How to Calculate the Effect of Point Loads on a Catenary
- 1). Find the cosine of the angle between the load's vector, which is the direction at which it acts, and the horizontal. Cosine is a ratio related to a triangle's measurements. Find it using a scientific calculator by pressing the cosine ("cos") button and entering the angle. For example, if the load acts at 40 degrees from the horizontal, find the cosine of 40, which is 0.766.
- 2). Multiply the load's size, measured in newtons, by this ratio. For example, if a load of 20 newtons acts on the catenary, multiply 20 by 0.766, giving 15.32. The point load leads to a 15.32-newton horizontal force on the catenary.
- 3). Find the sine of the angle between the load vector and the horizontal. Sine is a ratio similar to cosine. Find it using a scientific calculator by pressing the sine ("sin") button and entering the angle. Continuing the example, the sine of 40 is 0.643.
- 4). Multiply this ratio by the size of the load. Multiply 0.643 by 20, giving 12.86. The point load leads to a 12.86-newton vertical force on the catenary.
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