lehpron
Topic Author
Posts: 6846
Joined: Tue Jul 10, 2001 3:42 am

### How Do Delta Wings Affect CL & CD

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

MITaero
Posts: 485
Joined: Mon Jul 28, 2003 8:00 am

### RE: How Do Delta Wings Affect CL & CD

Hey,

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).

FredT
Posts: 2166
Joined: Thu Feb 07, 2002 9:51 pm

### RE: How Do Delta Wings Affect CL & CD

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...

Cheers,
Fred
I thought I was doing good trying to avoid those airport hotels... and look at me now.

B2707SST
Posts: 1264
Joined: Wed Apr 23, 2003 5:25 am

### RE: How Do Delta Wings Affect CL & CD

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.

--B2707SST
Keynes is dead and we are living in his long run.

MITaero
Posts: 485
Joined: Mon Jul 28, 2003 8:00 am

### RE: How Do Delta Wings Affect CL & CD

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.

lehpron
Topic Author
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Joined: Tue Jul 10, 2001 3:42 am

### RE: How Do Delta Wings Affect CL & CD

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.

vikkyvik
Posts: 12085
Joined: Thu Jul 31, 2003 1:58 pm

### RE: How Do Delta Wings Affect CL & CD

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?

Lehpron,
You may want to look at section 6.19 in Anderson 4th Ed....It might hopefully answer some of your questions. Best of luck.
~Vik
I'm watching Jeopardy. The category is worst Madonna songs. "This one from 1987 is terrible".

lehpron
Topic Author
Posts: 6846
Joined: Tue Jul 10, 2001 3:42 am

### RE: How Do Delta Wings Affect CL & CD

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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