When DME is calculating aircraft ground speed, is it doing it based off of the slant range? Wouldn't this mean that if the aircraft is at sea level and the DME is at sea level that the GS would be accurate. But if the aircraft is at altitude, then the slant range is changing differently, so won't the GS be different or inaccurate?
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$\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$– FedericoCommented Sep 30, 2022 at 16:05
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3 Answers
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DME dislayed ground speed (GS) is impacted by slant range. When you're close to the dme station (going directly to/from the station) the displayed GS is less than actual GS. When you are a few miles from the station going directly to/from it the displayed GS and actual GS difference is not functionally significant.
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$\begingroup$ Per some book (FAA IFH or IPH?), “very close” is within 1nm per 1000ft of elevation difference. $\endgroup$– StephenSCommented Sep 30, 2022 at 0:01
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$\begingroup$ @757toga I think what Stephen means is that DME GS is useful until you are closer to the station than 1 NM per 1000 ft elevation difference. In your example at 24,000 ft (assuming the DME is at sea level), the DME GS is useful until you are closer than 24 NM. $\endgroup$ Commented Sep 30, 2022 at 6:15
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$\begingroup$ Thanks @Bianfable - I think he is referring to the accuracy of the actual distance to the station vs the slant range distance (as opposed to ground speed accuracy). In any event, if at 12000 feet (agl) and 5nm actual distance from the station, the displayed dme (with the effect of slant range) would be about 5.3 NM (only about .3nm difference). Also, I do not believe that the dme displayed GS (at 24,000 feet (agl) is so inaccurate that it is not useful inside of 24nm from the station. $\endgroup$– user22445Commented Sep 30, 2022 at 17:20
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$\begingroup$ Ground speed error is not related to slant range error. It is related to the error in the rate of change in slant range. That is dependant on the Cosine of the line of sight angle to the DME station. $\endgroup$ Commented Sep 30, 2022 at 22:50
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Your slant range distance to the DME station is given by $s=\sqrt{s_g^2+a^2}$, where $s_g$ is the ground distance and $a$ is your altitude above the DME. Assuming you are in level flight, your computed speed is then $$\frac{ds}{dt}=\frac{s_gv_{gs}}{\sqrt{s_g^2+a^2}}$$
where $v_{gs}$ is the true groundspeed. Assuming that $d_g \gg a$, this can be approximated as $$\left(1-\frac{a^2}{2s_g^2}\right)v_{gs}$$ As an example, at 1000 feet above and 1 nautical mile horizontally from the station, this introduces an error of only about 1%. The error gets larger quickly as you get closer to the station.
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If the calculation is based purely on DME then yes slant range makes the DME groundspeed inaccurate.
However, DME groundspeed is a calculation not a measurement, so the computer could include DME station elevation and aircraft altitude in the calculation and remove the slant range error. In practical terms, significant error would remain when very near the station due to limits in the instrument precision and unfavorable trigonometry. The actual amount of error and zone of significant error would depend on the specific equipment.
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3$\begingroup$ In a stand-alone DME unit the computer (to the extent the simple circuitry in there can even be called a computer) could not include the DME station elevation, because it has no way to know which DME station it actually is. $\endgroup$ Commented Oct 1, 2022 at 9:15
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$\begingroup$ A DME receiver and a groundspeed computer are different devices, even if they happen to be packaged into one box. There are analog computers too. Anyway, how the information could be provided to the computer is not relevant. It could be a database or manual entry or something else. The user manual has all this info and more, including the known errors of the particular model number. $\endgroup$ Commented Oct 1, 2022 at 9:42
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$\begingroup$ How the information could be provided is very relevant, because it is a lot of information. That information is available in a flight management computer—that's it's purpose—but it wouldn't be a stand-alone DME, or even a stand-alone NAV radio, any more if it was connected to all the other data sources needed. $\endgroup$ Commented Oct 1, 2022 at 22:27