Coutinho's method for the altitude

In the first aerial crossing of the South Atlantic, by Gago Coutinho and Sacadura Cabral in 1922, several methods of astronomical maritime navigation were used with adaptions to aerial navigation. In order to apply these methods, the navigator needed to know the approximate altitude of the aircraft so that its position could be determined. The instrument available at that time, the altimeter, did not give reliable values for altitude. Therefore, Coutinho had to devise a method that enabled the navigator to determine the altitude quickly and efficiently. The method Coutinho devised is based on a mathematical and geometrical procedure. In this paper, we study in detail Coutinho's method to determine altitude, with diagrams to aid understanding of the deductions and calculations. We also present a real example of how this method would be used during the flight.