150 



Popular Science Monthly 



Estimating the Windings of the 

 Electromagnet Coils 



IT is frequently desirable to rewind 

 electromagnetic coils to obtain more 

 efficient windings, or to make and wind 

 the coil complete. It is usually difficult 

 to estimate coil-windings correctly, with- 

 out dealing more or less with complicated 

 technical formulae. 



The successful operation of every 

 electromagnet depends upon the number 

 of ampere-turns produced within the 

 winding when a certain current is flowing 

 through it. The value of this current 

 is, of course, determined from the 

 resistance of the coil and any of the 

 apparatus that might be in circuit with 

 it. For example, a certain electro- 

 magnet is connected alone in a 4-volt 

 circuit, the coil being wound with 500 

 turns of wire, giving a resistance of 

 10 ohms. By Ohm's law, the current C 

 equals .4 ampere. 



500 X .4 = 200 ampere-turns, which rep- 

 resents the strength or pulling power of 

 the magnet. 



It may happen that this pulling power 

 is not sufficient to produce the result 

 desired, in which case it can be increased 

 by either the number of turns or the 

 amount of current in the circuit. By 

 using a larger size of wire, the number 

 of turns may be increased and the 

 resistance reduced, thereby allowing 

 more current to flow, which means a 

 decided increase in the effective ampere- 

 turns. It is not always possible to do 

 this, however, on account of the small 

 winding space available. 



In this article we will consider only 

 spools having round cores, these being 

 the ones most generally used. The 

 calculations would be simplified if it 

 could be assumed that the convolutions 

 of the wire were lying together, as if the 

 wire were of square cross-section. Ex- 

 perience has shown, however, that this 

 is not the case. The condition more 

 nearly approached is where the second 

 and each succeeding layer of wire lie 

 in the grooves formed by the preceding 

 layers. To simplify matters, we will 

 take the square of the diameter of the 

 wire as the actual space occupied by 

 each turn, which will be approximately 

 correct and will give good results. 



The diameter of the insulated wire can 

 be determined by taking the diameter 

 of commercial bare wire and adding the 



thickness of insulation, which varies 

 with the manufacture. No fixed values 

 can be given to cover all cases. A 

 number of the leading manufacturers 

 furnish handbooks or cards showing the 

 average diameter over the insulation. 

 The following table of thicknesses for 

 different insulations will be found to 

 give good results: 



Unknown quantities are designated by let- 

 ters and are determined by the formula below 



Let 



L = Winding length. 



3' = Diameter of spool head. 



d = Diameter of core plus any insulated 

 covering wound over it. 



x = Depth of winding. 



Z> = Over-all diameter of winding. 

 Also let 



a = Diameter pf wire over insulation. 



n = Number of turns. 



K = Maximum winding space. 



Case I. Given a spool and the size 

 of wire, to find the number of turns and 

 resistance, it being understood that the 

 coil is to be wound as snugly as practic- 

 able. For convenience assume the 

 following values: 



L = 2'' d = 4" y=i" Wire = No. 34 



enamel. 

 a = diameter over insulation = ,007" for 

 No. 34 enameled wire. 

 .007^ = .000049 sq. ins. (space occupied 



by one turn). 

 y—d I — .4 



= .^ = x or maximum 

 winding depth. 



