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

### Lift-to-Drag Ratio Vs. Velocity For An SST...?

I made up this general graph based on pure theory. I need someone to criticize this mainly because I have never actually seen an L/D ratio graph for supersonic transports -- this type of graph doesn't exist in any of my aerodynamics' texts, but the formulas to make it do.

From this graph below, an (L/D) max exists for the two different speed ranges before and after Mach 1. I think the dip in the middle is due to the sound barrier and the second lift-to-drag max is due to compressed density that increases lift and drag to a point where it drops-off on the left due to wave drag overtaking compressed lift.

If something doesn't exist on the picture below, please tell me A.S.A.P, otherwise I will assume it to be a general approximation of what really happens.

note: if there is a second L/D max, i don't think it is that much higher than the one for subsonic flight. On the otherhand, an SST isn't designed to fly subsonically.
The meaning of life is curiosity; we were put on this planet to explore opportunities.

wilco737
Posts: 7275
Joined: Sun Jun 20, 2004 12:21 am

### RE: Lift-to-Drag Ratio Vs. Velocity For An SST...?

Well, I am not sure about the drop of the curve at M1.00!

What I learnt at flight school about supersonic aerodynamic is: the closer you get to Mach 1, the higher the drag is. THats why the concorde needed the afterburner to accelerate to cross the sound barrier and then switched the afternurner off again and accelerated to M 2. Without the afterburner she wouldnt have gone to M 1 or more!

WILCO737

zeke
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### RE: Lift-to-Drag Ratio Vs. Velocity For An SST...?

[Edited 2005-10-04 10:31:19]
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mrocktor
Posts: 1391
Joined: Mon Jan 24, 2005 12:57 am

### RE: Lift-to-Drag Ratio Vs. Velocity For An SST...?

Out of curiosity, could you plot ML/D?

mrocktor

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

### RE: Lift-to-Drag Ratio Vs. Velocity For An SST...?

I've seen that picture before, it was from a NASA website. What I got from that/it was that it showed the variances between zero-swept wings and higher swept back angles and their related L/D ratios through the speed of sound, concluding that the variable-sweep design, at the time, was the best of both worlds.

Concorde has a fixed variable sweep that curves from 70-degrees to 55-degrees; the data doesn't add up. I'm not claiming that a graph from a NASA website is wrong, just it was meant to describe a specific condition.

As of the second graph, I wish there were more points available for Concorde. I could conceivably come to the same conclusion with my plot if I gave 3 points. Also, which Boeing HCST was that? Though the one from 1969 and 1999 looked similar, I doubt they were.

Besides, density to stagnation increases with Mach, rho2/rho1 = (1+0.2M2)2.5 in air. If density affects lift and drag, why the drag drop after M1.0? Even wave drag depends on velocity (mach-wise) and angle of attack of surface. What equations/methods am I missing?

 Quoting Mrocktor (Reply 3):Out of curiosity, could you plot ML/D?

It was. If I took out the Mach factor, the max points would be higher but occur at slower velocities. Plus I don't know the real TSFC, e and CD,0 of Concorde, that data I cannot find online anywhere.

I had to average the fuel consumption by dividing the total fuel used for a 3 hour flight; I get 0.5 lb/lb/hr, average. I took as much as I could into account to minimize what I don't know. The resulting CL1/2/CD needs to be 12.3588 to have the range of 3600 Nmi, using Burguet eqns for range. So I made a formula estimating CD,0 as a function of the wing's efficiency factor, e. Concorde has a delta wing and having that vortex kills off any elliptical load distribution, so I know it’s shotty. I came up with having e = 0.60 and CD,0 = 0.0253 which gave the highest (L/D) max subsonic. But this max value was still smaller than the data I found on Concorde at the same speed.

No doubt, this is dirty math, it isn't accurate because it makes many assumptions -- which might account for it being different than the NASA graph. I'd like an explanation.
The meaning of life is curiosity; we were put on this planet to explore opportunities.

B2707SST
Posts: 1263
Joined: Wed Apr 23, 2003 5:25 am

### RE: Lift-to-Drag Ratio Vs. Velocity For An SST...?

I'm not an aerodynamicist, but I very much doubt the second (supersonic) peak will be higher than the subsonic peak. Even the best SST designs I've seen have supersonic L/Ds in the order of 10-12, which even Concorde could beat at Mach 0.95 (L/D = 12.5); it course, it was killed by subsonic SFC.

This chart shows the L/D for an F-111D with increasing sweep values (and implicitly higher Mach numbers). It's the only specific reference I could find that directly associates L/D with Mach number.

Some NASA publications might have these sorts of charts for fighters or supersonic research planes. I would imagine the bombers are still classified (I've never been able to find the XB-70's cruise L/D, let alone the B-1's).

--B2707SST
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zeke
Posts: 11219
Joined: Thu Dec 14, 2006 1:42 pm

### RE: Lift-to-Drag Ratio Vs. Velocity For An SST...?

 Quoting Lehpron (Reply 4):What equations/methods am I missing?

Considering super computers have trouble doing this sort of calculation I am not surprised.

Compressability, wave drag, shocks, bow wave etc..transonics is a black art.

This may help http://history.nasa.gov/SP-367/chapt6.htm

 Quoting Lehpron (Reply 4):It was. If I took out the Mach factor, the max points would be higher but occur at slower velocities. Plus I don't know the real TSFC, e and CD,0 of Concorde, that data I cannot find online anywhere.

This site http://www.concordesst.com/concordeb.html has Concorde CL and CL/CD, should be able to derive some data from whats given.

Nasa did some work with a TU-144, a bit of info on the internet about that.

This is a good link also for the sonic cruiser http://www.dlr.de/as/institut/abteil...s/hepperle-sonic-cruiser-paper.pdf

Also have a look at http://books.nap.edu/html/commercial_supersonic/ch3.html for the Boeing graph above.

Enjoy !
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phollingsworth
Posts: 635
Joined: Sat Mar 06, 2004 6:05 am

### RE: Lift-to-Drag Ratio Vs. Velocity For An SST...?

 Quoting B2707SST (Reply 5):would imagine the bombers are still classified (I've never been able to find the XB-70's cruise L/D, let alone the B-1's).

I don't know about the B-1, but from some of the flight test data I have seen (unclassified) the L/Dmax of XB-70 at Mach 3 is above 8.

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