Converting RAS to TAS
 

Does anybody have a formula for converting RAS to TAS, please?

Had a good look on the web with no luck. I can do it on my whizz wheel but I can't find a formula for it anywhere.

TAS = EAS/root(sigma)

sigma = local density/std SL density

The normal standard (troposphere) atmosphere derivation leads to the relationship

sigma = theta^4.25588

theta = local OAT/std SL OAT (temps in absolute deg K = deg C +273)

These relationships should give you something very close to what comes out of your whizz wheel activities.

Try looking in any of the standard undergrad engineering texts on aerodynamics etc for the background if you want an arithmetic headache ....

Mr Tullamarine, you are a mine of information - thanks very much.

JT,

...and of course there is always Ed Williams Aviation Formulary

http://williams.best.vwh.net/avform.html#Mach

R4D,

What an involved site .... I shall have to put a day aside and wade through it at some stage ....

... and hopefully life is treating you well ... ?

The above formulae are academically accurate if you need a computer algorithm or similar.

However, if you just want a reasonably accurate pilot's rule of thumb for use in the air:

TAS = CAS (or RAS) x (1.75% per thousand feet)

So, if you are at, say, 10,000 feet with a CAS of 100 knots, ten lots of 1.75% is 17.5 %, so your TAS is 117.5 knots.

Provided the temperature is fairly close to ISA, it's very accurate up to about 25,000 feet and not too bad even higher.

Another, quite accurate method is the 'Rule of Squares' taught in the RAF (a long time ago):

To get the percentage of IAS to add to get TAS use the following:

5000' 3² = 9%
10000' 4² = 16%
15000' 5² = 25%
20000' 6² = 36%

etc to

40000' 10² = 100%

and everyone (?) knows that TAS is twice IAS at 40000 ft.

If you're looking for a calculation to get TAS change after an altitude change - say ATC send you up 2000' - then take current TAS in miles per min and multiply by height change in 000s of feet. This is the increase in TAS you'll have got from changing altitude.

Stan,

Wouldn't it be easier and quicker to run the calc on the whizz wheel ? ... one-handed ?