Wing loading vs Stall speed

[Martin Hunter]

Hi gang,

Somewhere buried in a thread recently I saw someone post a formula for figuring out the approximate stall speed of an airplane given a wing loading in oz/sq ft and some other numbers. Now, I tried it myself and it worked decently for a few calculations but, silly me, I didn't write it down or bookmark the thread.

Help! What is that formula?

Thanks

Martin

[vintage1]

Dunno. i use motocalc :D

[BMatthews]

Foilsim. Set up the wing size and using the stall airflow modeling option keep reducing the flight speed with the angle of attack set to 8 degrees until the lift is equal to the model's weight. It's fixed to stall at 10 degrees but if you say 8 degrees it's more accurate for model applications.

Of if you know the max lift coefficient of your chosen airfoil before it turns the knee and produces a lot of drag for small increases in lift you can set up the wing size and then play with speeds and angles while flipping back and forth between total lift in pounds and lift coefficient until the max lift coefficient is met and the lift is equal to the model weight. The speed you see is what you can fly at.

A very handy and informative program applet.

[hul]

was it this one by Keith Shaw?

stall speed = 3.7 * square root of wing loading

speed in mph
wing loading in oz/sqft

Hans

[Sail 'n Soar]

Hi gang,

Somewhere buried in a thread recently I saw someone post a formula for figuring out the approximate stall speed of an airplane given a wing loading in oz/sq ft and some other numbers. Now, I tried it myself and it worked decently for a few calculations but, silly me, I didn't write it down or bookmark the thread.

Help! What is that formula?

Thanks

Martin

Formula at sea level standard atmosphere conditions is:

U = 7.25*sqrt((W/A)/CLmax), for U in fps, W/A in oz/sq ft

U = 4.95*sqrt((W/A)/CLmax), for U in mph, W/A in oz/sq ft

Unless you know the CLmax, use ~ 1.0 for a moderate camber & thickness foil and ~0.9 for a symetrical foil. This ignores the fact that the average CL for a wing at stall will be lower than the max CL, but in the grand scheme of things that's lost in the wash. Some others have published a factor of 3.7 rather than the 4.95 to calculate U in mph, but that is WRONG!

[Martin Hunter]

The 3.7 one is the one I was thinking of but 4.95 gives me much better results. Thanks, guys!

Martin

[Microbatman]

Lets do an example for my plane the MicroBat


Step 1 Get total wing area in inches

Find it from someplace like here
http://nesail.com/categories.php?subcatID=50&PHPSESSID=33cb9d0f9edc2d899603d7aaf7562587

385 inches

Step 2 Convert it to Square feet
This is the tricky step
there are 144 inches in 1 square foot
Get that by multiplying 12 by 12 = 144


So 385 inches/144 = 2.67 SQUARE FEET

Wingloading is defined as oz/area in square feet

Step 3 Solve for wingloading
Wingloading is OZ/Sqft

11 OZ on the micorbat
11oz/2.67sqft= 4.11 oz per square feet
Wingloading is 4.11

Then
Step 4 take the square root of the number in step 3
Square root of 4.11 is 2.02


Step 5 multipy number in step 4 by 4.95
2.02x4.95=9.99

So Answer is 9.99 miles per hour stall speed

[Sparky Paul]

And just -how- do you know -when- you're flying at 10 miles per hour?
The plane hasn't stalled?
With no way to get the information from the plane to the brain other than by looking at the way the plane is flying, the precise numbers for any performance criteria aren't too pertinent to the flight.
When observing the plane is -close- to stall, what more information could you need? What that airspeed may be? Not really.
Just be prepared, or don't fly any slower, with slower being defined as slower than it is flying now.

[Microbatman]

You are flying at over 10 miles per hour when a plane flys faster than you can walk.

If you fly at 30 miles an hour then it is hard to fly in a small flying area.
If you fly at 10 miles per hour it is easer to fly in a small flying area.

Ok sparky here is the question. You tell me if you have a better way of finding the answer.

If I can shave 2 or 3oz of weight off a 16 oz plane then how much slower can it fly? Feel free to give me an answer in takoff speed numbers as it looks like you have done alot of work in that area.

[Ollie]

The stall at maximum AoA and Cl will increase airspeed with power. If you make power zero it is simple. You can find the gliding stalling speed.

The gliding airspeed is porprotional to the square root of weight at one g. The airspeed is reduced by ~6% or ~10% depending on 2 oz or 3 oz reduced weight starting with 16 oz. The whole range of airspeeds are shifted by the square root of the wing loading including the stalling speed.

Example:
http://home.att.net/~jdburch/polar.htm

[davidfee]

I once read a general rule of thumb that said, since most airfoils will stall at around 15° AOA, just keep the fuselage at a lower angle than that. It's usually a lot easier to guesstimate the fuselage angle (esp. on landing) than it is to estimate the flying speed.

[Tom Harper]

Hunter,

The Sparkster is right. How would you measure the difference?

What are you trying to do?

[Microbatman]

Hunter,

The Sparkster is right. How would you measure the difference?

What are you trying to do?


Find out how much weight I need to shave off my plane to make it fly slower.
Right now my plane is
too fast now for small parks (still can be done but hard to fly)
Flys slow enought for big parks.
Want to shave weight and trying to figure out if I should buy the same plane I have and rebuild it this winter and make it lighter or buy a different plane. I like the plane that I have now alot and think I can shave off 3 oz (no landing gear and less better use of glue, lighter reciever,servos)

[Sparky Paul]

You are flying at over 10 miles per hour when a plane flys faster than you can walk.

If you fly at 30 miles an hour then it is hard to fly in a small flying area.
If you fly at 10 miles per hour it is easer to fly in a small flying area.

Ok sparky here is the question. You tell me if you have a better way of finding the answer.

If I can shave 2 or 3oz of weight off a 16 oz plane then how much slower can it fly? Feel free to give me an answer in takoff speed numbers as it looks like you have done alot of work in that area.
.
I have no need -for- the answer!
The plane flies the way the plane flies.
It's up to me to get a plane that fits the flying area.
I'll fly the Yard Stick in the recreational area of the park, but reluctantly.
I won't fly the 3D foamies there at all, although they can hover, i.e. zero airspeed.
Trees and buildings get in the way.
Wingloading all by itself is a good indication of how small an area a plane can be flown safely in, without knowing the airspeed.
Light AND manuverable are the criteria to look for.

[Martin Hunter]

I'd agree that stall speed means much less for general sport flying in a specific area, but my needs differ, hence my asking the original question. For calculations on multi-motor aircraft (such as my 10 foot Tupolev ANT-20), I was curious as to how close to "scale" I could fly it with X wing loading at Y scale. As it turns out, a 10 mph stall speed is still a scale 200 mph for the 1:20 ANT-20 but it's still much lower than most aircraft of the same size. It's with this in mind, I feel I can make scale aircraft that appear to fly scale as opposed to flying like the space shuttle (both up and down). As another example, if I have a 1:7 scale Beech Baron with a 6 oz wing loading, the stall speed calcs out to be a scale 77 mph which isn't so far off the mark. Also, doubling that for cruise speed is right where I want it to be.

All that being said, when it comes to my non-scale sport planes, I couldn't care less where the stall speed is unless it's radically high.

Martin

[Ollie]

Airfoils have AoA at inifinite AR. A real wing adds the airfoil AoA to the induced AoA for the whole wing. The induced AoA is proportional to Cl^2 and divided by the AR.

Make the question and answer simple. The airspeed is reduced by ~6% or ~10% depending on 2 oz or 3 oz reduced weight starting with 16 oz.




aoa

[Tom Harper]

10 foot ANT-20 has a dimensional scale factor of 20:1 (as you state). Velocity scales as the square root of dimension. So:

ANT-20 top speed 165 MPH........model 36 MPH

Model stall speed 10 MPH.........ANT-20 44 MPH

I think you are about on the money!

[Tom Harper]

Also, the original weighed 66,000 lbs, give or take a little, so your model would scale to 8.25 lbs. The original wing loading was 13 lbs per sq ft and that scales to 10.25 oz per sq ft.

I assume you are in the ball park.

[adam_one]

And just -how- do you know -when- you're flying at 10 miles per hour?
The plane hasn't stalled?
With no way to get the information from the plane to the brain other than by looking at the way the plane is flying, the precise numbers for any performance criteria aren't too pertinent to the flight.
When observing the plane is -close- to stall, what more information could you need? What that airspeed may be? Not really.
Just be prepared, or don't fly any slower, with slower being defined as slower than it is flying now.Knowing the model’s stall speed might not be much useful when flying but might be when one needs to choose the suitable prop pitch speed.

[Martin Hunter]

Tom, the difference is I'm looking for scale perspective more than true scale performance-based airspeed. Thus, at 140mph, the full scale would cover a little over 200 feet per second, or roughly twice the fuselage length. To give the same perspective at 1:20 scale, it's a true scaling down by a factor of 20, giving a perspective-based top speed of 7 mph - not doable at the scale I'm building but I'm not far off with a 13 mph cruise speed either :D

For what it's worth, I'm planning on a sub-7 oz wing loading. Somewhere in the scale forum someone mentioned volumetric wing area and that it can help decrease the stall speed further in a model this size. Know anything about that?

Martin

[Tom Harper]

Not quite sure I follow - humor me, I'm old. The scaling values I used were published by NACA years ago as the values they used for research with models.

Your 'true' scaling factor of 20 is what NACA called the scaling factor K. But all things do not scale linearly with K. For instance wing area scales as the square of K. Double the span and the area goes up by 4. The same is true of velocity. To scale down by 20 you divide by 4.4 (sq rt(20)). So your 140 becomes 32mph. That is the velocity that would be used to make a model appear realistic in a movie. One thing that does scale linearly is wing loading. Divide 13 lbs per sq ft by 20 and you get 10.25 oz per sq ft.

[Martin Hunter]

Yup, I follow all that but here's what I'm talking about with perspective. If, at full tilt (140 mph), the full scale ANT-20 would cover 200 feet in one second, or two fuselage lengths in one second, my ideal situation would be to have the model cover two fuselage lengths in one second as well, or about 9 feet in this case. 9 feet per second, if I recall, calcs out to a little over 7 mph. In other words, I'd love to see a video of this once done (were I able to hit a 3 oz wing loading, which I'm not) which would be indistinguishable from the full scale in terms of flying "presence" and perspective. Flying at 32 mph would make the model appear way too fast. Check out the models in "The Aviator" and then watch video of the full scale spruce goose to see what I mean here.

Martin

[Microbatman]

Airfoils have AoA at inifinite AR. A real wing adds the airfoil AoA to the induced AoA for the whole wing. The induced AoA is proportional to Cl^2 and divided by the AR.

Make the question and answer simple. The airspeed is reduced by ~6% or ~10% depending on 2 oz or 3 oz reduced weight starting with 16 oz.




aoa
Thank you
That is just the answer I was looking for.
I am going to rebuild my original plane this winter and try to make it lighter.
6% slower for2-3oz for me is worth the effort. By that time maybe with the way batteries are being developed I might be able to find another 20 grams.
BTW Running an 11 3.8 prop

[Tom Harper]

The issue in absence is viewing distance. If you view the original at a distance of 5 spans (~1000ft) and it is landing at 44 mph and if you view the model at the same span multiple (50ft) at 10 mph it will be very close in appearance.

NACA says that time scales as the sq rt of K. So 2 fuselage lengths of the model should not pass in one second. They should pass in 1/4.4 seconds.

[Martin Hunter]

Tom, it's the issue of distance I'm counting on to fudge my 13 mph cruise down to what looks right - particularly on video with a Polikarpov off each wingtip :D

Martin

[Tom Harper]

Sounds cool!

Are you gonna do the garrison flag in the cockpit thing?

[Martin Hunter]

Hmmmm... that's a new one on me and honestly I've not seen pictures of any flag. Got more details for me?

Martin

[vintage1]

If you wantteh model to bank at the rigfht abngle doing te right radius turn use the sqaure root scale factor for speed.

If you want it to approach at the right rate of getting bigger, use the linear. scale factor for speed.

If you want it right fir both, build it full size, or very heavy and film it underwater....

[Sparky Paul]

The problem for me is scaling linear processes (speed) and mass with respect to the air the thing flies in.
You can't scale the air.
The model most likely will not be scalable in size or weight and be flyable.
Build it to fly, and fly it at a speed and distance that looks right.
If it comes out close to the numbers you selected, consider that luck.

[Martin Hunter]

Paul, "right" is the hard part and very subjective

Martin

[Sail 'n Soar]

Lets do an example for my plane the MicroBat


Step 1 Get total wing area in inches

Find it from someplace like here
http://nesail.com/categories.php?subcatID=50&PHPSESSID=33cb9d0f9edc2d899603d7aaf7562587

385 inches

Step 2 Convert it to Square feet
This is the tricky step
there are 144 inches in 1 square foot
Get that by multiplying 12 by 12 = 144


So 385 inches/144 = 2.67 SQUARE FEET

Wingloading is defined as oz/area in square feet

Step 3 Solve for wingloading
Wingloading is OZ/Sqft

11 OZ on the micorbat
11oz/2.67sqft= 4.11 oz per square feet
Wingloading is 4.11

Then
Step 4 take the square root of the number in step 3
Square root of 4.11 is 2.02


Step 5 multipy number in step 4 by 4.95
2.02x4.95=9.99

So Answer is 9.99 miles per hour stall speed

You missed a variable, namely, CLmax. You math would be accurate IF you could achieve a CLmax of 1 with the MicroBat. If the MicroBat is a flying wing variant, then you would be lucky to get half that value, which would raise your value by sqrt(2), or about 14 mph.

[Sail 'n Soar]

I once read a general rule of thumb that said, since most airfoils will stall at around 15° AOA, just keep the fuselage at a lower angle than that. It's usually a lot easier to guesstimate the fuselage angle (esp. on landing) than it is to estimate the flying speed.


I'd say most airfoils at model scale will stall at less than 10 degrees AoA. Very low aspect ratio plan forms can go higher due to the impact of the tip or LE vorticees.

[Sail 'n Soar]

OK, so the Microbatman has a tail. Wing looks symetrical. That would be the CLmax at ~ .9, and with the planform the average CL when CLmax is reached locally will be something like 80% to 90% of that. Better than a flying wing, but still no 10 mph flyer.

[Sparky Paul]

Paul, "right" is the hard part and very subjective

Martin
.
Is it EVER! :)
Mach 1 Piper Cubs..
Mach 2 C-119s..
I like scale planes that make me believe I'm seeing the real thing at a distance.
Not twitchy, not instantaneous roll rates, big loops...
I get a lot of "thank yous" for the way I fly my Dynaflite PT-19, from guys that learned their trade in WWII in them.
An OS 120 which seldom gets past 1/2 power, just chuggin' away. the plane wallows just like it's supposed to.. drops out of rolls nicely.. Takes a lot of down elevator to keep the nose up going around inverted.. :)
And with the flaps down, it floats down nicely to a wheel landing..

[Ollie]

I like Sparky's attitude.

I like Michael Selig's attitude:
http://www.rcsoaringdigest.com/FlysFaster.html
http://www.rcsoaringdigest.com/SquareCube.html

I don't like Bob Boucher's attitude:
http://www.astroflight.com/e/env/0001RaWykiKFeWsg209Q0h1/articles.html?link=articles/scalespeed.html

All about facts but different points of view.

What's your point of view?

[vintage1]

Bob is correct in every respect.

If you want to make a film of a scale aircraft, you have to build it to the square root rule, and then use slow motion photography.

That is, if you do a quarter scale model according to Bouchers rules, and halve the playback speed, everything is correct, even the scale RPM is right.


You have to scale time, or the air, as well as the model..:D

However this does gove you models that are subjectively 'quick'.

If the model doesn't do much in the way of manouvering, then going lighter and slower is more realistic.

For warbirds I find te root rule is about right, but for WWI types. lightplanes and airliners/cargo carriers I thimnk a bit less wing loading is advantageous.

To know that perfection in all respects is unattainable is the key to making the right choices and compromises.....

[Sparky Paul]

In filming, models used for full-scale in movies always twitched unrealistically, particularly in "formation flying".
Many CGI models are also easily identified because of this.
The Schneider races at Lake Havasu used a linear rule for "scale speed".. which meant speeds slower than the model could fly, for the older Schneider racers.

[Ollie]

I enjoy reading vintage1's opinion! Like,"To know that perfection in all respects is unattainable is the key to making the right choices and compromises....." It has an ring to it. I like and admire you.

For the Hobby, I would like you to change this quotation from,"...right choices..." to,"...personal choices..." Who makes the choice? You? Sparky? Bob? A committee? ...
Not me! I am not into Scale models.

[Martin Hunter]

Bob Boucher's page is a little scary to read. I wouldn't call a 125 mph 1:10 scale P-51 scale in any respect :rolleyes:

Martin

[vintage1]

I enjoy reading vintage1's opinion! Like,"To know that perfection in all respects is unattainable is the key to making the right choices and compromises....." It has an ring to it. I like and admire you.

For the Hobby, I would like you to change this quotation from,"...right choices..." to,"...personal choices..." Who makes the choice? You? Sparky? Bob? A committee? ...
Not me! I am not into Scale models.


There are no choices except personal choices...;)

[jay flay tway]

I'm no expert but here's my two cents of nonsense on it:

I'm not sure what your plane is like but it seems to me that glue use and type is overrated. I just made a 2.2-gram plane and used unthinned normal plastic model glue for the covering. I wasn't very careful at all to avoid using excess glue.
The glue added negligible weight according to my 0.1-gram resolution balance.
I think to make a useable difference in speed, you need a fairly drastic measure...or many small--but not too small--changes.
I think, maybe the best way would be to add another wing to make it into a bipe. Even a crude wing would be okay as long as it "pulls its weight" so to speak. Separate the wings (vertically) as much as reasonable (to minimize "interference in airflow between the wings) without too much flex.
Should drop the stall speed by what...maybe...30-45% or so(guessing)Definitely not more than 50% if my rough mental math is right(twice the lifting area, but some increase in weight, so can't possibly halve the loading).
Stagger the wings and make the front one stall after the back one for stable stalling (AoA or washin).
May or may not need to add some size to the stabs to keep the same maneuverability. I think I'd lmake the other wing easily moveable and/or detachable. It might cause other problems which may be difficult to fix.

Good luck. Reducing flying speed is about the most interesting goal to me. :)

[vintage1]

I have done many calculations, and the only way to achieve a nearly decent compromise is to build very big, very liight and that's that. Stall speed goes down as the root of wing loading, so you need to slash model weight by a huge factor to get linear scale speed.

Whivh is probably what you are trying to achieve with a slow bomber or airliner type, since they don't do many manoeuvers anyway.

If you take about 13mph as a realistic stall speed, for out door use then - say - a modern airliner that stalls at about 130mph has to be 1/10th scale, and a WWII transport that might have stalled at 65mph has to be at least 1/5th scale.

These are NOT small planes.

E.g. a PBY catalina is 100ft span and fleqw at about 80-120 mph,

So a one fifth scale model is going to be 20ft wingspan, and need to fly at 16-24mph.

A giant parkflyer..

Go figure.

A 707 is 145ft span, so a one tenth model might be 14foot span, and need to still land at barely 13mph, and fly at 40mph cruise perhaps...that is a HUGE challenge..

[N9DP]

You are flying at over 10 miles per hour when a plane flys faster than you can walk.

If you fly at 30 miles an hour then it is hard to fly in a small flying area.
If you fly at 10 miles per hour it is easer to fly in a small flying area.

Ok sparky here is the question. You tell me if you have a better way of finding the answer.

If I can shave 2 or 3oz of weight off a 16 oz plane then how much slower can it fly? Feel free to give me an answer in takoff speed numbers as it looks like you have done alot of work in that area.

There is not enough information presented to calculate the reduction in Vs (stall speed). Tell me the wing loading now, or, equivalently, the wing area, and I'll calculate the approximate reduction in stall speed. The approach-to-landing speed is about 1.3 Vs.

Best regards,

Dennis

[Sail 'n Soar]

There is not enough information presented to calculate the reduction in Vs (stall speed). Tell me the wing loading now, or, equivalently, the wing area, and I'll calculate the approximate reduction in stall speed. The approach-to-landing speed is about 1.3 Vs.

Best regards,

Dennis

Shave 3 ozs from a 16 oz plane and it Vs will be reduced by about 10%!

sqrt((16-3)/16) = .901.

You need the wing loading to define Vs, but not the percentage change in Vs.

[N9DP]

Shave 3 ozs from a 16 oz plane and it Vs will be reduced by about 10%!

sqrt((16-3)/16) = .901.

You need the wing loading to define Vs, but not the percentage change in Vs.

Correct! Thanks. I should have remembered that -- guess the brain slows down along with everything else as we get older.

Dennis

[Sail 'n Soar]

Correct! Thanks. I should have remembered that -- guess the brain slows down along with everything else as we get older.

Dennis


Dennis,

It's not that we are getting older. It's that everyone else is getting younger!

Gerry

[Hasina75]

Martin Hunter >If I am not wrong, I may be one of the guys who post the formula that you are looking for. Just type my login name on the search engine. However, if you don't have a strong background in calculus, you won't be able to understand it because it's quite complicated.

[JetPlaneFlyer]

Martin Hunter >If I am not wrong, I may be one of the guys who post the formula that you are looking for. Just type my login name on the search engine. However, if you don't have a strong backround in calculus, you won't be able to understand it because it's quite complicated.

It's actually very simple, no calculus required

*** EDIT*** V = sq root (W x 9.81/(1/2p x S x Cl))

where:
V = Stall speed
p (rho) = air density
S = wing area
Cl = Coefficient of lift at stall
W = weight

Air density as sea level is about 1.2KG/M^3. Cl at stall depends mainly on wing section, and Re number... somewhere in the range of 1 - 1.5 would be typical for models.

***EDIT***
I've edited the formula to get everything into SI units. The 9.81 is to convert KG mass to force (in Newtons)

V : M/s
p (rho) : KG/M^3
S : M^2
Cl : no units
W : KG

[Hasina75]

Jjjjjjjj

[JetPlaneFlyer]

Hasina,
Stall speed is actually not related to wing loading in a linear fashion... Stall speed is proportional to the square root of wing loading. As an example if you increased the wing loading by 4X the stall speed would 'only' increase by 2X

Probably also best if aspect ratio is kept out of it because there is no simple relationship between aspect ratio and stall speed... Generally a higher aspect ratio will give a higher max Cl value and therefore a lower stall speed, but it's not a simple relationship... Also there is NO direct relationship between aspect ratio and wing loading ;)

Steve

[Hasina75]

ttttttttt-t

[MarkusN]

Aspect ratio and Stall Speed
Aspect ratio and Wing loading


It's up to your own judgement, but they there is a logical relationship between AR and SP...and between AR and WL.

Only if you specify more rules which other parameters are to be kept constant and which to vary.

If you keep span and weight constant, there is definitely a (simple)relationship between AR and WL. If you keep payload and basic structure constant, there is a more complex releationship between AR and WL. If you keep WL constant, which would be a very common thing to do in a model evaluation situation, there is none. ;)

Such statements only make sense if you define these constraints.

And please stop throwing around your degree. It is fine to know your background to be able to assess the trustworthyness of your statements. Boasting and intimidating as another thing altogether.

[JetPlaneFlyer]

C-Aspect ratio and Wing loading are reverse functions. The higher the aspect ratio, the lower the wing loading

ok Hasina, please use what you learned in your degree and from working for Airbus to explain to me how aspect ratio and wing loading have a direct reverse relationship:

here are a coupe of examples for you to work with:

Aircraft #1:

Span 1M
Chord 0.25M
Weight 1 KG

This aircraft has and aspect ratio of 4 and a wing loading of 4 KG/M^2

Aircraft #2

Span 0.5M
Chord 0.5M
Weight 1 KG

This aircraft has an aspect ratio of only 1 (one fifth of aircraft #1) yet it shares exactly the same wing loading as Aircraft #1 :rolleyes: Where is the linear relationship here? If there was a reverse relationship I'd have expected the wing loading of aircraft #2 to have increased four times.

Both aircraft have the same wing area and weigh the same, so the wing loading MUST be the same... Aspect ratio has no influence whatsoever on wing loading. Wing loading is simply the aircraft weight divided by wing area, aspect ratio is not even considered in the calculation.

Of course I just fly 'toy' planes and don’t have a degree in aeronautics and don’t work for airbus, so obviously I’m missing something that only a higher intellect could comprehend. Please enlighten me.

Steve

[kcaldwel]

Aspect ratio and Stall Speed
Aspect ratio and Wing loading


It's up to your own judgement,....
I am an airline pilot and an airframe engineer, who works for the Airbus Industry in Toulouse. A real test and experimention, by applying the principle of laminar flow and fluid mechanics but not just a subjective theory, prove the veracity of these relationships. Sure, they do not make sense to "folks", who just fly toy planes and toy jets unless they have a degree in aeronautical engineering and design and fly a full scale aircraft.


I'll never fly on an Airbus again! I'm only a very rusty aeronautical engineer, but I don't think most of your "relationships" are correct.

Your "D" makes no sense to me either. Power requirement is related to span loading, and Cl^2/Cd, not Watts/pound or wing loading.

And none of this has anything to do with laminar flow.

Kevin

[Sail 'n Soar]

Those who indicated that they either do not follow or definitely disagree with what Hasina75 wrote may want to reread his comments more carefully. What I believe he said is if you take a given sailplane and reshape the wing by, for instance, increasing the span while holding the inner wing or cord constant, you will increase both the wing area and aspect ratio simultaneously while reducing the wing loading, assuming only a modest structural weight increase with the wing modification.

The Schweizer SGS 1-23 is a case study for the basic concept. The original The area and wing span of the 1-23 were 149 sq ft and 43.83 feet, respectively, for an aspect ratio of 12.89. To increase the performance Schweizer extended the outer wing sections, which both increased the wing area to 164 sq ft, the wing span to 52.66 ft and the aspect ratiio to 16.9 for the 1-23 E, F, G and H models. The airfram empty weight did increase by 94 pounds and the max wing loading increased by ~ .1 lbs/sq ft, but the minimum sink speed decreased from 2.3 to 1.95 ft/sec in spite of the wing loading increase due to the improved performance at the higher aspect ratio.

You can also find more recent examples in such full scale glass ships with detachable wing tips that permit them to fly with either 15 M or 18 M sing spans, allowing them to be flown in different class contests.

[biber]

Yeah, but I second MarkusN's comment on the missing info in Hasina75's post.
It is not clear what conditions he assumed and that's nothing I'd expect to
come from an engineer, let alone from an airbus aero engineer.
I would recommend Hasina75 to read some posts of Mark Drela,
who can be seen as a perfect example for how toy planes and
science can go together without any hybris mixing into it.

biber

[JetPlaneFlyer]

Those who indicated that they either do not follow or definitely disagree with what Hasina75 wrote may want to reread his comments more carefully. What I believe he said is if you take a given sailplane and reshape the wing by, for instance, increasing the span while holding the inner wing or cord constant, you will increase both the wing area and aspect ratio simultaneously while reducing the wing loading, assuming only a modest structural weight increase with the wing modification.

The Schweizer SGS 1-23 is a case study for the basic concept. The original The area and wing span of the 1-23 were 149 sq ft and 43.83 feet, respectively, for an aspect ratio of 12.89. To increase the performance Schweizer extended the outer wing sections, which both increased the wing area to 164 sq ft, the wing span to 52.66 ft and the aspect ratiio to 16.9 for the 1-23 E, F, G and H models. The airfram empty weight did increase by 94 pounds and the max wing loading increased by ~ .1 lbs/sq ft, but the minimum sink speed decreased from 2.3 to 1.95 ft/sec in spite of the wing loading increase due to the improved performance at the higher aspect ratio.

You can also find more recent examples in such full scale glass ships with detachable wing tips that permit them to fly with either 15 M or 18 M sing spans, allowing them to be flown in different class contests.

But the point here surely is Hasina claimed there is a direct relationship between aspect ratio and wing loading ... in fact there is nothing of the sort. The example he quoted achieved a lower wing loading because by increasing span the wing AREA was increased, change in aspect ratio was irrelavant, you could have obtained exactly the same decrease in wing loading by increasing chord, which would actually decrease aspect ratio...
There is no relationship between aspect ratio and wing loading.. plain and simple.

[adam_one]

I agree, the typical wing loading has nothing to do with aspect ratio, that's why the simple formula:
Stall speed (mph) = 3.7 * square root of wing loading (in oz/square foot) - is not so accurate.
And that's why some people use cubic loading instead…

But you'll get a more accurate stall speed value by using following formula:

Stall speed (m/s) = [2*Weight / (Clmax*1.225*Wing Area)]^0.5

Where the Weight is in Newton, Wing Area in m2 and 1.225kg/m^3 is the standard air density.

[JetPlaneFlyer]

I agree, the typical wing loading has nothing to do with aspect ratio, that's why the simple formula:
Stall speed (mph) = 3.7 * square root of wing loading (in oz/square foot) - is not so accurate.
And that's why some people use cubic loading instead…

But you'll get a more accurate stall speed value by using following formula:

Stall speed (m/s) = [2*Weight / (Clmax*1.225*Wing Area)]^0.5

Where the Weight is in Newton, Wing Area in m2 and 1.225kg/m^3 is the standard air density.


Errr... this is the same formula i posted a couple of days ago in this thread, derived directly from the lift formula. I put a 9.81 conversion factor into mine so the input could be KG (Mass) rather than Newtons (Force)

[adam_one]

Wow, that means we must be right then...
:)

[JetPlaneFlyer]

Wow, that means we must be right then...
:)
Hopefully :D

[Flyingwingbat1]

Make the airplane ugly enough so the ground repels it, then you don't have to worry about wingloading.

[Sail 'n Soar]

But the point here surely is Hasina claimed there is a direct relationship between aspect ratio and wing loading ... in fact there is nothing of the sort. The example he quoted achieved a lower wing loading because by increasing span the wing AREA was increased, change in aspect ratio was irrelavant, you could have obtained exactly the same decrease in wing loading by increasing chord, which would actually decrease aspect ratio...
There is no relationship between aspect ratio and wing loading.. plain and simple.

The benefit of increasing the area by adding to the tip is that it will increase both the area AND the aspect ratio, which, in turn, will lower wing loading and raise the glide ratio (L/D) while lowering the stall speed. (I forgot that this thread was under "Modeling Science" and not under any of the sailplane topic areas, where improving glide ratio is good.)

[Sail 'n Soar]

I agree, the typical wing loading has nothing to do with aspect ratio, that's why the simple formula:
Stall speed (mph) = 3.7 * square root of wing loading (in oz/square foot) - is not so accurate.
And that's why some people use cubic loading instead…

But you'll get a more accurate stall speed value by using following formula:

Stall speed (m/s) = [2*Weight / (Clmax*1.225*Wing Area)]^0.5

Where the Weight is in Newton, Wing Area in m2 and 1.225kg/m^3 is the standard air density.

You are mostly right. The wing loading (W/A) has nothing to do with the aspect ratio, but the stall speed does. You have given your formula in terms of Clmax. You need to use Cl average in your equation and a higher aspect ratio wing will be able to achieve a higher Cl average at stall. Cl is not uniform along the span except for an elliptical wing with no washout. For any other planform most of the wing will be at a lower Cl when Clmax is reached at one point along the span. The Cl at stall will be the average CL when CL max is reached at one span-wise location.

The lower the aspect ratio, the bigger the difference between Cl average at stall and Cl max. For instance, the stall speed will be reduced by about 7% for a constant cord no washout wing with an aspect ratio = 5. Relatively small, but real. When you are giving everything else to three decimal places, a 7% change is significant.

[adam_one]

You are mostly right. The wing loading (W/A) has nothing to do with the aspect ratio, but the stall speed does. You have given your formula in terms of Clmax. You need to use Cl average in your equation and a higher aspect ratio wing will be able to achieve a higher Cl average at stall. Cl is not uniform along the span except for an elliptical wing with no washout. For any other planform most of the wing will be at a lower Cl when Clmax is reached at one point along the span. The Cl at stall will be the average CL when CL max is reached at one span-wise location.

The lower the aspect ratio, the bigger the difference between Cl average at stall and Cl max. For instance, the stall speed will be reduced by about 7% for a constant cord no washout wing with an aspect ratio = 5. Relatively small, but real. When you are giving everything else to three decimal places, a 7% change is significant.

Clmax in the equation above refers to the whole wing's Clmax not just the profile.
The whole wing's Clmax is obviously affected by the wing's aspect ratio.


.

[JetPlaneFlyer]

Anyone have a formula for calculating the reduction in Cl max from the infinite (2D) wing Cl number to figures for real world (3D) wings of given aspect ratio?

[MarkusN]

I don't think that a simple formula exists. Plan form plays into that, for example. I'd guess wing section properties as well ( is a wing section prone to be affected by lateral flow.)
There's a simple formula for induced AOA (reduction of effective AOA by 3d-effects), but not for Cl max.

[kcaldwel]

If you find the section Cl max for an infinite wing (wind tunnel 2D testing) at the proper Re, that will be section Cl max in a real finite span wing. The complication comes because of the 3D flows and induced angle of attack around a finite wing, so the local Cl along the wing varies. The entire wing does not reach Cl max possible for the section at each local Re.

A program like XFLR5 can do all the 3D planform effects, and give you local Cl's along the wing.

There is no formula for calculating the Cl max, at say Re = 200,000, from the data at 1 million. There are too many airfoil effects to do that without CFD.

Kevin

[Sail 'n Soar]

Clmax in the equation above refers to the whole wing's Clmax not just the profile.
The whole wing's Clmax is obviously affected by the wing's aspect ratio.


.

You point out the "obvious", but from the various authors posts, it most definitely is not obvious to a large number, if not the majority, of the writers. I didn't detect the definition subtlety in your earlier posts under this thread. It is too easy to confuse wing section Clmax for the for the effective Clmax for the finite wing wing when calculating stall speed, especially if you are relatively new to this topic, which is most likely the case for those who ask about what formula to use.

We obviously have a mixed audience here, which extends from university professors, e.g., Mark Drela, to current and former practicing aeronautical engineers, e.g., Ollie and Hasina75, to those who are just getting started in this hobby with little related formal training.

Therefore, the clarification and explanation seemed warranted.

For those who would like a tool to relate Cl average to Clmax locally try the following site. http://www.amadistrictii.org/cjrcc/wing2/wing.html#local
The lift distribution is calculated on the bases of vortex theory, which is a function of plan form, angle of attack and wing twist/washout only. The primary Reynolds Number impact will be related to the local section Clmax. For real fluids Reynolds Number will have a relatively small effect on the Cl distribution as a function of span and can be ignored for our purposes.

As a final thought, Hasina75 may not be the polished teacher that Mark Drela is, and is paid to be, but I have no doubt that he is fully credible. Please give the person a break. I imagine Hasina75 is paid to do, not to teach.

[adam_one]

You point out the "obvious", but from the various authors posts, it most definitely is not obvious to a large number, if not the majority, of the writers. I didn't detect the definition subtlety in your earlier posts under this thread. It is too easy to confuse wing section Clmax for the for the effective Clmax for the finite wing wing when calculating stall speed, especially if you are relatively new to this topic, which is most likely the case for those who ask about what formula to use.

We obviously have a mixed audience here, which extends from university professors, e.g., Mark Drela, to current and former practicing aeronautical engineers, e.g., Ollie and Hasina75, to those who are just getting started in this hobby with little related formal training.

Therefore, the clarification and explanation seemed warranted.


I see your point, but it is also difficult to guess everyone's background here and therefore difficult to know how detailed one should be in a single post.
For instance, does everyone know what aspect ratio stands for?
What induced drag, interference drag or parasitic drag stands for?
And so on.

By the way, it is not only the wing's aspect ratio that affects its Clmax, but also the wings' tip shapes, whether flaps or slats are used, and so on.

[Sail 'n Soar]

10 foot ANT-20 has a dimensional scale factor of 20:1 (as you state). Velocity scales as the square root of dimension. So:

ANT-20 top speed 165 MPH........model 36 MPH

Model stall speed 10 MPH.........ANT-20 44 MPH

I think you are about on the money!

Full scale aircraft with high lift devices and Re had a max Cl WELL over one. With a highly cambered airfoil your model achieve a max Cl a little over one. Your math needs to increase the model stall speed by the square root of the Clmax ratio.