Drag figures

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Does anyone have specific drag figures for any WWII aircraft type? Although 'low-drag' and similar terms are often used, actual coefficients and/or absolute figures in lbs. against velocity seem extraordinarily thin on the ground. The reason I am asking is an RAE report from 1940 (http://naca.central.cranfield.ac.uk/reports/arc/rm/2603.pdf) has the wing root interference drag of the Whirlwind as 2lbs at 100ft/s. This they record as 'reasonably satisfactory'. I am wondering what they are comparing it with - but I can find no other figures My interest was sparked when I worked out (on the back of an envelope, admittedly) that the wing root interference drag of the Arnold AR-5, famous for its low-drag design (especially wing roots) and capable of 213mph on 65hp, is 2.6lb at 100ft/s - more than the much larger and un-filleted WW.
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It's a difficult subject, since Cd varies with speed, for instance a 1945 NACA test on a P-39N revealed that: "The minimum drag coefficient at low Mach number ...was found to be approximately 0.022. The maximum Mach number attained in the course of the tests was about 0.80, which appears to be the terminal Mach number of the airplane. At this Mach number, the drag coefficient was about 0.060." I think there must be some RAE comparison reports available: via FAST maybe?
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Thanks SabreJet I'll keep digging through the AERADE stuff online - I hadn't seen that P-39 test. Here's the thing, though. In pure theory at least Cd should not change with velocity. It is meant to be a description of a shape in terms of how it interacts with an airflow, and actual drag - as a force - varies according to an equation into which you put that shape's Cd, reference area, and air (fluid) density and velocity. In practice around 1945 people were plotting charts left right and centre of Cd change against Mach! This threw me for a while, as it doesn't agree with the mathematical point of Cd - it's a constant for any given shape. Unless the P39N changes shape at higher Mach, this doesn't make sense - neither do the graphs I found presented by Jeffry Quill of Cd change as both the Spit and Mustang approach Mach 7 or 8. Then it dawned that there were compressibility / wave drag effects adding to the drag - a completely different and additional form of drag encountered at these speeds that wasn't properly understood by experimenters in 1944/45. If this wasn't literally added to the figures, the only way to make the figures from these experiments make any sense was to vary the Cd! Arm-waving stuff - any thoughts anyone?
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Agreed in essence: I hadn't thought Cd would vary either! I was tempted to say that many aircraft do change shape if they go fast enough: a good example being the RE.8 of the World War 1 era: go above about 120kt and the wings fall off!
Profile picture for user Beermat

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:) That 0.022 figure is useful though - I can add it to my CD collection! So far I have 0.020 for the P-51 and Whirlwind and 0.021 for the Spitfire IX and P-80

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In pure theory at least Cd should not change with velocity. It is meant to be a description of a shape in terms of how it interacts with an airflow, and actual drag - as a force - varies according to an equation into which you put that shape's Cd, reference area, and air (fluid) density and velocity...
But all that changes when the 'angle-of-attack' of the wing changes. To fly, an aircraft must balance lift against weight. So, as the weight increases, so must the lift generated by the wings (at a fairly constant speed); the trade-off for more lift is more drag... ...took me a while to figure this one out when I was younger. I couldn't figure out why aircraft carrying a bomb-load were slower if a faster aircraft generated more lift!
Profile picture for user Beermat

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Got it. So this lift -related drag is the CdI component of Cd, and why usually Cd0 (or in zero camber cases the very similar Cdmin) is often quoted (being the non-lift component, and constant) - though the drag DUE to Cd0 is still variable with speed etc.. am I close? 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? Why is this never explicit? And b), which of the above did Westland actually mean when they said the Whirlwind had a Cd of 0.020?

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It has been many years since I've done any drag-coefficient theory, and then mostly on cars (where lift is an unwanted by-product and the angle-of-attack, except for 'wings' is constant)... ...but you're on the right lines. The total 'drag' on an airframe will be made-up of various components and these will change depending on the 'shape' of the airframe, because this changes depending on how much lift is required (elevators / flaps), and at what angle the airframe is pulled (or pushed) through the air. A 'constant' drag-coefficient can be quoted for a known case: 'level flight' (plus 'zero' angle-of-attack), known weight (empty?), known speed and so on, but the aircraft will rarely fly in this condition. All the drag, from all causes, will vary with speed but the relationship is complicated by the fact that the drag-coefficient for the wing will effectively change depending on the weigh of the aircraft (or how much lift it is required to generate)!

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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. :)

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I don't think you can compair Cd for different aircraft as the desigers may have used different referance areas
Profile picture for user Beermat

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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.

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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!

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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?

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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.

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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.

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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.
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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.

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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!

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Genuinely fascinating stuff.
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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.

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