## Pilot Math – Compass Bearings

### Finding the reciprocal of a compass heading.

The easiest way to find the opposite direction on a compass is to use a two step process. If the current direction is less than 180, add 200 and then subtract 20. If the current heading is greater than 180, subtract 200 then add 20. So for a simple example, the opposite direction of 90° is found by adding 200 to get 290 then subtracting 20 to get 270°. The opposite direction of 270° is 270 minus 200 plus 20 equals 90°. For an arbitrary compass point, say 143°. Add 200 and subtract 20. 343-20 = 323.

You can use this method for any arithmetic involving compass points.

### VOR headings

VOR radials are arranged clockwise from 0° to 360°. If you are heading away from the VOR then set the OBS to the radial you are traveling on and the To/From flag will read “From”. If you turn around and head back to the VOR without changing the OBS then it will still read “From”. To get a “To” reading you need to rotate the OBS 180° so that the current radial is on the bottom. As an example, say an airway is on the 260° radial of the VOR. If you are headed TO the VOR your heading would be 260-200+20 = 80°.

### Runways

Runways are numbered based on their magnetic direction. Explanation That means that adding 180° to the runway heading gives the heading in the opposite direction. My home field usually uses Runway 29 in VFR conditions. The approximate heading of the runway is 290°. The runway heading in the opposite direction is 290 -200 -20 = 110, so the runway designation is 11. There is also a runway just off my hanger that I sometimes use. It is runway 07. The runway in the opposite direction is 07 + 20 -2 = 25.

### Holding Patterns

The standard hold at a VOR is given as a radial and direction. “Hold south of XYZ VOR on the 275 radial at 5,500 expect further clearance at 9:20”. The radial goes in the bottom of the OBS, so the heading inbound to the VOR is 275-200+20 = 95°. The outbound heading is 275. (Implicit in these instructions is standard turns to the right.)