86 DIRECT-CURRENT DYNAMOS AND MOTORS. 
from 24 to 100 per cent. of direct compensating ampere- 
turns; hence, the total number of compensating ampere- 
turns is from 1.25 to 2 times the direct compensating am- 
pere-turns and can therefore be expressed by the formula: 
ry ts Gap at 6 a 
Oh Rr A get eae sacle Mek 6 See ate Re +++-(45) 
in which k is a factor which usually varies from 1.25 to 
2.00, as follows: 
k = 1.25 to 1.75, average 1.5, for wrought tron and 
cast steel polepieces; 
k = 1.50 to 2.00, average 1.75, for cast tron pole- 
pieces. 
The average of k for wrought iron and cast steel corre- 
sponds to a mean flux density of about 105,000 lines per 
square inch; the lower limit is for 80,000 lines, or less, and 
the upper figure given refers to a density of about 120,000 
lines per square inch. For cast tron the average corre- 
sponds to a mean density in the polepieces of about 
45,000 lines per square inch; the minimum corresponds 
to 20,000 lines, or less. and the maximum is to be taken 
when the average density in the polepieces is about 
60,000 lines per square inch. 
66. Calculation of Ampere-Turns for Bipolar Smooth- 
Armature Dynamo.—The various dimensions of the 
magnetic circuit of the machine represented at the right 
in Fig. 25 having been determined, the ampere-turns 
required in the field coils are calculated as follows: 
The number of ampere-turns needed to overcome the reluct- 
ance of the two air gaps is obtained from (42), in which 
for the present case B,” = 30,500 lines per square inch 
(see page 72), and/,” = 2 x 4 X 1.25 =I1t inches. The 
average length of the magnetic lines in the gaps is here 
taken 25 per cent. greater than twice the distance across 
from polepiece to armature core, because. when the ma- 
chine is carrying current in the armature, the lines do not 
pass straight across in the direction of the radius, but are 
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