Accuracy of the coefficient expansion of the Transverse Mercator Projection

Problems of precision and accuracy in geographical information systems have often been undervalued. However, these are important issues when trying to avoid inaccurate computations that could distort the final result. A method is described for the Transverse Mercator Projection of the ellipsoid to calculate the necessary number of terms of their series development so that desired accuracy can be achieved. The first part describes one algorithm used to obtain the full development of the formulas by means of a symbolic calculus program. The second part studies the influence of each term in the final result in order to know which terms can be neglected while achieving the desired precision. Finally, the results are applied to a rectangle of 30° width and latitude varying from 30° to 50°.