Using a polar diagram, it is possible to visualize solar trajectories during a year at a certain place. This diagram, which is a projection of solar trajectories on a hori­zontal plane, can be obtained by the plotting the values of solar height and azimuth on a graph. These values are calculated using the eqns (5) and (6), for a certain place and as a function of the true solar time, as shown in Fig. 11.

Using this diagram, it is also possible to determine graphically the periods of time during which a surface point remains in shadow because of the obstacles which intercept solar rays. When the distance of the obstruction is large compared to the receiver’s dimensions (a solar collector, a window, etc.) it is right to consider the receiver as a punctiform one, since the shadow tends to move fast on the receiver so that it is completely in shadow or completely illuminated. To determine when the obstacle intercepts solar rays, in the diagram of solar trajectories, we have to represent the angle from the obstacle as seen from the considered

point, plotting on it (the diagram) the azimuth and the angle height of the obstacle’s contour points.

As an alternative to the diagram of solar trajectories we can use a Cartesian diagram of the Sun’s position in which the azimuth is plotted along the horizontal axis while the altitude is plotted vertically. The Sun’s position can be read by sim­ply reading the two axes. An example of this diagram is given in Fig.12. Of course, we may use this diagram to calculate the shadows [1].