# Turning Inbound: A mathematical solution

When should you start your turn inbound to exactly ensure the needle will be centered? This post explains and demonstrates a quick mental math solution. First, the answer:

Begin your turn no later than the CDI dot corresponding to one-half of the angle to intercept divided by 3 and divided by the time to pass from one CDI dot to the next.

This solution works for turning inbound & outbound for tracking a VOR radial, a LOC/ILS, or any situation where you can count intervals leading up to a desired track.

## Example

You are on a 45 degree intercept. The needle is alive and you count 4 seconds between CDI dots.

The mental math is: 45 divided by 3 is 15…..  15 divided by 4 is about 4…. Half of 4 is 2. Turn no later than 2 dots.

## Derivation:

The pilot needs a quicker and more intuitive solution. We can simplify this engineering-style intercept equation with a few steps.

Thus the pilot solution in words is: Begin your turn no later than the CDI dot corresponding to one-half of the angle to intercept divided by 3 and divided by the time to pass from one CDI dot to the next.

## Experimentally Developed Solution:

Full disclosure: I did not initially develop this intercept solution based on the mathematics. Rather, I experimentally flew many intercepts and developed the following rule of thumb. By a complete stroke of luck, the experimental solution happens to be exactly identical to the mathematical solution above.

## Disclaimer

This solution is only meant for intuition and the mathematical understanding of intercepts. You must follow ATC, the appropriate regulations and standard operating procedures when flying. Find and train with an instructor, preferably with a CFII. No exceptions!