combination of these intense tensile stresses in the leading part of the chimney (and also compressions on the trailing side) that causes the rupture of the chimney This type of breaking is more likely to occur at the positive maximum value of oL. This maximum value depends critically on the f ratio, for a certain angle of rupture 0, so it is possible, just by looking at the maxima of the solid curves in Fig. 6(marked by solid points), to roughly match the height of the rupture point to the angle at which the breakin started to occur. As far as the actual prediction of the point of rupture this would obviously depend on the building materials and the construction of the chimney or tower, an analysis of which goes beyond the scope of this work It is interesting to note, from Fig. 6 again, that the stress or is not always maximum at one third of the height (as for the bending moment of Fig. 5. For small angles of about 8a5-200 it reaches a maximum for F04-0.5, while for larger angles it approaches the typical ratio f<3. This means that if the chimney breaks early in its fall, for small angles, it is more likely to break near the center; on the contrary if the rupture occurs at larger angles, the breaking point is usually shifted toward one third of the height. This is the effect of the P term in Eq. 15, which modifies the position of the maximum oL(or or) As already mentioned, another factor to be considered is the ratio H, which is usu y in 20 for real chimneys, but can be increased up to about a 100 with our toy models. In Fig. 7 we plot the maxima of the leading edge stress curves, for several values of the ratio =5, 10, 20, 30, . 100( for the group of curves between the values of 30 and 100, the parameter is increased by 10 units for each curve These maxima are plotted as continuous curves, showing the corresponding values of the ratio f and the angle 0, at which the structure is more likely to break, for a given value of H. In other words, connecting for example the solid points of Fig. 6, we would obtain a corresponding continuous curve in Fig. 7, with the angle of probable rupture on the vertical axis, instead of the normalized stress The dependence of the rupture point on these quantities can be noted in several of the existing photos of falling chimneys, when the breaking occurs due to the bending of the of this section. The angle of rupture can be roughly estimated by measuring the angle th s structure and not for the transverse shear stress near the base mentioned at the beginnin upper part of the chimney forms with the vertical in the photos. This angle tends in fact not to change much after the rupture, since the upper part falls without much additional rotation. For example the photos in the paper by Bartlett 2 refer to chimneys with H2 10, breaking at about 0 a 200-25 and for I c0. 47, consistent with the values of Fig. 7, for the H =10 curve. Similar behavior can be seen in other photos, ,20 since real chimneys tend to break very early in their fall, due to the intense stresses originating within their structure IV. TOY MODELS In this section we discuss our efforts to reproduce the effects described above, with the help of toy models of the falling chimney. These models were constructed with simple toy blocks of different type and size, and their fall was filmed with a digital camera, so that we could analyze the events frame by frame, to test the theory. Complete details on the type of blocks used, experimental settings and video-capture techniques, as well as the complete set of our video-recordings and still photos can be found on our web-site, and in an upcoming publication. 33combination of these intense tensile stresses in the leading part of the chimney (and also compressions on the trailing side) that causes the rupture of the chimney. This type of breaking is more likely to occur at the positive maximum value of σL. This maximum value depends critically on the r H ratio, for a certain angle of rupture θ, so it is possible, just by looking at the maxima of the solid curves in Fig. 6 (marked by solid points), to roughly match the height of the rupture point to the angle at which the breaking started to occur. As far as the actual prediction of the point of rupture, this would obviously depend on the building materials and the construction of the chimney or tower, an analysis of which goes beyond the scope of this work. It is interesting to note, from Fig. 6 again, that the stress σL is not always maximum at one third of the height (as for the bending moment of Fig. 5). For small angles of about θ ≃ 5 ◦ − 20◦ it reaches a maximum for r H ≃ 0.4 − 0.5, while for larger angles it approaches the typical ratio r H ≃ 1 3 . This means that if the chimney breaks early in its fall, for small angles, it is more likely to break near the center; on the contrary if the rupture occurs at larger angles, the breaking point is usually shifted toward one third of the height. This is the effect of the Pr term in Eq. 15, which modifies the position of the maximum σL (or σT ). As already mentioned, another factor to be considered is the ratio H a , which is usually in the range H a ≃ 5 − 20 for real chimneys, but can be increased up to about H a ≃ 100 with our toy models. In Fig. 7 we plot the maxima of the leading edge stress curves, for several values of the ratio H a = 5, 10, 20, 30, ..., 100 (for the group of curves between the values of 30 and 100, the parameter is increased by 10 units for each curve). These maxima are plotted as continuous curves, showing the corresponding values of the ratio r H and the angle θ, at which the structure is more likely to break, for a given value of H a . In other words, connecting for example the solid points of Fig. 6, we would obtain a corresponding continuous curve in Fig. 7, with the angle of probable rupture on the vertical axis, instead of the normalized stress. The dependence of the rupture point on these quantities can be noted in several of the existing photos of falling chimneys, when the breaking occurs due to the bending of the structure and not for the transverse shear stress near the base mentioned at the beginning of this section. The angle of rupture can be roughly estimated by measuring the angle the upper part of the chimney forms with the vertical in the photos. This angle tends in fact not to change much after the rupture, since the upper part falls without much additional rotation. For example the photos in the paper by Bartlett5,21 refer to chimneys with H a ≃ 10, breaking at about θ ≃ 20◦ − 25◦ and for r H ≃ 0.47, consistent with the values of Fig. 7, for the H a = 10 curve. Similar behavior can be seen in other photos,5,20 since real chimneys tend to break very early in their fall, due to the intense stresses originating within their structure. IV. TOY MODELS In this section we discuss our efforts to reproduce the effects described above, with the help of toy models of the falling chimney. These models were constructed with simple toy blocks of different type and size, and their fall was filmed with a digital camera, so that we could analyze the events frame by frame, to test the theory. Complete details on the type of blocks used, experimental settings and video-capture techniques, as well as the complete set of our video-recordings and still photos can be found on our web-site,5 and in an upcoming publication.33 13