Aces High Bulletin Board
General Forums => Aircraft and Vehicles => Topic started by: Stoney on April 19, 2010, 09:06:10 PM
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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.
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Another thing I found interesting:
Between the 190 series and the Ta-152, the 190s generate a higher Clstall in the clean configuration than the Ta-152. They actually generate a higher Clstall than the Spit 5/9 (ignoring lift due to thrust and CG affects).
Using the stall speeds and other metrics collected during the tests:
Given the equation Clmax = L / q * S
Where:
Clmax = maximum lift coefficient
L = Lift (Weight)
q = Dynamic pressure (1/2*p*V^2)
S = Wing area
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the higher the aspect ratio (or more precisely, the wing span), the lower the stall AoA will be.
I don't understand how AoA is related to wingspan. AoA is the angle the wind hits the wing correct? How is that impacted by wingspan? Obviously, wingspan relates to wing area but unless there was a 'twist' in the wing, wouldn't the AoA of a given wing be constant?
Also, the 'Lift' variable, I mean isn't that a function of the speed of the air and the AoA as it crosses the wing? ie the same wing with the same AoA moving at 50 mph produces less lift than if it were going 150 mph?
Thanks
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Excerpt from the USN Fixed Wing Performance, Flight Test Manual:
(http://i125.photobucket.com/albums/p61/stonewall74/EffectsofAspectRatio.png)
If wing area remains constant, an increase in aspect ratio is purely an increase in wing span.
Lift variable in my equation isn't a variable--its fixed, given the plane's weight. Lift = weight in unaccelerated flight.
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Stony thank you for the information, I am by no means trying to discredit you or argue, only trying to understand. so given a 'real' values.
FW 190 A8(accoridng to wikipedia)
wing span 10.50 m
wing area 18.30 m²
Weight 3,490 kg
clmax = 3,490 / ((1/2*p*V^2) *18.30
Whats p and V?
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Stony thank you for the information, I am by no means trying to discredit you or argue, only trying to understand. so given a 'real' values.
FW 190 A8(accoridng to wikipedia)
wing span 10.50 m
wing area 18.30 m²
Weight 3,490 kg
clmax = 3,490 / ((1/2*p*V^2) *18.30
Whats p and V?
(1/2*p*v^2) is the common expression for dynamic pressure, or rho (q). So, in my formula Clmax = L / q*S, you have the weight of the aircraft divided by dynamic pressure * the wing area. For dynamic pressure, the "p" = air density at the specified altitude in slugs(I used sea level since my stall speeds were all at sea level). V is velocity in feet per second. To get this, multiply mph X 1.467 to get fps. Using this formula, you can determine the required lift coefficient for any condition of flight. Its an approximation that will get you very close. For example, if you wanted to find the required Cl at 20,000 feet and 385mph, you can plug in the air density for 20,000 feet, and 385*1.467 to get 564.8 fps. Therefore rho (or "q", or dynamic pressure) would = .5 * .1267(air density at 20,000 feet in slugs) * (564.8)^2 or 20208.6. Plug rho into the equation using your example and you have:
Cl = 3490 / 20208.6 * 34.4 (need area in ft^2) ~ .005. This would be the required lift coefficient for the 190 at the weight you listed, flying at 20,000 feet and 385 mph. If the required lift coefficient is higher than what the wing is capable of (Clstall), you could consider that condition of flight to be outside the envelope of the aircraft.
If you use the stall airspeed, you will find Clmax. If you use any other airspeed, you will find required Cl at that condition. Aircraft designers sometimes start with this formula in order to determine the wing-loading required to give them the desired landing speed.
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Ok, thats very interesting, thanks! Now one last question, I hear a lot about NACA airfoils and how their shape will change the behaviors of the wing, including the lift and stall characteristics. The above equation did not take airfoil shape into effect at all, is there an extension to the listed equation that accounts for the airfoil shape? Also, doesn't the overall shape of the wing have an effect too (ie 37 degree sweep on wings for fighter jets, or diamond shape wings of the yak, etc..).
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OMG!
I almost understood that!
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"Now one last question, I hear a lot about NACA airfoils and how their shape will change the behaviors of the wing, including the lift and stall characteristics. The above equation did not take airfoil shape into effect at all, is there an extension to the listed equation that accounts for the airfoil shape?"
That is a good question Ardy and I have been wondering exactly the same.
I think that the problem lies in the definition of Cl or CL depending on if we consider 2D or 3D lift characteristics since they provide approximations which are adequate for most uses. Ok there is alpha and according to airfoil data we know the limit at certain Reynolds number which determines the flow speed around the airfoil but I have understood that Re is not the speed itself i.e. Mach number.
http://en.wikipedia.org/wiki/Lift_%28force%29
http://en.wikipedia.org/wiki/Lift_coefficient
http://en.wikipedia.org/wiki/Lifting-line_theory
http://en.wikipedia.org/wiki/Reynolds_number
http://en.wikipedia.org/wiki/Mach_number
So where exactly does the airfoil geometry plug in? Calculating the general CL of a wing at certain alpha can it be just counted in as a modifier to result if wing profile characteristics are known?
http://en.wikipedia.org/wiki/File:Lift_curve.svg
I think that one of the competitors of Aces High is using some kind of a general lift curve for their FM since the maximum alpha is same for all their aircraft. If the airfoil data is counted in all along the calculation would it be too complicated calculation to run in real time?
-C+
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Ok, thats very interesting, thanks! Now one last question, I hear a lot about NACA airfoils and how their shape will change the behaviors of the wing, including the lift and stall characteristics. The above equation did not take airfoil shape into effect at all, is there an extension to the listed equation that accounts for the airfoil shape? Also, doesn't the overall shape of the wing have an effect too (ie 37 degree sweep on wings for fighter jets, or diamond shape wings of the yak, etc..).
The Cl of an aircraft is normally very close to the Cl value(s) of its wing profile in power off condition. So the Cl-value of an aircraft that comes out of the equation is very much dependent of the airfoil(s) that particular plane uses.
For example using AH 190A-8's stall speeds and weights from Stoney's testing (4245kg/172km/h) you get a Clmax value of ~1.6 which is very close to the Clmax values of NACA 23000-series airfoils which Fw190 used.
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Ok, thats very interesting, thanks! Now one last question, I hear a lot about NACA airfoils and how their shape will change the behaviors of the wing, including the lift and stall characteristics. The above equation did not take airfoil shape into effect at all, is there an extension to the listed equation that accounts for the airfoil shape? Also, doesn't the overall shape of the wing have an effect too (ie 37 degree sweep on wings for fighter jets, or diamond shape wings of the yak, etc..).
If I understand your question, I'd offer that, if you look, for example, at Stoney's plot above, you'll see that Cl = f(alpha) and that that function changes, airfoil to airfoil (2D) and 3d wing to 3d wing (as he shows here for varying aspect ratio) . If you're interested, take a look at, for example, Abbott and Von Doenhoff - it's a classic text on airfoil sections and plots out the cl versus alpha characteristics for many common 2d airfoils. My understanding of the development of most of these plots is that they're empirically derived (i.e., from test). Conceivably, you could "virtually" test 'em now, given CFD but A&vD predates computers as we know them.
And yes, the overall shape dramatically affects the wing characteristics. Consider, for example, cross-flow on swept wings causing higher relative velocities locally or the impact of elliptical planforms on drag and trailing vortex formation.
Speaking, as we were, of aspect ratio, one of the upsides of high AR is low induced drag - and this is related to Stoney's point, imj. Since induced drag is the "dragward" component of lift, and since a high AR wing produces more lift at lower relative AofA, his plot makes good sense. High AR planes tend to climb like demons for this reason - they can make lots of lift without making lots of induced drag - and THAT in turns, is corroborated, as expected, by our own AH Ta-152. The downside? Well, it gives it up in stall sooner too.
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Speaking, as we were, of aspect ratio, one of the upsides of high AR is low induced drag...
Sort of. High aspect ratio lowers the effect of wingtip turbulence. This vortex around the wingtip transport air from below the wing plane to above it and lowers the effective lift (lower CL). To produce the same lift, higher AoA is required and this builds more induced drag. At the same time, the lower pressure difference due to the vortex delays the stall and the wing can be pushed to higher AoA.
At high speeds level flight, the AoA is typically rather low and the effect of wingtip turbulence is less significant. Planes that need to maximize speed are typically designed with low aspect ratio wings (there are also other considerations). Good example is the Mirage 3/5/2000. With the short delta wings it cannot turn worth a damn, but it has a gentle stall and can "mush" into the turns at high AoA. It also has a very high top speed and rate of roll.
Wing profile matters. If you strap two doors of some size to a fuselage you can get any "wingloading" you want but it will not even get off the ground. High aspect ratio wings have a problem with the stalls, especially with some profiles as the whole wings suddenly stalls at once. Therefore sometimes the profile changes along the wing and sometime the wing has a twist to it - as far as I know this is the case with the spitfires. The idea is to lower the angle of attack at the outer wing at the ailerons section. The stall then develops gradually from the wing root outward and is much more gentle. It also leaves the ailerons effective even though part of the wing is in stall and significantly lowers the risk of snap stall. The price is the the wings produce less lift than what one might expect from its area (call it lower CL). It also has more drag at any AoA. So again wing-load is not the whole picture.
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Sort of. High aspect ratio lowers the effect of wingtip turbulence.
Therefore sometimes the profile changes along the wing and sometime the wing has a twist to it - as far as I know this is the case with the spitfires. The idea is to lower the angle of attack at the outer wing at the ailerons section. The stall then develops gradually from the wing root outward and is much more gentle. It also leaves the ailerons effective even though part of the wing is in stall and significantly lowers the risk of snap stall. The price is the the wings produce less lift than what one might expect from its area (call it lower CL). It also has more drag at any AoA. So again wing-load is not the whole picture.
Agreed, Your second para here clearly refers to washout - of both the aero and geometric variety. The FW appears to have actually had some "wash-in", per Stoney's (another thread) sourcing of the sections inboard and outboard on the venerable Focke...
As for wingtip vortices, I'd contend that, independent of AR, you can eliminate them altogether with an elliptical lift distribution. That's why I find your initial point cryptic since the AR dictates nothing about the pressure discontinuity at the tip - other than that it's likely to be a small-chord section, the way it's generally executed. But I find this distinction practical, as opposed to abstract and general, since a counter, as I 've stated, is readily available.
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In WW2 was the organic 3D shape of the wing targeted at a mission role or was it a choice by the designer to first achieve a unique performance specification then as circumstances unfolded in battel the mission roles? The Russian fighters all seem to have similar wing shapes to the yak9 and Lavotchkin or the 109 and 190 series have straight tapers. But then the U.S. and Britain had a mixture from elliptical to shapes like the Russians and germans.
Is this a chicken or an egg question?
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In WW2 was the organic 3D shape of the wing targeted at a mission role or was it a choice by the designer to first achieve a unique performance specification then as circumstances unfolded in battel the mission roles? The Russian fighters all seem to have similar wing shapes to the yak9 and Lavotchkin or the 109 and 190 series have straight tapers. But then the U.S. and Britain had a mixture from elliptical to shapes like the Russians and germans.
Is this a chicken or an egg question?
Bustr, its a good question. Basically, designers of the era did not have the full knowledge of aerodynamics we do now. Remember that WWII started only 35 years after the Wright Bros. first flew. A lot of the knowledge of planform, airfoil, wing sweep, and aspect ratio and how they impacted the efficiency of the wing, weren't really known. There was a lot of "almost" knowledge out there as a result of designers simply regurgitating NACA testing and documents, but, for example, Supermarine probably didn't consider that the washout they introduced to control tip-stall was both (a) contradicted by the airfoil thickness taper, and (b) only good for making the wing draggy as hell. Had they known a little more, they would have realized that an elliptical lift distribution can be approximated in ways that are much more cost effective than a true "elliptical" wing.
IMO, the two most important "aerodynamic" advances of the war were the design of the P-51D, which broke the mold, from an aerodynamic perspective, of the WWII fighter, and the Me-262. Obviously the Germans had figured out how important transonic considerations were for jets. Compare it to its peers in England and the U.S. who were still building "straight" winged jets. Another example can be seen in wingtip designs. Almost all early WWII aircraft had highly rounded wing tips, which were designed in the erroneous belief that they "mocked" elliptical shapes, and therefor, had lower drag. Had they had more wind tunnel data, you would have seen more straight wing tips that would have been more efficient, earlier.
We have the benefit of analyzing all of this stuff with 20/20 hindsight. At the time, all of these designs were considered by their manufacturers as "state of the art".
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Cool topic! Thanks! :salute
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
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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.
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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?
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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.
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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?
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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.
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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.
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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 ew/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.
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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.
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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.
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Well, I've got a way to approximate e. If we get some no-kidding Cd0 numbers, we're in there.
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this thread looked cool til i saw all the numbers..... :furious
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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.
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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.
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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.
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Thanks PJ. Equations don't speak to me but I appreciate your optimism. I'll try to figure out what you wrote. :headscratch:
I suspect the answer will show the relative importance of AOA. I don't usually fly the German planes so I don't have a feel for the performance differences but what I've read here seems to suggest that the Ta152 will have a higher sustained turn rate despite the higher stall speed because of the lower induced drag.
Stony I wondered that too. If I get a chance I'll see if I can get some stall numbers to compare.
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Actually, I do suspect that my 190A8 and D9 speeds are low because they work out to have a Clmax of 1.59, and that is a bit too high from what I think they should be. They probably should both be a little less than 1.5.
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Well, I've got a way to approximate e. If we get some no-kidding Cd0 numbers, we're in there.
Stoney, lookeehere... http://www.hq.nasa.gov/pao/History/SP-468/app-a2.htm
B-17G at tthe bottom of this one: http://www.hq.nasa.gov/pao/History/SP-468/app-a.htm
It looks like they link to source as well. I submit this to you and hope it helps (don't know if it will). It's only 5 types we care about but, it's a start.
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That's the link I posted for the WW1 glide ratio thread. Lots of good stuff there. Did you notice the DC-3 (C-47) glide ratio is a little better than the P-51?
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That's the link I posted for the WW1 glide ratio thread. Lots of good stuff there. Did you notice the DC-3 (C-47) glide ratio is a little better than the P-51?
I steer clear of the WW1 stuff - not that I'm not interested in general. I just think the WW1 topic has a ways to go yet with AH. It needs more purpose and variety.
I'm surprised at that slope thing. It seems like the CDo wpuld be higher for the C-47 - though I haven't checked their aspect ratios. C-47 definitely has a lot of wingspan.
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Even if you don't enjoy the WW1 arena I hope you've looped the Dr1. :joystick:
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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.
low aspect='fast' wing, laminar wing, Davis wing?
is L/D direct proportional or inversely?
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low aspect='fast' wing, laminar wing, Davis wing?
is L/D direct proportional or inversely?
The Davis Wings were all very high aspect designs. You see them on the B-24 and other Consolidated designs. They were typified by short chords and smaller wing area. Aspect ratio goes up, given fixed span, with decreases in wing area. Low aspect wings are sometimes associated with "fast" wings, because its easier to chop down a Reno P-51's wing span than it is to shorten the chord of the entire wing. Basically, they get rid of "excess" wing area that way, cutting down on parasitic drag. Usually, this is accompanied by higher wing loading.
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The Davis Wings were all very high aspect designs. You see them on the B-24 and other Consolidated designs. They were typified by short chords and smaller wing area. Aspect ratio goes up, given fixed span, with decreases in wing area. Low aspect wings are sometimes associated with "fast" wings, because its easier to chop down a Reno P-51's wing span than it is to shorten the chord of the entire wing. Basically, they get rid of "excess" wing area that way, cutting down on parasitic drag. Usually, this is accompanied by higher wing loading.
forgive me for asking such 'novice' questions.
so short cord, short span = low aspect...yes?
in the case of the 152, the wing got lengthened and so its aspect increased?
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forgive me for asking such 'novice' questions.
so short cord, short span = low aspect...yes?
in the case of the 152, the wing got lengthened and so its aspect increased?
Aspect Ratio = the wingspan squared / wing area.
So, for an aircraft with a 20 foot wingspan, and 70 sq ft of wing area, the aspect ratio would be:
20^2 / 70 = 400/70 =5.7
Or, for an aircraft with 30 foot wingspan and 157 sq ft of wing area would also have an aspect ratio of 5.7.
You could have a broad chord, short span wing that had a low aspect ratio. The Cassut III racer is a good example of a short span/broad chord aircraft.
And yes, the Ta-152 had a much longer wingspan than its FW-190 brothers, but it also got a bit more wing area as well. Overall, it had a higher aspect ratio than just about any other combat aircraft in the war.
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is L/D direct proportional or inversely?
Inversely - more lift for less drag means you glide better (smaller angle).
Intuitively, think about it this way: Since you do not have an engine, the energy lost to drag must come at the expense of potential energy. To maintain speed the glider must keep descending, but this need is only due to energy lost on drag. Loose less = descent less.
Alternatively, you can think in terms of forces:
The drag is slowing you down, so you need some forward force to replace the thrust. By tilting the lift forward (flying at an angle downward) the lift has a component that pulls you forward on the horizontal axis.
A simple drawing of a velocity vector at an angle "a" under the horizontal, a lift perpendicular to it and drag opposite to it will show you that in order to balance the forces in the horizontal axis:
L*sin(a) = D*cos(a)
So:
L/D = 1/tan(a) or: L/D~1/a for small angles in radians. Inversely proportional to the glide angle.
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so in the case of the 152 with the least wing loading but the highest stall speed.
might that be due to the increase of leading edge which negated any benefit in increase in span?
so then, would an increase in cord allow the same wing loading but a lower stall?
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so in the case of the 152 with the least wing loading but the highest stall speed.
might that be due to the increase of leading edge which negated any benefit in increase in span?
so then, would an increase in cord allow the same wing loading but a lower stall?
For your first question, no. Leading edge length (by itself) has nothing to do with with stall speed. Theoretically, a longer leading edge, if wing area is held constant, means higher span efficiency.
For your second question, if wing area is fixed, increasing chord length reduces aspect ratio which will (all other things being equal) reduce stall speed. This has to do with span efficiency.