Calculating ram rise?

[Founder]

does anyone know how to calculate ram rise?

Kind Regards
Tim

[captjns]

A quick calculation is to take ten percent of your indicated airspeed.

[Re-entry]

TAT/SAT=1+(g-1)/2 *M^2

g= gamma= cp/cv. The ratio of specific heats at constant P,V. (1.4 for air at STP.)

M= mach number.

The temp as measured by a probe (eg rosemount) is slightly different to the true TAT, due to a number of factors.

[Re-entry]

I suppose I should add that gamma varies with temp. For dry air g=1.401 @0 deg C. g=1.405 @ -80 deg C.
Also note TAT and SAT are expressed in deg K (ie deg C+273.16).

The value of gamma is an experimentally derived number. The theoretical value for a diatomic gas is 7/5 ie 1.4 . Air is of course only about 99% diatomic O2 and N2. The other 1% being other gases (mainly Ar).

[DesiPilot]

Another rule of thumb that we used was
TAT= SAT + (TAS/100)^2.

It works pretty well for approximation.

[411A]

Well, if you want the exact figure, there are graphs in most AFM's that are VERY accurate, and correct for any particular system/installation errors.

[Old Smokey]

Originally Posted by DesiPilot

Another rule of thumb that we used was
TAT= SAT + (TAS/100)^2.
It works pretty well for approximation.

True enough, an approximation. If you want the exact figure with Knots TAS as the entry variable -

TAT= SAT + (TAS/87.1)^2, which is exact

Or, if your entry variable is Mach Number -

TAT= SAT + (1+.2*M^2), which is also exact

Prop operators may prefer the former, jet jockeys the latter.

Regards,

Old Smokey

[Re-entry]

Old Smokey, I think for the second formula you meant

TAT= SAT*(1+ .2*M^2).

And the temps must be in deg K.

btw it is not exactly exact, due to the small variations in the value of gamma, as I mentioned before. But it is mighty close!

[Old Smokey]

Thanks Re-entry, my speed typing skills leave a lot to be desired.

Agreed abiout the small variations in Gamma, but most ADCs / FMCs etc use the 'standard' 1.4, so unless you're actually converting test flying results into standard results, using the standard will keep the results in line with standard instrument calibrations. As you said earlier, the difference is very small in any case.

Just in case someone copied my mis-typing, I'd better say again

TAT= SAT X (1+.2*M^2),

The problem was a cut and paste from the formula derived for TAS, didn't edit it as fully as I should have , Thanks again .

Regards,

Old Smokey

[westhawk]

Originally Posted by Re-entry

Old Smokey, I think for the second formula you meant

TAT= SAT*(1+ .2*M^2).
And the temps must be in deg K.
btw it is not exactly exact, due to the small variations in the value of gamma, as I mentioned before. But it is mighty close!

Just noticed the reference to absolute temperature. Is that right?

Best regards,

Westhawk

[Techman]

yes it is.

It is SAT(K)(1+0.2m^2)=TAT(K)

[westhawk]

Thank you.

So since SAT is displayed in degrees C, my cheat sheet ( for quick reference)should read like this:

TAT = SAT + 273 X (1+.2*M^2) - 273?

So if:
mach = .74
SAT = -54 deg C

Then:

-54 + 273 X (1 + .2 X .74^2) - 273 = - 30.015 deg C, or about 23.085 deg C of ram rise. Is that correct?

Sorry to drag this out. I just want to make sure I get it right.

Thanks for the clarification.

Westhawk

[barit1]

Without actually checking your math, the rise is remarkably close to my guess.

[Techman]

It would be :

SAT(K)(1+0.2m^2)=TAT(K)

TAT(K)/(1+0.2m^2)=SAT(K)

As 411 says, the quickest way would be a AFM graph.

[barit1]

Without actually checking your math, your rise is remarkably close to my guess.

[captjns]

Too much work when you can take 10% of your indicated airspeed to get the same result.

[westhawk]

Originally Posted by captjns

Too much work when you can take 10% of your indicated airspeed to get the same result.

That's probably right captjns. But it will be ever so much more fun to give the co-pilot the formula and the calculator and ask him to find the SAT from our mach number and our OAT/RAT reading, then explain about the 10% of IAS thing after!

Actually, I'll try both tomorrow. Then I'll compare the results to the SAT/TAS reading on the air data page. Gotta do something during cruise, and this seems both safer than, and preferable to, allowing any further discussions of religion or politics to commence!

Best regards,

Westhawk

[captjns]

Originally Posted by westhawk

That's probably right captjns. But it will be ever so much more fun to give the co-pilot the formula and the calculator and ask him to find the SAT from our mach number and our OAT/RAT reading, then explain about the 10% of IAS thing after!

Actually, I'll try both tomorrow. Then I'll compare the results to the SAT/TAS reading on the air data page. Gotta do something during cruise, and this seems both safer than, and preferable to, allowing any further discussions of religion or politics to commence!

Best regards,

Westhawk

Amen Brother... er uh you betcha