Drag figures

Or to put it yet another way, the way to scale up from the model forces to derive the full size ones is to scale up the reference area from the model’s wing area to the full size aircrafts wing area, keeping everything else in the equation (including Cd) the same. I have arrived at what I was trying to say at last – sorry it was a bit ’round the houses’ if only to get to something you already knew!

I am aware that there are slight qualifications to this.

Ah yes, I see – thanks Graham. I’m new to this.

I beg your pardon, I was thinking of the full-scale tunnel where there’d be no means of differentiating between velocity and mach.

Graham, I worry that something on the general discussion board has made you oppositional to me

I suspect the P-51 results you are referring to are those done in the Langley full scale tunnel – but certainly not based on Mach numbers as the Langley tunnel was unable to reach anything significant (AFAIK)..

No.. please read the report that I referred to and linked to before telling me what it contained and that I am wrong about it. It discusses Mach when describing matching the conditions of the test tunnel – at Ames, not Langley – and the full-size tests. A bit of reading around shows that it was known then that matching Mach was important, and not airspeed.

The Meredith effect is basically just flow through ducts – it would be present with or without propwash. The magnitude might be different, but it would not disappear. .

It would if the air was not heated by the radiator (the effect doesn’t tap into a magic source of energy). As in this case, because the engine is off.

“The squaring adjustment happens in the squared relationship change in reference area between model and full size – and that is what this apparently arbitrary element is actually for!” Sorry, I’ve no idea what you mean by this.

Look at the equations a bit longer (I had to stare until my forehead bled), think about how the units cancel out to make the result a dimensionless co-efficient and you’ll see it. Basically I was going full circle and realising the dimensionless nature of the coefficient meant that the dimensions of the body it applied to were irrelevant in deriving it, but doing it the hard way.

Here is it put another way, in “The Peenemünde Wind Tunnels: A Memoir” by Peter P. Wegener (which talks about the Mach4 tunnels):

[ATTACH=CONFIG]238675[/ATTACH]

The force varies with size – but the Cd doesn’t. It doesn’t because the reference area is scaled, cancelling out the change in force in the calculation.

My brain hurts:)

Despite your doubts, the performance can be and was calculated to a useful accuracy from drag and lift coefficients – or equivalent methods such as D100 as mentioned above. The basic equations of flight go back to WW1 or earlier. No, they weren’t as good at it then as they are now, but it still wouldn’t do to underestimate their capabilities. Most of the problems, then and now, come from allowing the correct values for engine power/thrust, intake efficiencies, and unexpected interactions. (And investigating the last is perhaps where this started?)

You are right about the scale speed problems in wind tunnels: look under the term “Reynolds Number”. However, this is only useful below high subsonic Mach numbers. The German supersonic wind tunnels were indeed run to investigate supersonic flight – the drag increase due to compressibility, and the movement of shock waves, made them totally useless for subsonic work. How many of them were capable of anything more significant than research work into configurations is another matter – we are talking about very small tunnels.

I suspect the P-51 results you are referring to are those done in the Langley full scale tunnel – but certainly not based on Mach numbers as the Langley tunnel was unable to reach anything significant (AFAIK). The Meredith effect is basically just flow through ducts – it would be present with or without propwash. The magnitude might be different, but it would not disappear. The Spitfire and Bf109, and indeed many other aircraft, also used the Meredith effect in their radiator systems.

“The squaring adjustment happens in the squared relationship change in reference area between model and full size – and that is what this apparently arbitrary element is actually for!” Sorry, I’ve no idea what you mean by this.

Me too.. but this is FASCINATING. My best Google find yet – http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CCoQFjAB&url=http%3A%2F%2Fwww.dtic.mil%2Fcgi-bin%2FGetTRDoc%3FAD%3DADB804999&ei=vzmNVefzOebT7Qb8voOoBw&usg=AFQjCNHg09CjCoP4Yy5fgLoCDpwqdMXchw&sig2=q8GcyAzIZMTudrrOwEsT9Q&bvm=bv.96782255,d.ZGU
..you have to download from here, I can’t find a better way of doing this.

P-51 drag tests. Lots of good stuff here. Note that this also used a model in a wind tunnel but run at the same velocities (or more specifically Mach numbers) as the full size test aircraft that it was compared with.

Check out the photo’s – the full-size one was the world’s fastest air-launched glider (until the Shuttle, I guess)

Also, a Cd 0f 0.022 is a lot higher than Mustang fans tend to quote. Pretty much what Creaking Door was saying. Of course, this was engine-off – so no Meredith effect!

Of course, Cd is dimensionless – so the size of the model surely doesn’t affect it? It just affects the force that the drag exerts. I guess in drag modelling the problems CD highlighted with the velocity squared rule don’t apply if all you are after is the drag co-efficient.

The squaring adjustment happens in the squared relationship change in reference area between model and full size – and that is what this apparently arbitrary element is actually for!

Lightbulb moment.

Now I’m even more confused than I thought I was.

Is it in fact possible to apply simple mathematical corrections to at least arrive at Cd.. for example, run at ‘real life’ speed, say 200mph, and square the result? After all, we are not trying to achieve the actual drag force, just a scale representation of it!?

Edit: This bears out the idea – http://www.nasa.gov/centers/dryden/pdf/87920main_H-1079.pdf – tests run on a 3% scale model in the same Mach regime as the full-size aircraft.

Genuinely fascinating stuff.

And when you use a wind-tunnel to gather experimental data the ‘velocity-squared’ law works against you; a half-scale model needs a wind velocity four times as fast and for a late mark Spitfire that would mean a supersonic wind-tunnel (and that causes problems in itself even if the data generated was representative of the full-size airframe)! Which explains full-size wind-tunnels for aircraft.

(Or have I got that wrong; half-scale needs twice the speed? Still, supersonic anyway?)

The numbers of many-times supersonic wind-tunnels found in Germany at the end of the war are not evidence, as some would have you believe, of Nazi fighters capable of twice, or three times, the speed of sound; they are evidence of smaller-scale model testing of fast, but subsonic, fighters!

Then you have interference drag and wave drag.. but the thing about coefficients is that they drop out of measurement. The complicated bit seems to be understanding what one is measuring. As I am beginning to understand it, actual Cd is what you get when you take the measured force acting opposite thrust (ie drag) and divide it by velocity squared, air density, and a reference area which I presume was introduced to cancel out units and keep the coefficient dimensionless. That’s it.

Now outside of aviation, the ‘classical’ view was that a shape acted on from a direction has a Cd. A sphere has one fixed value, an ellipse from the top another, from the side a third, and so on. All were arrived at by observation, and then applying the equation involving velocity and density. Values of Cd might get affected by skin roughness, but not massively. All fair enough.

But what I have learned here and from reading around is this..

When one is attempting to counter the weight of an aeroplane you have to borrow force from somewhere. So you use an aerofoil and increase incidence for any given speed to maintain lift. In truth what happens is the shape facing the airstream changes. That shape still has it’s own, fixed and specific Cd, its just a different, draggier, higher Cd shape.

It is very hard to calculate Cd from the complex form upwards, as it were (it takes a fair amount of computing power to get close), so is best arrived at through experimental measurement of forces. The value of Cd will be affected by interference, friction and possibly wave drag as well, but it will still remain the result of a simple equation into which is fed actual experimental data.

As for what it is all worth.. I expect it is very useful in the wind tunnel, where the designer is working ‘backwards’ unable to see max speed etc. experimentally (the model ‘flies’ at whatever speed you set the dial to) but can find improvements in efficiency by looking at the forces on the models, as expressed by Cd.

As has been said earlier drag coefficients are a complex thing to work out as there are there are three types of drag. Form drag (aircraft shape), Induced drag (from producing lift) and parasite drag (skin friction). At least I think I’ve got them right.

I doubt that any of these parameters, speed, range, payload or rate-of-climb, could be worked-out from the drag-coefficient with enough accuracy to be useful to any operator, above and beyond what was measured from actually testing a prototype; once you had a prototype of course.

How would drag-coefficients for World War Two aircraft be worked-out anyway? Wind-tunnel testing of models and full-size mock-ups (or prototypes) would presumably produce the best results but would calculations produce anything with sufficient accuracy?

Designers of (earlier) World War Two aircraft seemed to be constantly surprised, or more usually disappointed, by the performance of their aircraft at the flight of the first prototype. Even Roy Chadwick seemed to be surprised how good the Lancaster was, and could not offer a definitive reason why it was so good, and that was with the benefit of the experience of flying the Manchester airframe and in comparison of its performance, or lack thereof, with its (presumably) well-known drag coefficients.

The manufacturer (and indeed operators) require the drag coefficient (or D100, drag at 100 mph, which was also used in the 40s) to calculate speed, range, payload, rate-of-climb, ceiling and all these other wonderful pieces of information. Thus measured data from limited testing can be reduced to terms that can then be applied throughout the envelope, to produce the full Operating Data Manual for the aircraft. (Not that ODMs existed in precisely the same form in the early 1940s.) Compressibility is one (now) obvious factor preventing life being quite that simple.

Yes, calculation of drag coefficients does depend upon the chosen reference area, which is why it is necessary to be careful of comparisons. That doesn’t make them meaningless.

It has prevented me…..comparing unqualified Cd figures like they were straightforward measures.

Exactly, and it often depends where you see figures quoted; many publications intended for ‘general consumption’ like to quote figures to back-up the assertions of the author but these are often quoted out of context or in a way that means direct comparisons are not possible (or wrongly, simply because the author doesn’t understand the physics behind the statistic they have cherry-picked from a technical specification).

It also begs the question: what are these figures calculated or measured for?

Surely what really matters is the speed, range, payload, rate-of-climb, ceiling and manoeuvrability of a aircraft, not the comparison of an arbitrary coefficient of airframe drag?

I don’t think you can compair Cd for different aircraft as the desigers may have used different reference areas…

But the whole point of a coefficient is that is (almost) independent of size of the body; a party balloon and a hot-air balloon will have extremely similar drag-coefficients but one will take a lot more hanging-onto in a stiff breeze!

Thanks folks. That all helps. It has prevented me making a t(w)it of myself comparing unqualified Cd figures like they were straightforward measures. Proteus, I read that standard practice in aircraft drag calculation was to use wing area as reference area, but you have a point, as one source then went on to use the square of the mean chord instead.

Still, if anyone has wing/fuselage interference drag in pounds at 100ft/s I would still be very interested to compare with the unconventional Whirlwind’s 2lbs.

I don’t think you can compair Cd for different aircraft as the desigers may have used different referance areas

Which leaves the questions.. I have read that the Mustang II’s Cd0 was 0.016, and the Spit (though no clue as to Mk) was 0.018. Cd’s were 0.020 and 0.021 respectively. How were the latter arrived at, if at least one component is actually variable and down to angle of attack? Are these in fact Cdmin figures, ie including lift related drag in a very specific condition where this drag is at its minimum?

At the risk of getting dragged out of my comfort zone…

…basically, yes, figures quoted for a very specific condition. 🙂