Which of the distances shown on the diagram is displayed by a basic VOR/DME-based area navigation equipment using phantom waypoints?
Aircraft send out a signal which is sent back after a fixed delay by the DME ground equipment (50 µs).
The aircraft can compute its distance to the beacon from the delay of the signal perceived by the aircraft's DME equipment using the speed of light: the time difference between interrogation and reply, minus the 50 µs ground transponder delay and the pulse width of the reply pulses, is measured by the interrogator's timing circuitry and converted to a distance measurement (slant range in NM), then displayed on the cockpit DME display.
The slant range is the line-of-sight distance along a slant direction between two points which are not at the same level relative to a specific datum.
DME equipment in isolation does not have a height input, therefore it can only calculate direct, line-of-sight, Slant Range to the targe.
As a result, at close ranges where DME Slant Range and Ground Range differ significantly.
In our specific case the slant range distance measures 12 NM ( refer to fig.062-12409°).
The most extreme case of "slant range error" occurs when the aircraft passes directly over the station; instead of reading zero, the DME shows the altitude of the airplane above the station (in NM).
Dist = Rate x time
The rate in the calculation is the velocity of the radio pulse, which is the speed of light (300,000,000 m/s)
The time in the calculation is (total time – 50µs-pulse width of reply pulse)/2.
Be Carefull: using this formula make sure that all the measurement units are congruent !!
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