ATPL theory questions

[keith williams]

geraldflyagain,

I suspect that your difficulty stems from the fact that ATPL studies concentrate only on the effects of northerly and southerly movement. But movement in any direction over the surface of the Earth will cause coriolis effect.

If you do a google search of Eotvos Effect you will find a link to a wikipedia article. The maths may prove to be a bit off-putting, but the diagrams and explanations (particularly in the section of motion along the 60 degree latitude) will probably be more helpful.

[joshuahsong]

Calculating exact TAS

Here's question.
We are cruising at pressure altitude of 9000ft.
The OAT is -5 degrees celsius.
Calibrated airspeed is 170 knots.
What's the exact true airspeed under these circumstances?
I do know the answer, I need to know the formula.
Please help.

[EC DKN]

Hi,

You need to use the CRP-5:

1. Set Press Alt 9000 with -5 OAT.
2. Find 17 (170 kts CAS) in the inner scale
3. Read the outter scale which is 194 kts (TAS)

TAS= 194 KTS.

Alex or Paco can correct that as I am just student

[Cat3C.ATPL]

Absolutely correct EC DKN.

Of course, there will be a mathematical formula which can convert a CAS to a TAS but this type of question can be calculated simply and quickly using either a manual flight computer such as the CRP-5 or an electronic flight computer, the latter of which are permitted by some aviation authorities, e.g. FAA, but not by EASA.

I will expand your answer slightly:

1. Refer to the CRP-5's AIRSPEED window.
2. Set the Pressure Altitude of 9,000' on the scale inside the window against the Outside Air Temperature of -5 degrees on the scale outside the window.
3. Look up 17 (170 kts CAS) on the CRP-5 inner scale
4. Read the TAS of 194 kts on the CRP-5 outer scale.

(*I don't have a CRP-5 to hand - unforgivable!! - but I have 100% confidence in EC DKN's answer )

I hope this helps.

[latecoere240]

You can calculate it.

Density correction : You add 1% / 600ft. In this case 9000/600=15%
170*1.15=195 kt

Temperature : In standard atmosphere at 9000 ft it should be -3 (15-9*2).. The OAT is -5.. It's 2 degree colder..
you correct 1% per 5 degree difference.

170*1%*2/5=0.7

195-0.7=Approximately 194KT

[oggers]

Here's question....I do know the answer, I need to know the formula.

Hello Josh,

The formula is: TAS = CAS/√Relative Density

1.225 kg per cubic metre being standard SL density, the relative density is: air density at altitude/1.225

Note the above does not include correction for compressibility which is generally considered insignificant at the lowish speed and altitude in your example. To correct for compressibility you would substitue Equivalent Airspeed for CAS in the formula. I lifted the formula straight from my RAF gorundschool notes. There is a similar formula in "Aerodynamics for Naval Aviators" which is freely available online if you search for it.

[latecoere240]

eggs, there is no need in this example to talk about compressibility. Speed is less than 250 kt.
Regarding density of the air the most important to know>>> what does affect it :
-Pressure (Altitude)
-Temperature
-Humidity

[EC DKN]

Wrong, compressibility error is applied above 300kt TAS!! Look the CRP-5, it doesn´t make sense 250/100-3 DIV!

[Alex Whittingham]

Er compressibility is corrected for 'initial' TAS in excess of 300KT on the CRP-5, it is true, but FAA docs say compressibility can be ignored below 200KT and 10,000ft. EASA questions seem to say 200KT and ignore the 10,000ft bit. It's a matter of judgement, at what point can a very small compressibility be ignored? How do you express what is essentially a mach number in terms of TAS/CAS/altitude? Is the FAA 200KT a CAS or a TAS? Depends on the reference material. The reference material isn't quoted of course, that would be too partisan.

[oggers]

Latecoere:

eggs, there is no need in this example to talk about compressibility. Speed is less than 250 kt.

Actually the guy asked for an "exact" answer and a formula, so I gave the formula both with and without compressibility. And I also wrote "compressibility is generally considered insignificant at the lowish speed and altitude in your example".

Regarding density of the air the most important to know>>> what does affect it :
-Pressure (Altitude)
-Temperature
-Humidity

I was answering the question the OP asked, as opposed to the question you think is more important

The formula is: TAS = CAS/√Relative Density.....the rule of thumb you gave is a useful approximation. We all use them. But it is an approximation and the OP asked for an "exact" TAS.

[latecoere240]

Well, I already know the formula.
Everybody can find easily this formula and it's not only part of your RAF notes and aerodynamics for Naval aviators.Now demonstrate your calculation with this formula and your answer..

Indeed It's an approximation but quiet representative.it's more pratical and it seems we found the same result of the CRP-5, AVIAT 617 or any kind of flight computer..

[oggers]

The OP specifically asked "I do know the answer, I need to know the formula". So, I gave him the formula and cited my source. You didn't

Why do you have a problem with that? Genuine question.....

[latecoere240]

Well i can give another source with a different way of formula:

TAS : CAS +/- density error +/- compressibility error or EAS +/- density error

The source : OAA

I don't have any problem, but i guess you don't know to use it !
He does know the answer but doesn't know to calculate it.. You don't help that much...

[oggers]

Latecoere

The OP asked for the formula for TAS. Neither of us know whether he wanted the proper formula I gave or the - admittedly useful - approximation you gave. I simply answered the question, if you want to be the arbiter of the best formula fill your boots. Nobody else cares. Both are up there, the OP can take which one he needs. The end.

[s4ex]

I've came across interesting question, which I cannot understand, so maybe somebody could give an idea why.

At 10:15 the reading from VOR/DME station is 211deg/90NM, at 10:20 the reading from the same VOR/DME station is 211deg/120NM
Magnetic Heading = 200deg
Variation = 31W
Drift = 12L
What is the True Track ?

a 163
b 157
c 180 // Correct answer
d 181

So at first, I saw the 211 Radial and calculated 211 - 31 = 180, which gave me the correct answer.

But then I started thinking more, and though, that given MH, Var and Drift and ignoring VOR radial should give the same result, so I decided to check. If I wasn't given the Radial information, then True Track calculation would be :
(MH) 200 - (VAR West) 31 - (Left Drift) 12 = 157(T)

So obviously it was a wrong approach, however in the questions, where the VOR radials are not mentioned, only MH, Var and Drift given, that is the way how True Track is calculated.

In reality I'd expect both calculations give the same result (ignoring the Deviation). So why the VOR reading in this case is given the priority, or am I missing something ?

Thanks.

[Alex Whittingham]

Looks like the drift is given incorrectly in the question. Had it been 11° right (or 12°) you would have calculated a track of 180° (or 181°). My guess is that whoever set the question got left and right muddled up. Where was this from?

[s4ex]

Thanks for explanation. That might be true, or just a typo. Got the Q together with the list of questions from somebody I know while preparing for my PPL exams. Not a public source.

[gerardflyagain]

Thanks Keith.

I have another question. Are there mini quizs available any where?

I am about to transition from Pooley's books to Phil Croucher's EASA ebook. I think the book is excellent (although I'd like a bit more colour ) but one thing I miss is the mini quizs per section of a given topic. For example, in Pooley's air law, when I finished the chapter on Visual Flight Rules, I could then do a quiz on it. If I had to finish the whole of air law before I could do a quiz (which is how ppl tutor et al have it) then I'd have forgotten half of it by then!

[paco]

A good suggestion - I will schedule that in for the next update.

[selfin]

Originally Posted by latecoere240

TAS : CAS +/- density error +/- compressibility error or EAS +/- density error

TAS cannot be obtained from CAS or EAS by using independent linear terms.

Originally Posted by oggers

... the proper formula I gave ...

Originally Posted by oggers

The formula is: TAS = CAS/√Relative Density ...

This formula requires a loss of distinction between EAS and CAS which may be an acceptable assumption at low speed and low altitude. As either speed or altitude increase above some threshold - see Wittingham's post here on 2016/06/03 - the assumption leads to an increasingly erroneous TAS value and it is the difference from the correct value which is referred to as, rightly or wrongly, a "compressibility error." Latecoere240 therefore probably wanted to write your formula but with the addition of a corrective term. That is, I suspect the intention was TAS = CAS/sqrt(sigma) + compressibility_error; sigma being the ratio of ambient air density to the ISA MSL value as you've given.

It is incorrect to state TAS = EAS/sqrt(sigma) + compressibility_error; EAS might as well be defined by the expression TAS * sqrt(sigma), i.e. no corrective term is needed when mapping EAS to TAS or vice versa.

It's crucial to note that this compressibility_error is a function of CAS and altitude and that the effort needed to compute TAS this way is not less than working it out directly in the first instance. The function needed to do this mapping which is mechanically effected in modern airspeed indicators, and has been since the Tiger Moth, may be found in William Aiken Jr's NACA report 837 (1946), Standard nomenclature for airspeeds with tables and charts for use in calculation of airspeed, available from the Aerade Reports Archive hosted by Cranfield University here: NACA UK Mirror report description page. Eqn 3 can be rearranged to set TAS (V) or CAS (V_c) as the subject as required.