Vertical Accuracy?

[+rutson]

Now I know that vertical accuracy is streets behind horizontal, but I've noticed passing J22 M62, where there is a big sign that says "Highest motorway in Britain 1221feet", my GPS reads 1400' or so. Is it really that far off?

 

Actually just checked OS 1:50 map and 1221 feet seems about right. Wierd.

[+Simply Paul]

At the top of Snowdon in September my GPS said 1085m - And my OS map said 1085m. Now, the big question is do the OS people work from the top of the mountain, or the top of the trig pillar?

 

SP

 

P.S. OS 1:50 map? Now that's what I call a large scale map. Or do I mean a small scale one?

Edited December 27, 2004 by Simply Paul

[+Cryptik Souls Crew]

The marker here says 654m, my gps says 652m. I thought that was pretty good.

 

[+Stuey]

Now, the big question is do the OS people work from the top of the mountain, or the top of the trig pillar?

I don't know, but I put my GPS on a Trig pillar once and it was spot on too. It impressed me... but I did have about 10 satellites at the time.

[+Simply Paul]

Top of a mountain/big hill = nothing much between you and the satellites I guess.

[+klaus23]

On top of Snowdon I took three readings, all wrong... until I averaged them out, and that figure was correct.

 

SP, I think that the OS people, in the case of Snowdon, go from the OS pillar as the summit cairn is a construction rather than a part of the mountain.

 

I'm sure I saw something about that in the lodge on the summit... or was it my girlfriend's Uncle, who I was climbing with... hmmm

[Deego]

. Now, the big question is do the OS people work from the top of the mountain, or the top of the trig pillar?

 

The Height on the Trigpoint is measured at the top of the FB plate. Thats what the 2 holes are for above the number,

[+Simply Paul]

SP, I think that the OS people, in the case of Snowdon, go from the OS pillar as the summit cairn is a construction rather than a part of the mountain.

You're right Klaus - the trig point is NOT a part of the mountain, it's an addition. Therefor is it right that they measure from the plate on top of it, or do they allow for the height to the base, or just down to the plate with the numbers and bench mark on it...?

 

Also, the OS pillar on Snowdon is ON TOP of the artificial summit cairn, so I'm not sure how that works. If you can include artificial things on top of hills and mountains then where do you draw the line? A tall building on top of a small hill could end up being a mountain

 

More on topic, I'd add that I found vertical figures 'catch up' much slower when I stop than lateral position and take ages to settle down. While climbing Ben Nevis (well, the bottom 2/3 of it) last year the figures kept climbing for about 5 minutes after I'd given up and stopped!

 

SP

[+kewfriend]

Slight digression - but in the same vein:

 

I launched a 'vertically challenger TB' not so long ago. The LADDER

Ok so its a very long way from going anywhere but I was pleased to see that the first person to pick it up did at least concur with my vertical reading, which means that its a valid experiment.

 

It's only got to get to 2000 metres, but I'm taking the long view on this one.

 

[+The Forester]

Is it really that far off?

The reason why GPS vertical accuracy is so much less than horizontal error is to do with how GPS pseudoranging works.

 

If you have a dozen sats spread out around the horizon, the Northerly ones tend to cancel the random errors of the Southerly ones and vice versa, Same goes for the East/West ones of course. The sats which are most useful for calculating horizontal position are the ones below about 30° above the horizon and the ones much more than about 60° above the horizon are increasingly useless for obtaining Lat/Long

 

The sats which are most useful for measuring height above sea level are the ones which are highest above the horizon, but they have the disadvanatage that they do not have the error-cancelling effect of being able to counterbalance those pesky random errors by 'looking' at sars which are below the local horizon.

 

That having been said, the difference between the measured height and the observed height which you quote is exceptionally large.

 

Cheers, The Forester

[+The Forester]

do the OS people work from the top of the mountain, or the top of the trig pillar?

Heights plotted on an OS map at a trig pillar are the height of the natural ground around the base of the pillar.

 

The height shown in the database of trig pillars is the height above Ordnance Datum of the horizontally flat bit of the little metal bracket which is set into the side of the pillar.

 

Heights shown on your GPSr are related to the WGS84 spheroid and then have a fudge factor applied to convert from the mathematical model which your GPSr has of the geoid into an approximation of height above theoretical sea level.

 

Ordnance Datum is an average of a year's worth of tidal readings at Newlyn in Cornwall taken in the 1920s. It is not local mean sea level, even at coastal locations.

 

Cheers, The Forester

[+Snosrap]

Where does the gpsr measure height from? I understood this was from the centre of the earth with height above mean sea level approximated from an ellipsoid model of the surface of the earth (which is also used as an additional datum when the GPSr registers a 2D fix from only 3 satellites).

 

This is surely likely to be much less accurate than an OS measurement taken from the actual sea level? Which means that accurate height readings are most likely to be pure coincidence.

 

Have I misunderstood this?

[+ribel]

On a flight to Tenerife in July, I tracked the entire flight with the GPS. I was astounded by the apparent accuracy of the height (or more correctly, altitude) readings.

 

A brief lesson - commercial air traffic flies at pre-determined flight-levels (FL). Flight levels differ from height (which is the height above ground level) and altitude (height above mean sea level), in that above a certain altitude, when terrain clearance is not an issue, all aircraft set their altimeters to a common datum to ensure seperation from each other. Globally this is 1013.2mb (or 29.92inHg in the States). Incidentally, this transition altitude is 3000ft in the UK, and 18000ft in most of the US (where they have higher mountains).

 

Anyhow, getting back to flight levels, aircraft heading South may fly at say odd flight levels (FL310, FL330, etc.) and opposite traffic will fly at even flight levels (FL320, FL340, etc.). FL340 equates to roughly 34000ft AMSL. It will only be actually at 34000ft AMSL in a standard atmosphere. This is where it gets complicated, so I'll shut up now.

 

So getting back to my flight to Tenerife, I was astounded to see that during most of the cruise, my GPS was indicating 36000ft, give or take a few feet. So I guessed we were at FL360, which the crew confirmed during their usual progress reports. Does that mean we were flying in a standard atmosphere? That's rare, but possible. Or was it just co-incidence.

 

Right, I'll really shut up now...

[+Birders]

<<Incidentally, this transition altitude is 3000ft in the UK>>

 

Jolly excellent lesson, Ribel! The TA varies depending on where in the UK you are - it's 6000 ft in the London area. (Bren's just showing off, having beena Heathrow controller for 30+ years!)

 

Thanks to The Forester for more interesting info too.. a real ace in navigation matters. I wonder how my one time boss, AVM DCT Bennett - who wrote the standard text on navigation - would react to GPS. I can guess, but won't say!

 

HNY to all..

Edited December 28, 2004 by Birders

[+klaus23]

SP, I think that the OS people, in the case of Snowdon, go from the OS pillar as the summit cairn is a construction rather than a part of the mountain.

You're right Klaus - the trig point is NOT a part of the mountain, it's an addition. Therefor is it right that they measure from the plate on top of it, or do they allow for the height to the base, or just down to the plate with the numbers and bench mark on it...?

 

Also, the OS pillar on Snowdon is ON TOP of the artificial summit cairn, so I'm not sure how that works. If you can include artificial things on top of hills and mountains then where do you draw the line? A tall building on top of a small hill could end up being a mountain

 

More on topic, I'd add that I found vertical figures 'catch up' much slower when I stop than lateral position and take ages to settle down. While climbing Ben Nevis (well, the bottom 2/3 of it) last year the figures kept climbing for about 5 minutes after I'd given up and stopped!

 

SP

Sorry SP, I had to go and check my pics - for some reason I remembered the summit cairn to be seperate from the trigpoint...

 

I would say Deego is right (he is the authority on trigpoints after all!), that the plate on the top is the altitude.

 

In the case of Snowdon however, the cairn is manmade, as is the trigpoint, so the measurement off the top of the trigpoint is a good 5m/15ft higher than the mountain originally was, before cairn and tp were added.

 

Mad, eh?

[+pieces_of_8]

I'd say near enough for most of the time...when you have a good signal. I use a barometric altimeter as well... that only has 10ft increments and is also dependent on the weather pressure changes... so that can also be quite away out....need to reset it at known spot hights.

Anyway you should have seen the gps altitude before SA was switched off!! My house at 510ft could vary between 60ft and 1300ft.....not very helpful!

 

Mart

Edited December 28, 2004 by pieces_of_8

[+Pengy&Tigger]

a big sign that says "Highest motorway in Britain 1221feet", my GPS reads 1400' or so.

I've also tried this and get about 1215' going east and 1220' going west. The sign reads the same on both sides, but one side is slightly higher.

 

T

[+rutson]

The mystery deepens....

 

On the beech today my etrex read 2', by BT GPS 180' or thereabouts. Methinks something is wrong.

 

OOOOooooo P&T are alive

[+The Forester]

Where does the gpsr measure height from?

 

 

Your GPSr's GPS 'engine', its inner core, calculates its 3-D position in Cartesian co-ordinates: X,Y,Z.

 

Let's do a worked example.:

 

Let's say it takes a fix from four (or more) sats and comes up with a 3-D fix of:

X = + 3,756,096.444

Y = - 95,419.405

Z = + 5,136,715.016

 

Your GPSr then converts those Cartesians, whose origin is already defined as being the WGS84 geodetic datum, onto the WGS84 spheroid. That spheroid is a very simple mathematical model of the shape of the earth and is used because it is so simple to perform calcs using it. It is simply an ellipse of rotation, with its semi-major axis being the average distance from the centre of the Earth to mean sea level at the Equator and its semi-minor axis being the average distance from the centre of the Earth to mean sea level at the poles. "Average" is a key word here.

 

One of my heros, Albert Einstein, once said that "the truth should always be expressed as simply as possible, but never more so". Modelling the Earth as a simple spheroid is an excessive oversimplification if we wish to calculate altimetry to the sub 100 metre level. We need a more sophisticated model, but one upon which we can perform manageable calculations. That model is called the geoid.

 

The geoid is a model of the shape that the Earth at mean sea level would be if it was covered with a continuous and very deep ocean. This is the equipotential surface of the Earth. The average tidal range would be about 52cm and the general shape of the Earth could be modelled to a vertical accuracy of a metre or better. For several decades satellites measured the gravimetric 'pull' of the sea surface by radar and by laser, while having the gravitationally induced perturbations in their own orbits measured by very accurate tracking from ground stations. From this work a model of the Earth's gravimetric shape was produced which maps the variations in the density of rocks and minerals in the crust of the Earth. Mean sea level in the deep oceans is not at all a level surface. In one place it is a hundred metres below the spheroid, in another it is a hundred metres above.

 

Your GPSr has a simplified version of the gravimetric model, which enables it to convert 3-D from the WGS-84 spheroid to the altimetric model by interpolating your position from a lookup table which has a resolution of about 5° of Lat/Long. It then applies the corrected altitudinal difference between the spheroid and the geoid to your height and calls it height above sea level.

 

Now, let's go back to the worked example and follow through.

 

The 3-D Cartesian co-ords above are easily converted to a Latitude of:

53° 59.976' N 01° 27.315'W

with a spheroidal height of 99 metres.

 

Your GPSr then dips into its lookup table to read the spheroid to geoid height difference at your location and then and makes the suitable correction. In this case it finds that the difference means that the spheroidal height should be reduced by 49 metres, so it shows a height of 50 metres.

 

That's how your GPSr 'measures' height.

 

Cheers, The Forester

Edited December 29, 2004 by The Forester

[+Stuey]

Good grief, that actually made sense! Thanks for that

[+Brenin Tegeingl]

Re the cairn on Snowdon, I remember reading about one of the mountains in Wales, which on one survey was found to be under the hight to be classified as a mountain. The local community actually raised the hight to qualify as a mountain by building a cairn, this was then used for the measured hight, I seem to remember that a few years ago, on re-surveying it, the cairn had actually slumped slightly, and the hight was now slightly bellow the qualifying hight, to be classified as a mountain. From this I would presume that the Snowdon Cairn is used when measuring the actual hight.

 

Dave

[JackiePenn]

I remember reading about one of the mountains in Wales, which on one survey was found to be under the hight to be classified as a mountain. The local community actually raised the hight to qualify as a mountain by building a cairn

That story was made into a movie starring Hugh Grant. "The Englishman Who Went Up a Hill But Came Down a Mountain" Rather sweet really.

Edited December 29, 2004 by stonefisk

[+The Forester]

The Forester for more interesting info too.. a real ace in navigation matters.

Well, thank ye, kind Sir.

 

All my many years of grovelling with London Information on 124.6 have finally paid off!!

[+The Forester]

my flight to Tenerife, I was astounded to see that during most of the cruise, my GPS was indicating 36000ft, give or take a few feet. So I guessed we were at FL360, which the crew confirmed during their usual progress reports. Does that mean we were flying in a standard atmosphere? That's rare, but possible. Or was it just co-incidence.

It's an interesting observation. I'd never thought of it before, but I suppose you could use GPS to back-calculate the regional QNH (atmospheric pressure at sea level) if you know the flight level of the aircraft.

 

Can you tell us the point of departure and the date and approximate time? With that information we can calculate the position of the aircraft throughout the flight and look up the weather records to see what the QNH was at various points along the route.

 

For example, if we take a hypothetical mid-day departure from Newcastle on the 15th of July, we can estimate that your aircraft reached Top of Climb FL360 after say a couple of hundred miles with a step climb from an initial cleared level of FL320. Top of descent would have been about 120 miles from touchdown. We can calculate your position reasonably accurately throughout the cruise segment

 

So, you passed the NorthWestern corner of France at around 13:00, where the atmospheric pressure at sea level (QNH) was 1021mb and the surface wind 240°/6kts at Brest.

 

Then you passed La Coruña on the NorthWestern corner of the Iberian peninsula at about 13:45z, where the surface wind was 010/7 and the QNH was 1017. Then past Lisbon before heading out over the West Atlantic, where the METAR shows the surface wind was 200/11 and the QNH was 1015.

 

Upon arrival at Tenerife, at around 15:50, the local pressure setting was 1019 and the surface wind 310° at 12knots.

 

The above data is real, but is meaningless because it does not refer to your actual departure time and place. If you let me know your estimate of what time your holiday jet got airborne and from which airport and on what date, I'll crunch the numbers and come up with some useful data about the actual pressure along your track.

 

Cheers, The Forester

[+ribel]

Ok then Forester, I hope you know what you're doing!

 

I've done a bit hunting around and found I'd exported and saved the tracks from the GPS to memory map. I can email the entire tracks, both inbound and outbound if they'll be of any interest to you (about 80kb each).

 

Here are some key points:

 

Outbound

 

Newcastle (EGNT) - Tenerife South (GCTS)

27th July 2004

 

1st 3d position fix (approx. 15mins after departure)

 

09:00 (BST), 54°08.341'N, 2°06.784'W (Arncliffe, Yorkshire Dales), climbing through 19,682ft.

 

Subsequent fixes:

 

09:05, Salford (Gtr Manchester), 27,633ft

 

09:31, Berry Head VOR (BHD), 36,467ft

 

10:00, 47°17.073'N, 5°27.278'W, 36,614ft

 

11:00, 40°39.955'N, 9°28.111'W, 37,732ft

 

12:00, 34°09.550'N, 12°59.360'W, 39,065ft

 

13:00, 28°01.283'N, 17°03.194'W, 3,380ft

 

Last Fix:

 

13:05, 28°02.846'N, 16°34.062'W, 1759ft

 

I trust you can crunch something out of that lot.

 

Incidentally, looking at the GPS tracks, I seem to recall a lot of the flight was at 36,500ft, not my original quote of 36,000ft. The latter part of the flight was at 39,000ft.

 

ribel

[+ribel]

Oh, and I've just checked the top of descent - 137 nautical track miles from the last position fix on final approach!

[+The Forester]

I trust you can crunch something out of that lot.

I certainly can, though I'm initially puzzled by some things, such as the very unusual use of FL365 out of Berry Head. At first glance, I think this may have been an RVSM validation thing. I'll look at the spatial data later in the evening (hopefully before I open my Hogmanay bottle!) and get back to you.

 

Cheers, The Forester

[+The Forester]

I hope you know what you're doing!

I do and I've got a couple of pilot's licences to prove it.

 

OK, I've crunched the numbers and here are the results for the three fixes which are clearly made at cruising altitude.

 

09:31BST, Berry Head

QNH 1021mb. Presuming a cruise level of FL365, this equates to a pressure altitude of 36,740'. Your GPSr indicated an altitude which was just 33' different from this. Quite remarkable, considering that the 'view' of the higher elevation angle satellites through an airliner window is not very good.

 

10:00BST, abeam Brest

QNH 1021mb. Still at the same cruise level, but the altitude indicated by your GPSr equates to a pressure altitude of 36,854'.

 

The 11:000BST fix is inconclusive in altitudinal terms as it appears to have been taken during the step climb from FL365 to FL390. By this time your aircraft had burned off sufficient fuel to get up to its optimum altitude for fuel economy and you had flown far South enough for the tropopause to have raised high enough to make the climb worthwhile in terms of fuel savings.

 

The 12:00BST fix was taken approximately mid-way between Casablanca (QNH 1015) and Funchal Madeira where the QNH was 1018. Taking an average of these two, we have a pressure altitude for FL390 of 39,105'. Your GPSr readout of height above the geoid of 39,065' is in pretty good agreement, with a difference of just 40'.

 

Now, a word about accuracy. Modern airliners which want to use European or North Atlantic airspce between 29,000' and 41,000' are obliged to demonstrate a height-keeping accuracy of better than ±65' for a continuous five-minute period. Your airliner was quite certainly so qualified. An unaugmented GPSr which has a good view of all satellites above about 45° to 60° of the horizion can be expected to produce vertical accuracy of about 15m or 50', but from an airliner window your GPSr antenna can only see about 80° of a vertical arc and about 150° of the sky horizontally, so the fixes are not particularly well conditioned.

 

The 09:31 and 12:00 fixes are remarkable, having a comparison with the aircraft's intended altitude of just 33' and 40' respectively. Even the 10:00 fix, with a difference of 114' is not bad, when you consider the potential for the two errors each of about 50' to have the awkward habit of combining instead of mutually self-cancelling.

 

I've just checked the top of descent - 137 nautical track miles from the last position fix on final approach!

That doesn't surprose me at all. The normal rule of thumb is to commence descent at least three miles per thousand feet, increasing by a mile for every couple of knots of tailwind. A jet flying at 500 knots almost 8 miles above the ground has a huge amount of expensively bought kinetic and potential energy, so the fuel-cost conscious crew want to avoid having to dump energy with the speed brakes if at all possible. They fully close the throttles to idle at the top of descent and don't apply any power until it's necessary to dangle the Dunlops and hang some tin off the sharp edge of the wing and overcome the consequent and unavoidable drag. You approached Tenerife from the NorthEast with a surface wind of 060°/34knots, so the letdown had to commence by about 134 miles from touchdown. No Captain or handling pilot wants to get 'behind' his aeroplane, so most prudent jet-jocks add another couple of miles so that they can finesse the approach profile with a gentle trickle of power rather than having to deliberately dump energy through being late.

 

Cheers, and thanks for the data, The Forester

[+ribel]

Forester, thanks for that, a very informative piece, especially to a wannabe (but can't be) ATPL, so has to make do with a PPL!

 

Incidentally, the flight was on a Iberworld A320, perhaps the Spanish crews local knowledge led to the accuracy of the TOD? Having said that, the A320 has some particularly good FMC's.

 

So what do you fly?

 

Thanks again.

 

ribel

[+The Forester]

perhaps the Spanish crews local knowledge led to the accuracy of the TOD? Having said that, the A320 has some particularly good FMC's.

The rule of thumb of 3 miles per thousand feet holds good for all the main jets, whether Boeing or Airbus.

 

Having initiated the descent, with an input to the autopilot telling it the cleared level to descend to, the nav display shows a blue arc in front of the aircraft showing the projected point of arrival at the current speed and rate of descent. With that, the crew can tweak to descent rate to arrive spot on the allocated altitude at the initial point of the STandard ARrrival. They can tell the autopilot the rate of descent they want or the airspeed (in either IAS or Mach number). Either way, they can adjust to arrive at the assigned altitude at the waypoint of choice. It's a hi-tech equivalent of a bug-smsher pilot doing the 3° glideslope mental arithmetic with the DME readout.

 

Incidentally, there is a nifty trick you can use to calculate the drift if you listen to the QNH at the beginning and end of a sector. It's called Bellamy's Rule.

Drift (nm) = 635 *(p2-p1)/(sin(latitude)*TAS) (p2-p1 in mB)

Wind Correction Angle= 36300* (p2-p1)/(sin(latitude)*TAS*Dist)

 

p2-p1 is the difference between the destination and departure pressures. latitude is the average latitude on the route. TAS is the true airspeed in knots. Dist is the distance in nm. If the destination pressure is higher, the drift is to the left, and the required WCA is to the right (and vice-versa).

 

It's a handy trick and one which does not directly need a knowledge of the upper winds, nor does it need any plotting onto a whizzwheel, just a few seconds with the simplest of scientific calcuators.

 

what do you fly?

Nothing larger than the Beech Baron and Duchess and the good old Cessna 310. I fly for fun, not for profit, though I did do the CPL flying training at AST Perth and the ATPLs technicals with PPSC many years ago (sadly, both institutions are long gone).

 

Airmanship got me into seamanship and seamanship got me into hydrography and geodesy, which is just a very advanced form of high precision nav.

 

Cheers, The Forester