Let’s consider how a cable winds on a drum.

The cable takeup rate will be smooth until the drum is covered with one layer of cable, then it will start a new layer in the opposite direction. The new layer will be winding on a drum with a diameter that is the empty drum diameter plus two times the cable diameter. Therefore the rate of winding will increase in jumps followed by a smooth increase. In the graph below, each point indicates one revolution. The drum length is 10 inches, the drum diameter is 6 inches, the cable diameter is 0.5 inches. The plot shows forty-five revolutions, so there will be 45 x .5/10 = 2.25 layers of cable on the drum. Beginning with the third layer, the drum diameter will be nine inches – 6 +(2 x .5 x 3) = 9 – fifty percent bigger than the empty drum, so the takeup will be fifty percent faster. The graph shows this.

Let’s try the following parameters in order to make the increasing rate of takeup more clear: drum length = 6, drum diameter = 4, cable diameter = .5, 100 revolutions.

One can clearly see that the slope of each segment is greater than that of the previous segment. In other words, the rate of takeup of each layer is greater than the rate of takeup of the previous layer because the drum daimeter increases with each layer.

See “cablewindwithggplot_good.R”" to be able to play with user input.

That’s all for now.