Quote:
Originally Posted by Crumpp
It is not hard to do at all. We can use the first entry for flaps up turn performance at 12000 feet.
V = TAS/SMOE = EAS
Standard Means of Evaluation at 12,000 feet = 1.2011
Flaps up TAS at 12,000 feet = 160 mph TAS
160/1.2011 = 133 mph EAS
133 mph EAS * .869 = 115.6 KEAS
Oh check it out....They give you EAS on the report. Gee, wasn't that another 100 page discussion on these forums?
Anyway, once you have EAS you can easily convert the performance to any atmospheric condition you want.
I like working with BGS but the units do not matter. Just don't put the correction factors like "1091" and "11.26" if you are using metric and keep your units straight.
Our formula becomes:
Radius = (VKeas * SMOE)^2 / 11.26tan <theta>
<theta> = angle of bank which is a fixed relationship with load factor irregardless of altitude
If you use the above formula and knots, our radius calculates out to be 693 feet and the RAE measurement is 695 feet. Pretty good agreement.
Radius is not the primary turn characteristic in a fighter. It not so important how small the circle but how fast we can bring the nose around to put guns on target.
So lets check our rate of turn based on the document:
Flaps up = 160 TAS * .869 = 139 KTAS
1091(tan 68 ) / 139 KTAS = 19.42 degrees a second
360/19.42 = 18.56 seconds to complete a 360 degree turn
18.6 and 18.56 are a match....
Now let's see what it does at 20000 feet:
160 TAS at 12000 feet = 133 mph EAS
133 mph EAS * .869 = 115.6 KTAS
SMOE @ 20000 feet from our Standard Atmospheric Data = 1.3700
Radius = (VKeas * SMOE)^2 / 11.26tan <theta>
Radius = {115.6*1.3700}^2 / 11.26tan <68>
= 899.97 or just 900 feet @ 20,000 feet
Rate = 1091(tan 68 ) / (115.6KEAS*1.3700)
= 17.05 degrees a second
= 360/17.05 = 21 seconds to complete a 360 degree turn at 20,000 feet
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As you yourself said there have been many 100 page discussions about your use of EAS to estimate turn performance in the forums you post in and it seems that you still have not mastered the art.
The way you simply use EAS above to derive results for 20,000 ft gives erroneous results that bear no relation to actual performance of the Spitfire at this altitude and a more realistic turn time under these conditions would be about 30 to 31 s.