Paging Stranger on a Train and other engineering types!
I happened to see a photo of a pair of Thorp T-18s, and it reminded me of the free-flight Midwest ‘Sniffer’ model I built when I was a kid. Notice the dihedral. The Sniffer not only has the normal dihedral at the fuselage, but also dihedral on the outer wing panels. The T-18 has a flat midsection with dihedral on the outer panels.
The purpose of dihedral is well-known and obvious, and it’s also obvious why the extra dihedral would be beneficial on a free-flight model. But it got me to wondering about the structure on a manned aircraft. Most fixed-wing aircraft have dihedral only at the fuselage. This is where the wing is thickest, so the structure can be larger for more strength. In many designs I would assume that additional strength would come from the wing/fuselage junction. The spar would be a single piece (actually a single piece of metal, or else built-up) running from root-to-tip. With dihedral on the outer panels the wing is thinner (less room for a beefy structure), and a bending moment would be applied to a non-continuous spar.
Obviously the design works, as seen on the T-18, the F-4 Phantom series (on which the panels fold), and other aircraft. But is it really a logical design on light aircraft? How much weight does it add? How strong are the bent wings relative to traditional ones with continuous root-to-tip spars?
Do you mean continuous but bent spars? There’s no effect on either stiffness or overall spar stress, although there can be local stress concentrations at the bend. You’ll have a slightly more complex control linkage system, too.
The main reasons not to do it are mostly aerodynamic. You’ll get some flow disturbances on the top surface in the joint, and those can cause stall to initiate out there instead of at the root, leading to loss of aileron authority earlier than you’d like. Even in cruise, the extra turbulence, along more of the wingspan than with a straight wing, will produce more drag.
With composite construction, “bent” spars are no big problem. As multi-planar wings offer certain handling and performance advantages, they are starting to become common for high-performance sailplanes. Here are photos of a new 2-seat design.
Warning: Five hours of sleep, just got out of bed, no coffee yet. What I meant by ‘continuous’ is a ‘single piece of metal’ running from the root to the tip. By ‘single piece of metal’ I mean, for example, a thick-walled 4" diameter aluminum tube or an I-beam to which the ribs are attached, or a ‘built-up’ structure whose main component is a single piece of metal from the root to the tip. For a built-up structure, what I mean is that the main bit of the spar would be a thick-ish piece of flat aluminum, perhaps tapered, that is ‘on its edge’ with perhaps angle aluminum bonded and/or riveted to the edges to make (for example) a tapered I-beam. Or perhaps concentric square or round tubes so that the tip is smaller than the root (i.e., tapered). Obviously I’m talking about a small general aviation aircraft and not a ‘heavy’, which I imagine would make use of more milled parts than a small aircraft would. And I’ll just mention lightening holes on G.P.
With a multi-panel wing, I’m curious about the bend. A tubular spar can be bent easily enough without (I think) too much weakening of the metal where it’s bent. What about an I-beam? Not being a structural engineer I’m curious about weakening of the metal since ISTM an I-beam would be harder to bend in that direction. Is it a concern? Would there be doublers at the bend for added strength?
Or would the spar be ‘non-continuous’? That is, each panel would have its own spar segment that is joined (possibly with doublers – I don’t knot) at the bend? That is, instead of one continuous root-to-tip piece of metal, there are two pieces of metal.
It’s an interesting point about flow disturbance at the joint. Wouldn’t it be better to simply wash out the tip so that the tip has a lesser angle of attack (or incidence) than the root?
Structurally, the wing spar carries the greatest load at the root. Thus keeping this straight allows it to be stronger. To avoid dropping a wing on stall, most wings have washout, so the wingtip operates at significantly lower angle of attack than the root. This tends to unload outboard dihederal joints even more.
Metal wing spars were typically made up of numerous pieces riveted togethor, so arbitrary shapes are possible without concerns about how to bend them. Besides allowing simpler fabrication, this allows repair without having to replace the entire spar. A notable exception is the B-1, which used titanium forgings, but again, that allows pretty much any shape. I’m pretty sure the center section of the B-1 still holds the record for the largest titanium forging.
Stability. If a wing with dihedral is raised, the lift vector is rotated and the aircraft slips in the toward the lowered wing. The lower wing has a greater angle of attack than the higher wing, so it makes more lift and tends to rotate the aircraft back to an ‘even keel’.
But that’s not the question. I’m interested in the structure, and the advantages and disadvantages of polyhedral wings.
Um, no, it doesn’t. The lower wing creates more lift because it has more projected area when seen from above - it “flattens out”.
Next, you’re going to ask why high-wing airplanes like the C-5 have zero to negative dihedral, aren’t you? That’s because pendulum stability (from the CG being below the wing) is enough to provide roll stability. Adding dihedral would make the plane *too *hard to roll and would introduce control problems, including Dutch roll. Low-wing planes have negative pendulum stability and dihedral is needed to counteract it.
Washout does help make sure the stall progresses from the fuselage outboard, btw, but it’s at the cost of optimizing angle of attack across the span. Creating a local disturbance, as discussed above, makes even more washout necessary and costs even more efficiency.
This is what I was taught. The way it was explained is that as the aircraft banks the wind is coming from a greater angle to the descending wing. This jibes with what I was taught about ‘flapping’ in helicopters.
But I’ve just done a search, and I found this (emphasis mine):
I have to admit that I am unfamiliar with ‘free-stream velocity’, so maybe that’s what you’re getting at.
Really? I’ve never seen an explanation other than what I just posted.
Free-stream velocity is just the airspeed at enough distance from the aircraft not to be affected by it - the ambient air velocity relative to the direction of flight.
The description you posted sounds like it’s including sideslip in the scenario, with the lower wing further forward. If you picture the orientation of the chord line at any particular location on each wing, and limit the aircraft axis to be parallel to the direction of flight, you can see the angle between the chord line and the free-stream velocity is the same.
It’s true that the high wing, at a steeper angle to the ground, will have more effective camber (it will be “thicker” in vertical cross-section), and that will produce more lift per unit area that has to be offset by the higher total projected area of the lower wing. But that higher lift also produces higher induced drag, pulling it aft, maybe more than the increased induced drag of the flatter wing. Maybe the net difference is the sideslip that your NASA cite is getting at?
Possibly. I’ve only heard the ‘flapping’ (sorry, I’m more of a rotorhead) explanation – at least until just a bit ago.
But if we could take that as read, I’ve kind of got this worm in my head that wants to know about polyhedral on full-sized aircraft. (Not that aerodynamics in general isn’t interesting!)
And that’s the wrong explanation that I said I’ve seen so much of. Sure, the lower wing has more projected area when seen from above, but why should that matter? Lift isn’t exclusively upwards, so why project it to vertical? Both wings would still put the same torque on the plane.
You’re both right. The angle-of-attack effect improves transitional stability. When the wing is upset, the lower wing starts flying at a higher angle of attack, which creates an additional lifting force that acts in opposition. This makes the airplane more dynamically stable - it’s an almost viscous effect that dampens oscillations.
The projected area model is correct in terms of static stability. If you put the airplane in a static position where one wing is lower than the other, the lower wing has a force vector closer to vertical, which forces it back towards an equilibrium position.
I was going to point out that I’ve seen polyhedral wings on a bunch of GA aircraft but I could only think of the Culver V off the top of my head. I know I’ve seen others.
Yeah, that’s the thing. There’s the Culver, and there’s the T-18, and there’s the… ? It’s like you notice them when you see them, but when you try to think of them they’re gone.
I see that the Culver, like the Thorpe, has a flat center section. On a light aircraft I can see that it would be easier to build it that way than to have dihedral on the outer panels and the center section as well. And I understand that it makes no sense to have the extra bend if you don’t need it. But I’m still not sure what the advantage is of having outboard dihedral in the first place, over the conventional layout.
I suspect the higher AOA explanation has a dynamic element that isn’t explained.
Imagine an aircraft with 3 degree dihedral. Imaigine it is in wings-level flight. The AOA on left & right wing is the same. Now magine it is in a steady-state bank of 10 degrees right wing low. The AOA on left & right wing is the same.
Now imagine it is rolling to the right at 10 degree/sec and now passing through 10 degrees right wing low. At that instant the AOA is greater on the descending wing. Not becasue of dihedral or bank angle, but because of roll rate.
