ATPL Instruments exam
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ATPL Instruments exam
Having a tough time with this one and exam on Monday. 
Any last minute tips/suggestions gratefully received!
Other mocks going well, meteorology a little mixed. Fingers crossed.
Thanks guys
Any last minute tips/suggestions gratefully received!Other mocks going well, meteorology a little mixed. Fingers crossed.
Thanks guys
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A question from the last exam... the CAS is 230KT at FL100, what is the Mach number?
(a) M0.405
(b) M0.420
(c) M0.485
(d) M0.525
(a) M0.405
(b) M0.420
(c) M0.485
(d) M0.525
Last edited by Alex Whittingham; 8th Dec 2014 at 09:06. Reason: to change answer (b)
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mach ?
Hello Alex,
there is a formula : EAS = 661xMxroot of greek letter delta
delta= pressure ratio P/Po
at fl100 P= 700hpa(see wx charts)
at sea level Po=1013hpa
700/1013=0,69 => square root= 0,83
CAS~EAS( difference= compressibility error)
661kt is speed of sound at sl std
so finally as an approximate ; 230kt=661xMx0,83
I let you work out the Mach number
there is a formula : EAS = 661xMxroot of greek letter delta
delta= pressure ratio P/Po
at fl100 P= 700hpa(see wx charts)
at sea level Po=1013hpa
700/1013=0,69 => square root= 0,83
CAS~EAS( difference= compressibility error)
661kt is speed of sound at sl std
so finally as an approximate ; 230kt=661xMx0,83
I let you work out the Mach number
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Merci blackmail, I thought this was more interesting as it relies on the knowledge that a constant CAS and flight level produces a Mach number that is independent of temperature. There is no need to assume ISA, any temperature will do, then it can be very quickly calculated on the nav computer without using formulae.
Using your last equation I get an answer of M0.419, the nav computer gives M0.445. The multi-choice answers above were made up, if this question comes up again I'd be interested to know what they are.
(edited to add: my mistake, I am getting M0.420 now so there is no real discrepancy)
Using your last equation I get an answer of M0.419, the nav computer gives M0.445. The multi-choice answers above were made up, if this question comes up again I'd be interested to know what they are.
(edited to add: my mistake, I am getting M0.420 now so there is no real discrepancy)
Last edited by Alex Whittingham; 8th Dec 2014 at 09:06.
For readers who have difficulty with the idea that changing temperature at any given combination of flight level and CAS will not change the Mach number the link below illustrates this effect well.
Just insert a pressure altitude and temperature then select CAS and insert a CAS value. Click on the "Submit" button and read off the TAS, LSS and Mach number. Then change the temperature and click the "Submit" button. The TAS and LSS will change, but the Mach number will remain unchanged.
For 230 knots CAS at 10000 ft the App gives Mach 0.417 ish. The difference between this and the nav computer result of 0.445 is caused by slightly different approximations used in the two methods.
https://www.google.co.uk/url?sa=t&rc...TNrM_Z5ikZzt2Q
And the link below includes a CAS/TAS/MACH/EAS converter which illustrates the ECTM/ERTM graphs well.
To test the effects of climbing or descending with one speed (CAS, EAS, TAS or Mach) constant, just input a pressure altitude and a value for whatever speed is to be constant. Click "compute" and read of the other speeds. Repeat this for several pressure altitudes and trends will become obvious.
https://www.google.co.uk/url?sa=t&rc...80642063,d.d2s
Just insert a pressure altitude and temperature then select CAS and insert a CAS value. Click on the "Submit" button and read off the TAS, LSS and Mach number. Then change the temperature and click the "Submit" button. The TAS and LSS will change, but the Mach number will remain unchanged.
For 230 knots CAS at 10000 ft the App gives Mach 0.417 ish. The difference between this and the nav computer result of 0.445 is caused by slightly different approximations used in the two methods.
https://www.google.co.uk/url?sa=t&rc...TNrM_Z5ikZzt2Q
And the link below includes a CAS/TAS/MACH/EAS converter which illustrates the ECTM/ERTM graphs well.
To test the effects of climbing or descending with one speed (CAS, EAS, TAS or Mach) constant, just input a pressure altitude and a value for whatever speed is to be constant. Click "compute" and read of the other speeds. Repeat this for several pressure altitudes and trends will become obvious.
https://www.google.co.uk/url?sa=t&rc...80642063,d.d2s
Last edited by keith williams; 7th Dec 2014 at 14:34.
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I have reworked this using accurate data. It looks like the difference was mostly due to me making a mistake with the nav computer, rather than differing assumptions. CAS has to be almost the same as EAS, even the online calculators show only a knot and a half of compressibility, which has no real effect. I have reworked it several times to find M0.420 so have amended the answers above in red and annotated previous posts to point out my mistake.
Interestingly the CRP5 nav computer is still giving a TAS some 4KT higher than the online sites. I remember this discrepancy was noticed some ten or so years ago when the JAA exams first started, other nav computers gave different speeds. It led to the UK CAA at least saying we should use the Pooleys or Airtour CRP5 for TAS calculations as that was the one they used when they wrote the questions.
Interestingly the CRP5 nav computer is still giving a TAS some 4KT higher than the online sites. I remember this discrepancy was noticed some ten or so years ago when the JAA exams first started, other nav computers gave different speeds. It led to the UK CAA at least saying we should use the Pooleys or Airtour CRP5 for TAS calculations as that was the one they used when they wrote the questions.
We have always known that different versions of the nav computer produce different results.
There is also considerable scope for errors when using the nav computer. If we use 2 degrees per 1000 feet for the lapse rate we get -5 at 10000 feet. If we use 1.98 we get -4.8. Distinguishing between –5 degrees Celsius and –4.8 degrees Celsius in the airspeed window for example is clearly subject to errors. These types of error are what I meant when I said that the differences were probably due to the approximations used.
There is also the question of differences between individual examples of any given type of nav computer. At EPTA we had one of those large classroom versions of the CRP5 which rarely if ever produced the same results as any normal sized version.
When I do the 230 knots CAS at 10000 feet question on my rather old and tatty CRP5, I get 268 TAS and Mach 0.42. These figures are pretty close to those produced by the two Apps. But the first couple of times I misread 0.42 as 0.44, which I suspect is what you did. (Damned treacherous thing this age related brain fade!)
As you say, hopefully the “incorrect “ options are far enough apart to enable exam candidates to pick the “correct” option. I do think that going for answers to three decimal places is a bit over-optimistic on the part of the author of the question.
On the up side, researching this question did lead me to find those two rather entertaining Apps, which i hadn't seen before.
There is also considerable scope for errors when using the nav computer. If we use 2 degrees per 1000 feet for the lapse rate we get -5 at 10000 feet. If we use 1.98 we get -4.8. Distinguishing between –5 degrees Celsius and –4.8 degrees Celsius in the airspeed window for example is clearly subject to errors. These types of error are what I meant when I said that the differences were probably due to the approximations used.
There is also the question of differences between individual examples of any given type of nav computer. At EPTA we had one of those large classroom versions of the CRP5 which rarely if ever produced the same results as any normal sized version.
When I do the 230 knots CAS at 10000 feet question on my rather old and tatty CRP5, I get 268 TAS and Mach 0.42. These figures are pretty close to those produced by the two Apps. But the first couple of times I misread 0.42 as 0.44, which I suspect is what you did. (Damned treacherous thing this age related brain fade!)
As you say, hopefully the “incorrect “ options are far enough apart to enable exam candidates to pick the “correct” option. I do think that going for answers to three decimal places is a bit over-optimistic on the part of the author of the question.
On the up side, researching this question did lead me to find those two rather entertaining Apps, which i hadn't seen before.
Last edited by keith williams; 8th Dec 2014 at 13:30.
