In order to design and construct a canopy walkway, one must know the attributes of all of the materials used, e.g., tensile strength of the cables and the weights of all of the component parts as well as the load of equipment and people. The tensions on the supporting cables must either be measured or calculated, and a sufficiently large safety factor assured. The canopy walkways typically built by CCA are supported by two strong and flexible cables fastened at the two ends on a horizontal plane. The treads are distributed along the cables and the resulting walkway, when not loaded, take the natural shape of a catenary curve. This is a reasonable assumption because the walkway very nearly weighs a constant amount per unit of length and the cables are quite flexible. It is nearly impossible and certainly not feasible to actually measure the tension on the cables as installed. Therefore it is necessary to calculate tensions and stresses. The results are accurate since the mathematical model is a very good approximation to what actually occurs at the construction site.
Even after calculating the parameters of a specific canopy walkway, such as its span, catenary length, sag, and angle from horizontal of the catenary curve at the end attachment points, there still remains the matter of actually constructing it. When considering the degree of precision required, the length of the span is extremely difficult to measure as is the angle. This is best illustrated by comparing measurements errors of the sag, the angle and the span length; a change of 3 inches in the sag is equivalent to a 0.56 degree angle change and only 1 inch difference in span length. It seems certain that the most feasible way to construct a walkway is to use the measured value of sag, which can be altered by simply shortening or lengthening the span cables until the required sag is obtained. At this point the walkway will be the correct shape for its calculated no load situation with the specified safety factor.
A design calculation requires the following parameters to be specified:
1. Span - horizontal distance between attachment points
2. Weight per foot - includes cable, treads, separators and attachment hardware
3. Minimum Breaking Strength of cables - from manufacturer
4. Load - consists of all equipment and/or people on a walkway
5. Safety Factor - CCA uses minimum of 5:1
The QBASIC program requires a first approximation as a starting point for the Sag. This calls on a root extraction procedure that employs Newtons method which iterates changes until the root is reached. Fortunately, the root equation is very malleable and an analytical derivative of it is easily found. With this derivative function, the Length is then easily calculated.