How Far Away is that Waypoint?

Imagine you are on patrol and your OPCON contacts you to respond to a boater who needs assistance at a given location.  Where is that waypoint and how do you get there?  Of course you are familiar with your chartplotter and can enter that waypoint and get underway.  But with just a few seconds of mental math you can derive a rough solution and respond.

You are at the following location (which happens to be the coordinates of Blossom Rock Buoy in San Francisco Bay):

37° 49.1’N

122° 24.2’W

Also recall that one minute of latitude is equal to one nautical mile.

You are given the following coordinates of the boater requiring assistance (at Harding Rock Buoy):

37° 50.3’N

122° 26.7’W

By quick inspection of the numbers you can see that both the latitude and longitude are greater than your current position so you know it is roughly northwest of your current position.  The latitude is 1.2 minutes greater so they are 1.2 miles of “northing” from you.

Also note that the longitude is 2.5 minutes greater and therefore they are west of you.  But those would only be miles if we were at the equator and we are at latitude 38 degrees.  At this latitude, the longitude scale is shorter than the latitude scale (by an amount equal to the cosine of our latitude…) or about 80% as long.

So 80% of 2.5 is 2.0, therefore they are 2 miles of “westing” from you.

The triangle is therefore 2 miles west and 1.2 miles north.  If you guessed the actual distance of around 2.5 miles you’d be close – it’s actually 2.35 NM.  If you were to roughly sketch the triangle, you’d be very close if you guessed that the course is about 30 degrees north of due west, or 300 degrees True.   At least you could proceed in the right direction while you fine-tuned your navigation plan.

Now, knowing your cruise speed is 15 knots and that 2.5 miles is one- sixth of what you can travel in an hour, your estimated time enroute is around 10 minutes (one-sixth of 60 minutes). 

If you practice this you’ll be amazed in how quickly you can come up with a reasonable estimate.  Remember that this does not replace proper navigation and hazard avoidance.