This is where I got my formulae
from the site
Local, flat earth approximation
If you stay in the vicinity of a given fixed point (lat0,lon0), it may be a good enough approximation to consider the earth as "flat", and use a North, East, Down rectangular coordinate system with origin at the fixed point. If we call the changes in latitude and longitude dlat=lat-lat0, dlon=lon-lon0 (Here treating North and East as positive!), thendistance_North=R1dlat
distance_East=R2cos(lat0)*dlonR1 and R2 are called the meridional radius of curvature and the radius of curvature in the prime vertical, respectively.
R1=a(1-e^2)/(1-e^2*(sin(lat0))^2)^(3/2)
R2=a/sqrt(1-e^2*(sin(lat0))^2)a is the equatorial radius of the earth (=6378.137000km for WGS84), and e^2=f*(2-f) with the flattening f=1/298.257223563 for WGS84.
In the spherical model used elsewhere in the Formulary, R1=R2=R, the earth's radius. (using R=1 we get distances in radians, using R=60*180/pi distances are in nm.)
In the flat earth approximation, distances and bearings are given by the usual plane trigonometry formulae, i.e:
distance = sqrt(distance_North^2 + distance_East^2)
bearing to (lat,lon) = mod(atan2(distance_East, distance_North), 2*pi)
(= mod(atan2(cos(lat0)dlon, dlat), 2pi) in the spherical case)These approximations fail in the vicinity of either pole and at large distances. The fractional errors are of order (distance/R)^2.
I took the Micromega examples and changed the great circle method to the one above.