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?

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.

A Better Game....
 

L.D.D. Is Lift Dependent Drag. It's another way of saying Induced.:)

very quick reply
 

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!

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

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'.:ok:

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.)

Thanks old smokey
 

cheers old smokey:ok:

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!!:) .

- you can look forward to experimenting with all sorts of changes to the a/c and seeing the effect on the graph.:ok:

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…..

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 ...

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.

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.

You might like to reconsider that statement

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

Hi John Farley
Could you please explain?Are you saying that induced drag is only from lift production??

May I recommend Google and 'induced drag' to save JF some typing?

Thanks BOAC

This formula is not homogeneous, so something must be missing.
Where does it come from? What assumptions are behind?

I suspect it is simply stating Total drag is the sum of induced drag + form drag.

For induced drag see:
https://en.wikipedia.org/wiki/Lift-induced_drag
Since Lift = Weight (at 1g).
Induced drag is proportional to W^2/v^2

Form drag is proportional to v^2.

Hence Total drag is proportional to W^2/v^2 + v^2.

One factor that often get's overlooked (though not by glider pilots!!) is that a change in AofA ALSO changes profile drag, as the airframe is presented at a different angle also.

That's why you can actually achieve a better LD ratio in some gliders with a small amount of flap deployed.

For the glider example, it likely has to do with the basic design philosophy of the builder, as well as nomenclature.

If a glider is actually a high-performance sailplane, focused on competitive long-distance soaring, then the wing will be designed as much for speed as for glide ratio (L/D). A "1 degree" flap setting or similar may be incorporated to get better L/D at lower speeds for thermalling. OTOH, other sailplane mfgrs will instead incorporate a "negative flap" setting for high-speed dashes, while the normal 0 deg setting is used for thermalling.

You actually go for minimum sink (Min drag) during thermalling, and thus often use a positive flap setting.

This will be at a lower speed and thus higher deck angle than best L/D (which isn't always the most efficient inter-thermal speed) in a glider with no flaps. Thus, if the gliders incidence is set such that it produces minimum profile drag at best L/D, you will present the bottom of the fuselage to the airflow, increasing profile drag.

A positive flap setting will give approximately the same wing performance, while putting the deck-angle back to optimum.

You are correct that then a reflex, negative flap setting will do the same thing at speeds greater than best L/D.

I've often thought variable incidence would be a better solution than flaps, though obviously mechanically more complex.

After only 12 years of hibernation, this query raises it's ugly head on the 1st April. What planet am I on??

That's between you and your therapist.

Well. it's only been necro-ed the same number of times as Jesus.

I think a lot of the posters who are saying the Parasitic Drag... increases... have forgotten one thing... The Axis of the fuselage is not the axis of the mean chord line. Airplane designers ( model or full size.) include about 3 degrees difference in these two axis.


So it might just be that the fuselage will align more into the prevailing airstream at an increased weight, if the airplane was initially flying somewhat nose-down. There should only be one speed where the fuselage is level, at all other speeds it is either Plus or Minus.
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Post #21 was 12 years in the making!

Yeah- this was exactly my point four posts up....

Hi Wizzy.. I think you mean 6 posts up, not the therapist post...


For Gliders the figures are soooo small. A typical 350kg glider with 35:1 L/D
has a drag of just 10kg... 5kg Induced drag and 5kg Parasitic. So even sticking your hand out of the DV window is likely to double your Parasitic Drag. I also think that the fuselage may not contribute much to this drag, as the tailplane is providing negative lift, so it's Induced drag gets counted towards the parasitic drag. One reason for putting water ballast in the tail.


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I never had these sort of complex problems in hang-gliders. Just stuff the bar out in thermals and up she went. Pull in for best glide inbetween. Unless you had that fancy Variable Geometry (Billow) system not much else to worry about. No tailplane either. ;)

I am afraid most information you find through Google will be very simplicstic... Real life is a bit more complex, probably even too complex to discuss it in a forum with the restricted possibility to draw up some graphs.

Unfortunately if we talk transport airplane we can not ignore mach number. In typical cruise the upper wing surface is 30-50% supersonic and profile drag is strongly influenced by this. A little change in lift may change transsonic drag significantly.
If we strictly talk subsonic, turbulent and moderate Cl your simplification is correct. If we go transsonic, consider laminar airflow and go closer to Cl max it becomes quite complex.
As Cl is limited, a weight increase typically means a speed increase (starting already before you even fly with Vr calculation...), this makes the induced lift discussion a bit academic. Nobody would (only) increase Cl to compensate for heigher weight.

Your total drag will increase as well because total drag=profile drag+induced drag. Therefore, even though the change in the weight will only affect your induced drag, it will ultimately affect your total drag, hope it is clear..

Is this a bit of an academic question anyway, there are not too many ways for aircraft to gain weight in flight, but lots of ways to loose weight... Some with disastrous consequences...


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