202 PROCEEDINGS OF SECTION A. 
If we have m spokes in the wheel, and if 7 = tension in a 
2 WG 
spoke, we may assume 7 = —— x 1, and we have from (5) 
i bd Os YxH 
2% a? 
In a particular case, 
n = 32 spokes 
K = 480 ft. (lbs. weight) per unit change of curvature 
a == 1,02 41 
= .0951 sq. ze 
H = .0046 sq. i 
Y = 28,900,000 ative: weight per sq. inch, 
so that A = 630, 500 Ibs. weight. per sq. inch, 
ite 9: 
: =, 256a: 
Bapecwn me Ne ii S 
—— ] a / 
H ve Ye XO? 4 000 
K p) 
er oe i/ Nan gi 
a ae | ee — 2 
; l ~ 14 4.2848 
pe? p* = 37.720 
V 
je — 27.64602 = Sa + (144° 0’) 
3 = 26.92255 
~~” OS 
and we have (¢’ = ¢,+ ¢ 
Wa? id 
i +36 ~ 4py (pe? + 9?) K * 
27a YG 
i = 
= ¥8 ) —V (20-8) 
| {neon Or» sinpohe + [eos (am 0) +v sin (27 — 8) Fe | 
cn ree oe J Snean 
When @ = x, =t, + cs 1k) 7 a x 
( VG. 
h ; Ww W a® i % 
When” 0—"0, ¢ = % eet “Ay (uw? + v2) K 
( ya) 
W WwW 
= pecs ~ 8S x 13.81, XS ae 
27 a 274 PLE Se) 
Hence, in order that the spokes shall always be in tension, 
i.e, Us > o, we must have 
f W 
274 
and the necessary initial tension in the spokes— 
27a t Wok As: 
x 13.0 
hy ee 
pee Sesser ies .4 x W, say, 
Te > - x re) 32 y 
‘tf t 8 W 
T= Oo = 
27a 
, Ty = if 
i == Ts ave 8 W ze a me WG 
