Basic Aeronautical Knowledge: Altimetry and margins of error
 

According to the Australian Bureau of Meteorology:You are a diligent pilot and have set your altimeter to the current forecast Area QNH for the area in which you are flying. It happens to be 1013 hPa.

Assume, for the purposes of the first question, that:

• The forecast QNH is representative in accordance with the BOM’s explanatory material quoted above.
• 1013 hPa is exactly sea level pressure in the ISA.
• 1 hPa = exactly 30’ in the ISA.
• The temperature is exactly ISA.
• Your altimeter is perfectly accurate and you are flying over the sea.
• Your aircraft’s static source is at the same height above the sea as the altimeter.
• Your altimeter is indicating 500’.

Question: What is your altimeter’s actual height above the sea below?

Is it:

(a) 500’.
(b) It could be anywhere between about 350’ and 650’.
(c) It could be anywhere between about 425’ and 575’.
(d) None of the above, the correct answer is [explain].

Background to question 2.

Two hours earlier from the scenario in question 1, you took off from a Class D aerodrome with ATIS. Before take off, you did a pre-flight altimeter check in accordance with ENR 1.7. For simplicity, assume that both altimeters in your aircraft were exactly 50’ ‘off’ in the same direction. (For present purposes, I’m not going to reveal ‘which way’.) In accordance with ENR 1.7, that error is acceptable (for both VFR and IFR flight) and you take off.

Fast forward two hours and 150 nms, when the circumstances and assumptions as are set out for question 1 apply. But you now know that that the altimeters in the aircraft have a 50’ error.

Question: What is your altimeter’s actual height above the sea below?

(a) 500’.
(b) It could be anywhere between about 400’ and 700’ (if the altimeter error is a 50’ under-read) or between about 300’ and 600’ (if the altimeter error is a 50’ over-read).
(c) It could be anywhere between about 475’ and 625’ (if the altimeter error is a 50’ under-read) or between about 375’ and 525’ (if the altimeter error is a 50’ over-read).
(d) None of the above. The correct answer is [specify].

I think you'll find the correct answer is (e) who cares Clinton :8

The question relates with margins of error.
The question gives the answer for the QNH margin of error : +/-5hPa is +/-150ft.
The altimeter is said to be perfect. However, is the static pressure source perfect ? I will assume so. In real life, there will always be a small error due to propwash on the ground and relative wind in the air.
I don't see any other source of error (instrument misread maybe?).
So theoretically the answer would be b), or D), there is always a margin of error but hopefully much lower than 150ft in this case.

But, I would add something. QNH represents the air surface pressure. It's something that evolves slowly over large distances. So it's rather continuous. 5hPa of error seems very big. Plus, QNH can be measured accurately at multiple locations to help the forecast. In practise, I rarely noticed more than 1-2 hPa of error when applying the right QNH on the ground when compared to the charted airfield altitude.

For the second question I will ignore this remark and assume my first answer was b)
B for the second question would be tempting, but if there is a measurement error on the ground, I think this error will only ever increase with altitude, because if 1hPa is 30ft close to the ground, it's more (much more) up in the air. The effect won't be very noticeable at 500ft (1hPa = 30.5ft) so the answer is close to b) but I specified some aspects according to d)

That's ok for the purposes of this question but I have seen some people studying for ATPL exams who didn't realise that this value (ft per hPa) increases with altitude. For example, it's about 70'/hPa at 30,000ft.

Not relevant to your post but thought I'd just throw that in.

e) whatever the RADALT says it is. Wings level of course.

Not sure what the purpose of your question might be, however, some comments ...

The forecast QNH is representative in accordance with the BOM’s explanatory material quoted above.

That's fine. BOM is maintaining their defined reporting standard.

1013 hPa is exactly sea level pressure in the ISA.

Not quite but close enough for Government business

1 hPa = exactly 30’ in the ISA.

Not the case, other than at one specific altitude, which is of no great interest to pilot folk. Providing you are in the lower atmosphere, the error is not great. However, get up in the flight levels and the 30 ft/hPa is way out of line. Some discussion here

Bob Tait's Aviation Theory School - Altimetry Rates - Bob Tait's Aviation Theory School Forums

might be of use for those who are interested.

I presume that you are suggesting that the atmosphere on the day has a pressure distribution which is the same as postulated in the ISA ?

The temperature is exactly ISA.

I presume you mean both the standard SL OAT and standard lapse rate ?

Your altimeter is perfectly accurate and you are flying over the sea.

If you wish.

Your aircraft’s static source is at the same height above the sea as the altimeter.

Not generally the case, but OK.

Your altimeter is indicating 500’

OK

Question: What is your altimeter’s actual height above the sea below?

I suggest very close to 500 ft assuming you are nearby the departure aerodrome as the instrument check would have been done by comparing a known elevation for the test point to the instrument indication ie the BOM tolerance is irrelevant at this point. Which answer were you running with ?

Background to question 2.

Not too sure what Q1 and Q2 refers to, but, let's not worry too much about that.

assume that both altimeters in your aircraft were exactly 50’ ‘off’ in the same direction
Fast forward two hours and 150 nms, when the circumstances and assumptions as are set out for question 1 apply. But you now know that that the altimeters in the aircraft have a 50’ error.
Question: What is your altimeter’s actual height above the sea below?

I suggest, again, pretty close to 500ft but, assuming we remain in the same forecast QNH area, we might see up to the relevant difference for the BOM tolerance. I'll leave you to run the actual sums or look up an approximate figure from the linked reference. We would expect to see an error related to the 50 ft altimeter check error. I don't believe we can be certain what that error might be.

The question gives the answer for the QNH margin of error : +/-5hPa is +/-150ft.

But, as noted before, that figure is incorrect in this case where the OP is looking to split hairs.

However, is the static pressure source perfect ? I will assume so.

For the purposes of the question, one would include the plumbing in the statement that Your altimeter is perfectly accurate

In real life, there will always be a small error due to propwash on the ground and relative wind in the air.

Providing you have zero sideslip, no. The purpose of the quite lengthy certification flight test work done to establish the AFM PEC data is to cover all this sort of stuff.

In practise, I rarely noticed more than 1-2 hPa of error when applying the right QNH on the ground

Not the point in question. Using A/QNH data, you may only assume the accuracy declared by the BOM.

I think this error will only ever increase with altitude,

Why is that ? You have no indication regarding the source of the error which you observed on the ground ?

because if 1hPa is 30ft close to the ground, it's more (much more) up in the air.

Close to sea level, the rate is around 27 ft/hPa. Indeed, it does increase with height as that is the nature of the equation for ISA pressure variation with height.

The effect won't be very noticeable at 500ft (1hPa = 30.5ft)

Only because I'm totally confused, whence comes 30.5 ?

That's ok for the purposes of this question

Not really, as the OP is playing with splitting of hairs, so the pressure rate variation becomes materially significant.

Hopefully, I will learn some material techo stuff with the OP's response ?

JT, you've confused some assumptions I provided, for the purposes of simplicity, for assertions of fact, then added your own assumptions that were not made in the questions.

For the record, I know that:

- 1013 hPa isn't the precise sea level pressure in the ISA

- no altimeter is perfect

- an aircraft's static source isn't necessarily at exactly the same level as the altimeter/s to which it is input, and

- etc

all of which looks to me very much like 'splitting of hairs' by you, unless that all adds up to 100's of feet of error? (I did spend the odd decade or so working on avionics, BTW.)

You've added your own assumptions that weren't in the questions I asked. You've assumed that we "are nearby the departure aerodrome" and "remain in the same forecast QNH area". So when you "note" that a figure is "incorrect", it's based on your assumptions. I could assume that BOM's forecast Area QNHs are accurate to within plus or minus 0.1 hPa, but that would be imprudent because, as a matter of fact, BOM states that "[a]n altimeter set to Area QNH will be representative to within ±5 hPa of any actual QNH of any location within the defined area."

You are flying YCBP - YFRT - YPKG. You have forecast Area QNHs for the 4 Areas through which you're going to fly. Let's pick 2,500' 'indicated' on the altimeter as the cruising altitude. What do you say is the range of heights above MSL within which the aircraft will definitely remain during the cruise? Make whatever assumptions you want about the height of static source compared with the altimeter and lapse rates etc. If you can bring yourself to do it, assume you nail the long pointer on the altimeter to the '5' for the entirety of the cruise.

2,500' plus and minus what? PI insurance level of confidence.

Would have thought between 310 and 670 ft depending on which way the altimeter error is and the which side of the +/- 5 HPa you are.

What an incredible waste of band width this thread is 😳

It's a big plus and minus, isn't it, swh!

But provided all the aircraft in an Area have altimeters that are within the accuracy tolerances and set to forecast QNH, the potential variations of actual QNH from forecast QNH will affect all 'nearby' aircraft equally. (I'll track down the BOM's parameters for maximum differences in QHNs as between adjacent areas.) It makes sense, and has done for a long time.

The next questions:

What is the margin of error of a 'blind' Mode C encoder output?

What is the maximum allowable 'delta' between an aircraft's Mode C encoder output and the reading on the aircraft's altimeters (when set to 1013 hPa)?

A nice big Chocolate Easter Egg seems good about now……..

In the hope that On eyre might change his or her mind, I'll ask another question. As background, I note that the AOPA CEO went before a Senate Committee on 20 November 2020 and raised a number of concerns, one of which was about a pilot accused of low flying, which accusation the pilot said is not true.

Who said this to the Committee, in response:That quote and the answer to my question are here.

I'm pretty sure the maker of that statement wasn't in the cockpit at the time and hasn't much of a clue about the subject matter of this thread.

Pot........Kettle

Not interested in getting into willy waving contests. You are free to interpret the intent of my comments as you may choose.

Are you sure about this?
You can't be perfect, there is always some sort of turbulence around the static pressure source, the dual static source is useful to counted sideslip but does it counter it perfectly ?
I don't know the specific term in english but during flight test they use some sort of pole/rod to measure air data very far away from the aircraft.
The pressure vs altitude follows approximately an exponential law, so if the pressure is 10% lower, the pressure rate with altitude is 10% lower as well.
30.5ft/hPa is the figure at 500ft, IF you assume the figure at sea level was 30ft. It was just to give an idea of the difference it made at 500ft : not much.
That's a very technical question.
I'll try to make a parallel with what I know.
In the black boxes, all values are rounded down to one resolution.
For example, if the altitude is coded with a resolution of 4ft, an altitude of 3ft will read 0.
This problem is most visible on the latitude/longitude parameters, since the resolution can be some meters..

Are you referring to the same kind of problem ?

Tolerance for the Mode C encoder is +/- 125ft at all altitudes.
Tolerance at your theoretical 500 ft on your altimeter is +/- 20ft. This tolerance gets wider as you increase altitude, for instance at 10,000ft, the tolerance is +/- 80ft.

Both these hypothetical threads smell of a CASA exam, absolutely impractical, nothing to do with the real world.

In the real world, Cedrik, a real Australian pilot is being prosecuted for ‘low flying’. My understanding is that the pilot is the pilot to whom the CASA person I quoted earlier was referring when he said to a Senate Committee: “[T]hat’s not what the instruments on his aircraft say. They say he was at 125 feet.”

I confidently predict that the pilot isn’t you, Cedrik, because rather than carrying on like a petulant child as you are in the threads I’ve started, you’d be under constant stress, having sleepless nights and spending large to defend yourself against an allegation you consider to be untrue. Maybe you’d end up like Glen Buckley: a heart attack and penniless as a consequence of what’s been done to you. Pray your turn never comes.

Whilst I am well aware that there are always at least three sides to every story, in the case of “what aircraft instruments say” there are some unassailable facts about the potential delta between “what they say” and a thing called “the truth”. That’s because there are tolerances and margins of error in every gizmo ever fitted to any aircraft, tolerances and margins of error in every gizmo ever used in air traffic control and surveillance and tolerances and margins of error in every forecast ever produced by any met forecaster. And all of that should be BAK.

(Chronic Snoozer nailed it by nominating the RADALT as the most accurate gizmo to measure the distance between a point on an aircraft’s airframe and the ground or water. These days I think the margin of error in RADALTs is specified in centimetres. But why do some aircraft have RADALTs? Precisely because the other gizmos aren’t precise enough when an aircraft is getting close to the ground in zero or bad viz.)

Out of many examples, a prosecution for ‘drink driving’ recently collapsed in the ACT because a legislated period of time was measured by reference to a clock on the wall of a hospital. No evidence was led to prove, to the requisite standard, the accuracy of the clock. When ‘speed cameras’ first came out, many prosecutions for speeding collapsed because no evidence was led to show the serviceability and accuracy of the ‘camera’.

What a speed camera “says”, what a breathalyser “says” and what a clock “says” are all just hearsay. (There are now laws to the effect that provided evidence is led to show a ‘speed camera’ and ‘breathalyser’ were serviceable and ‘in calibration’, the reading is taken to be the actual speed or BAL unless evidence is led to disprove the reading.) And what an altimeter “says” and what a Mode C transponder “says” and what a TAAATS screen “says” are all just hearsay.

Of course we all rely and make decisions on the basis of what these things “say” and it is possible – and necessary – to show the accuracy of “what aircraft aircraft instruments say” if you want to convict someone on the basis of what those aircraft instruments “say”. But simple BAK (such as that provided to us by swh and RedwireBluewire and others in this thread) demonstrates that – depending on what the “instruments” are – there can be hundreds of feet of accumulated difference between the truth and what those instruments “say”. Not a few feet of difference. Not a few tens of feet difference.

As the CASA person who made the statement in front of the Senate Committee wasn’t in the aircraft with the pilot, the CASA person can’t be referring to the aircraft’s altimeter or the display on the aircraft’s transponder. As the pilot involved denies the allegation, I can only assume - reasonably I suggest – that the pilot doesn’t reckon the altimeter was "saying" 125’. I can only assume – reasonably I suggest – that the CASA person was referring to some gizmo on the ground relying on Mode C transponder / ADS-B data.

Acceptable VFR altimeter accuracy when tested against a known accurate QNH and known elevation below 3,300’? +/- 100’. It’s in AIP.

Maximum allowable delta indicated altitude and Mode C data? +/- 125’ (and there’s a margin of error in the Mode C data itself). I’m confident there’s an equivalent of FAR Part 43, Appendix E in Australia’s rules.

And then take off and fly with the altimeter set to forecast Area QNH, which is representative to within +/- 5 hPa of any actual QNH of any location within that Area. The BOM says so.

And what does TAAATS use as the QNH reference to generate the Mode C altitude to display for a particular aircraft?

A pilot diligently nailing 500’ indicated on an altimeter serviceable for VFR and set to Area QNH could, on the published tolerances, be anywhere between about 250’ and 750’ AMSL in fact and squawking a 125’ delta from any number in that range.

There is also the possibility of eyewitnesses. But laypeople are notoriously unreliable in estimating heights and distances of aircraft. When the city of Gunghalin was originally built in the ACT, lots of new residents complained about low flying aircraft. Air Services literally went into people’s lounge rooms with equipment to show that the aircraft (on SIDs out of 35) were, based on the transponder data, at least 2,500’ AGL by the time they were overhead. (I think the data usually showed around 5,000’ AMSL and, taking into account tolerances and the ground level, that meant the aircraft were at least 2,500’ AGL.) The Facebook page for the Brisbane airport noise complaint group includes people complaining about aircraft “shifting gears” above their homes.

To most laypeople, just about every ‘little aircraft’ is a Cessna. But as we know, e.g. a C152 isn’t the same size as e.g. a C208. And when someone sees something that they think is small but is in fact much larger, it appears much closer.

For everyone who thinks this is all trivia and hypothetical, pray you don't come to the attention of someone who wants to hang you on the basis of "what your aircraft instruments say".

You can't be perfect, there is always some sort of turbulence around the static pressure source, the dual static source is useful to counted sideslip but does it counter it perfectly ?

No measurement is perfect and the closer to perfection, the greater the cost. However, a major proportion of the flight test dollars go into PEC workups and the resulting AFM charts will be as good as one can get. I suggest, in terms of the thread questions, we can take the PEC to be near as close to correct for all practical purposes. Introduce some sideslip and it goes a bit out the window. For most aircraft, in most operations, sideslip will be minimal and unintentional so all usually is OK.

I don't know the specific term in english but during flight test they use some sort of pole/rod to measure air data very far away from the aircraft.

Probably you are thinking of the various air data test boom and trailing cone kits. Some links at

Air data boom - Wikipedia
Design, Testing, and Calibration of a Custom Air Data Boom to Obtain Flight Data For the UTSI Cessna-T210J (N33UT) (tennessee.edu)
What Is The Shuttlecock That Hangs Off The Tail Of Test Planes? (simpleflying.com)

These bits of kit keep the source away from the bulk of the aircraft airflow interference so the crew can determine the errors inherent in the aircraft's pitot static system by reference to the free stream measurements taken with the test kits.

The pressure vs altitude follows approximately an exponential law,

Actually, the ISA model (and any other of which I'm aware), is exponential, as is the derivative to figure the rate (on a given day, the numbers will be a bit off ISA, as you infer). For SL, the figure is around 27 ft/hPa (rather than 30) and the graph in my first post's link is the model for the derivative with altitude. Not sure that I concur with your calculation but, no matter.

a real Australian pilot is being prosecuted for ‘low flying’.

Then I suggest that the pilot in question secures the services of one of the lawyers who both specialises in aviation and has a significant flying background (presuming that he/she has not done so already). There are a few of those folk around (JM and GP - both long term mates of mine - come to mind, for starters) and they would then engage an appropriate engineering expert (and, again, that is an easy ask) for the courtroom punch up. If the ins and outs of the thread are relevant to the case, I would have thought it would be a relatively easy exercise to have it thrown out of court without an excessive waste of time.

A side issue might be if the other side can involve your friend in strict liability matters along the way ? Part 91.267(4) would be a point to consider ...

And when someone sees something that they think is small but is in fact much larger, it appears much closer.

.. and, hence, slower. Well can I remember the first B747 I saw coming into land donkeys years ago. I was sure that it was about to stall and make the headlines that evening ...