Compute Lat/Long Waypoints For A Sinusoidal Track Given: Start & End Waypoint, Delta-Bearing, and Number Cycles

I want to compute a bunch of waypoints along a sinusoidal path from a starting waypoint to an ending waypoint as depicted in the diagram below.

I am given:

1. a starting and ending waypoint, [lat1 lon1] & [lat2 lon2]
2. the delta-bearing, in degrees
3. the number of sinusoidal cycles

The distance between the starting and ending waypoints is ~25 nm if that matters.

The bearing is typically in the range 145-210 degrees, and the delta-bearing 10-25 degrees.

I'm new to the mapping toolbox so am not very familiar with all the functionality. I have an idea on how to solve it, but I think it is overly complicated, and, am betting that there is a simpler solution.

Thanks in advance.

Answer 1

[Dhruv]

Here are the steps you can follow to compute a series of waypoints along a sinusoidal path:

1. Determine the distance between the starting and ending waypoints using the distance function in the Mapping Toolbox.
2. Find the initial bearing from the starting waypoint to the ending waypoint using the bearing function in the Mapping Toolbox.
3. Determine the delta-bearing based on the range provided.
4. Determine the wavelength and amplitude of the sinusoidal path by using appropriate formulas.
5. Use the distance, initial bearing, and delta-bearing to compute a series of intermediate waypoints along the great circle path using the reckon function in the Mapping Toolbox.
6. By using the cross-track distance function in the Mapping Toolbox. Calculate the perpendicular distance to the sinusoidal path by projecting the waypoint onto the great circle path for each intermediate waypoint.
7. Use the wavelength and amplitude to compute the latitude and longitude offset for each waypoint based on its perpendicular distance from the sinusoidal path.
8. Compute the latitude and longitude of each waypoint by adding the offset to the latitude and longitude of the corresponding intermediate waypoint and output the series of waypoints.

Note that this solution ignores the curvature of the Earth. You may also refer to the documentation below for guidance. Hopefully, these suggestions will help getting you started with the mapping toolbox and help with your problem statement.

Mapping Toolbox Documentation (mathworks.com)