Use the ruler to measure the diameter of the central core cylinder of the thermal roll. The core cylinder is found in the middle of the roll. The core may be an empty cylinder or a solid structure made from a material other than thermal paper. The diameter is a measurement taken through the center of the core, from one side of the core circumference to the other. Repeat this measurement three times. Add the four core diameter measurements to obtain a total core diameter. Divide the total core diameter by four to obtain the average core diameter.
Represent the average core diameter with the letter C. For example, if the core diameter measurements are 5.0 x 10^-2 m, 5.1 x 10^-2 m, 5.1 x 10^-2 m, and 5.2 x 10^-2 m, then the total core diameter is 20.4 x 10^-2 m = 5.0 x 10^-2 m + 5.1 x 10^-2 m + 5.1 x 10^-2 m + 5.2 x 10^-2 m. The average core diameter C = 5.1 x 10^-2 m = (20.4 x 10^-2 m)/(4).
Measure the diameter of the thermal roll. The thermal roll shares the same center point as the core. Use the ruler to measure from the outer edge of the paper through the center of the core, to the opposite outer edge of the roll. Repeat this measurement three times. Add the four roll diameter measurements to obtain a total roll diameter. Divide the total roll diameter by four to obtain the average roll diameter.
Represent the average roll diameter with the letter D. For example, if the roll diameter measurements are 45.0 x 10^-2 m, 45.1 x 10^-2 m, 45.1 x 10^-2 m, and 45.2 x 10^-2 m, then the total roll diameter is 180.4 x 10^-2 m = 45.0 x 10^-2 m + 45.1 x 10^-2 m + 45.1 x 10^-2 m + 45.2 x 10^-2 m. The average roll diameter D = 45.1 x 10^-2 m = (180.4 x 10^-2 m)/(4).
Use a micrometer to measure the thickness of the paper. Take six measurements of the thickness of the paper at various points on the paper. Add these measurements to obtain a total thickness. Divide the total thickness by 6 to obtain an average paper thickness.
Represent the average paper thickness with the letter T. For example, the thickness of the paper at six different points on the roll is measured as 1.2 x 10^-6 m, 1.3 x 10^-6 m, 1.2 x 10^-6 m, 1.1 x 10^-6 m, 1.3 x 10^-6 m, and 1.3 x 10^-6 m. The total thickness is 7.4 x 10^-6 m = 1.2 x 10^-6 m + 1.3 x 10^-6 m + 1.2 x 10^-6 m + 1.1 x 10^-6 m + 1.3 x 10^-6 m + 1.3 x 10^-6 m. The average thickness T = 1.2 x 10^-6 m.
Find the length (L) of the paper on the roll using the formula: L = (3.14/4) x [(D^2 -- C^2)/T]. For example, if the thermal roll has an average core diameter of 5.1 x 10^-2 m, an average roll diameter of 45.1 x 10^-2 m, and an average paper thickness of 1.2 x 10^-6 m, the length of the paper on the roll is: L = 131356.7 m = (3.14/4) x [(D^2 -- C^2)/T] = (3.14/4) x [((45.1 x 10^-2 m)^2 -- (5.1 x 10^-2 m)^2)/(1.2 x 10^-6 m)] = (3.14/4) x [(D^2 -- C^2)/T].