Ih

Figure 5. The estimated straight line at 64° degree on the horizontal plane projection. The values in the figure represent the difference between the calculated points and the surveyed ones.

Figure 5. The estimated straight line at 64° degree on the horizontal plane projection. The values in the figure represent the difference between the calculated points and the surveyed ones.

4.1 Research of the curves connecting points defined by constant zenithal angles

The constant zenith points were projected on the horizontal plane and the line which best approximates these points was researched.

Then with the least square method the approximating lines can be found.

Figure 4 shows these constant zenith points are not straight lines but they differ a little from it especially in the middle area of the web. These deviations have been computed through projections of these points on the horizontal and vertical planes.

The results have been shown (Figures 5,6), for the sake of brevity, only for the angle 64°, where the greatest deviations are noticed.

Out of Figure 5 the maximum deviation in the horizontal plan projection is 0.083 m, while in the vertical plane projection is 0.089 m (Figure 6). As the length of the chord is 10.666 m, the deviation is at about 0.8%. So it can be observed that this deviation is very modest and it can be disregarded in the global geometry of the dome.

The following step was to consider the intersection of two such neighboring lines determines a point of the curve intersection of two border web (Figure 4).

The next one was to discover the surface on which these points are placed. This surface is a plane and then, by projecting these points on this plane, the curve which best approximates these projections was studied: these curves are circles (Figure 7). The two surveyed arches radii are respectively 36,11m and 36,23 m.

The authors leave to the proposed future research of Chapter 2 a study on the surveyed differences pictured

Figure 6. The estimated straight line at 64° degree on the vertical plane projection.

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