Why is DME calculated via slant range?

Question

I've always wondered why DME is calculated via slant distance! Since we have two sides of the right triangle, hypoteneuse and height, distance from the NAVAID should be easy to attain via a simple algorithm. Why, then, do we calculate DME using slant range?

I appreciate the answers provided, but I don't they answer my question. I understand how DME works in that it is line of site from the VOR/TACAN to the aircraft and, thus, a slant range distance. I, too, am a pilot. I understand HOW it works. My question, however, is why we haven't created course indicators that compensate for this! This is how I see it:

Right now the DME we read in the cockpit is slant range distance to the VORTAC. This is the hypoteneuse of the right triangle. We also know the MSL of the VORTAC as well as the MSL of the aircraft. Their difference is the aircraft's height above the VORTAC, and one of the other sides of the right triangle (B). Thus, it seems to me that it wouldn't be difficult to add a formula in the cockpit VOR to reduce slant range to actual distance!
IE: C^2-B^2=A^2
or
Slant Range^2-Aircraft Height Above VORTAC^2=Distance from VORTAC^2.

Boston seems to have grasped my question, but the answer of "because it doesn't" just doesn't "fly" with me! Why hasn't someone thought of incorporating an algorithm for adjusting DME for horizontal distance into the onboard VOR? Clearly, since the MSL of the VORTAC is known and can be "broadcast", and the airplane knows it's MSL altitude it shouldn't be too difficult for onboard Course Indicator to calculate horizontal distance rather than simply reporting slant range! I still don't think a sufficient answer has been offered, though Boston's comes closest.

Answer 1

I'd say that it's a gap in instrumentation: light aircraft don't have accurate enough equipment to perform that calculation, and airliners have equipment that's accurate enough that they already do it and then some.

I have experience working on light aircraft avionics, and the aircraft's altitude generally isn't calculated electronically by the altimeter, but instead by a very coarse instrument called an altitude encoder, which embeds altitude information in the transponder signal. To adjust it, a mechanic on the ground hooks it up to a pressure rig during IFR certification. The encoder has two adjustment screws. The mechanic adjusts one screw at "0 ft" pressure, and adjusts the other screw at the maximum altitude the aircraft's rated at (usually 20,000 or 30,000 ft). Furthermore, it's permanently set at 29.92 in Hg, regardless of actual local sea level pressure. Because of these limitations, the encoder's not very accurate, and is usually off by 100-200 ft on a good day.

Airliners, on the other hand, have inertial navigation systems and GPS as well as DME. I also have some experience studying the Boeing 767's instrumentation, and the flight computer on that aircraft mixes all three sources to estimate the aircraft's location, rather than relying on a single source.

Answer 2

DME can only show absolute distance from the VOR. The DME on your aircraft "pings" the VOR with a pulse of radio waves the VOR acknowledges with a "ping" of its own the DME knows when it sent the original "ping" and how long it took to hear back from the VOR knowing the speed of the radio waves the DME can now calculate a distance from the VOR. The DME doesn't know what direction the VOR is all it knows is how long it took to hear reply from it so if you are 5820 feet directly above the VOR you are still a mile away from it in absolute distance.

I think what you are describing is basically a INS system on the CRJ the FMS uses up to six VOR/DME indications to locate were it is but you have to tell it were it is every time you start it up otherwise it is lost with the advent of GPS it makes what you are describing obsolete DME as it stands now is cheap and relatively accurate

Answer 3

DME measures slant range because of the way it works: an interrogation signal goes from the aircraft to the DME station, and after a specified short delay an answer signal is transmitted back. The aircraft uses the round trip transit time (subtracting off the delay) to determine the distance. (Divides the time by the speed of light, of course.) Obviously, this will be the slant range because the radio signals travel in a straight line between the aircraft and the station.

Answer 4

Because it depends on your altitude.
An important thing to understand is that DME provides the physical distance from the aircraft to the DME transponder in your aircraft. This distance is referred to as 'slant range' and depends trigonometrically upon both the altitude above the transponder and the ground distance from it.This is where you get your triangle from.

For example, an aircraft directly above the DME station at 6000 feet altitude would still show approx. one mile on the readout. The aircraft is a mile away, but a mile straight up but right over your intended position. Slant range error is most pronounced at high altitudes when close to the DME station.
So if you do not calculate with your altitude you can be very far off especially at high altitudes and range.

Hope I was clear enough.

Answer 5

I think the simple answer is VOR technology is old. Things went from simply deadreckoning to airways to VORs and now GPS (yes that is simplified). I doubt whoever created the system envisioned your possibility. They were probably quite happy that you could track a radial and also calculate distance. This was a huge jump over previous technology. Of course someone probably came along with your idea, but this would require retrofitting a lot of equipment and retraining people that had become accustomed to slant range. VOR technology is on the way out though as GPS takes over. Certainly it will linger around for awhile, look at all the NDBs still out there. IMHO.

Answer 6

Quite simply because DME equipment does not take into account either your altitude or the altitude of the navaid -- it has no way of knowing that information. You have to calculate the distance to the equivalent "point in the sky" above the navaid yourself based on those altitudes, i.e. your altitude above (or below!) the navaid.