1:60 Rule

The purpose of this rule is to calculate a new heading when we are found to be off track.

For practice see here.

Definition

The definition is that, \(1nm\) subtends an angle of \(1^{\circ}\) at a distance of \(60nm\).

Mathematically speaking, this is a statement of arc-distance as follows;

The distance traveled along an arc is equal to the arc radius times the arc angle divided by 60.

Proof

By definition, circumference equals \(2 \pi r\) and that a circles angular circumference is \(360^{\circ}\).

A proportion of a circle is therefore \(\frac{\theta}{360}\) and therefore;

\(\require{ams}\) \begin{align} d & = \left( 2 \pi r \right) \left( \frac{\theta}{360} \right)
& = \frac{\pi r \theta}{180} \text{ and } \frac{180}{\pi} \approx 57.296.
& \implies d \approx \frac{r \theta}{60} \text{ where } \theta \text{ is in degrees}. \end{align}