0,73-0,75
P-51: 0,77-0,8
Spitfire: 0,87-0,88
Fw 190: 0,79

The aspect ratios are following:

Bf 109G: 6,13
P-51: 5,81
Spitfire: 5,61
Fw 190: 6,02

The taper ratios:

Bf 109G: 0,44 (0,5 without wing tips)
P-51: 0,46
Spitfire: elliptical
Fw 190: 0,44

The washout:

Bf 109G: 0
P-51: 2 deg
Spitfire: 2,25 deg
Fw 190: 2 deg

If we look these numbers and compare them to generalized formulas (like Wood's or the one in the Zigrat's sheet), we can see that  except the case of the Spitfire, generalized formulas seem to give somewhat  higher values (around 10%, and in the case of the Spitfire the accuracy seem to be more or less accidental). We can also see that this very limited data set supports assumption that the e factor decreases when the aspect ratio increases. In addition we can also see that taper ratios are somewhat lower than assumed in the Wood's formula and except the case of the Bf 109, the planes have some washout (I don't know if the generalized formulas assumed washout).

Anyway, this is by far too limited data set; it would most interesting to have drag polars of the planes with higher aspect ratio (like the Ta 152H and the P-38) and the P-47 would be also interesting due to elliptical wing shape.

gripen

[Crumpp]

Firstly Wood's and the NADC formula's for e are all approximations based mainly on AR. If you're expecting values to match up perfectly with everything you're expecting a bit much.

If we look these numbers and compare them to generalized formulas (like Wood's or the one in the Zigrat's sheet), we can see that except the case of the Spitfire, generalized formulas seem to give somewhat higher values (around 10%, and in the case of the Spitfire the accuracy seem to be more or less accidental).

I was not referring to Lednicers flat plate comparisons.  I was referring to his discussion on the elliptical shape of the lifting wet area.  

The Spitfires physical elliptical shape was an attempt to produce an elliptical wet lifting area, correct.  The problem he states with that is the stall characteristics.  To eliminate the problematic stall of a truly elliptical wing, the Spitfires wings are twisted just like most fighters.  That twist according to him, removes the major advantages and eliminates the huge advantage everyone thinks the spitfire had in "e" factor.

He states that of the loading distribution of the spitfire is NOT elliptical.  Of the three it probably has the best "e" factor but it does not have a huge advantage.

case of the Spitfire the accuracy seem to be more or less accidental

That seems highly suspicious. Especially since all the other data lines up perfectly with Lednicer's conclusions.  He used the actual German drag plots as noted in his references.

Crumpp

[dtango]

...according to him, removes the major advantages and eliminates the huge advantage everyone thinks the spitfire had in "e" factor. ....He states that....Of the three it probably has the best "e" factor but it does not have a huge advantage.

Firstly, Dave Lednicier doesn't say anything about the quantitative advantage of one aircraft over another based on the lift distribution so it's unfair to claim that he says anything about the magnitude of the advantage.

2ndly most students of aerodynamics are aware of the famous elliptical wings of the Spitfire, what they were trying to achieve with it and HOW it didn't meet the ideal.  This is nothing new.  Dave Lednicer points out specifics of WHY it didn't.  I'm not sure where you get the notion about what "everyone" believes about the Spitfire.

3rdly I'm not sure why we're even talking about this since this thread was a discussion regarding estimating span efficiency factor using AR as the prime variable.

Tango, XO
412th FS Braunco Mustangs

[gripen]

Originally posted by Crumpp

He states that of the loading distribution of the spitfire is NOT elliptical.  Of the three it probably has the best "e" factor but it does not have a huge advantage.
 

I wonder what you are trying to prove?  If you look my numbers, you will note that the e factor of the Spitfire is not 1. My numbers also show that the Spitfire has best e factor of the three. Those Generalized models give the best e factor for the Spitfire just because it has the lowest aspect ratio of the three and therefore relative difference between planes is wrong.

gripen

[Crumpp]

I wonder what you are trying to prove? If you look my numbers, you will note that the e factor of the Spitfire is not 1. My numbers also show that the Spitfire has best e factor of the three. Those Generalized models give the best e factor for the Spitfire just because it has the lowest aspect ratio of the three and therefore relative difference between planes is wrong.

Knowing your prejudice for the Spitfire, Gripen.  Just look at the merry -go-round we just went through in the last thread.

http://www.hitechcreations.com/forums/showthread.php?s=&postid=1391720#post1391720

First you make a bunch of assumptions that show the FW-190 way behind the spitfire in flat plate areas that are proved wrong in the math.  Even using ALL the values you claimed!

Then you claim it is only JL 165 that has a drag disadvantage.  
When that is proved wrong your story changes again.

Then it changes and is the Spitfire Mk VIII which has the drag advantage.

In fact, when the numbers are run ONLY ONE Spitfire Mk IX had the advantage.  The one with an new style of air intake.  And of course the Spitfire Mk VIII which is a at totally different plane.  

None of the Spitfire's had a parasitic drag advantage.

Now your making calculations off of assumptions AGAIN.

Anyway, this is by far too limited data set; it would most interesting to have drag polars of the planes with higher aspect ratio (like the Ta 152H and the P-38) and the P-47 would be also interesting due to elliptical wing shape.

In fact lets review what the Aeronautical engineering instructor says about taper ratio:

 

However, the formulae presented by Professor Wood is for a taper ratio of 0.57 which yields an almost elliptical lift distribution, which is why it fits the experimental data so closely over a wide range of examples. Most WWII aircraft had a taper ratio close to that value  (Me109 was approx 0.52) because the designers knew about the benefits of elliptical lift distribution and that it could be achieved quite closely with a wing of that taper, that’s why a formulae that only includes aspect ratio could still be of such good practical use.

Spitfire: elliptical

Your making the assumption in your calculations that the Spitfire gains benefits for it's elliptical shaped wing. The entire point is that when tested, the wing was not elliptical due to the twist in the outboard portion.  

Your simply changing the formula to one that better suits your plane.
You explain away the "fluke" of the NACD and woods formulas for Oswald's efficiency coming so close the your favorite plane, the Spitfire, by declaring:

If we look these numbers and compare them to generalized formulas (like Wood's or the one in the Zigrat's sheet), we can see that except the case of the Spitfire,

I say baloney. You're playing the shell game again.

The values of the Spitfire and P-51 are suprisingly close to the values which are calculated from the drag data above.

There is no drag data on the P51 accept a number you calculated.  Only actual data you present is the Bf-109G, which is not the A/C in question.

Crumpp

[gripen]

Originally posted by Crumpp
First you make a bunch of assumptions that show the FW-190 way behind the spitfire in flat plate areas that are proved wrong in the math.

Hm... My assumption regarding the e factor was 0,9 for the Spitfire  (calculated 0,87-0,88) and 0,8 for the other two (calculated 0,77-0,80) so with my assumptions the errors were small and overall smaller than with generalized model.

Regarding data, the Mustang data is available from the PRO as DSIR 23/14544 and the Spitfire data  as DSIR 23/12576.

gripen

[Crumpp]

Hm... My assumption regarding the e factor was 0,9 for the Spitfire (calculated 0,87-0,88) and 0,8 for the other two (calculated 0,77-0,80) so with my assumptions the errors were small and overall smaller than with generalized model.

No, not really.  Your third or so assumptions might have been in that ballpark but not your original ones.  After you were confronted with calculations.  Pretty sure that is not the right ball park either.

overall smaller than with generalized model

Which is much more accurate than your assumptions.

Right now your trying to argue that the 190's design team, using a wing designed after the Spitfire, in a time when designers knew about the benefits of elliptical distribution, did not plan for it.  Seems kinda silly to me.


 
Crumpp

[joeblogs]

I was under the impression that Heinkel designed their pre-war commercial plane (can't remember the model number) with an elliptical planform in mind because of prandtls work. And I thought this had influenced the designers at supermarine too.

So wouldn't this be old news by 1940?

-Blogs

Originally posted by Crumpp
...

Right now your trying to argue that the 190's design team, using a wing designed after the Spitfire, in a time when designers knew about the benefits of elliptical distribution, did not plan for it.  Seems kinda silly to me.

Crumpp [/B]

[Crumpp]

I was under the impression that Heinkel designed their pre-war commercial plane (can't remember the model number) with an elliptical planform in mind because of prandtls work. And I thought this had influenced the designers at supermarine too.

It was old news by then.  That is the point.  Once you understand the physical shape has little to do with the wet area shape you can see planes like this one:

http://www.anycities.com/user/j22/j22/index.htm

Have an "e" factor of .95

http://www.anycities.com/user/j22/j22/aero.htm

And that just because the spitfire had a physically elliptical shape has nothing to do with it's "e" factor given the wingtip twist.  

Lednicer explains the elliptical shape was more an attempt to better deal with the problem's of wing mounted landing gear than induced drag. That allowed the spitfire wing to be relatively thin.  We all know Willey went around it by putting the landing gear in the Fuselage.  That has it's own set of unique problems though.  

Crumpp