12 DIRECT-CURRENT DYNAMOS AND MOTORS. . 
surface can in most cases be considered as cooling sur- 
face. If, however, the construction of the armature is 
such that the inner surface or one of the end surfaces is 
covered up, the area so covered must be excluded from 
the calculation of the cooling surface. The total surface 
of a ring having a diameter D,, a length L,, and a radial 
depth B,, Fig. 6, is given by the formula: 
S, = (D, — Ba)e * AB, +B eee ee (9) 
Expressing both the length and the radial thickness of 
the ring as multiples of its diameter, L, = mD, and 
B, = m'D,, we obtain: 
S, = 2a x (D, — m'D,) XK (mD, + m'D,) 
= 2a X D,* X (1 — m’) X (m + m’).......(10) 
16. Determination of Armature Diameter by Cool- 
ing Surface.—lIt is found that from 4 to 1 square inch 
of cooling surface is needed to liberate the heat resulting 
from each watt of power lost in the armature. This in- 
cludes not only the copper, or C*R, loss due to the resist- 
ance of the armature winding, but also the iron loss, or 
core loss, due to hysteresis and eddy currents. These losses 
are not definitely known in the beginning, but it is rea- 
sonable to assume that they will be from J to 3 per cent. 
of the total power in large machines of 400 K. W. and 
over; 3 to J per cent. for machines of about 100 K. W.; 
4 to 6 per cent. for sizes of about 50 K. W.; 5 to8& per 
cent. for 10 K. W.; 6 to 10 per cent. for  K. W.; 8 to 12 
per cent. for 7. K. W.; and up to 20 and even 24 per cent. 
for very small machines, such as battery motors, etc. 
The cooling surface, in square inches, required in any case 
is, therefore: 
Sax kh eH, Coco ne ccceccc cr sestccce (11) 
in which W = capacity of dynamo, in watts; 
s = specific cooling surface, 
= .5to 1 square inch per watt of power loss; 
and k = percentage of power loss in armature (see 
Table 3 for average values). 
