I have read some articles mentioning that a full dihedral reduces the lift produced by a wing. So what about a tip (or cranked) dihedral that has the angled part starting from the mid-wing rather than the root of the wing?
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$\begingroup$ What does your analysis tell you? $\endgroup$– JimCommented Jul 3, 2022 at 13:12
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$\begingroup$ That resembles something they did with the Phantom jet. But look at its tail. $\endgroup$– Robert DiGiovanniCommented Jul 3, 2022 at 17:44
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2 Answers
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The ratio of vertical lift to total lift in a bank angle is cosine bank angle. Cosine of 5 degrees is 0.996. Dihedral "banks" each wing very slightly from vertical. Typical dihedral angles affect lift very little.
Working this problem a bit further, we find that the cosine function is non-linear as angle increases. This means that half a wing at a steeper angle with half a zero angle actually has less vertical lift than a full wing dihedral of the same fuselage to wing tip angle.
A "cranked dihedral" would also be more complicated to build and not as strong. The design is sometimes seen in older model gliders. Some full scale aircraft may have winglets, but are plenty stable without extra dihedralling at the wingtips.
answered Jul 3, 2022 at 14:39
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$\begingroup$ It's not harder to build at all. You have to put the joint for the change in angle in there somewhere. The Thorp T-18 did it to allow each wing to be single 4 ft skin wraps, with a straight spar carrythrough and the joint at mid span. $\endgroup$– John KCommented Jul 3, 2022 at 17:43
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$\begingroup$ Yes, but the "joint" now has a sharp angle. I'd rather brace the whole dihedral angle with a cross beam inside the fuselage. The tips do provide a bit more ground clearance. $\endgroup$ Commented Jul 3, 2022 at 18:46
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1$\begingroup$ The angle is unimportant. You are creating a splice at the change in angle, and putting it at mid span means the splice can be much lighter, the stresses being lower, and you now have a straight one piece spar carrythrough through the fuselage without any splices at the highest stress location. Most designers do it at the wing root because the wing is designed to be removeable so the connection is done at the root and might as well put the dihedral break there as well. $\endgroup$– John KCommented Jul 3, 2022 at 19:23
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$\begingroup$ I can see along an entire rib structure a splice is feasible, but if anything I would favor a bit of anhedral (from a dihedralled wing). Birds such as seagulls and geese do this naturally to improve crosswind control. But it is a workable design. $\endgroup$ Commented Jul 3, 2022 at 21:35
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$\begingroup$ Minor observation--if the design objective definitely includes a wing that can be disassembled into at least two pieces, much weight can be saved by making a one-piece center section with removable tips, as opposed to a wing that breaks apart right at the center section. (I.e. don't put a junction at the point where the bending load is greatest.) In such a case, if the tips are removable anyway, there may not be a significant weight (or roll inertia) penalty incurred by designing a dihedral break coincident with the point where the removable tip joins the wing center-section. (ctd) $\endgroup$ Commented Jul 4, 2022 at 20:42
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The main performance penalty incurred by dihedral is arguably not the slight loss of "verticality" in the lift vector generated by each wing, but rather the fact that if any accidental sideslip is present, the angle-of-attack of the "upwind" wing will be increased and the angle-of-attack of the "downwind" wing will be decreased. (That's how dihedral "works" to create roll stability, after all.) Even disregarding the additional drag incurred by whatever aileron input is needed to cancel this roll torque, due to the shape of the curves of the lift and drag coefficients (versus angle-of-attack), flying around with the two wings at different angles-of-attack is generally less efficient than flying around with the two wings at the same angle-of-attack.
Making the wing flat in the middle and reserving the dihedral for the tips-- where it will have the most benefit in terms of maximizing the stabilizing roll torque generated by a sideslip-- minimizes this drag penalty during accidental (and perhaps transient) sideslips, for any given desired degree of overall "effective dihedral", i.e. any desired amount of roll torque generated by a given sideslip angle.
answered Jul 4, 2022 at 18:15