How do I determine which radial intercept angle to use?

Question

I'm studying for the (EASA) Instrument Rating exam and I found several questions about radial intercept angles in sample exams but nothing in the books I've studied and my flight instructor doesn't know of any specific rules either.

Based on the answers, it appears that, depending on the current and desired positions and headings, the intercept angle can be 30°, 45°, a third of the heading difference or a combination of a 90° then 45° turns.

What is the rule to determine which intercept angle to use and where is it documented?

Sample questions:

1. current QDM 330, HDG 060, desired QDM 350, what should be the new heading? (answer: 305 for a 45° intercept)
2. current QDM 120, HDG 120, desired QDR 060 after flying over VOR, what should be the heading after flying over? (answer: 040 for a 20° intercept angle, a third of the 60° heading difference between 120 and 060)

_{Note: I've found this document online that mentions the 45° and 90-45 techniques page 20 but it doesn't cover the other cases.
QDM: magnetic bearing to station
QDR: magnetic bearing from station}

Answer 1

There is no definite answer to this question.

If you are far away from the beacon radials are far away from each other and thus small intercept angle would be insufficient to reach desired track in feasible time. Also, if you are, say, five miles away from the beacon intercept angle of thirty degrees would be acceptable for C172 but an overkill for transport category jet traveling at 450kts of ground speed. Then again, the mentioned jet would assume the same 30 degree intercept angle to join final track for an approach.

The question has also to do with current aircraft track in relation to the desired track. If you are for example tracking radial 150 inbound towards a beacon and you want to change to radial 180 an intercept angle of 30 degrees would keep you on radial 150 and you will not intercept the desired track until you are overhead the beacon.

The only rule seems to be that when vectoring for approach ATC gives a maximum intercept angle of 30 degrees.

Answer 2

The "other case" is the flyover. If you arrive at a VOR on a certain course and are requested to leave on another course. In this case you take the difference of these two courses divide it by three. Thats your intercept angle to the outbound radial. if its more than 15, its gonna be 15. (Example you arrive on a course 180° (from the north) and you're asked to leave on radial 90. Difference is 90°, divided by three is 30°, as max. is 15° you intercept the new course by 15°: means you turn left to (90°-15°=)75°.)