'Time to station' question

[WinglessAviator]

Hi everyone.
Hope you all are doing great.

Someone please help me with the following question:

Q: While maintaining a constant heading, a relative bearing of 15(deg) doubles in 6 mins. The time taken to the station being used is:

A: 3mins
B: 6mins
C: 12mins


According to my working:

Time to station = 60 x number of minutes flown / change in bearing

number of minutes flown: 6
change in bearing: 15 (because the RB doubles)

60x6/15 = 24mins. How come?

[paco]

I read that as 30 degs, or double 15. Must be my English.

Phil

[hetfield]

I read that as 30 degs

Me too...........

[DFC]

Ah the old "double bow method"!!

Wish I could draw the answer but I hope you can draw what I explain and see the reason behind it.

At "A" the relative bearing of the Station "C" is 015

The aircraft flies on a constant heading until the relative bearing has doubled (030 in this case). Call this position "B"

Draw a line from A to B to C and back to A which makes a triangle.

The angle at "A" is 15 degrees.

By simple geometry, the angle at "C" is also 15 degrees.

If two angles of a triangle are equal then the sides opposite them are also equal.

The line A-B is opposite angle C which is 15 degrees

The line B - C is opposite angle A which is also 15 degrees.

Therefore A to B = B to C

So if it takes 6 minutes to fly from A to B then (assuming constant groundspeed) it will also take 6 minutes to fly from B to C (the station).

Far easier with a diagram but I hope that helps.

Regards,

DFC

[WinglessAviator]

Thank you very much DCC. Helped a lot! :ok:

[aristoclis]

@wingless aviator

Your formula is correct if you put your bearing pointer on the 90 degrees index (abeam) and note the bearing change. In your example this formula doesn't apply.

I guess DFC's method is the best answer.

Regards.

[bfisk]

http://i32.tinypic.com/4tomrk.jpg
I made a quick sketch of the problem.

By trigonometry default when B=C then b=c also :)

Edit: whoops! That turned out larger than expected. I hope I'm better at flying than computers.
Edit2: I see that with regards to one of the previous explanations A and B is swapped but you get the picture.