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I was reading Ray Whitford's Design for Air combat and came upon a passage that said that on the SR-71 conical camber "gives a useful reduction in the otherwise very high rolling moment due to sideslip inherent in the highly swept delta wing."Text from Design for Air Combat

I could not understand how this would happen and dug a little deeper to find a paper NACA RM A56DO2 where as per my understanding the opposite is said.

If what the book says is true, then an aircraft with a conical camber wing flying with the relative wind from the left (sideslip) should roll to the right with less torque/ rate of roll compared to a normal delta wing.

Here's what the paper says:Graph from the paper. x-axis= Cl= rolling moment coefficient

y-axis= Angle of attack Here the wing is facing relative wind 6° off to the left. We can see that the conical cambered wing with relative wind from the left produces a stronger roll to the right compared to a normal wing. The book says the opposite.

The paper further adds that the conical camber increases maximum effective dihedral. Which will again promotes stability. So am I having a brain fart or is this a contradiction?

P.S Here's the entire graph page:enter image description here

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  • $\begingroup$ Thanks for showing the whole graph page, that helps. $\endgroup$ Apr 12, 2023 at 14:35
  • $\begingroup$ I'd be interested in seeing a new question that simply asked, "Does conical camber in fact decrease rolling moment due to sideslip at positive angles-of-attack, and if so, how does this happen, aerodynamically speaking?" Maybe will have to ask it-- $\endgroup$ Apr 12, 2023 at 15:17
  • $\begingroup$ I edited the opening sentence because your quote did not exactly match the quoted sentence from the book. If you like your wording better, you can put it back, but I'd suggest removing the quotes. $\endgroup$ Apr 12, 2023 at 16:00
  • $\begingroup$ I created a chat room to discuss further-- feel free to post there--chat.stackexchange.com/rooms/145487/… $\endgroup$ Apr 21, 2023 at 13:35

2 Answers 2

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I was reading Ray Whitford's Design for Air combat and came upon a passage that said that on the SR-71 conical camber "gives a useful reduction in the otherwise very high rolling moment due to sideslip inherent in the highly swept delta wing."

...

If what the book says is true, then an aircraft with a conical camber wing flying with the relative wind from the left (sideslip) should roll to the left or at least the rate of roll to the right should be reduced.

(Bolding added)

There's a huge difference between simply reducing the rolling moment due to sideslip, and reversing the rolling moment due to sideslip! Delta wings are well known to have a strong positive rolling moment due to sideslip, and in the absence of a clear and direct statement, it would be unreasonable to assume that the book was trying to convey that the direction of this rolling moment would be reversed by introducing conical camber, as if the wing had a great deal of anhedral. Nothing that you've quoted supports that conclusion. The bolded sentence in particular clearly references a reduction in rolling moment due to sideslip, not a reversal in the direction of the rolling moment due to sideslip.1

However, you are correct in noting that there is a contradiction between the idea expressed in the book-- namely that introducing conical camber on a delta wing reduces the rolling moment due to sideslip-- and the graph from the NACA paper, which shows that-- at least between about 4 and 10 degrees of positive angle-of-attack-- delta wings with conical camber show a stronger rolling moment due to sideslip than does a delta wing without conical camber.

Footnotes:

  1. It would not be unreasonable to imagine that a design feature that reduced the rolling moment due to sideslip over most of the positive angle-of-attack range, might reverse the direction of the rolling moment due to sideslip at very low positive angles-of-attack (i.e. very near zero). For example, that's what we'd expect to see if we added a mild amount of anhedral to a delta wing. So we need to be a bit careful about blanket statements as to whether a given design feature reduces the rolling moment due to sideslip, or reverses it-- it may well depend upon what part of the flight envelope we are looking at. This is particularly relevant in the case of a very-high-speed aircraft that will cruise at very low angles-of-attack. However that nuance is clearly not the root of the observed discrepancy between the two sources. Unlike what we'd expect to see in the case of a delta wing with anhedral, on the plot you've provided from the NACA paper, it appears that the delta wings with and without conical camber all experience nearly zero rolling moment due to sideslip at angles-of-attack near zero degrees.
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  • $\begingroup$ Obviously we're speaking in broad generalities here. The effect (on rolling moment due to sideslip) of adding conical camber to delta wing could well depend on the aspect ratio of the wing. Look at photos of hang gliders, especially the old "Rogallo" designs with tremendous amounts of conical camber. This can be viewed as essentially adding dihedral to the inboard portion of the wing, and adding anhedral to the outboard portion. $\endgroup$ Apr 12, 2023 at 15:34
  • $\begingroup$ (ctd) Highly tapered (low-aspect) ratio designs have so little area in the outboard (anhedral) portions that resulting shift in "effective dihedral" is distinctly in the positive direction; with less tapered (higher-aspect) ratio designs the reverse appears to be true, so that the effective dihedral is shifted in the negative direction and reaches negative values at low (but still positive) angles-of-attack. $\endgroup$ Apr 12, 2023 at 15:47
  • $\begingroup$ (ctd) We don't see anything like this in the NACA graph, and I'm not sure the geometry of the conical camber in the Rogallo wing is really very similar to geometry of the conical camber that NACA is graphing. In the Rogallo case, the leading edge remains linear, while the camber is created by sail billow such that the trailing edge rises from root toward mid-span area and then descends again back toward the tip. That's not the geometry we see when we look at a SR-71! $\endgroup$ Apr 12, 2023 at 15:47
  • $\begingroup$ The second quoted passage from the question was changed during the time that I was creating and posting this answer-- the question no longer interprets the passages in the book to suggest that conical camber creates a reversal in the direction of the roll torque due to sideslip. $\endgroup$ Apr 12, 2023 at 16:11
  • $\begingroup$ Nonetheless I'm just going to let the answer stand as is, at least for now. $\endgroup$ Apr 12, 2023 at 16:11
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... using my desert cooler as a wind tunnel

That's the spirit!

Let's first evaluate the degrees sweep of the B-58 Hustler and F106 Delta Dart vs the NACA paper. The former are 60 degrees sweep and the paper covers 45 degree sweep.

This becomes important because highly swept delta wings use vortex lift, which can be easily broken in a sideslip. This may explain why the book and the paper provided conflicting results. Add in the effects of engine nacelles acting as fences and you have a fairly complicated situation even before Mach effects.

From personal paper airplane experience, 45 degrees seem to be in a "transition zone" between straight wing and slender (highly swept) wing cross wind behavior.

Straight wings with dihedral effect tend to roll away from a cross wind, while slender deltas roll into due to loss of upwind wing lift.

Flying a model Delta Ray, which did fine > half throttle, a real "bricking" tendency was noted banking low and slow (you know how). The feeling at the RC forum was the wingtips may have been better pointed downwards!

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