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Converting Mode C flight levels to altitudes

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Converting Mode C flight levels to altitudes

Old 24th Jun 2009, 16:45
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Converting Mode C flight levels to altitudes

Hi

I know transponder encoders send out pressure altitude, and I know ATC can convert this value into an altitude to display on the screen.

I remember it is to do with the difference in QNH from 1013mb and then times it by 28ft and add that to the flight level reported???

What formula is used and what are the variables based on? Is it based on the pressure at the aircraft position or the ATC location? And does the altitude of the aircraft change the 28mb/ft bit of the formula? (I think this is related to temp and pressure???)

cheers
smithgd
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Old 24th Jun 2009, 17:04
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You really need 3 variables - level sent by transponder, TA/TL, and current QNH. At my unit, approach controller updates the QNH in the radar system, and then computer uses it to calculate altitude for a/c below TA/TL.
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Old 24th Jun 2009, 17:40
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Aviation Formulary V1.44 is helpful for formulae.

There are two reasons why altitude is important to aircraft:

A) Avoiding terrain and obstacles
B) Avoiding other aircraft

For B, which is what ATC is involved in, you can use any datum you like, provided all the aircraft that are being separated from each other are using the same datum. So ATC would much prefer to use flight levels all the time -- it's those damned aircraft that insist on using a datum that approximates to true altitude at lower levels (for purpose A).

That should give you a clue to help with "Is it based on the pressure at the aircraft position or the ATC location?"

"And does the altitude of the aircraft change the 28mb/ft bit of the formula?" takes a bit more thought to get your head around. If you imagine the atmosphere stratified into flight levels, then consider what happens if sea level happens to be offset from FL000, you'll notice that the difference in level between e.g. FL350 and 35,000 ft is the same as the difference between FL001 and 100 ft, or FL000 and sea level. So while the 28 ft/mbar bit will vary ever so slightly depending on the QNH, the altitude of the aircraft makes no difference to the correction applied.
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Old 24th Jun 2009, 18:46
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To expand on criss's answer, it's basically transparent to the controller.

Here in the UAE, the transition altitude (TA) is 13,000 ft, and the lowest available flight level is FL150 (as opposed to most places where the lowest usable FL would be whichever is separated from 13,000 ft by 1,000 ft or more). Our radar screens are set with a TL of FL145. We manually input the QNH (pressure at MSL) into the system. At and above FL145, the display shows flight levels. Below FL145, it shows altitudes based on the QNH without any calculation required by us.

To expand a little further, as bookworm says, altitudes are used for separating aircraft from terrain as well as from each other. However, the atmospheric pressure at MSL can vary enormously over relatively short distances (especially when it's windy, for the meteorologists among you!). I've seen a helicopter on the radar about 70 NMs away, displaying an altitude of MINUS 200 feet, simply because of the pressure difference over those 70 miles. Our radar showed information based on the pressure at our location only.

Thus, when aircraft need to be separated from each other over long distances and are well above terrain, flight levels are used so they're all on the same pressure setting.

When aircraft are close to an aerodrome and terrain needs to be taken into account, the QNH is used. We have no way of knowing what the exact atmospheric pressure would be at mean sea level where the aircraft is; only at the aerodrome. Even in that case, it's actually a calculated pressure as we can't bore a hole down to MSL and place a barometer at the bottom! In essence, QNH will be used within 40 NM or so of an aerodrome so we have reasonable assurance that it's close enough to the actual MSL pressure at the location of the aircraft, and in any case we're using a minimum of 1,000 ft separation above terrain just in case. It also means that all aircraft within that bit of airspace are on the same pressure setting, and thus can be separated from each other using vertical separation.

As an aside, for those of us using Flight Refueling kit on which we input the QNH manually, there is possible embarrassment as the pressure drops out after 2 hours and must be entered again. If you don't do so, it reverts to 1013 below the TL. If you don't notice the pressure display flashing and then disappearing, verifying an aircraft's Mode C becomes interesting to say the least!
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Old 24th Jun 2009, 22:20
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Hi

Thanks for the replies...

So the general feeling is that it is QNH at the ATC unit not the aircraft, that makes sense, OK.... about the 28ft per mb...

Having searched the www I have found that the pressure lapse rate does vary with height quite a bit, 27ft/mb at SL, 36ft/mb at 10000ft and 48ft/mb at 18000ft are just a few examples. These are calculated from ISA values and are based on temperature and pressure using a formula:

ft/mb = (96*Temp in Kelvin)/Pressure in mb

so that gives me all the info to calculate altitude given QNH the lapse rate and the PA from the encoder...

As an aside does anyone know the highest transition altitude in use?

Cheers
smithgd
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Old 24th Jun 2009, 23:21
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USA is 18,000ft - don't know if there's any higher

Bookworm - those of us in the terminal environment would rather use Altitude than Flight Levels as it makes life a lot easier. 6000ft TA is coming
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Old 25th Jun 2009, 01:25
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I believe Papua New Guinea Transition layer is between 20,000ft and FL210.
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Old 25th Jun 2009, 06:57
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<<6000ft TA is coming >>

It's been in the London TMA for yonks..
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Old 25th Jun 2009, 07:36
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so that gives me all the info to calculate altitude given QNH the lapse rate and the PA from the encoder...
You don't need lapse rate to convert between altitude as ATC will see it. Nor do you need a formula like that. All you need is to know the pressure variation with altitude in the standard atmosphere to determine the offset for a particular QNH.

Bookworm - those of us in the terminal environment would rather use Altitude than Flight Levels as it makes life a lot easier.
That's only because you're assisting aircraft with objective A by assigning levels at or above the MVA.
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Old 25th Jun 2009, 09:48
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The lapse rate with altitude isn't used.

Climbing from FL50 to FL60 will be nearly 1000 ground feet.

Climbing from FL250 to FL360 will be more than 1000 ground feet.

The altimeters in my plane are calibrated for the standard atmosphere i.e. 27mb/100 feet.

If I reach cruising flight level, FL350, over an area of high pressure and fly to an area of low pressure, then the planes absolute altitude will decrease. It will happen at such a slow rate that it will be impercetible to me.

My altimeter will continue to show FL350, and so will everyone elses nearby, so no loss of separation
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Old 25th Jun 2009, 11:26
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It's been in the London TMA for yonks..
Contrary to popular belief there is a world beyond Watford that is also part of the UK

That's only because you're assisting aircraft with objective A by assigning levels at or above the MVA.
And thereby doing quite a bit of objective B too.
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Old 25th Jun 2009, 12:28
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Renard:
Climbing from FL250 to FL360 will be more than 1000 ground feet.
Your not wrong there - it would be more like 10,000 feet. I think you missed a zero off.
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Old 25th Jun 2009, 16:24
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Contrary to popular belief there is a world beyond Watford that is also part of the UK
OK, it's been in the Scottish TMA and the Belfast TMA for yonks
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Old 26th Jun 2009, 10:22
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Renard
You said.......The altimeters in my plane are calibrated for the standard atmosphere i.e. 27mb/100 feet.

Is that correct given in the standard atmosphere it varies?

Is 27ft/mb considered to be an ISA lapse rate for all altitudes?

So given the following info:
Aircraft at FL180
QNH = 1025mb

Using 27ft/mb (ISA lapse rate?) gives an altitude of 18,324ft AMSL.
Using 48ft/mb (Calculated lapse rate at 18000ft) gives an altitude of 18,576ft AMSL.

cheers
smithgd
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Old 26th Jun 2009, 15:44
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I believe a reasonably accurate formula for the height difference between two millibar levels is:

h2 - h1 = 221.1T (logP1 -logP2)


... where h1/h2 are the two heights, P1/P2 are the two pressure (mb) levels and T is mean temperature in degrees Kelvin.

By appropriate substitution (i.e. P1=1013.25, P2=1012.25 and T=15C=288K), this indicates that 1Mb corresponds to 27.3ft/mb at MSL in ISA.

I would have thought this would form the basis of calibration for a standard altimeter.


JD
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Old 26th Jun 2009, 16:39
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So given the following info:
Aircraft at FL180
QNH = 1025mb

Using 27ft/mb (ISA lapse rate?) gives an altitude of 18,324ft AMSL.
Using 48ft/mb (Calculated lapse rate at 18000ft) gives an altitude of 18,576ft AMSL.
(FWIW, the term "lapse rate" is conventionally used to describe temperature variation with height, not pressure variation)

If you start at FL180 in an aircraft with 1013 set, and wind the subscale to 1025, you'll find the altimeter reads about 18,300 ft, not 18,600 ft. Why? Well it's true that levels separated by 1 mbar are about 48 ft apart. But you didn't make the aircraft "12 mbar higher", you changed the subscale by 12 mbar. That's like adding a 12 mbar column of air at the bottom of the column on which the aircraft sits, and therefore the appropriate multiple is 27 ft/mbar.
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Old 27th Jun 2009, 15:41
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Finger trouble in my first post.

It should read FL350 to FL360.
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Old 27th Jun 2009, 19:57
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It should read FL350 to FL360.
In which case, I don't understand the point you're making.

FL350 to FL360 is 1000 ft in the ISA.
FL350 to FL360 is less than 1000 ft when the atmosphere is colder than ISA.
FL350 to FL360 is more than 1000 ft when the atmosphere is warmer than ISA.
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Old 29th Jun 2009, 13:45
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Bookworm, your post at 17:39 is exactly what I was thinking, but since I couldn't find any "formal" confirmation of this I thought I'd ask the good people of PPRuNe for help, and help you all did! Thanks.

smithgd

PS. If anyone should find a suitable "formal" confirmation please feel free to pm it to me
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