Determine Paper Roll Size

Determine Paper Roll Size-58
If all conditions are met the shelf life of the paper is up to seven years.As well once the thermal paper has been used the image life of the paper is up to seven years as long as all storage conditions are met.

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If the conditions aren’t met then that will change how long the shelf and image life are.

First thing, make sure the paper is placed in the printer correctly if it is thermal paper the side that has the coating that allows the image to appear should be facing outward.

Let D the outer diameter of the roll, h the thickness of the tape and N the number of turns. First, the number of turns is easy to compute, since it's just the difference of the two radii divided by the thickness of the tape or, in terms of diameter: The circumference of the first turn is πD 2(N–1)h).

The total length of the tape is therefore: By rearranging the terms we get: Now, the sum of the integers from 1 to N-1 can be expressed in the form N(N–1)/2 (Gauss's formula).

Knowing the length of a roll just by measuring its diameter can be useful in many situations, since many everyday objects are in rolled form, like tapes, paper, plastic films, and so on.

There are two ways of calculating the length of roll (mathematically speaking a "spiral"), an exact and complex formula derived from integral calculation and an approximate and simpler formula derived from the sum of circumferences of concentric circles.

This method start with an approximation or a guess of the solution (zero of a function) and iteratively refines it by finding the intercept point on the abscise axis of its tangent line.

Since this point is a better approximation, so the process can be repeated until the desired precision is achieved.

The approximate formula is enough in many situations as long as the thickness of the tape is small compared to the diameter of the roll.

Now let's have a look on how these formulas are deduces.

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