Wing shape and spar

[techbear]

I've been thinking about wing behavior recently, and I'm not sure about something.

Suppose I made a tapered wing, so the wing tip had a smaller chord then the wing root. Normally, I'd also taper the spar, so the spar was narrower at the tip, to keep the airfoil shape uniform.

But what if I didn't?

If the spar was the same size along its length, the airfoil at the tip would be thicker than at the root. What would this do to the wing stall? Is this a good, or un-wise idea? Would it promote or inhibit wing-tip stalling?

 

[danskis]

I'm willing to be wrong on this but I think a thicker airfoil at the tip might create more lift at slower speed - acting like washout or undercamber and preventing tip stall.

 

[Pieliker96]

I'm willing to be wrong on this but I think a thicker airfoil at the tip might create more lift at slower speed - acting like washout or undercamber and preventing tip stall.

Yes, a thicker foil will generate more lift at lower speeds, but the critical factor that determines stall behavior is the angle of attack of each airfoil section along the wing. In this case, all angles of attack are the same (assuming a flat-bottom wing with no wing twist), just with a thicker foil at the tip. Thicker foils tend to stall at a higher angle of attack, meaning the root will probably stall before the tips do in an ideal situation. Also consider that since the chord changes along the span, the Reynolds number does as well - smaller sections will tend to stall earlier than larger ones, which contributes to "tip-stall" in the case of a conventionally tapered wing.

I'd expect this method to work somewhat in specific configurations, but the two effects - as the taper is increased - decreasing Reynolds number decreasing the stall AoA and increasing thickness increasing the stall AoA - fight each other, which could lead to the effects cancelling each other out (or, if the Reynolds Number effects win out), a reduced (not inhibited) tip-stall. There are also some practical considerations to be made here: This effectively moves more lift outwards on the wing, which both increases the bending moment on the wing's spar as well as increases induced drag from the vorticity caused by a (now higher) difference in pressure across the tip foil.

Having given the long answer that brings up more questions than it answers, here's my short answer:
Keeping the absolute wing thickness constant along the span of a tapered wing has the potential to cause the inner portion of the wing to stall first, decreasing or inhibiting "tip stall". The specific combinations of foil thickness, chord, and taper ratio that accomplish this require further investigation and experimentation.

 

[JasonK]

hmm...
I believe a flat bottomed airfoil has a positive angle of attack when the bottom is line with the direction of travel, meaning a shorter cord with the same amount of airfoil shape means more, not less angle of attack.

this seems to be a 'flat' bottomed shape, and notice the zero angle of incidence line goes from the 'fold' to the tail, not along the flat bottom of the airfoil:
http://airfoiltools.com/airfoil/details?airfoil=s7055-il

which would mean doing the above would put your wing tips at a higher angle of attack then the root of your wing.


which puts my conclusion to be the opposite of Pieliker96's

 

[clolsonus]

I found this article which seems interesting:

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1038&context=aere_conf

My takeaway is yes, probably some increase of critical angle of attack with a thicker airfoil, but there is quite a bit more going on if you want to dig in an think about it.

My 2c is for RC models, RC scale, RC speeds you aren't going to notice much of a difference so it's probably just as well to go with whatever is easiest to design, build, or what gives you the look that you want.

If it helps, I have been making a quick tool to help layout/unfold tapered wings including the spar (and considers dihedral.) It's a python script so if that doesn't throw you off, you can find the code here: https://github.com/clolsonus/madesigner/tree/master/sandbox. Pick any root chord, tip chord, leading edge offset (sweep), and even define inner/outer dihedral and the script generates an svg cut file which you can import into inkscape/lightburn, create tiled pdfs, or just print directly if it fits on a single page. Script is open-source so feel free to examine and modify to your taste:

https://github.com/clolsonus/madesigner/tree/master/sandbox

The link will likely change at some point when I'm happy enough with the results and I'll put it in it's own proper subdirectory.

 

[Pieliker96]

hmm...
I believe a flat bottomed airfoil has a positive angle of attack when the bottom is line with the direction of travel, meaning a shorter cord with the same amount of airfoil shape means more, not less angle of attack.

this seems to be a 'flat' bottomed shape, and notice the zero angle of incidence line goes from the 'fold' to the tail, not along the flat bottom of the airfoil:
http://airfoiltools.com/airfoil/details?airfoil=s7055-il

which would mean doing the above would put your wing tips at a higher angle of attack then the root of your wing.

which puts my conclusion to be the opposite of Pieliker96's

Good catch. Consider that the effective increase in angle of attack of the wingtips still may not cause them to stall before the root. Say, for example, the root foil stalls at 10 degrees AoA and the tip foil at 13, due to being thicker. With a decent taper ratio, the angle of attack of the tip is 2 degrees higher than that of the root. But when the wing is placed at 10 degrees of AoA, the root foil will be stalled, but not the tip (13 - 2 = 11 degrees > 10 degrees). This is ultimately another variable to consider, I stand by my original conclusion: It's a complex system, the easiest way to find out if it works is to test it!

 

[techbear]

Wow, great analysis! I hadn't considered the effective increase in AOA caused by the non-symmetrical airfoil. I CERTAINLY hadn't considered the change in the Reynold's number affecting the tip's stall.

 

[JasonK]

Good catch. Consider that the effective increase in angle of attack of the wingtips still may not cause them to stall before the root. Say, for example, the root foil stalls at 10 degrees AoA and the tip foil at 13, due to being thicker. With a decent taper ratio, the angle of attack of the tip is 2 degrees higher than that of the root. But when the wing is placed at 10 degrees of AoA, the root foil will be stalled, but not the tip (13 - 2 = 11 degrees > 10 degrees). This is ultimately another variable to consider, I stand by my original conclusion: It's a complex system, the easiest way to find out if it works is to test it!

ah ok, and that seems to correlate with the research paper showing the thicker airfoil dropping lift at a greater angle of attack. Thanks for the counter point... it does appear to be a fairly complex system.

 

[Merv]

...... Keeping the absolute wing thickness constant along the span of a tapered wing has the potential to cause the inner portion of the wing to stall first, decreasing or inhibiting "tip stall". .....

If the root of the wing stalls first, this increases tip stall. That is when the wing stalls, it will be a very bad stall. It will literally drop out of the sky with out warning.

You want the tip to stall before the root. This will allow the tip to drop more gently, giving you some warning a complete stall is coming.

 

[Pieliker96]

If the root of the wing stalls first, this increases tip stall. That is when the wing stalls, it will be a very bad stall. It will literally drop out of the sky with out warning.

You want the tip to stall before the root. This will allow the tip to drop more gently, giving you some warning a complete stall is coming.

I think you've got it backwards. The ailerons are generally located outboard on the wing for generating the maximum moment per aileron area around the CG. Having the root of the wing stall first results in a loss of lift while retaining aileron control, which manifests as a relatively benign partial stall with little "snap" or "tip stall" effect. The stalled portions of the wing here are closer to the CG, so any asymmetry results in a less pronounced rolling moment. Having the tips of the wing stall first results in loss of roll control - and, if one tip stalls before the other due to any amount of sideslip or yaw rate, a wingtip will drop, as the stalled region is now far from the CG and as such results in a larger rolling moment. Of course, if the angle of attack is increased enough to stall the entire wing, what results will be a "very bad" or full stall, but that will happen regardless of which configuration is used. Having the root stall first gives the pilot more controllability and stability in the region of flight where the wing is partially stalled, and allows the pilot to bring the plane out of the stall with a reduced possibility of a second stall or spin.

See:
Washout: Reducing the angle of attack of the wingtips through wing twist so the root stalls first,
Leading Edge Cuff: Another method of reducing the angle of attack on the wingtips, similar to the undercambered tips on some FT planes, and
Tip stall: Self-explanatory.

 

[Tench745]

If the root of the wing stalls first, this increases tip stall. That is when the wing stalls, it will be a very bad stall. It will literally drop out of the sky with out warning.

You want the tip to stall before the root. This will allow the tip to drop more gently, giving you some warning a complete stall is coming.

Sorry Merv, you have that backwards. You want the root to stall first and the tips to keep flying.

Edit: Pieliker beat me to it.

 

[quorneng]

Never mind the tip stall effect a constant depth spar is structurally inefficient.
With a tapered wing use the extra wing chord to make the spar deeper. Yes it makes construction a bit harder but overall a tapered wing spar is lighter for a given stiffness and strength than a constant depth one.
One other tip is to arrange that the spar is swept back, say a swept leading edge and a straight trailing edge. This will mean under load the wing will twist slightly effectively giving some washout so reducing the chances of the tip stalling first.
Something like a modern airliner swept wing not only has a significant taper, 4:1 or more, hence a structurally efficient spar (no surprise) but due to load twisting and Reynolds number effects at model sizes has a forgiving stall.
The wing of my EDF Airbus A350

 

[TEAJR66]

The FT Bloody Wonder has a tapered wing and the spar stays the same.

Build one and fly it. They are squirrel. Fun, but squirrely.