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Density height calculation question

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Old 7th Nov 2020, 04:58
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Density height calculation question

I have an assessment for the Qantas pilot academy. They have sent me a practice test with the following question:

"The elevation of Echo is 3480ft AMSL. The QNH is 1021 hPa and the temperature is 24C. What is the density height of Echo?"
A. 1920 ft
B. 5105 ft
C. 3820 ft
D. 5560 ft

I calculate this as follows:

PH = 3480 + (1013-1021) x 30))
= 3480 - 240 = 3240 ft PH

ISA Temp @ 3240 PH = 15 + (3 x -2) = 9C

ISA Deviation = OAT - ISA
= 24 - 9 = +15C

Density Height = PH + (ISA Deviation x 120)
= 3240 + (15 x 120)
= 5040 ft DH

Can someone please explain what I'm doing wrong?
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Old 7th Nov 2020, 05:43
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Can someone please explain what I'm doing wrong?
Applying for the Qantas Academy is what.
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Old 7th Nov 2020, 05:49
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Originally Posted by MB00086
I have an assessment for the Qantas pilot academy. They have sent me a practice test with the following question:

"The elevation of Echo is 3480ft AMSL. The QNH is 1021 hPa and the temperature is 24C. What is the density height of Echo?"
A. 1920 ft
B. 5105 ft
C. 3820 ft
D. 5560 ft

I calculate this as follows:

PH = 3480 + (1013-1021) x 30))
= 3480 - 240 = 3240 ft PH

ISA Temp @ 3240 PH = 15 + (3 x -2) = 9C

ISA Deviation = OAT - ISA
= 24 - 9 = +15C

Density Height = PH + (ISA Deviation x 120)
= 3240 + (15 x 120)
= 5040 ft DH

Can someone please explain what I'm doing wrong?
Using more accurate 3.24 instead of 3 in the ISA dev formula gets a final answer of 5098ft which is closer to (B)
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Old 7th Nov 2020, 06:10
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Yea that's what I did, and apparently B is the correct answer. It's just in all the study material it tells me to round to the nearest 500ft to calculate temp drop. I was expecting as it's multiple choice I would get the exact answer.
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Old 7th Nov 2020, 06:52
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ISA temp is 2*C / 1000' which is 0.5*C per 250'.

So ISA T* at 3240' is nearer 8.5*C, not 9*C

That gives 5100' for an answer, so B
==========
Or using my CR whiz wheel a fraction over 5000' which is also more than close enough to pick B
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Old 7th Nov 2020, 07:46
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Wait till you do some plotting, the thickness of the pencil they used for the questions determines the answer. :-(
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Old 7th Nov 2020, 07:58
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PH = 3480 – [(1021-1013)x30]

= 3480-240

= 3240

ISA at 3240 = 15-(2x3.2)

= 15-6.4

= 8.6

ISA dev = 24-8.6

= 15.4

Density Alt increases approx. 1000ft for every 8C above ISA

Therefore Density Height of Echo = 3240+[(15.4/8)x1000]

= 3240+1925

= 5165, which is pretty close to ‘B’.
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Old 7th Nov 2020, 08:15
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Originally Posted by Tinstaafl
ISA temp is 2*C / 1000' which is 0.5*C per 250'.

So ISA T* at 3240' is nearer 8.5*C, not 9*C

That gives 5100' for an answer, so B
==========
Or using my CR whiz wheel a fraction over 5000' which is also more than close enough to pick B
One of the few bizarre things that actually took hold during my Met lessons sometime last century was the Dry Adiabatic Lapse Rate is 1.98C per 1,000ft. So the ISA Temp at 3,240ft is 8.5848*C rounded to 8.6*C, not 8.5*C. Pretty much what eckhard calculated.

That would round out the result a foot further from 'B'
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Old 7th Nov 2020, 08:17
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The correct answer: "My calculations lead me to conclude that the answer is 5040'. I therefore don't understand where I may have gone wrong."

5,040' feet is, in principle, a 'less safe' answer than the 5,105' in B, as you're erring 65' on the 'dangerous' side for your planning. But, as binzer has observed, and as you will find in the real world, there are hundreds of feet in a pencil width and rounding assumptions. Just avoid any operation in which 65' either way make a real difference.

Qantas put a Jumbo into a golf course - or was it a rice paddy? I forget - but I reckon that 65' either way wasn't the cause.
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Old 7th Nov 2020, 09:25
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I don't think it is a case of what you are doing wrong. As they say in FAA land: B 'is the most correct answer'. I am not even joking.
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Old 7th Nov 2020, 10:57
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I've only ever used Density Altitude.
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Old 7th Nov 2020, 12:15
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Looks like the type of questions haven't changed much since the old DCA SCPL theory exams of the 1950 - 1960's.

I well remember scratching my head around the complexity of gyro steering questions centred on the South Pole. After joining DCA in 1969 my office was next to Ted Steele the former wartime RAAF navigator who set the SCPL navigation and flight planning exams in those days. He came across as an embittered old man who hated pilots for some reason. I tackled him on the uselessness of South Pole gyro steering questions for the average GA charter pilot flying Chieftains to Tasmania which was SFA. He said the SCPL exams were first vetted and approved by Qantas as that was the standard demanded of Qantas recruits. That could be an urban myth but it came from the horse's mouth so to speak.
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Old 7th Nov 2020, 12:50
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Closest answer, don’t worry if it’s not exactly one of the given answers.
You don’t know if they’ve used 2C or 1.65 or 1.98 and 30’ or 25’ and if they’ve rounded up or down.
These are fun to do on the back of a paper napkin but in real life you use tables to reduce the possibility of errors.
That is if you fly analog piston aircraft.
Anything bigger and it’s provided for you.
Pretty much.
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Old 7th Nov 2020, 14:54
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Originally Posted by MB00086
I have an assessment for the Qantas pilot academy. They have sent me a practice test with the following question:

"The elevation of Echo is 3480ft AMSL. The QNH is 1021 hPa and the temperature is 24C. What is the density height of Echo?"
A. 1920 ft
B. 5105 ft
C. 3820 ft
D. 5560 ft

I calculate this as follows:

PH = 3480 + (1013-1021) x 30))
= 3480 - 240 = 3240 ft PH

ISA Temp @ 3240 PH = 15 + (3 x -2) = 9C

ISA Deviation = OAT - ISA
= 24 - 9 = +15C

Density Height = PH + (ISA Deviation x 120)
= 3240 + (15 x 120)
= 5040 ft DH

Can someone please explain what I'm doing wrong?
Essentially you have done nothing wrong, CASA does not require you to know that relative humidity/dew point also impacts density height. Their answer assumes a relative humanity of 85% or a dew point of -5 deg C.
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Old 7th Nov 2020, 15:02
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Calc

For some reason, my computer asks to input dew point temperature, too. I left it that in blank and it came up with density alt 5043 ft, press alt 3268 ft, ISA 8.5C, and ISA Dev 15.5 C
🤔
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Old 7th Nov 2020, 16:23
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So some bloke at Qantas has no knowlege of how to calculate density height, and simply plugged the values into a computer, without understanding the algorithm, and wrote down the resultant answer ...

Sounds about right for an airline training department.
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Old 7th Nov 2020, 20:09
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Originally Posted by Checkboard
Sounds about right for an airline training department.
What a load of codswallop. QANTAS has a pretty good training department from my experience, full of blokes (and even sheilas), with plenty of knowledge and both the desire and the ability to impart it to their trainees.

It’s a pretty fair bet they had nothing to do with the writing of this question either.
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Old 7th Nov 2020, 21:22
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Not codswallop in the slightest. Ask an airline pilot to calculate an off-track PNR in flight sometime. Airline training does not review many ATPL subjects. Calculating a density height would be a head scratcher for most airline pilots - including trainers.
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Old 7th Nov 2020, 21:30
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An airline pilot would have no need to work out density altitude. Just like they don’t need to use a sextant or do DR plots!

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Old 7th Nov 2020, 23:43
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Originally Posted by Checkboard
Not codswallop in the slightest. Ask an airline pilot to calculate an off-track PNR in flight sometime. Airline training does not review many ATPL subjects. Calculating a density height would be a head scratcher for most airline pilots - including trainers.
You’re probably right - but that has stuff all to do with airline ops and airline training and nothing whatsoever to do with the level of involvement that QANTAS training would have had in this question - precisely zero. Your post was casting aspersions against QF training. It’s irrelevant.
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