Bridging form and function
The old Poole lifting bridge was built in the 1920s. It is a lifting bridge comprising two sections that split apart in the centre.
A new bridge called the 'Twin Sails' is due to be completed in February. This is designed somewhat differently, comprising two triangles, each of sufficient length to span the gap they are to cover.
The old bridge can be modelled as two rectangles, meeting in the centre of the span to create one large rectangle, as in figure 1:
Figure 1: Old lifting bridge (plan view).
The new bridge can be modelled as two triangles that each span the gap, and tesselate together so as to form a large rectangle, as in figure 2:
Figure 2: 'Twin Sails' (plan view).
In both cases the two sections pivot at their ends to allow the bridge to lift. The closer the centre of mass of each section is to the pivoting ends, the less strain will be imposed on the motors. The centre of mass of each rectangular section of the old bridge is just halfway along the section, i.e., one quarter (0.25) of the total span of the bridge.
In the case of the triangular sections, for a triangle of uniform thickness, the centre of mass is at a distance from the pivot (i.e. the base of the triangle), such that the surface area of triangle above it is half the total surface area:
Figure 3: Triangle, showing line on which centre of mass rests.
The area of a triangle = (base x height)/2.
If the small triangle in figure 3 is half the size of the total, then (b(1)h(1))/2 = (b(2)h(2))/2.
The height to base length ratio is the same for each triangle, therefore: b(1)/h(1) = b(2)/h(2), therefore, b(1) = ((b(2)h(1))/h(2)
By substitution:
(b(2)h(1)^2)/h(2) = b(2)h(2)^2
From this, H (the distance of the centre of mass from the pivot point) = h(1) - h(2) = h(1)(1-(2^(-1/2)), roughly = h(1) x 0.292.
So, the centre of mass of the triangle is slightly further from the pivot point than is the case for the more conventional design spanning the same distance, and the Twin Sails design is therefore less efficient than its conventional predecessor. Essentially a triumph of form over function.
The old Poole lifting bridge was built in the 1920s. It is a lifting bridge comprising two sections that split apart in the centre.
A new bridge called the 'Twin Sails' is due to be completed in February. This is designed somewhat differently, comprising two triangles, each of sufficient length to span the gap they are to cover.
The old bridge can be modelled as two rectangles, meeting in the centre of the span to create one large rectangle, as in figure 1:
Figure 1: Old lifting bridge (plan view).
The new bridge can be modelled as two triangles that each span the gap, and tesselate together so as to form a large rectangle, as in figure 2:
Figure 2: 'Twin Sails' (plan view).
In both cases the two sections pivot at their ends to allow the bridge to lift. The closer the centre of mass of each section is to the pivoting ends, the less strain will be imposed on the motors. The centre of mass of each rectangular section of the old bridge is just halfway along the section, i.e., one quarter (0.25) of the total span of the bridge.
In the case of the triangular sections, for a triangle of uniform thickness, the centre of mass is at a distance from the pivot (i.e. the base of the triangle), such that the surface area of triangle above it is half the total surface area:
Figure 3: Triangle, showing line on which centre of mass rests.
The area of a triangle = (base x height)/2.
If the small triangle in figure 3 is half the size of the total, then (b(1)h(1))/2 = (b(2)h(2))/2.
The height to base length ratio is the same for each triangle, therefore: b(1)/h(1) = b(2)/h(2), therefore, b(1) = ((b(2)h(1))/h(2)
By substitution:
(b(2)h(1)^2)/h(2) = b(2)h(2)^2
From this, H (the distance of the centre of mass from the pivot point) = h(1) - h(2) = h(1)(1-(2^(-1/2)), roughly = h(1) x 0.292.
So, the centre of mass of the triangle is slightly further from the pivot point than is the case for the more conventional design spanning the same distance, and the Twin Sails design is therefore less efficient than its conventional predecessor. Essentially a triumph of form over function.
posted by Iansonuk at 7:20 AM
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