Intragrated Elevation Into Coordinates

[+EraSeek]

Beam me down Scotty, to W122 34.457 N47.48.765, but dammit, this time get the elevation right.

 

"A minimum of four GPS NAVSTAR satellites (more can be used in overdetermined PVT solutions) are used to determine three position coordinates and time. Position coordinates are computed by the receiver in Earth-Centered, Earth-Fixed X, Y, Z (ECEF XYZ) coordinates.

Most receivers compute (and store) positions in geodetic coordinates (datum WGS-84) latitude, longitude and height above the ellipsoid (HAE). Note - height calculations are independent of any user selected horizontal datum.

 

The height displayed on most consumer handheld GPS receivers is orthometric height, the height above mean sea level (MSL). It is straight forward to approximate MSL world wide by interpolation of the GEOID model (table) and making the simple calculation."

 

A satellite fix is a 3D solution. However, coordinates and elevation are displayed seperate from each other on the user end. A waypoint is not elevation dependant. Whether you are above the waypoint or on the ground at the waypoint, it is the same. Doesn't it make more sense for the waypoint to include elevation in its calculations. Lat, Long, Elev. 3D instead of 2D. At present a GOTO operates in the world of Flatland. Why?

 

If you are 5000' feet above a point on the ground, in the real world you are still 5000' away from that point. Anyone know why the Global Positioning System has not included this obvious step into our 3 dimensional world?

 

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Edited September 20, 2004 by EraSeek

[davidbrit2]

Well, if doing a goto on a waypoint requires going several thousand feet vertically, chances are the environment is such that using a standard GPS would be either impractical or impossible (i.e. inside a large building, etc.). In most cases, the user is on relatively flat land, and someone who really needs the elevation info probably has some kind of topo maps, too.

Edited September 20, 2004 by davidbrit2

[+NightPilot]

Elevation is the most imprecise part of the position. The FAA commissioned WAAS precisely because of this. The *only* reason WAAS was implemented was for aircraft use in precision approaches, which require some sort of vertical guidance. But even with WAAS, precision GPS instrument approaches still aren't being used. Some approaches have been published, but I'm not aware of any hardware that is certified, and the altitude is still less accurate than the horizontal position.

 

It would be possible for GPS receivers to calculate the distance to a waypoint from above it (or below it) if the altitude were given, but no production receivers even try to calculate altitude, and no waypoints that I know of give elevation. If you don't have the elevation information, then there is no way to calculate distance to it, and all waypoints are assumed to be on the surface of the earth. I don't see that as a huge problem for normal outdoor use. Why would you try to put a waypoint thousands of feet in the air? If it's not on the earth, then how could you get to it? If it's inside a building, then your GPS isn't going to work inside there anyway.

 

It is always possible to propose a solution to a nonexistant problem.

[+BattleBug]

ERASEEK's post made me wonder so I grabbed the old Garmin and sure enough; waypoint elevation makes no difference to distance calculations. I was hoping that slant range would display but alas, 'twas only ground range. I guess that commercial, recreational grade GPSr's only really compute 2-D distances. Seems that they assume current HAE is equal to the GoTo HAE. This explains why my GPS odometer doesn't match my car's odometer on cross country trips--vehicle trip mileage is always more--especially over significant terrain elevation changes. I wouldn't say this problem is nonexistant; however, it surely doesn't use the full capabilty of GPS. Though, for most GC activities it's trivial.

[+EraSeek]

I had aviation applications in mind for the most part. I suppose you are correct. No real practical purpose. Perhaps complicating things unnessecarily so. It was for the most part a concept I had not considered before and wanted to put it out there to get feedback on. Actually elevation accuracy is not as bad as most people think, and accuracy of both horizontal and elevation is improving each year from improvements in the system, but yes, elevation generally runs about 1.5 times behind horizontal.

[+BattleBug]

Regarding aviation applications: My (military) aerospace vehicle does, in fact, use all three dimensions dynamically. For what I do, relative elevation calculations are often the difference between success/failure.

[+Prime Suspect]

You also have to ask what you would be trying to accomplish. Let's say you're at sea level, and your waypoint is 3 miles away and 10,000' above sea level. What exactly do you want to calculate? The straight-line distance between you and the waypoint? But GPSs aren't designed to do straight-line distance calculations, because we have to travel over the earth's surface. And the farther apart the two points are, the less useful a straight-line distance becomes for our purposes, as few of us have the ability to bore straight through the earth to reach our destination.

 

We say the GPSs calculate distances "as the crow flies", meaning a straight line. But it's truer than we think, as crows, like GPSs, have to follow the curve of the earth.

[+Prime Suspect]

Seems that they assume current HAE is equal to the GoTo HAE. This explains why my GPS odometer doesn't match my car's odometer on cross country trips--vehicle trip mileage is always more--especially over significant terrain elevation changes.

I seem to recall reading that the Garmins that have built-in altimeters do take the elevation change into consideration when updating the odometer value.

[davidbrit2]

I had aviation applications in mind for the most part. I suppose you are correct. No real practical purpose. Perhaps complicating things unnessecarily so. It was for the most part a concept I had not considered before and wanted to put it out there to get feedback on. Actually elevation accuracy is not as bad as most people think, and accuracy of both horizontal and elevation is improving each year from improvements in the system, but yes, elevation generally runs about 1.5 times behind horizontal.

Ah yes, for aviation, this sort of thing would be very useful. But you can bet that if I were doing something as mission critical as landing an airplane, I certainly wouldn't be using a little $200 eTrex hooked to an autopilot. Heh. My Legend can vary by as much as 20 or 30 feet for elevation, and I'm sure that's more than enough to leave you in a smoldering heap on the runway, or with a hefty repair bill at least.

[peter]

This explains why my GPS odometer doesn't match my car's odometer on cross country trips--vehicle trip mileage is always more--especially over significant terrain elevation changes.

I'm afraid you'll have to look for another cause for this discrepancy unless you spend lots of time driving up and down the block of Filbert St. which has the steepest grade (31 %) in San Francisco. Even that would show a difference of less than 5% between horizontal and slope distance. Mountain highways in the US are generally limited to grades of 6% and then the discrepancy is less than 0.2% - much less than the variation between car odometers.

 

Hikers familiar with the South Kaibab trail know that it's a strenuous climb and considerably steeper than the other main route (the Bright Angel). Yet the slope distance on the Kaibab is only about 1% greater than the horizontal distance.

 

Overall I think computing the GOTO distance including altitude would introduce more problems than it would solve. Many of our maps don't include altitude data so we enter destination waypoints without knowing the elevation with any precision. In that case the GPS would probably just take the current altitude as the default.

 

Let's again take the Grand Canyon Kaibab trail as an example. Say I get the lat/long of Phantom Ranch at the bottom and enter it as a waypoint for my GOTO destination as I start down. Then when I reach it, the unit will say that I still have almost a whole mile to go since the elevation is down 4800'. That wouldn't make me think much of the GPS accuracy. Even if I guessed the altitude I might easily be off by hundreds of feet and not get a good indication of how far I still need to go. And that's not even including the possibility of inaccurate altitude readings from the GPS which isn't unlikely in canyons where many of the satellites will be blocked.

 

OTOH, the current system has the disadvantage that the unit will initially tell me the distance is only 6.24 miles to the river when it's really 6.3 miles for the slope distance. I'd rather have that 1% error in exchange for an accurate indication as I'm nearing the destination.

[+NightPilot]

Your odometer doesn't match the GPS odometer because your vehicle odometer is incorrect. I'll bet the speed doesn't match the GPS speed, either. Automobile odometers don't actually measure distance, they just count turns. The distance your car travels per each revolution of the tires varies with tire size, and tire size varies with wear, inflation pressure, and the pressure varies with temperature. The vehicle's odometer is just a SWAG, not an accurate measurement.

 

I fly helicopters in instrument conditions, making instrument approaches to offshore platforms as well as to airports, using an IFR-certified GPS, which lets me fly down to 200 feet above the ground with 3/4 mile visibility or less. This GPS does not compute distance using altitude at all. With a standard VOR (VHF Omnirange Radio) transmitter and DME (Distance Measuring Equipment), the distance displayed is slant-range distance, and if you fly directly over a VOR you will never see the distance go to zero, because you'll always be some distance above the transmitter. Using a GPS simultaneously, you can see the distance go all the way to zero if you fly very precisely. Flying over a transmitter at 6000', the distance will never go under 1 mile (a nautical mile is 6000), but with a GPS the display will go all the way down. For altitude information we have 2 independent calibrated barometric altimeters and a radio altimeter. All three of these must match within 70 feet to be serviceable, but you'll often see 200' or more difference between them and the altitude shown by the GPS. 20 or 30 feet error is well within tolerances for IFR altimeters, because 200' is the usual minimum descent altitude without seeing the ground. For some airliners using Category III approach minimums, it's zero, though, using radio altimeters. These have autoland capability, and can land without the pilot touching the controls. GPS isn't even in the ballpark for this.