How to obtain an elliptical lift distribution along the wing - RC Groups
Nov 02, 2010, 01:21 PM
Registered User
Mini-HowTo

# How to obtain an elliptical lift distribution along the wing

Hi everyone,

Some people ask me how to adapt an airfoil to a wing design. The aim is to obtain an elliptical lift distribution along the wing.
First of all i would like to thanks Thierry Platon, Jean CLaude Tournaire, Marc Pujol and Franck Aguerre for their helps concerning this method.

Subject :

A 4 meter all around glider with NM32 airfoil i designed for a friend.

wing design Tools:

XFLR 5 or better but in french, software Predim RC

Requirements :

24cm of chord root and 198cm long for a wing. 30% of chord for the hingelines.

See Picture 1 for the result.

In XFLR5 "Xfoil direct design":

-Perform a Type 1 polar for your airfoil.
-My batch analysis parameters for this 4m glider are: alpha between -4 and 8°, Reynold between 20000 to 600000 with 20 000 step.

To do this for the flap degree value (-2°, -1°, 0, 1°, 2°, 3°)

Go to XLFR5 "wing and plane design"

-Design your wing and introduce the same airfoil 0° in each panel.
-Then perform a Type 2 polar (fixed lift), fill the weight of your model (5kg here), In XCoG put the wing aerodynamic center point
_Choose LLT Calculation, it's very Important, the other choice doesn't work to do that

You will obtain a first set of values and graph.

Do this again with all the flap deflection.

The choice of my friend is to optimize the Cl/Cd ratio. Other choices are possible : min sink rate, Cdmin etc...

Look the graph Cl/Cd(Cl) and choose the flap defection which correspond the maximum value (look at picture 2). Here the -2° flap deflection.
The Cl domain associated is in the range of 0.5-0.7

Reynold number determination

Calculate the local REynolds number corresponding to each chord at the chosen speed. Here 28 m/s.

Re=70 * C * V, C = Chord in mm, V speed in m/s.

I found : at root 460000,then 440000, 370000, 290000, 190000, 90000 at tip

Return In XFLR5 "Xfoil direct design":

Select you -2° flap airfoil.
Perfom a single Type 1 polar at Reynolds corresponding to the local chord.

The goal is to overlap the curve Cl(Apha) for each previous Reynold number and in the Cl domain previously selected.

To adapt the foil, 3 paramaters:
_change the camber to shift up or down the curve
_change the thickness, decreasing normally when you go to the tip
_change Maximun thickness and camber position forward for lower Reynolds.

Result in picture 3. The curve overlap the Cl domain previously selected.

Result in OpPoint view at the graph local lift (Y-span). Don't forget to tick "show the elliptic curve" to have the reference.
Look at the last picture.

We have finally what we want an elliptical lift distribution along the wing for all speed.

Don't hesitate to ask you have a question.

Best regards

Nicolas

### Images

Last edited by kipecoul; Nov 03, 2010 at 11:05 AM.
 Nov 02, 2010, 02:09 PM Registered User what's the application? Thermal? Slope racing? 28 m/s (62 mph) seems quite fast for an "all around glider". Jon
 Nov 02, 2010, 02:27 PM Registered User Very nice explanation! I must admit that I don't understand everything! Hope to not disapointed you with the bulding of this wing. For the application, I ask for what we call in France "le mouton à 5 pattes", don't know if you have a similar expression in english. I want a glider to use "everyday" in "everyconditions". I know it's difficult to obtain, we have to make some compromises. Hope to build this glider during winter, so, rendez-vous this summer for my impressions! Amitiés, Ludo
Nov 02, 2010, 02:36 PM
Registered User
Quote:
 Originally Posted by nuevo what's the application? Thermal? Slope racing? 28 m/s (62 mph) seems quite fast for an "all around glider". Jon
The application of the method or of the glider?

The application of the method is available for all the flight domain, from F3k to F3F.

for the glider it is more a fast all around glider which can do aerobatic easily.

Nicolas
Last edited by kipecoul; Nov 02, 2010 at 02:46 PM.
Nov 02, 2010, 02:38 PM
Registered User
Quote:
 Originally Posted by Ludovic 07g Very nice explanation! I must admit that I don't understand everything! Hope to not disapointed you with the bulding of this wing. For the application, I ask for what we call in France "le mouton à 5 pattes", don't know if you have a similar expression in english. I want a glider to use "everyday" in "everyconditions". I know it's difficult to obtain, we have to make some compromises. Hope to build this glider during winter, so, rendez-vous this summer for my impressions! Amitiés, Ludo
Hi Ludo,

Which part you don't understand?

Nico
 Nov 02, 2010, 02:45 PM Registered User I don't understand the reading of the curves... Maybe one day I will take time to study that, but as you know, at the moment, I don't have a lot of free time! And I think that in french it will be easier to me to understand. ;-)
Nov 02, 2010, 03:08 PM
Registered User
Quote:
 Originally Posted by kipecoul The application of the method or of the glider? The application of the method is available for all the flight domain, from F3k to F3F. for the glider it is more a fast all around glider which can do aerobatic easily. Nicolas
Sorry for the ambiguous question. I meant the glider. You answered my question. Thanks.

When I saw 400k Re, I assumed the plane's purpose was not F3J.
 Nov 02, 2010, 09:03 PM Registered User Looks like a powerfull program. Now that you have the airfoils selected how does the wing lift distribution look when lift is higher or should I say closer to stall speeds (CL of 1.0) and then at high speeds (CL 0.02)?
 Nov 02, 2010, 09:12 PM Registered User After looking at the plots a little longer, I am very interested in what changes were made at the tip airfoil MH32-3-2deg T1_RE0.090_Mo.00_N9.0? Thanks again....
 Nov 03, 2010, 01:04 AM Registered User You will do well to calculate the local "load" distribution, or the actual lift at each station based on those local Cl's. That wing appears to very narrow tip chords and it looks like you are combating tip stall by using wing twist. Beware of very low alpha where the tips become negative and the rest of the wing is still at positive alpha. At high alpha, make sure your airfoil is capable of dealing with those local Cl's. If it can't produce the local Cl, then you will stall in that area, even though you may have a smooth lift distribution. My gut reaction says that this wing will have a stalling probllem.
 Nov 03, 2010, 01:14 AM Registered User Ok, after a second look, it appears that you have plotted the local "load" distribution and not the local Cl distribution. The difference being the local Cl's are the operating Cl in that area, where the local load is the slice of the wing CL that is over that small panel of the wing. A fine but important detail. Can you please plot local Cl and local "load" (lift)? It also looks like I was wrong about the twist in the wing panel..is that correct?
Nov 03, 2010, 03:31 AM
Registered User
Quote:
 Originally Posted by Robert-CSD Looks like a powerfull program. Now that you have the airfoils selected how does the wing lift distribution look when lift is higher or should I say closer to stall speeds (CL of 1.0) and then at high speeds (CL 0.02)?
I attached the corresponding graph. This method allows, with a variation of the flap deflection, to obtain an elliptical lift distribution for all Cl domain. Here for low Cl, Put the flap up of 1°, for higher value (Cl of 1.2) put the flap down of 2°.

The mods done is thinner airfoil (be careful to the nose radius when you decrease the thickness), forward maximum thickness and camber position and higher camber. But when you modify the airfoil, do it step by step to understand the consequence on the Cl(alpha) curve.
Regards

Nicolas

### Images

Last edited by kipecoul; Nov 03, 2010 at 05:16 AM.
Nov 03, 2010, 04:24 AM
Registered User
Quote:
 Originally Posted by Avaldes Ok, after a second look, it appears that you have plotted the local "load" distribution and not the local Cl distribution. The difference being the local Cl's are the operating Cl in that area, where the local load is the slice of the wing CL that is over that small panel of the wing. A fine but important detail. Can you please plot local Cl and local "load" (lift)? It also looks like I was wrong about the twist in the wing panel..is that correct?
Yes no twist at all at tip.

I attached the asking local lift and Cl function of Y span for 16m/s.

Concerning the tip stall, i'm pretty sure it will be gentle. But don't forget we have here a 4 meters glider of 5 kg, all this kind of plane need a minimum speed to fly. You can also reduce the speed of tip stall, with flap down of some degree. I estimate the critical speed of the tip airfoil with 0° of flap (i.e. the Critical Reynolds of the airfoil tip) at 12 m/s i.e 55 000 of reynolds number. With 4° down you can reduce the speed to 9 m/s i.e 35 000 Re number.

To evaluate the Critical Re number of an airfoil, go to Cl (alpha) and plot Type 1 polar to overlap the curve.
plot same polar with a decrease of the Re number associated. The critical Re is the value when you have no more overlaping curve at all. The transition is not easy to observe but you can have an idea +- 10 000 Re.
Best regards

Nicolas

### Images

Last edited by kipecoul; Nov 03, 2010 at 06:02 AM.
 Nov 03, 2010, 09:47 PM Registered User Your reply answers my question, thanks! It looks like your wing is built in panels but I don't see the local lift (Y-span) changing or showing that at the corresponding panel breaks. Is this a smoothing or averaging setting you have set in XLRF5?
Nov 04, 2010, 03:52 AM
Registered User
Quote:
 Originally Posted by Robert-CSD Your reply answers my question, thanks! It looks like your wing is built in panels but I don't see the local lift (Y-span) changing or showing that at the corresponding panel breaks. Is this a smoothing or averaging setting you have set in XLRF5?
It 's normal because you adapt the airfoil to local Reynolds corresponding to each root and tip of the panel.

Nicolas