An Angle of GPS Navigation

On low-level VFR flights, we typically enter the next destination airport into the GPS unit and deal with deviations forced by high towers, controlled airports, TFRs, restricted areas, and so on, with temporary deviations from the direct course. 

This approach forces us to track the course on the sectional chart— a good thing. If the navigation equipment ever fails, we will be well prepared for appropriate action. 

For the same reasons, we never let the autopilot execute the flight plan in the GPS unit. Instead, we input the GPS bearing to the destination into the autopilot, and adjust that setting manually as needed.

Suppose we are approaching an obstacle forcing a course change. If we detour close to the obstacle, we add some distance—a bad thing. We avoid that through a course correction for the autopilot while we are relatively far from the obstacle.

In the past, we carried out estimation of the course correction 30-60miles out as follows.  We would dial in a larger-scale display for the GPS so that both the current position and the obstacle were displayed, estimate the required angle change for avoidance, and use that value for the autopilot.

That estimation process is rather tedious and quite inaccurate. There is a different way that is easy to use and gives precise estimates for the required course correction. This note describes the process.

Suppose we are L miles away from an obstacle, and at the obstacle the course needs to be moved to the right or left by D miles. Then the required correction angle α of the course, in degrees,  is 

α = D x 60 / L 

where α is added to the current magnetic course for deviation to the right, and is subtracted for deviation to the left.

Here is an example. Suppose we are 30 miles from an obstacle. At the obstacle, the course should be moved 5 miles to the right.

Thus, L= 30 and D = 5, and the course should be corrected by

α = D x 60 / L = 5 x 60 / 30  = 10 degrees to the right.

Once we are abeam the obstacle, we read the GPS bearing to the destination and dial that course into the autopilot.

The formula is quite precise when the ratio D/L is less than 40%. It should not be used very close to an obstacle. This restriction does not pose a problem since very close to the obstacle we can visually correct using the detailed, low-scale GPS display.

We typically make corrections 30 and 60 miles out. For the 30 miles case, the formula simplifies to 

α = D x 2;    case L = 30 miles

For the 60 miles case, the formula becomes 

α = D;   case L = 60 miles

These facts are summarized in the following rule.

--------------------------------------------------------------------------------
Rule: When 60 miles away from an obstacle, the desired displacement of the course at the obstacle, in miles, directly gives the course correction in degrees. When 30 miles out, the displacement value must be doubled.
--------------------------------------------------------------------------------

Derivation of the rule: The exact formula is 

sin(α) = D / L 

For small values α, sin(α) is approximately equal to α  when the angle is expressed in radians. Conversion to degrees yields 

α = D x (360 / 2π) /  L = D x 57.3 / L 

Rounding up the factor 57.3, we have the formula

α = D x 60 / L.