DYNAMIC MEASUREMENTS ON V! »•,•',??<»>! \. . \ i i k DKVK K.s llCii 



a compromise for this effect. Actually the rise curves do not cross, but 

 they do approach each other. 



Coil to core constant ratios now in use range from 2 upwards, the case 

 of 2 being the best condition for 25 watts power. An examination of this 

 particular curve shows some curvature for small times. This effect of an 

 initial increased rate of rise reduces the operate time of an electromag- 

 net, and is automatically taken advantage of in the experimental design 

 of windings. 



With a winding as part of the system, an elementary consideration 

 shows why this curvature exists. This follows from 



N^^E-iR, (23) 



where: iV = number of winding turns, E — applied battery voltage, 

 R = resistance of winding, i = instantaneous current, and ^ = in- 

 stantaneous flux. This equation is exact and holds whether or not there 

 are eddy currents. At the instant of circuit closure there are no winding 

 or eddy currents (because of leakage inductances if for no other reason) 

 and the initial rate of flux rise is dependent only upon the number of 

 turns and the applied voltage. After a transition interval, the eddy cur- 

 rents become effective and slow down the rate of flux rise. For any given 

 total flux, the time required, therefore, is less than that given by the well 

 known equation: 



^ = 1 - e-'/^i(«.+<'.). (24) 



However, for large coil constants where Gc predominates the effect 

 diminishes and the above equation is an excellent representation and 

 desirable for its simplicity. 



NEW FIRST APPROXIMATION FLUX RISE EQUATION 



Returning to Fig. 24, while the effect we have been discussing is all 

 important for open circuit flux decay, practical coil constants at present 

 do not have ratios to the core constant much below 2. These curves do 

 not diverge greatly from straight lines on this plot. Can a minor correc- 

 tion term be made a part of the simple equation heretofore used which 

 will retain its simplicity and extend its accuracy to windings now used? 



One such equation is 



^ = 1 - c-'i^ii<'c+o.*-<''''''\ (25) 



