![]() To find out the length, we need to integrate from the initial angle to the final angle. Now we have the dependence of the length dl on the angle dφ. Using the polar equation of a spiral, we can replace ρ with kφ, and dρ with kdφ Hence:Īn infinitesimal spiral segment dh can be replaced with an infinitesimal segment of a circle with radius ρ hence its length is ρdφ. Please be careful with unit control when you enter the known dimensions! 20 meters are not the same as 20 millimeters.Īn infinitesimal spiral segment dl can be thought of as hypotenuse of the dl, dρ, and dh triangle. Theory and formulas, as usual, can be found below the calculator. You can also solve an inverse problem (when you know the roll length) - calculate thickness and number of turnings using roll length and both diameters. For example, you can calculate roll length from inner and outer diameters and roll thickness or number of turnings. You can easily find out some of these objects' dimensions, like diameters and thickness, or a number of turnings, and, using the calculator below, calculate the missing ones. We can see spirals in everyday life in any objects that are in the rolled form: rolls of paper, tapes, films, and so on. These dimensions are related (see formulas below the calculator), and you can calculate any two if you know the other three. We have five spiral dimensions: outer diameter - D, inner diameter - d, thickness, separation distance or distance between arms - t, spiral length - L, number of turnings - n.
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