Question the whole class doesn't understand

[neil_1821]

Ok, so were getting along ok with questions i guess, but were all fumbled on this qustion, not sure if were using the right formulae or not, were just trying to figure it all out.

Q. Given MN 0.70, measured impact temp = - 48° C, the recovery factor
of
the temperature probe (Kr) is 0.85, the OAT is:

a) - 60° C
b) - 45° C
c) - 65° C
d) -51° C

Answer: c) -65° C

So we now know that the equation is Ts = Tt/(1 + 0.2KrM²)

Ts IS the OAT, so it’s a question of working the rest of it out, I cant
get
anywhere near to -65° C.

[Blues&twos]

Might be something to do with using degrees Kelvin rather than degrees C, then converting back to degrees C afterwards.

I'm not familiar with your equation (not being a pilot) but after pressing some buttons on my calculator using Kelvin, then converting back to deg C, I got -65.3.

This might be total rubbish!!!!

I might have converted back to deg C incorrectly, thinking about it....

No wait a minute, I did convert correctly...I think....give it a try.

[neil_1821]

It might well be that you need to convert it into kelvin, but can you go through a step by step process at all?

[Old Smokey]

As other posters have mentioned, the calculation must be done in Absolute Temperature (°K). For the scenario given, if the calculation is done in °K,

SAT = - 65.3°C : TAT = - 44.9°C : RAT = - 48.0°C

Regards,

Old Smokey

[Blues&twos]

I've made some assumptions here (as I said before, I don't know what all the letters stand for in your equation, but I had a guess). So in Absolute Temperature

-48 Deg C = 225 deg K (273-48)

Ts = 225/1 + 0.2 x 0.85 x (0.7)²

Ts = 225/1 + 0.2 x 0.85 x 0.49

Ts = 225/1.0833

Ts = 207.7 deg K

Now convert to Deg C:

207.7 deg K - 273 = -65.3 deg C

Old Smokey seems to know what's going on, so hopefully will be able to confirm this is how it is calculated. Otherwise, maybe tell me what I've assumed incorrectly!


Edited later: I've since found out what the letters all mean...calculation above is OK I think.

[neil_1821]

thanks very much, makes sense now i know what formula to use and where things go.

Very clever person

[Old Smokey]

Yes, Blues&twos, that's correct Reviewing the associated algorithm might help for understanding on the original poster's part, i.e. -

SAT = RAT / (1 + .2 X Ct X M^2)

Where SAT = Static Air Temperature, RAT = Ram Air Temperature, Ct = Temperature coefficient (recovery factor) for your temperature measuring system, and M = Mach No.

For RAT = -48°C, RAT = 273.15 - 48 = 225.25°K

SAT = 225.15 / (1 + .2 X .85 X 0.49) = 207.84°K - 273.15 = -65.31°K

If your aircraft has a TAT system (100% recovery, or >99%), Ct =1, and you can dispense with the Ct input in finding SAT.

Regards,

Old Smokey