When was cloth tape invented? 

The mixture of cloth and adhesive to create a conformable, protective material for repair has been used throughout history, although the first documented appearance of a cloth tape similar to modern duct or gaffer tape dates back to the 1840s when it was patented by Dr Horace Day as a medical tape.

Modern duct tape was patented in 1942 when it was developed as part of the war effort and was first used as a water-resistant seal for ammunition cases.

Gaffer tape is a more recent invention and was introduced in the early 1950s as a product for the film industry as it was easily torn and suitable to use on set.