Dead reckoning is a reasonably accurate method for predicting position if the vehicle is able to maintain the planned course. Aircraft and ships can be pushed off the planned course by winds and current. An important step in navigational planning is to calculate the required drift correction.
In the standard drift correction problem, the desired course and wind are known, but the heading needed to stay on course is unknown. This problem is well suited to vector analysis. The wind velocity is a vector of known magnitude and direction. The vehicle's speed relative to the moving air mass is a vector of known magnitude, but unknown direction. This heading must be chosen so that the sum of the vehicle and wind velocities gives a resultant in the specified course direction. The ground speed can be larger or smaller than the air speed because of headwind or tailwind components. A navigator would like to know the required heading, the associated wind correction angle, and the resulting ground speed.
What heading puts an aircraft on a course of 250° when the wind is 38 knots from 285°? The aircraft flies at an airspeed of 145 knots.
course = 250; airspeed = 145; windfrom = 285; windspeed = 38; [heading,groundspeed,windcorrangle] = ... driftcorr(course,airspeed,windfrom,windspeed)
heading = 258.65 groundspeed = 112.22 windcorrangle = 8.65
The required heading is about 9° to the right of the course. There is a 33-knot headwind component.
A related problem is the calculation of the wind speed and direction from observed heading and course. The wind velocity is just the vector difference of the ground speed and the velocity relative to the air mass.
[windfrom,windspeed] = ... driftvel(course,groundspeed,heading,airspeed)
windfrom = 285.00 windspeed = 38.00