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I am currently struggling to understand the following question regarding a VOR station and an aircraft. The aircraft is found in the 30 degree radial from the VOR station at time T(1) and T(2). During the 10 minutes between T(1) and T(2) the aircraft maintains a heading of 120 degrees from magnetic north at 120 knots ground speed. The question goes like so:

At time t(1) an airborne VOR receiver shows that the aircraft is on the 30deg radial from a VOR station. The pilot maintains a ground track heading of 120deg with respect to magnetic North and 120 knots ground speed. At time t(2) , 10 minutes later than t(1) , the VOR receiver indicates that the aircraft is on the 30deg radial from the same station. Assuming no errors, what is the pilot’s distance from the VOR station at time t(2) ? If the pilot had access to airspeed, can the range be determined from the VOR measurements? Can it be determined if the pilot had access to ground speed and ground track heading?

I'm not quite positive of my understanding of the situation. To my understanding the heading indicates the direction the aircraft is pointing in is 120 degrees with respect to magnetic North however its course must be either be 30 degrees with respect to magnetic North or 210 degrees with respect to magnetic North, allowing it to stay in the station's 30 degree radial. Would my understanding of the situation be correct?

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    $\begingroup$ If the a/c is located somewhere on the 30 deg radial and is on a heading of 120 degrees, it is flying exactly perpendicular to that radial. So, it's hard to imagine how after 10 minutes the a/c would still be located on the 30 deg radial (unless the a/c is not moving). Can you go back and check to ensure you have the specifics of your question correct. It would make more sense if after 10 minutes the aircraft was located/crossing on the 50 or 60 degree radial. $\endgroup$ – 757toga Oct 5 '18 at 17:34
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Bad news: the question is unanswerable.

Good news: you're right to be confused!

  • With a groundspeed of 120 knots and a constant ground track, after 10 minutes the airplane will have moved 20 miles in a straight line. There's no getting around this fact.

  • If the airplane doesn't parallel a radial, and yet it moves, the radial it's on must change.

  • If it's still indicating the same radial after non-parallel movement, the only option is that the indicator is in error. But the question removes that possibility.

  • The only way I can think to make this situation possible is that maybe you've tuned the world's most bizarre VOT. But even still there's no possibility for a valid answer for the question.

The original question:

At time t(1) an airborne VOR receiver shows that the aircraft is on the 30deg radial from a VOR station. The pilot maintains a ground track heading of 120deg with respect to magnetic North and 120 knots ground speed. At time t(2) , 10 minutes later than t(1) , the VOR receiver indicates that the aircraft is on the 30deg radial from the same station. Assuming no errors, what is the pilot’s distance from the VOR station at time t(2) ? If the pilot had access to airspeed, can the range be determined from the VOR measurements? Can it be determined if the pilot had access to ground speed and ground track heading?

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  • $\begingroup$ Years ago it was not uncommon for an Inspector/Examiner to have the CFII applicant determine how far he/she was away from a particular VOR station (freq was covered up and not viewable by applicant). Technique was essentially the same as in the question, i.e., center cdi, start time, turn perpendicular to the radial, reset cdi to radial 10 degrees away from centered radial, stop time when new radial was centered on cdi. Simple calculation would give a good estimate of time/distance to the VOR. Perhaps this is what is shown above and second point should be 40 deg (not 30 deg). Just a thought. $\endgroup$ – 757toga Oct 5 '18 at 22:05
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    $\begingroup$ Agreed, that's probably what was meant. Minutes*60/degrees=ETA to the station, but the question is flawed $\endgroup$ – Steve V. Oct 5 '18 at 22:09
  • $\begingroup$ "Flawed" is a real polite term for that question. It's a mess! $\endgroup$ – Wayne Conrad Oct 6 '18 at 2:18

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