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# Increased drag with weight

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# Increased drag with weight

26th Dec 2006, 07:59

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Increased drag with weight

I know that LDD (induced) increases with increased weight, but profile drag should only increase with speed.
So my question is, how will my total drag graph change with increased weight?

Last edited by Smells like...; 26th Dec 2006 at 08:00. Reason: spelling error
26th Dec 2006, 12:39

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I'm not sure if I've seen the term LDD before, but the TAS for minimum total drag will increase with an increase in weight, and the value of minimum drag will increase also. So, the curve will move up and to the right. However, I see no reason why the curve itself will retain the exact same shape. Perhaps some others have a comment on that.
26th Dec 2006, 13:53

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26th Dec 2006, 17:38

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A Better Game....

26th Dec 2006, 23:54

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L.D.D. Is Lift Dependent Drag. It's another way of saying Induced.
28th Dec 2006, 10:41

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http://i28.photobucket.com/albums/c2...ndSparrows.jpg
If I temporarily neglect the changes in drag due to changes in pitch. If I make a nod in the direction of compressibility drag with a simple algorithm such as Cdc = (1-(CL-0.25))/400.... By heck I'll make a lot of enemies but a graph of CL squared versus CD will be linear and at the "interview" I'll hope to discuss why this isn't exactly so.
Such devices as these allow me to concentrate on increasing weight purely in terms of increasing CL assuming everything else such as pressure altitude and speed are constant. I drew the accompanying graph based on a fixed Cd0of 0.01563 and Cdi = CL^2/26.295 using logarithmic values purely to compress the data values into a conveniently small range.
Any resemblance to a Company "A" or "B" product that may or may not have served on QF575/580 must be the result of a fevered mind.
The outrageous "dings and sparrows" is my flippant aside. It doesn't take long for a sleek and svelte airframe to become as dimpled as a baby's bottom.
Incidentally I've been parked up the last few months having had a mild stroke through overwork (okay overeating) and demyelinating nerves and have reluctantly concluded that Company "A" (or is it "B") can happily go to the dogs without my assistance. Mrs "E" demands that I pprune but occasionally so its back to Oz when I'm fit enough. No more Frogs Legs!!
Best wishes to all, especially those at home and I hope the Poms are enjoying the seasonal stuffing this Chrissie!
29th Dec 2006, 05:49

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The big E is back! Sorry to hear of your setback enicalyth, my sincere wishes for a speedy accommodation of, and adaption to your new condition. If you feel disposed towards it, a post in the Medical section regarding the effects of and adaption to the mild stroke would be appreciated, it’s something that a lot of us may have to face one day.

Smells Like…, your question requires a dual answer, depending upon the condition. It depends upon whether you’re referring to the same aircraft at differing weights at either (1) the same speed, OR (2) the applicable aerodynamic performance speed, for example, Vmd.

If you consider a conventional drag curve, that is, Drag/Thrust required on the vertical axis, and Equivalent Airspeed on the horizontal axis, the drag curve for the heavier aircraft will move up, elongate, and move horizontally to the right.

Same Speed – The heavier aircraft at the SAME speed (e.g. 200 KEAS), will have to fly at a higher Angle of Attack AND body angle (important), to generate the increased lift required. The lift vector will therefore be greater, inclined more rearwards, with the horizontal component of drag increased by both the greater magnitude of the vector, and the higher trigonometrical vector due to the greater rearward inclination. That explains the increase in Induced Drag. As this higher angle of attack occurs at a higher body angle, the frontal area of the total airframe ‘facing’ the relative airflow is greater, thus a greater value of S (Surface Area) in the

Drag = Cd ½ Rho V^2 S formula.

Thus, induced drag increases, as does profile drag to a generally lesser extent. Total Drag is greater.

Same aerodynamic performance speed (for example, Vmd) – Vmd and other aerodynamic performance speeds such as MRC generally occur at the SAME Angle of Attack, thus change in frontal area need not be considered. To produce the requisite lift at the same AoA, speed must be increased. The Total Lift vector will be at the same inclination for both aircraft, thus the trigonometrically derived rearwards factor is the same, but the magnitude is greater for the heavier aircraft, thus, Induced drag is greater. Frontal (profile) area will be the same for both aircraft, thus S may be taken out of the comparison, but as higher speed is required, the greater speed will lead to greater profile drag – V is the important determinant in the

Drag = Cd ½ Rho V^2 S formula.

Again, Total Drag will be higher, and again, it all depends!!!!!

Caveats galore - Compressibility, transonic shock waves, kinematic viscosity etc. not considered.

Regards, and Happy New Year,

Old Smokey
29th Dec 2006, 07:54

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It would be nice to hear from the OP? After all, the answer to his question is at post#3. We are already 'wandering' into compressibility and soon I expect Reynold to appear .

Hello 'smells like' - you there?

Best wishes 'E'.
29th Dec 2006, 09:08

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The algebra/calculus is not too hard for this. Considering only lift-dependent drag and profile drag as a function of speed v and weight W, the drag curve (in arbitrary units) looks like:

D(v, W) = W^2/v^2 + v^2

So e.g. for W = 1, the minimum of 2 is at v = 1.

More generally, the minimum is D_min = 2W at v_min = sqrt(W). So if you increase W, the curve shifts right and up.

Interesting that D_min scales with W. That's consistent with the idea of a "best L/D" AoA, at which D simply scales with L (which is W).

(Introducing drag with other than a quadratic or zero dependence on lift will change the results a bit, but the effect will be similar.)
29th Dec 2006, 13:44

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Thanks old smokey

cheers old smokey

Thats what I was looking for on the proflie drag side. I fully understood the CL induced drag relationship, but was getting a bit confused with the profile drag side of the graph. It would probally be better for to use 2 graphs for different weights, therefore different speeds.

BOAC, so sorry for not coming back sooner, i've been having a nightmare with local, slow and restricted internet ( I'm still on a contract in the sticks!!! ), so i can't access those pages yet. But i'll be able to in 2 weeks, can't wait!! .
29th Dec 2006, 14:23

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It would probally be better for to use 2 graphs for different weights, therefore different speeds.
- you can look forward to experimenting with all sorts of changes to the a/c and seeing the effect on the graph.
29th Dec 2006, 18:27

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Originally Posted by Old Smokey
As this higher angle of attack occurs at a higher body angle, the frontal area of the total airframe ‘facing’ the relative airflow is greater, thus a greater value of S (Surface Area) in the
Drag = Cd ½ Rho V^2 S formula.
Smokey, I’m having a wee bit of a problem with an item from your last post.

From what I’ve read here at PPRUNE, the use of the area term is just a reference number, and has in the past been used, among other things, as the value of wetted area, wing area, frontal area, or just plain the number “1.000”. As long as it was a constant, it was the choice of the person presenting the data.
And thus I’m not sure when using the equation for profile drag D = .5 rho Cd Vsq S that it is fair to say that the profile drag depends on weight because of a changing frontal area. Consider if S was wetted area, for example, then weight certainly would not have any effect on S. Certainly though, increased weight has an effect on total drag, but I thought it was only in the term induced drag…..

Perhaps MFS or the newly returned E have an input…..
29th Dec 2006, 19:29

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Yes, usually the "S" is just the wing reference area, and doesn't change.

However, it IS true to say that as AoA varies from the optimum for the body for profile drag, the drag contribution from the body will increase. You can think of it as either a change to profile-Cd or an area change - I prefer the former - but the effect is the same...more drag.

ASSUMING that the lighter aircraft is closer to the optimum AoA, of course ...
29th Dec 2006, 20:05
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And thus I’m not sure when using the equation for profile drag D = .5 rho Cd Vsq S that it is fair to say that the profile drag depends on weight because of a changing frontal area.
Not in reference to S, but induced drag is made up of elements of parasite, form and skin drag so it is probably technically correct to say that at higher AoA it isn't just the increase in CL that contributes to the additional drag but the larger surface area too.
30th Dec 2006, 18:31

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OK, thanks for the replies. I'll have to read up some more. And yes, I should have known better than to question something Old Smokey says.
30th Dec 2006, 20:39

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but induced drag is made up of elements of parasite, form and skin drag
You might like to reconsider that statement
31st Dec 2006, 02:50

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Hi pstaney, I would usually respond to a question sent my way, but I think that Mad (Flt) Scientist did it for me. Thanks MFS.

Regards, and Happy New Year,

Old Smokey
31st Dec 2006, 06:24

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Hi John Farley
Quote:
but induced drag is made up of elements of parasite, form and skin drag
You might like to reconsider that statement
Are you saying that induced drag is only from lift production??
31st Dec 2006, 07:37

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May I recommend Google and 'induced drag' to save JF some typing?
31st Dec 2006, 11:20

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Thanks BOAC