How to Calculate an Azimuth Angle

When you set out on a voyage, you want to know a few things, including where you trip begins, where it ends, how far it is and what direction you go to get there. A chart can tell you where the voyage begins and ends, but exactly what course do you take to get there? To learn that, you have to calculate the azimuth angle. On one hand, you might begin to tremble; after all that's spherical trigonometry, right? Once you know the formula, though, you can plug in the numbers and never look back.

Things You'll Need

• Calculator with sine, cosine, arcsine capabilities.
• Chart

Instructions

1. Do some research: use the chart to find out the latitude and longitude from which you wish to determine the azimuth angle, the starting point. Find out the latitude and longitude of the destination. In the following formula, "L" is the latitude of the starting point. "D" is the is the latitude of the destination. "t" is the difference of longitude between the the starting point and the destination.

2. Multiply the sine of "L" by the sine of "D". Multiply the the cosine of "L" by the cosine of "D" and the cosine of "t." Determine the arcsine of the result and call it "H."

3. Multiply the cosine of "D" by the cosine of "t." Divide the result by the cosine of "H." Determine the arcsine of the the result and call it "Z, " the azimuth angle.

Tips & Warnings

• On short voyages, those that can be undertaken using a single chart, determining the azimuth angle is as simple as laying down a line between the starting point and the destination, and reading the azimuth angle directly from one of the chart's compass roses.

• The prudent mariner is aware that the differing navigational procedures can provide results that are similar but vary slightly. The prudent mariner picks one navigational method for an entire voyage: if you choose one method, you will always know where you are. If you do not, you will never know where you are.

References

• The Math Forum at Drexel University

Resources

• The American Practical Navigator