Calculating the latitude/longitude from known distance

[Ben Arnold]

For a small distance (in the range of 10's of metres) how can I calculate the latitude/longitude of a point if I know the distance in ΔN and ΔE from a known latitude/longitude using the 'flat earth' assumption?

Thanks in advance :)

 

[jtbell]

What are ΔN and ΔE?

 

[nasu]

For the latitude is easier. One minute is approximately one nautical mile, 1852 m. So your displacement of 10m N (let's say) will corespond to 10/1852 minutes change in latitude. The change in longitude is trickier. It depends on the latitude. One minute of longitude is approximately one nautical mile along the equator but decreases as you approach the pole. Still not too hard a problem if you draw a diagram.

What is the flat Earth assumption? How do you define degrees of latitude and longitude in this assumption?

 

[Ben Arnold]

I'm basically looking at a simple way of calculating the latitude and longitude of a point from a known datum point, with distance traveled north and east known (from the azimuth and total distance travelled, using Pythagoras). It will be a relatively small distance so I've read you can use a 'flat earth' assumption? Sorry I'm very new to this.

 

[nasu]

Can you provide a reference? Where have you read this?

 

[rumborak]

I think all the "flat earth" assumption means in this case is that the triangle you will calculate will be a regular triangle, not one with an arc on one side. A reasonable assumption provided you're not close to the poles and your deltas are small.

 

[Ben Arnold]

Aye, basically what I'm asking is what deltas would correspond to what change in long/lat roughly? I'll dig up the source now.

 

[nasu]

Then what are these deltas? The distance traveled to North and South? You also mentioned azimuth.

 

[Ben Arnold]

I've got a basic grid set up over an area of roughly 100m x 100m with y direction being north and x direction being east, I'm testing the dead reckoning capabilities of a tracking unit so will have a read out in long/lat from the device after a certain period of time of movement. I plan on measuring the distance traveled in the y (north) and x(East) direction using a laser measuring device from a known datum and compare it with the readout. Using the distance and azimuth I can use basic trig to work out the north and east components, and wondered if there was a way of converting the distances to a new longitude and latitude and comparing it with what the tracking device is telling me.

 

[Ben Arnold]

https://www.physicsforums.com/threads/calculating-lat-long-with-range-bearing.605218/

I guess it's just using this, what does it mean by 'then convert these to the difference in degrees to angular measure to add to your existing lat long' ?

 

[Filip Larsen]

You can derive a very simple approximation for change in latitude and longitude from the line element of, say, spherical coordinates [1]. Here you can see that changes north/south is proportional to changes in latitude, and changes east/west are proportional to cos(latitude) times changes in longitude.

[1] http://en.wikipedia.org/wiki/Spheri..._and_differentiation_in_spherical_coordinates

 

[sophiecentaur]

This link tells you what you need to know. The section on the length of a degree longitude shows you how to work out what it is for any particular latitude. For a small range of distances, such as you want, you can treat the geometry as Cartesian (x,y) with the x scaled according to the angle of lattitude.