ESTIMATION AND COXTUOL OF Ol'EKATE TIME OF RELAYS 159 



Tji ,' the iiuhi('taiic(> foi' one wiiidiiiu; iui'ii is: 



Also 



NI = VGcW. (15) 



From the network of Fig. 7, 



Tlie armature force developed is 



-^ = 84- (") 



When the magnetic pull has reached F\ , the waiting time is over, deter- 

 mining (p« , which in turn determines NIo , and hence q. 

 Substituting (U), (15), (16), and (17) in (13) we have 



h = 47r 



J_ 1 



(s\l (Ro + ■a/a_ 



(Gc + G'^) In 



1 (18) 



as the desired expression for the waiting time in terms of the funda- 

 mental constants. Use will be made of this later when an expression for 

 motion time has been developed. 



Motion Time 



The motion time immediately follows the waiting time and is the time 

 required for the armature to move from the backstop position Xi , to the 

 location of the last contact xs . From Fig. 1, it is permissible to omit any 

 consideration of contact spring load, and consider the motion to be 

 controlled entirely by the armature mass and magnetic pull developed 

 after the waiting time is over. The determination of motion time is 

 simplified because the initial velocity and net force on the armature are 

 both zero, the latter following from the definition of the end of d . In 

 any problem involving motion, there must be established the initial 

 velocity, position, and a suitable expression for the ensuing force. With 



