Why wing-loading isn't always the most important characteristic

[Bino]

Cool topic!  Thanks!   

FYI:
I'm told* that some progress in aerodynamics was delayed in the first few decades of flight due to the failure to properly scale air density into measurements made inside scaled-down wind tunnels.


* by my Dad, who has a B.S. in Mechanical Engineering and recently retired after 20+ years teaching A&P mechanics

[bozon]

Bustr, its a good question.  Basically, designers of the era did not have the full knowledge of aerodynamics we do now.

True, but the real advantage that we have now is computing power. Hydrodynamics is notoriously difficult to calculate. On the pure theory side, this is one of the most disappointing fields of science where all the major problems of 100 years ago are still around. Even brute computing power can only take you so far and many calculations rely on various shotcuts and empirical data for anything but the simplest conditions. This, coupled with over 100 years of trial and error are what gets aerodynamics advancing. As Stoney said, they had only 35 years of trial and error and only pen, paper and ruler instead of supercomputers.

[Kenne]

Just an example I discovered doing the stall testing on the 190 family...  It also shows an interesting phenomenon related to aspect ratio.  When testing the standard airframe 190s (A5, A8, D9), the wing-loading and how it affected stall speeds was intuitive--i.e. the higher the wing-loading, the higher the stall speed.  It surprised me to find that even though the Ta-152 has the lowest wing-loading of the 4 aircraft, it has the highest stall speed of the four tested.  Stall test results can be found here:

http://bbs.hitechcreations.com/smf/index.php/topic,287289.0.html

This is basically a function of its aspect ratio, where the Clmax is achieved at a much lower AoA compared to the other 190s.  Generally speaking, the higher the aspect ratio (or more precisely, the wing span), the lower the stall AoA will be.

then ur saying the A5 has a better glide ratio than the 152 given their respective wingloadings?
Aspect ratio...from wing SPAN or wing AREA?

given AC with the same WL, would flap design make for lower stall speed?

[Stoney]

then ur saying the A5 has a better glide ratio than the 152 given their respective wingloadings?
Aspect ratio...from wing SPAN or wing AREA?

given AC with the same WL, would flap design make for lower stall speed?

Don't know about the glide ratio--haven't tested that.  If you have a formula for that I'd be interested in seeing it. 

Aspect ratio is both span and area.  Basically, AR = Span^2 / Area.

[Kenne]

Don't know about the glide ratio--haven't tested that.  If you have a formula for that I'd be interested in seeing it. 

but would it not be logical to conclude that the higher WL would reguire more airspeed across the wings to remain aloft than the AC with lower WL?

[Stoney]

but would it not be logical to conclude that the higher WL would reguire more airspeed across the wings to remain aloft than the AC with lower WL?

No.  Too many other variables that aren't being considered.

[bozon]

The glide angle at a given speed is a function of the efficiency - that is the lift/drag ratio. Low aspect wings can still have very good L/D and therefore a shallow glide angle, but it just means that they have to glide at a higher speed. The drag part is very important and it includes the parasitic drag as well and this is why optimum glide speed is close to the minimum drag (best climb) speed.

For real planes it is a little difficult to compare between two wings, because in addition to the aspect ratios other factors (shape, profile, twist, total area) will differ.

[PJ_Godzilla]

The glide angle at a given speed is a function of the efficiency - that is the lift/drag ratio.

Yep, and L/D (max) is given by .5*((pi*AR*e)/CD0))^.5

So, this thing goes like the square root of Aspect Ratio. Note that some of the really extreme AR sailplanes have L/D(max) = Cl/Cd (max) of on the order of 70.

The only really cryptic term here is e - the Oswald efficiency factor - some sample values I'll add below:

B26F, DC-3, Piper Cub = .75
Su-27 = .71
F-22 = .82
Mig-29 = .85

blar, blar, blar...

I ran across, in the course of finding these examples, an analytic method to approximate Oswald's e... HERE: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VK4-41MJ1YS-3&_user=613487&_coverDate=09%2F30%2F2000&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1312830550&_rerunOrigin=google&_acct=C000032038&_version=1&_urlVersion=0&_userid=613487&md5=f4014adea2261dd39022f69479adab26  (quoted below)

e=ew*kf

where ew = ( e _w/se=1*e _w/se=0 )/( S _e * e _w/se=0 - ( 1 - S _e * e _w/se=1 )

 ew denotes the Oswald efficiency factor reflecting the difference between the actual wing circulation distribution and an elliptical one, and the influence of the leading edge suction force, and kF is a correction factor to incorporate the influence of a fuselage cross section shape on the induced drag.

Thus the following tasks should be solved for calculating the aeroplane is Oswald efficiency factor:

• wing Oswald efficiency factor calculation with full implementation of the leading edge suction force e_w/Se=1;

• wing Oswald efficiency factor calculation at zero leading edge suction force ew/Se=0;

• calculation of the relative leading edge suction force Se;

• calculation of the fuselage cross section shape factor kF.

Solutions of all mentioned tasks are considered below in brief.

Wing Oswald efficiency factor calculation with full implementation of the leading edge suction force is based on a vortex model of a simple shape wing flow.


(end quote)

Developing those terms is a little complicated but they give you some empirical forms for the e terms, if you want to go there.

There are other methods as well, or, you can dig up test data for the type in which you're interested, with any luck.

[Stoney]

The suction method for determining "e" is really only useful for aircraft that operate in the transonic/supersonic range.  For our purposes, the conventional approximations of e work.  I'd contend that finding a legitimate Cd0 is the toughest part of using that equation.

[PJ_Godzilla]

A cursory look shows .022 for Spit XIV, .0268 for P-38, and .0211 for F6F. However, I think I see your problem. First, a zl Cd is going to be hard to get without test data. Second, even given test data, there's a lot of potential sources of change - i.e., version, loadout, etc... If that stuff's not doc'd in the source data, you're kind of screwed, especially given the sensitivity of 1/cd0)^.5

I just sort of assumed good Cd0 data was widely available for these old ac. I guess you could always go to a numerical method, given the time, expertise, and computing power.

[Stoney]

Well, I've got a way to approximate e.  If we get some no-kidding Cd0 numbers, we're in there.

[IrishOne]

this thread looked cool til i saw all the numbers.....

[FLS]

I'm still trying to understand why a high AR wing has a higher stall speed despite a lower wing loading when it has a higher CL for a given AOA and apparently a higher max CL compared to a lower AR wing of the same area. I understand it stalls at a lower AOA and it stalls completely after CL Max with less additional AOA compared to a lower AR wing. I'm guessing the increased CL doesn't offset the lower AOA but it seems like it should at some point where the difference in wing loading is great enough and that point isn't reached in the difference between the Ta152 and the FW190.

[PJ_Godzilla]

I'm still trying to understand why a high AR wing has a higher stall speed despite a lower wing loading when it has a higher CL for a given AOA and apparently a higher max CL compared to a lower AR wing of the same area. I understand it stalls at a lower AOA and it stalls completely after CL Max with less additional AOA compared to a lower AR wing. I'm guessing the increased CL doesn't offset the lower AOA but it seems like it should at some point where the difference in wing loading is great enough and that point isn't reached in the difference between the Ta152 and the FW190.

VStall =(2*W/(S*rho*CLMax))^.5

In the case of the 152 versus 190, the weights are similar and the denominator under the radical looks as though it'd favor the 152 as well. Thus, I'm a little baffled as well.

Recall that this Vstall equation is simply derived by doing W=.5rhoSCLMaxVstall^2 and rearranging.

[Stoney]

Maybe my stall speed on the Ta-152 is bad.  Or, perhaps the other 190 stall speeds are a little low.  I tried to derive one from Badboy's bootstrap program, but haven't gotten anything nearly as precise as I'd hoped.