BRAKES AND DYNAMOMETERS 345 
- effort will be required on the lever at D to keep the brake in full 
action. 
It is obvious that if AC is greater than AB, a downward motion of 
the end D of the lever will loosen the band from the wheel. 
If the ratio ce is made less than then, when the brake is in 
action, the force P must act downwards, as shown at (4), Fig. 534; but if 
this force be increased beyond what is sufficient to balance the turning 
action of T, and T, on the lever, the end D will drop, and the band will 
be disengaged from the wheel. 
At (c), Fig. 534, the tight’end of the band is shown anchored at A, 
the fulcrum of the lever. Here Px AD=T, x AC. At (d) the slack end 
of the band is shown anchored at A. Here Px AD= T, x AB. Com- 
paring the arrangements at (c) and (d), it is obvious that, for the same 
effort P, the latter arrangement will require a larger leverage for P to 
produce the same resistance at the circumference of the wheel. 
293. Band and Block Brakes.—By lining the band of the brake 
discussed in the preceding Article with wood blocks, as shown in Fig. 535, 
a higher coefficient of fric- 
tion is introduced, and the RX o 
wear is confined to the wood T. 34 
blocks, which may easily be 7 of 
renewed from time to time. | ~\ 7 
The ratio of the tensions (4) 420 
T, and T, at the ends of ‘i 
the band is obtained as fol- ‘ 
lows. Let there be n blocks, 90°-0- 
each subtending an angle 20 To (29 
at the centre of the wheel. XY (b) ag 
The first block at the tightest FRgpt 94's 
end is shown separately at 
(a). The forces acting on 
this block are T, and T,, the tensions in the band where it leaves the 
block, and R, the reaction of the wheel on the block ; the latter force is 
inclined to the normal at an angle ¢, as shown, when slipping is taking 
place, ¢ being the friction angle. The triangle of forces for the block 
under consideration is shown at (bd). 
From the triangle of forces it follows that 
sin{(90 — 6) + : T, 1+) tan 0 
tT, nant 0 = a “ which reduces to T rae. ‘an 8” 
where p= tan ¢ is the coefficient of friction between the block and the wheel. 
T, l+ptané T, 
T,7 ~l=ptan 0~ T, 
Fia@. 535. 
In like manner for the second block ®, and for 
| Re TY 4 Ry 
] on pat PRR Bi ei od VO fee abboncsaly 
all the blocks qT, T, T, tS tanent 
ae en} 
l—ptan 0) 
294. Block Brakes.—In a block brake a block is pressed against the 
rim of a revolving wheel. This is the type of brake which is nearly 
