Calculating True Airspeed

[FlyingLapinou]

Yawn. Yes, I know...

But being fairly new to aviation AND mathematically challenged (you don't know how much :{), I'm having a hard time with some of the questions cropping up in past papers which I'm revising for an exam later this year. So maybe someone brainy might be able to explain the following to me? :ok:

Anyway, here's the question:

An aircraft is flying at an altitude of 15 000 ft. The machmeter indicates 0.4 and the outside air temp. is – 15°C. The true airspeed is:

a) 200 kt.
b) 250 kt.
c) 250 km/h.
d) 338 kt.

Gulp. Where do I start? :confused:

Very hypothetical when you're bimbling around in a Cessna or a Jodel, I know, but...

All hints gratefully received (btw, I've managed to grasp the idea that TAS is likely to be (considerably) greater that IAS as altitude increases?) but that's as far as I've got.

[BackPacker]

It's a very easy calculation on a flight computer, such as the CRP-5, E6B or whatever mechanical or electronic variant you use. (And that computer should come with a manual with examples of calculations like this.)

As for doing it with pen and paper, or a generic scientific calculator - I have no idea..

[what next]

Hello!

Gulp. Where do I start?I don't think this is a question that needs to be ansered by claculations, but rather an excercise about knowing the orders of magnitude of the speed units!

The speed of sound is roughly 1000 km/h at low level (and this includes the 15000ft in the question). Therefore Mach 0.4 is 400km/h. The only value in the list that comes close to that figure is 200kt.

If you want to now the exact answer you can also google for "mach number calcuator".

Happy landings
max

[Whopity]

As stated above you need a Navigation Computer then follow the instructions on the front of the device:
SET Corected OAT against Arrow, or Indicated OAT against Mach No (In Mach Window) READ TAS on Miles scale against Mach No on Minutes Scale. Its that easy no maths involved.Very hypothetical when you're bimbling around in a CessnaLets say you opt to fly at 10,000 ft then the TAS will exceed the IAS by 15% so it is in your interest to know how to work this out.

[24Carrot]

The speed of sound in air depends only on temperature, and it is pretty much the square root of the absolute temperature (degrees C + 273).

So you can construct a formula which will be some constant in knots times the square root of T+273.

I did this for my exams and I think it was 40 x sqrt(T+273), giving 661 knots at zero C.

Edited to add the answer:
0.4 x 40 x sqrt(273-15) = 257 knots so I would go for 250 kts.

Edited again:
I checked my notes and it was 39, not 40, giving 661 kts at 15C,

and so the answer to your question is:
0.4 x 39 x sqrt(273-15) = 250 kts.

[peterh337]

Just google for e.g.

TAS calculator

and you get loads of hits e.g. here (http://www.hochwarth.com/misc/AviationCalculator.html).

[Whopity]

I got 250 kts on my Wizz Wheel in less than the time it took to find it in my bag! Sorry Max you are outvoted; good job they stopped negative marking. Follow-on Question: Is the OAT given Indicated or Corrected?

[Genghis the Engineer]

Given this is the private flying forum, I'd assume that OAT=IOAT

A quick bit of back of envelope algebra by the way tells me that (within about 3%):

TAS = IAS / SQRT ((288 * air pressure) / ( Absolute Temperature * sea level air pressure))

[clarifying, TAS = EAS/SQRT(sigma); sigma is relative pressure = rho/rho_0, but I just worked it out with temperature and pressure. Below 0.8 Mach and FL100 it's reasonable to assume that EAS=CAS, and certification requirements permit a maximum of 5% error between IAS and CAS.]


In this case however you've got altitude, mach number and temperature. Dead easy.

Speed of sound in metres per second, c = SQRT (gamma * R * T)

Gamma = 1.4 (always is because air is a diatomic gas)
R = 287 J/kg.K (constant for air)
T = 273.15 - 15 = 258.15K

So c = 322 m/s

So, at M=0.4, TAS = 0.4 * 322 = 129m/s

None of your answers are in metres per second, but 1 knot = 0.514 m/s, so let's try that. 129 / 0.514 = 250 knots.

Bingo: 250 knots is your answer.

G

[MIKECR]

The Mach Number = TAS/LSS(local speed of sound)

Local Speed of sound = constant(38.94) x square root of temp(in degrees kelvin)

Just transpose the 2 formulae above.

And remember that the speed of sound is dependent on temperature.

Years since i did that in ATPL studies.....frightening thats its still in my head!!

And having just rattled it out on the calculator i get 250 knots!

[BabyBear]

Ah, my belief was that speed of sound was temp sensitive, but not altitude/pressure.

Genghis, is this a rule of thumb ignoring insignifficant effect of altitude/pressure, or is it important to consider altitude/pressure?

BB

[Genghis the Engineer]

BabyBear

My first equation is based upon ACTUAL temperature and pressure - temperature is easy (use the OAT gauge), pressure is also easy (use the altimeter calibration and adjust for the subscale setting - correcting to 1013.25 hPa/mb). The rest are standard values. So, I'd stand by my max 3% error for airspeed measurement and you could remove that by using the PEC chart in the manual.

My second equation is exact, so long as you have an exact air temperture to work with. There's a small error due to humidity, but it's going to be around the 4th significant figure, so I'd really not worry about it. Altitude / pressure / density do not affect the speed of sound in air, only temperature.


MIKECR

Your ATPL notes formula is correct, but just a simplification of the universal formula I made. Being really picky, it's just "Kelvin" not "degrees Kelvin". Obviously Kelvin = degrees Celcius + 273.15. "degrees centigrade" = "degrees Celcius".

G

[BabyBear]

Genghis, thanks for the confirmation.:ok:

BB

[MIKECR]

It'll be in the atpl notes somewhete Gengis, probably in a box under the xmas decorations in the attic! Havent read them in years and hope never to have to ever again.....bloody awful syllabus!

The formula is just one of those bizarre things i seem to remember. God knows why. Must've interested me at the time. I just look at the mach indicator or the FMS these days. Funny how we all remember strange things! The human brain is trully amazing.

[FlyingLapinou]

Delighted to get so many helpful replies! :ok: Thank you all. I'm still chuckling over this thread and on my tenth slow re-read (so far). Bear with me, I feel like I've jumped in at the deep end.

I like all the different approaches. Thanks for the link to the aviation calculations and conversions Peter - bookmarked (now you're really talking dead easy..:D)

I agree with what next in that it's good to keep in mind the big picture, and that's mostly how I try to approach the questions in the aerodynamics/flight mechanics section - I have to admit it, the maths is way above my head, so trying to understand the overall principles is my only hope. It's all ridiculously difficult (but in an exciting grrr-I'm-determined-to-crack-this-sort of way, if you see what I mean).

Flight computers? Well, we don't use them in PPL training/exams over here in France, so this Wizz Wheel/CRP-5/E6B I keep hearing about is still a mystery to me. I can see they must be useful. But not allowed in the exam - just a simple calculator is all we can use, so I was really looking for the sort of thing that 24Carrot, MikeCR and Genghis have come up with. Thanks for checking your notes! I'll make a note of that little formula 24Carrot posted. I also followed through your calculations Genghis - very helpful, thanks.

Now, Whopity, about OAT....I just have to ask :E Corrected for what, exactly?

And why would I want to know my TAS? IAS is all I need in terms of aerodynamic performance, right? And GS is what I need for navigation? Right? Wrong?

Oh yes, I forgot! The answer is 250 kt (but you knew that...)

[peterh337]

It sounds like an ATPL paper.

AFAIK, no JAA PPL or JAA IR syllabus has any mach number related stuff in it; they were removed within the past year or so. I certainly did not do any of this for the JAA IR7-exam set.

Maybe JAA CPL, or you are doing the whole JAA ATPL 14-exam set.

Maybe in France the 7 JAA IR exams are simply a subset of the 14 ATPL exams, which AIUI used to be the case in the UK also, until ~ 10 years ago, so maybe the French IR exams do indeed contain this dross.

Much as I hate to say this, the silly circular slide rule is good for this kind of stuff because you just line up the numbers you are given and read off the one(s) you are not given. I have a little Jepp CR-5 which does this.

One never does these calcs in real life.

why would I want to know my TAS?In modern flying you don't really need to know it, because what matters is the GS, the ETE, the fuel flow, and the LFOB, and you get these off the GPS linked to the fuel totaliser :)

The TAS is useful if you want to work out roughly what the wind is when you are flying, by comparing the GPS GS with the TAS. But again without a GPS (or getting a DME GS reading if flying more or less direct to/from a DME) that's not much good, either :)

But on any half decent speedo there is a subscale where you set the current altitude and OAT and you read the TAS straight off

http://www.langleyflyingschool.com/Images/PPL%20GS%20Flight%20Instruments/581px-True_airspeed_indicator-FAA_SVG.png

[Genghis the Engineer]

Now, Whopity, about OAT....I just have to ask Corrected for what, exactly?

Corrected for Mach Number. Not really an issue at M=0.4.



Airspeeds work like this

(1) IAS, what you can see on the dial, which corrects for position errors (there's a graph in the back of the aircraft manual) to...

(2) CAS, which is what aircraft limitations are really in, which you can correct for compressibility (although don't bother below 10,000ft and M=0.6, the errors are trivial) to....

(3) EAS, which is what all the structural limits were worked out in, which corrects for density to....

(4) TAS, which is what the "V" term is in all the aerodynamics textbooks, and if you correct for wind you then get...

(5) Groundspeed!

G

[what next]

Hello!

I agree with what next in that it's good to keep in mind the big picture and that's mostly how I try to approach the questions in the aerodynamics/flight mechanics section ...

Know the order of magnitude (or the "power of ten") and where to look up the details or what tool to use to compute them and you will be fine. That's what they told us back at university and it served me well, both for engineering and for flying.
Sometimes one over-simplifies this way (my memorising the speed of sound as 1000 km/h rather than the precise value of 1235) but for me it was good enough to get more then the 75% of correct answers required in the exams :)

And why would I want to know my TAS? IAS is all I need in terms of aerodynamic performance, right? And GS is what I need for navigation? Right? Wrong?

Right. In the aeroplane I fly at work, the TAS is displayed in the lower corner of a secondary display and I swear that I didn't bother to look there for the last 1.000 flying hours (maybe it has vanished from the display in the meantime, who knows?). Totally irrelevant. You could compute your GS knowing your TAS, but then you must also know your exact wind. At any moment. Nobody does.

[peterh337]

You could compute your GS knowing your TAS, but then you must also know your exact wind. At any moment. Nobody does.

It sounds like you fly a jet. On those, the airdata computer gets IAS, OAT, pressure altitude, computes the TAS from the foregoing, then gets the heading (from the fluxgate compass system), gets the track and GA (from the FMS i.e. INS or GPS), and calculates the wind vector from those.

One can get the same in GA (example (http://www.aircraftspruce.com/catalog/inpages/shadin_fadc200.php)) but it's hardly worth it for the cost.

[BackPacker]

Totally irrelevant.

You must not be working for the marketing department...;)

Most aircraft sales/marketing brochures show the TAS instead of IAS because the TAS is invariably higher. Only when you read the fine print do you realize that that TAS is obtained at some ridiculously high altitude, which nobody flies at in real life, for instance due to oxygen/airspace issues.

Anyway, FlyingLapinou, I can't believe you are not allowed to use some sort of dedicated flight computer. Whether that's a mechanical one or an electronic one doesn't matter. But they are specifically designed for calculations like this, plus things like fuel volume/mass conversions, working out your GS and track based on TAS, heading and wind, and so on and so forth. (I can imagine that it's not allowed for Aircraft Technical, but for a subject like Navigation...:confused:)

With such a flight computer, at the PPL level you can forget about all the math that people showed you in this thread. As Peter said, you simply line up the numbers that you know, and read off the number you are looking for. It really is that simple.

And why would I want to know my TAS?

For the PPL exam you need to be able to calculate TAS based on IAS, temperature and altitude, and then you use that TAS in combination with the forecasted wind to calculate GS and heading. Although you won't find any Mach numbers on the PPL exam, just knots.

After the PPL you will find that the difference between TAS and IAS, at typical PPL flight altitudes, is less than the error in the wind forecast, so you can save yourself the trouble. Although "trouble" is a big word for having to line up two numbers, and reading off a third.

[FlyingLapinou]

Thanks all, I'm very grateful for the help. Just for background: I already have a PPL, this is for a national French exam called the Certificat d'Aptitude à l'Enseignement Aéronautique which I'm doing purely for my own interest.

I hope I'll be able to contribute a bit more myself one day. In the meantime, I'll keep reading and learning :)

[BackPacker]

FL, I'm intrigued. How did you do the various aviation calculations on your PPL exam, including calculating wind corrections, TAS from IAS etc., without some sort of flight computer (mechanical or electronic)?

Did you have to memorize the various conversion factors, for instance, and draw a wind triangle on the map? Or was there some other clever way of doing stuff like this?

[FlyingLapinou]

Aw flip, BackPacker, I was rather hoping to slip away unnoticed, but since you ask.. :O

I've never seen the UK PPL exams, but if the truth be known, I suspect the French syllabus might be slightly easier, or perhaps the emphasis is placed in different areas? We sit five exams, for example, not seven - meteorology, navigation and flight planning & performance are grouped together as one paper. We don't have to know how to calculate TAS from IAS at PPL level and other navigation calculations are very simple ones, so no need for flight computers or electronic calculators. Most PPL pilots over here have never seen a flight computer, and at instructor level there seems to be a perception that they are too complicated.

In short, I feel that many things were glossed over during PPL training. It's frustrating, and that's why I'm trying to do something about it. On the other hand, there are very few club pilots who do long flights. Most stay in the local area: short flights, low altitudes, that kind of thing. Perhaps the DGAC feels the current syllabus covers those needs adequately.