4120.11 – Insulating Tape

A long strip of insulating tape is to be wrapped around a hot water pipe. If the width of the strip is $w$ and the diameter of the pipe is $d$, at what angle must the strip be placed at the edge of the pipe so that no overlapping and no spaces occur?

Solution

Cut open and flatten out the pipe, as shown below. Then $\dfrac{w}{d\pi} = \sin\Omega \implies \Omega = \arcsin\left(\dfrac{w}{d\pi}\right)$.

Note, one would normally overlap the tape a bit; would the angle change?