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I am trying to calculate the point from a given lat/long, a bearing, and a distance.

This is for plotting weather given a aeronautical way point.

For example:

Given a waypoint with a known lat/long (LAX airport control tower), with a bearing of North by Northwest and a distance of 45 nautical miles, where is the point?

I could treat the world as flat, but I think the resulting calculations would be inaccurate the further north the point is since longitudes get more narrow near the poles.

I am mainly interested in plotting these points in the US. Is there a projection that would help me do this?

This is for a Python application I'm writing, and the libraries I have access to are GDAL and Proj4 for projections. So no fancy tools like ArcGIS are available to me.

Ultimately I want to combine 4 or these calculated points to form a polygon that should roughly be about 100-200 miles in width and height.

Thanks!

LeeMobile
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  • Hi LeeMobile, what software are you trying to plot in? – Michael Stimson Jun 24 '14 at 00:54
  • This is for a Python application I'm writing. I have access to the GDAL and Proj4 libraries, but that's it. – LeeMobile Jun 24 '14 at 00:56
  • That is interesting, there are mixed units involved, nautical miles can't be measured in DD and bearings don't hold true in UTM. What kind of accuracy are you expecting? I can suggest is project the point, draw a circle, project the circle back and intersect with a bearing line. – Michael Stimson Jun 24 '14 at 01:02
  • Would you be able to edit your Question to include those additional details that seem highly relevant to what you are asking, please? – PolyGeo Jun 24 '14 at 01:06
  • Michael Miles-Stimson: which projection should I project the point to? – LeeMobile Jun 24 '14 at 01:20
  • That depends on where the point is and what your accuracy expectation is. If you want good accuracy use NAD or WGS84/UTM but you have to specify the zone from your airfield https://www.e-education.psu.edu/natureofgeoinfo/c2_p22.html, if you aren't too concerned with a dozen feet or so then do the whole thing in Lamberts Conformal Conic Projection http://spatialreference.org/ref/esri/north-america-lambert-conformal-conic/ which is EPSG:102009. – Michael Stimson Jun 24 '14 at 01:27
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    Off-topic, but I always thought that "north by northwest" was a great film, but isn't a real direction – Stephen Lead Jun 24 '14 at 01:48
  • No, you're right, it's not a direction. I am thinking that the op means something like I have a bearing 245.36 and want to plot a point at 45.0 nautical miles otherwise there's no point debating accuracy as the direction is vague at best. – Michael Stimson Jun 24 '14 at 01:51

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Funnily enough I have just answered a similar question a couple of minutes ago.

Calculating a circle in Lat/Lons

This link will take you to a page that has describes algorithms for calculating forward azimuths, which is the type of calculation you have described in your question. I don't know if it will have all of the details you need but it should get you started.

Inverse/Forward Azimuths

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