The shape of the earth is approximately to an ellipse of which the bipolar is slightly flat and the equatorial has the biggest radius. The standard of model used for GPS is WGS-84 coordinate system promulgated by defense department of United State. In this model , the cross section parallel to equatorial plan is a circle while the cross section perpendicular to equatorial plan is an ellipse.
Mathematically, the surface of ellipsoid can not be expanded into plane. To calculate distance or area precisely, we spread such surface into plan by the way of projection approximately. For large scale maps we usually use Gauss Kruger projection to realize transformation in our country. But in this case, the meridian and parallel are no longer lines anymore in the figure 1, and it is complicated and calculate and hard to be realized by MCU. Because the distance is very short and the area is very small in field measurement, we have made simplifications as follows to find a simple way to expand the earth surface into plane and then to calculate distance and area.
1. It is considered that field is horizontal or just has a little slope, which means to ignore the influences caused by height difference to the distance between two points.
2. All of the cross section parallel to equatorial plane are standard circles that just has different radius; and all the cross section perpendicular to equatorial plane are standard ellipses that in the same size.