Expert: Paul Soderman - 10/26/2008

Question
QUESTION: Dear Paul

Watching videos of aircraft at the Hobby Lobby site and comparing wing loadings of aircraft, it appears that the aircraft with low wing loadings are able to fly slower.
for example the "ember" model:

http://www.hobby-lobby.com/ember.htm

Slow speed is important to fly a model at 'scale speed'. If the wing loading of a model aircraft is kept below a certain limit, say 1 kg/ sq meter is it guaranteed that the model will be able to achieve slow flight? Does airfoil shape and aspect ratio matter if aspect ratio > 6 for example?

Also, in designing for low weight, is it true that most of the stress in a wing is concentrated wings spars close to the fuselage and the fuselage side section over the wing and behind the wing - so these areas have to be strong?

please see: http://www.aircraftdesigns.com/stress-analysis.html
Thanks

ANSWER: Gehan
Yes, low wing loading goes with low speed.  Consider the basic aerodynamic lift equation which shows that lift is proportional to air density, velocity squared, and wing area.  Low wing loading suggests that weight is low so lift required is low and velocity required is low, or wing area is large so velocity required is low for a given lift.  Conversely, if we want high speed we need to keep drag low (drag has the same relationship to density, velocity, and area as lift), so we want low wing area (or wing sweep).  I don't know about the 1 kg/sq meter limit, but it is clear that airfoil shape is always important. An ugly wing will have trouble flying no matter what we do.  And high aspect ratio is important to minimize induced drag.

Generally speaking, maximum stress of a wing occurs at the root since load times moment arm is maximum there.  Of course there might be an exception if someone designed a weak point in a wing outboard of the root.  But why would they do that...maybe to hold up a heavy engine or have a big flap cutout.  Wing stress is something that is very configuration dependent; it is unwise to generalize too much except to say -  check the wing root first.  That is where wings usually fail when they do.
Paul

---------- FOLLOW-UP ----------

QUESTION: Dear Paul

Thanks for your answer, that was very helpful, I have some further questions.

I think you have answered the query about aspect ratio nicely -"high aspect ratio is important to minimize induced drag".

The 1 kg/ sq metre limit was arbitrary based on some basic calculations and measurements - a paper plane made out of a single A4 paper will have about 0.3 kg/sq. m and a typical small R/c model will be 4 kg/sq m.

Now about airfoil shape - especially for models of 12" or so wingspan - I have read that thin airfoils are the best because air is relatively viscous at that scale. Also, how does airfoil shape affect lift - is the NASA foilsim applet
http://www.grc.nasa.gov/WWW/K-12/airplane/foil2.html a good way to gain an accurate view of how airfoil shape affects lift? I think the foilsim program could answer most of my questions.

Thanks

Gehan


Answer
Gehan
I am not familiar with the NASA foilsim code, but it looks like a nice interactive tool.  I would be curious to see how it compares to the data in Abbott and von Doenhoff: Theory of Wing Sections.

You are correct, you do not need a thick airfoil because you don't need the strength.  But you also don't want the airfoil to stall readily.  You have a low-Reynolds number environment much like gliders experience.  They are susceptible to laminar flow separation on the upper surface.  To that end I would consider a glider airfoil shape designed to allow a laminar or weakly turbulent boundary layer to stay attached to the upper surface as long as possible.  One that I like is the McMasters-Henderson airfoil described in:  McMasters, Henderson, Sandvig:  Two Airfoil Sections Designed for Low Reynolds Number.  Technical Soaring, vol VI, no. 4, XVIIth OSTIV Congress, Paderbon, Germany.  Coordinates are listed in my chapter of Aeroacoustic Measurements, Thomas Mueller ed. (page 15).  You can also google:  McMasters Henderson airfoil.  I am reminded that that airfoil has 30 thickness-to-chord ratio.  It was built for strength.  There are thinner designs described at:
http://www.gliders.dk/airfoils.htm
You could get some nice airfoil shapes and try them out in your NASA code.
Good luck.
Paul