PROCEEDINGS OF SECTION A. 197 
10.— THE BICYCLE WHEEL. 
By B. A. Suir, M.C.E. 
WE assume that the number of spokes, supposed radial, is very 
great, so that we may regard the tension applied to the rim to 
be uniformly distributed 
round it and to amount 
to ¢ per unit length. Let 
a=radius of wheel mea- 
sured to c. g. of rim, and 
suppose that there is an 
initial tension in thespokes 
amounting to ¢ per unit 
length of arc. This pro- 
duces a radial displace- 
ment — 2, throughout, and 
a corresponding rim ten- 
sion — T,, the centre being 
supposed fixed. When 
the load is applied a 
further radial displace- 
ment w is produced (to- 
gether with a corresponding tangential displacement v), which 
gives rise to a tension ¢= wu, which is to be superposed on éo, 
ay: a ,in which x is the number of spokes, H 
where \ = 
27 a a 
the sectional area of a spoke, and Y is Young’s Modulus of the 
material. Calling T, L, M the rim tension, the shear and the 
bending moment respectively at P measured as Fig. 1, we have 
for equilibrium of the element P Q of the rim 
T + 6 Ef \--L oe — T= 6 
L+6L+7T760+ta60-—-L=o0 
M+656M+Laéé@ -M-=o 
or 
at 
do = ie a: eA.) CD) 
di 
aqetitta=o ai) tes) 
d M ; 
d 6 =I a= oO Ble’ (3) 
We have also 
3 d*u 
M=Kéx=- g («+ dB: (4) 
where K is the bending moment required to produce unit increase 
of curvature in the rim. 
