Compute Latitude and Longitude 1 nm ahead (given heading)

[ZenMusic]

How do you Compute the Latitude and Longitude 1 nm ahead given the heading?

C# or c is my programming language. I can compute, distances and headings for position to position, but this must be some trig functions.

thanks, happy new year!

 

[tgibson]

Here's an online caclulator.

Find Terminal Coordinates, Given a Bearing and a Distance

This function will calculate the end coordinates, in degrees, minutes and seconds, given an initial set of coordinates, a bearing or azimuth (referenced to True North or 0 degrees), and a distance.

www.fcc.gov

You can use this to test your eventual calculations?

And the formula is here. You have to scroll down to the correct section, the top section is not what you want.

Formula to Find Bearing or Heading angle between two points: Latitude Longitude

Formula to Find Bearing or Heading angle between two points: navigation purpose calculating angle, bearing or heading or course in GIS. Find bearing angle and find direction A and B as two different points, where 'La' is point A longitude and 'θa' is point A latitude.. angle between two lat lon...

www.igismap.com

• Let first point latitude be la1,
• longitude as lo1,
• d be distance,
• R as radius of Earth,
• Ad be the angular distance i.e d/R and
• θ be the bearing,

Here is the formula to find the second point, when first point, bearing and distance is known:

• latitude of second point = la2 = asin(sin la1 * cos Ad + cos la1 * sin Ad * cos θ), and
• longitude of second point = lo2 = lo1 + atan2(sin θ * sin Ad * cos la1 , cos Ad – sin la1 * sin la2)

Hope this helps,

 

[ZenMusic]

THANKS!

public (double newLatitude, double newLongitude) CalculateNewPosition(double latitude, double longitude, double heading, double distance)
{
const double EarthRadius = 3440.065; // Earth's radius in nautical miles

// Convert latitude, longitude, and heading to radians
double latRad = latitude * (Math.PI / 180);
double lonRad = longitude * (Math.PI / 180);
double headingRad = heading * (Math.PI / 180);

// Calculate new position
double newLatRad = Math.Asin(Math.Sin(latRad) * Math.Cos(distance / EarthRadius) +
Math.Cos(latRad) * Math.Sin(distance / EarthRadius) * Math.Cos(headingRad));
double newLonRad = lonRad + Math.Atan2(Math.Sin(headingRad) * Math.Sin(distance / EarthRadius) * Math.Cos(latRad),
Math.Cos(distance / EarthRadius) - Math.Sin(latRad) * Math.Sin(newLatRad));

// Convert new position back to degrees
double newLatitude = newLatRad * (180 / Math.PI);
double newLongitude = newLonRad * (180 / Math.PI);

return (newLatitude, newLongitude);
}

 

[hervesors]

Tom provided links referring to great circle calculations that should be enough precise for small distances
If a more precise result is required (especially for longer distances), calculation based on the earth ellipsoid model (WGS84) would be more appropriate
A script from Chris Veness is available here (easily translatable in C language)
Ellipsoid calculation
Other useful scripts for the spherical model are also available here
Spherical model scripts

Hervé

 

[DragonflightDesign]

My go-to page for all formulae aviation-related:

Aviation Formulary V1.47

Aviation Formulary

www.edwilliams.org

Most are easily translated into C/C++.