TAS Question

[suckerdin]

Good day all,
Question regarding TAS.

FL330
CAS = 262
OAT = -24
Temp Rise = 20

TAS=?

The answer given to me by my colleague was TAS=437

My question is: Why do you include the Temp rise?

I get a TAS of 456.5, which is incorrect according my good friend...

Can someone please help if possible

Thanks

[horus23]

The key information to find out the answer is: the temperature given is TAT (that is also know as RAT or IOAT) or SAT (COAT or simply OAT).

I understand that it's referring to SAT, then TAT = SAT + Ram rise, TAT = -24 + 20, TAT = +4,
therefore 262 cas is 500 TAS, correct for compressibility and you will get 479kts

Correct me if I'm wrong.
Cheers

[horus23]

Actually, normally they give you data so you need to find the temp rise. But giving the temp rise you could just directly read speed against 20 on the blue scale of crp5, which would give the right answer 437ish.
Maybe this is the right way to solve it.

I might have just messed everything in the previous post.

[eckhard]

ISA Temp at FL330 is approx -51C

If the "OAT" given in the question is -24C, then that has to be RAT or TAT.
Temp rise given is 20C which then gives a SAT of -44C

I don't have access to an E-6B or CRP-5 but an on-line calculator gives a TAS of 459.

I guess if you correct for compressibility you would get close to the 437 that your colleague gave you?

Edited to add that I just found an on-line compressibility correction chart which shows a 12kt correction to CAS. Plugging in 262-12=250 EAS gives a TAS of 438

[Alex Whittingham]

Under normal circumstances the term OAT means SAT but who knows? Also air temperature gauges on aircraft may show SAT or TAT, there is no rule and you cannot really deduce whether the temperature is SAT or TAT by looking at the ISA and saying 'that's too hot'.

With the data given my interpretation is the same as that of the OP, OAT is given and the temperature rise is irrelevant. Some of the online calculators give results too far apart to be serious, the old CRP-5 gives me a first TAS reading of 469KT without compressibility which corrects down to 455KT, as the OP says.

Suggest OP asks his colleague why this is wrong!

[eckhard]

While I agree that the data is ambiguous, a quick look at some atmospheric temperatures for FL330 today suggests a warmest area over India at approx -31C, so I still say that -24C is unfeasibly warm for a SAT.

But, as Alex says, who knows?

[chr2017]

Good morning everyone,

Someone had recommended that I use this formula to convert KCAS/KIAS to KTAS:

(note: the forum would not allow me to post the link)

If you scroll down to "True Airspeed, TAS," you will see this formula:

=KIAS*SQRT(SEA LEVEL AIR DENSITY/AIR DENSITY OF DESIRED ALT)

Entered into an Excel spreadsheet cell, the formula looks like this:

=100*SQRT(1.225/0.905)

100 is the KIAS, 1.255 is air density at sea level, and 0.905 is air density at 10,000 feet.

This formula gives us 116 knots for KTAS.


This formula works for low airspeeds, but as airspeeds get higher, the KTAS that is given is not accurate. As I have learned, this formula does not take into account "compressibility," and therefore the KTAS will not be accurate at higher airspeeds.

I am interested in a formula that I can enter into an Excel spreadsheet that will give an accurate KTAS for all airspeeds up to Mach 3, and altitudes up to 100,000 feet.

Is there one particular formula that will work?

[selfin]

chr2017,

In the subsonic regime use the Saint Venant equations by Aiken (1947) in NACA Report 837. The report is available at: NACA UK Mirror report description page (http://naca.central.cranfield.ac.uk/report.php?NID=2451)

To the best of my knowledge calibrated airspeed has never been defined for the supersonic regime. I don't think a closed form solution can be obtained even if a definition is pursued. In the supersonic regime the pressure at the mouth of the pitot probe can be determined, for a calorically perfect gas, using the Rayleigh supersonic pitot formula. The formula accounts for the reduction in total pressure caused by the normal shock ahead of the probe, see equation 100 in NACA Report 1135 available at: https://www.nasa.gov/sites/default/files/734673main_Equations-Tables-Charts-CompressibleFlow-Report-1135.pdf Don't use the supersonic total pressure in the Saint Venant equation because it will produce a meaningless CAS value (and an erroneous TAS value).

In the hypersonic regime, say beyond about Mach 3 to 5, rotational modes become excited so the calorically perfect gas assumption becomes inappropriate and it will be necessary to work out how the adiabatic index reduces; I have a decade-old spreadsheet archived for this problem if it helps.

[suckerdin]

Thanks all. I guess the answer is closest to 437 as I was given......as per ECKHARD the temp was taken as -44, which confused me.