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.

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):

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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.

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.

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?

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?