Explain this and win the prize!

[Angus]

Oh, come on.
I mean, is this a duel or what?

[Crumpp]

et's look it again, below is Crumpp's version (his post 01-04-2005 12:50 AM) of the NACA 921 which was supposed to support Wood's claim on validity of the Glauert corrections for tapered wings:

You just told a story Gripen.  You posted nothing I quoted!

Typical.

Crump says:

Your ridiculous calculations off Lednicers lift distribution chart. The one three aeronautical engineers working in the field could not figure out how you could make any conclusions about efficiency factor.

Gripen says:

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:

Crump says:

2. You did not realize that the differences in values comes from an element of parasitic drag. Niether did I until Badboy pointed it out.

 

Gripen says:

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).

In spite of his being told:

Joeblogs says:
Getting back to Grippen's point, though, Oswald's e is used to correct for departures from eliptical planform and is therefore not just a function of the aspect ratio.

Even I said on page 2 of this thread:

A correction is made for the variation of parasitic resistance with angle of attack and nonelliptical wingloading by including in the induced drag term a factor e, called the "airplane efficiency factor". The correction is thus assumed to be proportional to CL^2.

He continues on and on about the differences formulas calculated values.

Another pearl of wisdom from Gripen.

Gripen says:
Overall the exact speed (if below Mach 0,5) is not important if we know the Cl and/or value of the K.

 

Crumpp says:
If you want to compare planes it certainly is important. Nobody cares that when the FW-190 and the Spitfire have the same CL the spitfire's wing is more efficient. What matters is under the SAME conditions of flight.

And yet another:

Crumpp says:

Lets Check out your claims:
1. All aircraft have the same e factor ".8"!

Gripen says:

The problem is that that the WWII fighters generally had lower e factor which means that the both formulas give too high estimates and therefore also a constant value works better in most cases.

I could be here all night cutting and pasting!

Lastly for g00b:

 

Crumpp and Dweeb could use a serious lesson from Miss Manners.

Dweeb is Badboy's pseudonym.

Crumpp

[gripen]

Originally posted by Crumpp
You just told a story Gripen.  You posted nothing I quoted!

Anyone can check this from Crumpp's posting.

Originally posted by Crumpp
Even I said on page 2 of this thread:

Anyone can check that there Crumpp just quotes Oswald's report which I linked earlier.

Otherwise Crumpp just continues his cut and paste game. It has been pointed out that so called generalized formulas were actually formulas for rectangular wing only and can't be used for entire airframe nor other wing types

gripen

[Crumpp]

Crumpp just quotes Oswald's report which I linked earlier.

Sure you linked it Gripen but you sure did not understand it!

Crumpp

[gripen]

Originally posted by Crumpp
Sure you linked it Gripen but you sure did not understand it!

So why I have pointed out several times during this thread that also viscous drag rise should be counted for e factor?

Besides just two days ago you announced that "There are TWO e factors's".

Basicly you continously quote sources without understanding them, Oswald and NACA 921 are good examples.

gripen

[Crumpp]

Crumpp says:
You did not understand what Badboy pointed out did you? There are TWO e factors's. Only Oswalds includes an element of viscous drag.

Yep, Gripen. And there are two e factors.  

Badboy says:

I didn’t realize what was happening until I saw your recent posts, and I think I can explain what you are seeing. We have been referring to Oswald’s efficiency factor, (Airplane Efficiency factor) and we have been using the character e to represent it, which is what normally happens, but there is a catch...  There are two values associated with it and they are not the same, and they don’t measure the same things. Take another look at the explanation I posted previously:

ONE

Badboy says:
you may see the induced drag for the wing expressed using a value for e that does not include the effects of the lift dependant component of the parasite drag for the fuselage or tail, or anything other than the induced drag of the wing.

TWO

Badboy says:
The number normally represented by the character e in induced drag calculations was originally known as Oswald’s efficiency factor, and his original paper is available for download from the NACA report server. More commonly it has a component of parasite drag lumped in with it and is just called the airplane efficiency factor and can be estimated depending on the aspect ratio, taper ratio, sweep angle and twist. Theoretically an elliptical wing would have an efficiency factor of 1, meaning that it will have a coefficient of induced drag close to the theoretical maximum. Even though it is a function of aspect ratio, sweepback angle, taper ratio, camber, Mach number and twist, the largest influence on the wing of a WWII fighter with very little sweep or twist comes from aspect ratio and taper ratio and so there are approximate formulae for estimating e that only include aspect and taper ratio, and even more approximate methods that only include aspect ratio. The important thing you must appreciate is that they are only approximate. But better than just assuming a constant value for every aircraft..

Thanks for proving my point again!

Crump says:
Sure you linked it Gripen but you sure did not understand it!

Crumpp

[gripen]

Originally posted by Crumpp
Yep, Gripen. And there are two e factors.

As noted earlier there is just one e factor which is for entire airplane and it includes induced drag rise and viscous drag rise just like noted in the Oswald's study. In the Wood's book, the author separated this to two pieces, ew for wing and ef for fuselage.

The factor which include just induced drag is not the e factor, in the Anderson's study it's called the factor u.

Regarding Badboy's postings, he has allready admited missunderstandings. However, unlike you Badboy is capable to discuss about this rational way as others have noted. And I don't want to mix him in this discussion like you continously do.

In addition I noted a funny thing above when you wrote about exact speeds in the Fw drag chart. If the shape of the lift/drag curve below compressibility speeds (say mach 0,5) is not practically constant, it means that measurements in the low speed tunnel like Chalais-Meudon (around 45m/s) are worthless.

gripen

[Crumpp]

Regarding Badboy's postings, he has allready admited missunderstandings.

Umm Looks to me like your the one with the misunderstandings, Gripen.

When are you going to admit them?

In addition I noted a funny thing above when you wrote about exact speeds in the Fw drag chart. If the shape of the lift/drag curve below compressibility speeds (say mach 0,5) is not practically constant, it means that measurements in the low speed tunnel like Chalais-Meudon (around 45m/s) are worthless.

You should let Kurt Tank know!!

Crumpp

[Badboy]

Just to summarise the technical aspects of this discussion…

Anyone reading this thread could be forgiven for wondering why the value of e should be so important. Why argue about the difference between something as small as 0.8 and 0.85 for example, when it only has a small influence on the overall drag coefficient. But before we get into this, let’s just apply a crude reality check to see if we have a realistic range for the fighters we are interested in? This diagram:



taken from NACA 408 shows that Oswald’s estimate agrees with the values that arise from approximate equations solely based on aspect ratio, for example, values between 0.85 and 1 for a cantilever monoplane. It is worth noting that he also quotes values between 0.95 and 1 just for a wing on its own, which is similar to approximate values produced earlier in this thread for a wing also.  

Well, let’s put that in terms of air combat, and look at the difference that would make to an aircraft at the very bottom of Oswald’s range 0.85, and one even lower, say 0.8 corresponding to a value at the high end of the range of average values Gripen posted from drag polars for various WWII fighters earlier in this thread.

Well, here is a diagram that shows the difference that these two values would have on the sustained turn rate of the same aircraft. Firstly, it would make very little difference at all to any other performance characteristics, the top speed for example being only 0.4mph different (and hardly distinguishable on the chart). You can see from the diagram that there is only 0.6 degrees per second difference (less than 3%) in the sustained turn rate, and no difference in the sustained turn radius, or any of the instantaneous values.  



Alternatively, the pilot in the aircraft with an e = 0.8 could choose to match the turn rate of the less draggy counterpart, but to do so he would have to lose altitude in the turn at the rate of 260ft/min.

That’s a bout the size of it, not a decisive advantage by any means and because in a real engagement, that difference is small enough to be overwhelmed by other factors, such as pilot ability, fuel or other ordnance loads, or the significant differences between the dissimilar aircraft more likely to have been involved in real combat.

Lastly, the diagram also includes the equations used in a modern context to describe Oswald’s efficiency factor, and they demonstrate three things. Firstly, that the definition of e as Oswald intended, includes the factors that have been discussed here in that context correctly by Gripen, but separately on occasions by me Those factors are the value for the wing alone, indicated by the Greek character delta in those equations, and the value for the fuselage indicated by the character k. Some modern analytical methods estimate those values together or separately, while practical methods provide the value of e directly from the slope of a graph produced from either wind tunnel or flight test data.

I think that just about sums it up…

Hope that helps put things in perspective…

Badboy

[Crumpp]

Good Post.  

Definately puts things in persepective.

Crumpp

[gripen]

Originally posted by Badboy

Anyone reading this thread could be forgiven for wondering why the value of e should be so important. Why argue about the difference between something as small as 0.8 and 0.85 for example, when it only has a small influence on the overall drag coefficient.

Well, the point of this thread was clear up the methods to determine the e for performance calculations and we (me and Badboy) have a consensus now here.

Originally posted by Badboy
But before we get into this, let’s just apply a crude reality check to see if we have a realistic range for the fighters we are interested in? This diagram:



taken from NACA 236 shows that Oswald’s estimate agrees with the values that arise from approximate equations solely based on aspect ratio, for example, values between 0.85 and 1 for a cantilever monoplane. It is worth noting that he also quotes values between 0.95 and 1 just for a wing on its own, which is similar to approximate values produced earlier in this thread for a wing also.

Just a little correction. The chart linked above is from NACA 408 which is Oswald's report where he introduced the e factor, mentioned NACA 236 is the reference Wood used for his partial e factor for fuselage.

Generally the values in the Oswald's chart are probably a bit on high side; the value of e must be always be less than 1 as Wood notes. Practical maximum is probably around 0,95 for the flying wings. Here is some values for modern planes from Navy web site:

"The value e can be estimated for a particular model of aircraft by various methods.
One of the simplest is by comparison with aircraft of similar configuration. For most
aircraft e has a value of about 0.6 to 0.8. Some values of e for various aircraft as
measured at Mississippi State University are

Bellancer Crusair (low-wing) 0.55
Learstar (twin engine mid-wing) 0.67
Cessna 170 (high-wing) 0.74
RJ-5 Glider (high-wing) 0.79"
 

Originally posted by Badboy
Lastly, the diagram also includes the equations used in a modern context to describe Oswald’s efficiency factor, and they demonstrate three things. Firstly, that the definition of e as Oswald intended, includes the factors that have been discussed here in that context correctly by Gripen, but separately on occasions by me Those factors are the value for the wing alone, indicated by the Greek character delta in those equations, and the value for the fuselage indicated by the character k. Some modern analytical methods estimate those values together or separately, while practical methods provide the value of e directly from the slope of a graph produced from either wind tunnel or flight test data.

A practical comparison can be done with the Spiteful (no washout) wind tunnel data and calculation for entire airframe using the estimated value of K 0,01 (viscous drag) from Perkins&Hage and Glauert correction factor 0,011 for taper ratio about 0,5 (induced drag):

Wind tunnel => e=0,81
Calculated => e=0,84

Which is a pretty good result given the generalized form of the estimation. The effect of the wash out is much more difficult to calculate using the Glauert corrections because the effect varies with the AoA. Maybe the software used by Badboy could used for that case?

Originally posted by Crumpp

You should let Kurt Tank know!!

Tank certainly knew that below compressibility speeds the shape of the drag polar is practically constant, therefore the polars measured below these speeds (say mach 0,5) are comparable. Basicly if you are saying something else, it means that the polars measured at low speed tunnel are not good for other speeds than the speed used in the measurement (about 45m/s in the case of the Chalais-Meudon).

gripen

edit: The link to the Navy site corrected.

[Crumpp]

Tank certainly knew that below compressibility speeds the shape of the drag polar is practically constant, therefore the polars measured below these speeds (say mach 0,5) are comparable. Basicly if you are saying something else, it means that the polars measured at low speed tunnel are not good for other speeds than the speed used in the measurement (about 45m/s in the case of the Chalais-Meudon).

I am saying your calculated value is not close to the value you get off the polar, Gripen.

Crumpp

[gripen]

Originally posted by Crumpp
I am saying your calculated value is not close to the value you get off the polar, Gripen.

Hm... You said that there is something wrong in my statement regarding the speed in which the value of the K for climb in the Fw chart was given assuming that there is about linear stage in the Cd/Cl^2 curve:

 "Overall the exact speed (if below Mach 0,5) is not important if we know the Cl and/or value of the K".

If this statement is not true, the polar which is measured in the low speed tunnel can't be used for other speeds.

If this statement is true, the polar which is measured in the low speed tunnel can be used for any practical flying speed below compressibility speeds.

gripen

[Badboy]

Originally posted by gripen
Just a little correction. The chart linked above is from NACA 408 which is Oswald's report where he introduced the e factor

Thanks for picking that one up, that's what I get for not reading it back before posting... I've corrected it.  

Badboy

[Crumpp]

A practical comparison can be done with the Spiteful (no washout) wind tunnel data and calculation for entire airframe using the estimated value of K 0,01 (viscous drag) from Perkins&Hage and Glauert correction factor 0,011 for taper ratio about 0,5 (induced drag):
Wind tunnel => e=0,81
Calculated => e=0,84

Here is a good example.  Your saying the Spiteful has a more efficient wing than the FW-190A not be just a little but a rather large margin.  Your calculations using "K" from Focke Wulf's data say the e factor is around .78!!

Lets look at the Spiteful's wing:

http://www.fortunecity.com/marina/manatee/272/spiteful.html

Now we all know wingtip efficiency can be very easily manipulated thru structural design.  Designers were very aware of the benefits of wing efficiency in the late 1930's and were familiar with how to manipulate the design to attain an efficient wing.

The FW-190 and the Spiteful have almost the exact same wingtip.  As you know wingtips are extremely important to wing efficiency.

Both the FW-190 and the Spiteful have sharp cornered wingtips.  Figure (c) in this diagram.  As you can see the wingtip design is not far behind an elliptical tip.

http://www.centennialofflight.gov/essay/Theories_of_Flight/Reducing_Induced_Drag/TH16G6.htm

Another tool designers use manipulate efficiency is twist.

They include (1) planform taper to obtain an elliptic planform, used for the Spitfire wing, which was remarkably elliptic; (2) a geometric twist and/or aerodynamic twist to obtain elliptic lift distribution; or (3) a combination of all of these methods.

The FW-190 wing was twisted 2 degrees specifically to achieve an elliptical distribution.  As Lednicer points out it was not far behind the Spitfire and neither was the P51.  The lift distribution chart puts the wingtips almost equal.  All three aircraft are very close with the Spitfire having a slight advantage.

Now as we all know the Spitfires elliptical distribution was purposely destroyed by it designers to lessen the harsh stall characteristics inherent with a perfect ellipse.

The other problem with elliptical wings is the stall characteristics. It is much safer to design an airplane so that the wing stalls first at the root, leaving the outer portion of the wing, (where the ailerons are) still flying. An elliptical wing however, will tend to stall uniformly all along the span (see the diagram below.) The "fix" for this situation is washout, but that will reduce the theoretical gains in induced drag. Therefore, we are unlikely to see a great resurgence in the use of elliptical wings, except in situations where appearance dictates.

http://142.26.194.131/aerodynamics1/Drag/Page8.html

So I think we can all agree that .88 is about right for the Spitfire.  This is backed up by EVERYONE's calculations.

Another factor is aspect ratio.  The FW-190 had the advantage over the Spiteful with a higher aspect ratio.

6.02 = FW-190
5.81 = Spiteful

The efficiency factor e and wing span are physical factors that may be controlled by proper design. A plane with a longer span wing (higher aspect ratio) has less induced drag and, therefore, greater efficiency.

So frankly your calculations do not make sense putting the FW-190 so far behind the Spitfire.    

Spiteful - Same wingtip, no twist, lower  aspect ratio, e factor = .84
FW-190 - Same wingtip, 2 degree twist, higher aspect ratio,  .78!!

Aeronautical engineer using the same data calculates the FW-190's e factor to be .87.  

Every formula I have used puts its the FW-190's in the same ballpark.  .86-.87.

Crumpp says:
I am saying your calculated value is not close to the value you get off the polar, Gripen.

Is a true statement.

Now you might be tempted to state that e factor includes an element of parasitic drag.  Well we both know the FW-190 has less parasitic drag than the Spitfire so I find that hard to imagine that the viscous drag portion of "e" would make a .10 difference!


As for the polars themselves, Gripen.

The polar include multiple pages and multiple aircraft configurations.

The include prop mounted, no prop, low power high power, gear up, gear down, flaps up, flaps down, cooling gills open cooling gills closed etc...

Even graphs for different hardpoint racks.  Your numbers do not correspond to any of them.

Each configuration and speed has it's own graph.

I would look to your math before I looked to FW documents.  Your numbers do not make sense.

Crumpp