32 PRINCIPLES OF ELECTRICAL DESIGN 



Thus in both cases the inclined gap has the effect of increasing 

 the initial pull for the same total length of travel. This is 

 sometimes an advantage, and conical poles are occasionally 

 introduced in designs of electromagnets when the total travel is 

 small relatively to the diameter of the plunger. In this manner 

 it is possible to obtain increased length of travel without adding 

 to the weight of the magnet. For the same initial pull, the 

 length of travel obtainable by providing conical surfaces is, 



COS 2 



where l\ is the length of the normal gap which corresponds to 

 the required initial pull. This formula is easily derived from 

 the expressions previously developed. 



There is a limit to the amount of taper that can be put on the 

 conical pole pieces, and a large amount of taper will prove to be 

 of little use. It should be noted that a limit of usefulness is 

 reached when the flux density in the iron core approaches satura- 

 tion limits, because the air-gap density which determines the 

 magnetic pull cannot then be carried up to high values, even 

 with greatly increased exciting ampere-turns. A reference to the 

 curves of Figs. 2 or 3 (pages 16, 17) will enable the designer to 

 judge when the density in the magnet is approaching uneconom- 

 ical values. Thus, in the case of cast iron it will rarely pay to 

 carry the induction above 11,000 gausses, while, in wrought iron, 

 or cast steel as used for electromagnets, 1 the upper limit may be 

 placed at about 19,000 gausses, although, as will be explained 

 later, it is often advantageous to force the density up to higher 

 values in the teeth of laminated armature cores. 



9. Materials Wire and Insulation. Before going further into 

 the design of electromagnets it will be advisable to consider 

 briefly the qualities of the materials used in their construction. 

 The most important of these materials is the iron, which con- 

 centrates the magnetic flux and so provides the necessary dis- 

 tribution and density in the air gap where it performs the duty 

 required of it. The effect of iron in the magnetic circuit has 

 however already been discussed at some length, and as its various 

 properties will be considered further in the course of subsequent 

 articles, it is proposed to confine the remarks immediately fol- 



1 This is practically pure iron, with magnetic characteristics very similar 

 to those of soft annealed iron of good quality. 



