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How Do Delta Wings Affect CL & CD  
User currently offlineLehpron From United States of America, joined Jul 2001, 7028 posts, RR: 19
Posted (12 years 3 months 3 days 3 hours ago) and read 5595 times:

In my textbook, "Introduction to flight", 4th Ed, by John Anderson Jr. they talk about flow over wings and how the induced flow interferes with the angle effective and gives formula approximations and stuff which are based on finite wings of a certain shape, incompressible flow, etc; but I can not find anything with regards to how supersonic planformed wings affect their subsonic force components since their induced flows actually goes over the top rather than at the tips of the wings. Can someone tell me what is up with that?

Actually I just want a formula.  Smile

The meaning of life is curiosity; we were put on this planet to explore opportunities.
7 replies: All unread, jump to last
User currently offlineMITaero From United States of America, joined Jul 2003, 497 posts, RR: 7
Reply 1, posted (12 years 3 months 2 days 21 hours ago) and read 5549 times:


I gotta look into this some more, but I believe that using the induced drag equation (CDi = CL^2/pi*e*AR) should help here. The aspect ratio of the wing (b^2/S) is much smaller, and the span efficiency ratio e is much worse (lower), leading to higher induced drag on these wings.

I'm not sure how CL is affected.. at cruise it seems that CL would not need to be as high, due to the high area of the wing (could produce L=W with a smaller CL since L=W=1/2*rho*V^2*S*CL).

User currently offlineFredT From United Kingdom, joined Feb 2002, 2185 posts, RR: 25
Reply 2, posted (12 years 3 months 2 days 20 hours ago) and read 5542 times:

Basically, CL just keeps increasing with increased AoA, rather than falling off as it does when a normal wing stalls. I would not be surprised to see a change in gradient in the CL curve at about the alpha where the vortices start to shed along the LE. I'll see if I can find any hard data in the library tomorrow.

On the downside, CD goes right through the roof as well...


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User currently offlineB2707SST From United States of America, joined Apr 2003, 1384 posts, RR: 58
Reply 3, posted (12 years 3 months 2 days 13 hours ago) and read 5499 times:

I found a couple of diagrams in Mach One and Beyond, one relating wing sweep to several performance characteristics, the other showing the effect of vortex shedding on a double-delta or ogee wing at low speed. I'm not sure if they answer your questions.


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User currently offlineMITaero From United States of America, joined Jul 2003, 497 posts, RR: 7
Reply 4, posted (12 years 3 months 2 days 12 hours ago) and read 5485 times:

Didn't know about that lift coefficient effect at low speeds, pretty cool.

It makes sense that a/c designed for supersonic flight (or M close to 1) have swept wings - decreases relative Mach number, helps wave drag.

User currently offlineLehpron From United States of America, joined Jul 2001, 7028 posts, RR: 19
Reply 5, posted (12 years 3 months 2 days 7 hours ago) and read 5475 times:

Yeah they do kind of answer my question expect there are not many numbers on the graphs. Most of my transonic projects have wings ranged between 40 and 60 degrees. But my primary interest is in hypersonic and I figure that shoe horn shaped lifting bodies behave just like deltas expect their leading edge sweep angle goes from 75 to 87 degrees at some points to fit into high Mach number flight cones.

Like I have this design that follows a hyperbolic curve in meters, where 'x' is span and asymtote is cruise Mach:

L = 69.4 – (47.4-47.4x)0.5 + (47.4)0.5

Can someone estimate the CL and CD based only on planform?

I am certain wedge bodies behave like delta wings.

I asked my professor who supervises those students in their senior projects if instead of a subsonic concept like everyone else, i want do subsonic tests on a hypersonic concept plane. I have not read much done in that particular sequence of flight so I am curious. He at first suggested otherwise because of the complexity as they are not shaped as simple as say most airliners. Then I told him that I've been studying this for years and to me it is not that complex, he let it slide as long as I knew what I was getting into but suggests i wait and watch how other students deal with "different" shapes.

[Edited 2003-11-14 07:00:24]

The meaning of life is curiosity; we were put on this planet to explore opportunities.
User currently offlineVikkyvik From United States of America, joined Jul 2003, 11904 posts, RR: 24
Reply 6, posted (12 years 3 months 2 days 3 hours ago) and read 5454 times:

Swept wings help subsonic jetliners that fly at speeds close to Mach 1, as was stated by MITAero, but the swept wing design on most commercial jetliners is specifically designed for the approximately M~0.8 range, as far as I know. This is due to the fact that the flow over a straight wing at these speeds would be supersonic, causing shock waves and wave drag. From what I understand, given certain conditions, the flow over airliner wings will occasionally be supersonic, and visible shock waves will develop. As far as delta wings for supersonic aircraft go, I know that the design is incredibly complex. One of the factors I've heard of is having a wing that will not penetrate the (bow?) shock generated by the airplane, as it travels past the side of the airplane. My question, though, is how is flow kept unseparated along the upper surface of this kind of wing? And even if it's not separated, wouldn't the boundary layer flow be significantly turbulent by the time it reached the trailing edge, causing more drag?

You may want to look at section 6.19 in Anderson 4th Ed....It might hopefully answer some of your questions. Best of luck.

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User currently offlineLehpron From United States of America, joined Jul 2001, 7028 posts, RR: 19
Reply 7, posted (12 years 2 months 3 weeks 2 days 4 hours ago) and read 5376 times:

I talked to my aerodynamis professor, he says that delta winds and wedge-cone bodies may have a similar vortex effect and perhaps thus similar characteristics. I think there will be more Newtonian than Bernoulli here, I donno. His feild of study was not even supersonic, he based everything on the book.

Vik, we just got into chapter 6 and I dont think we will cover up to section 6.19 so I have dont it on my own. I keep playing with eqn 6.143 and I'm having trouble, my range is always small, but I'm working with it. What sux is that I get the impression from Chapter 11 on hypersonics that they assumed the lift was primarily from a "winged-vehicle" those shapes in the figures do not have the shapes I am familiar with. I could assume planform but for how long?

The meaning of life is curiosity; we were put on this planet to explore opportunities.
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