### Overview

The math for the pulleys is pulled from my Flat Belt Pulley page and my Coal Breaker page 3 which in turn was compiled from “A Treatise on Belts and Pulleys” by John Howard Cromwell published 1888. Like the title suggests also belt information. The Diameter of a Pulley is dictated in part by the desired end-speed of the shaft it is on (the other part being the driving pulley diameter and speed). The width depends on the belt width – and the belt width is calculated by the HP transmitted, RPM and pulley diameter to get Vm and P which you can then use the ‘Width Table’ on page 3 to find..

### Crusher Pulley

• $\textbf{HP=45}$
• $\textbf{Pulley Diameter = D}$
• $D = 64"$
• $D = 33.87\text{ mm - O scale}$
• $\textbf{Pulley Circumference = C}$
• $C=16.755'$
• $\textbf{100 RPM}$
• $\textbf{Pulley Circumferential Velocity}$ $v_{m}$ (Pulley Circumference in Feet x RPM)
• $v_{m}=C_f*RPM$
• $v_{m}=1689 \text{ FPM}$
• $\textbf{Pulley Power = P}$
• $P = 33000H/v_m$
• $P = 33000*45/1689$
• $P = 879$
• $\textbf{Shaft Diameter = d}$
• $d = 3"$
• $d = 1.6\text{ mm - O scale}$
• $\textbf{Belt width = b}$
• $b=10"$
• $b=5.29"\text{ mm - O scale}$
• $\textbf{Face Width = B}$
• $B = \frac{5}{4}b$
• $B = 12\frac{1}{2}"$
• $B=6.61\text{ mm - O scale}$
• $\textbf{Rounding of Pulley Face = s}$
• $s=\frac{1}{20}*b$
• $s=\frac{1}{20}*10$
• $s=1.05"$
• $s=.56\text{ mm - O scale}$
• $\textbf{Rim Edge Thickness = k}$
• $k = 0.08 + \frac{B}{100}$
• $k = 0.08 + \frac{12.5}{100}$
• $k=.205"$
• $k=.11 \text{ mm - O scale}$
• BREAK
• $\textbf{Pulley Nave Width = w}$
• $w = 0.4 + \frac{d}{6} + \frac{R}{50}$
• $w = 0.4 + \frac{3}{6} + \frac{32}{50}$
• $w = 1.54"$
• $w=.815 \text{ mm - O scale}$
• $\textbf{Pulley Nave Length = L}$
• $L = 2.5w$
• $L = 3.85"$
• $L=2.04 \text{ mm - O scale}$
• $\textbf{Number of Arms = N}$
• $N = \frac{1}{2} (5+\frac{R}{b})$
• $N = \frac{1}{2} (5+\frac{32}{10})$
• $N = 4.1$
• $N=\text{5 - Rounding up}$
• $\textbf{Arm Width at Nave = h}$
• $h=0.24+\frac{b}{4}+\frac{R}{10*N}$
• $h=0.24+\frac{10}{4}+\frac{32}{10*5}$
• $h=0.24+2.5+.64$
• $h=3.38"$
• $h=1.8 \text{ mm - O scale}$
• $\textbf{Arm Width at Rim = }h_1$
• $h_1=\frac{2}{3}*h$
• $h_1=\frac{2}{3}*3.38$
• $h_1=2.25"$
• $h_1=1.2 \text{ mm - O scale}$

### Crusher Drive Pulley

• $\textbf{HP=45}$
• $\textbf{Pulley Diameter = D}$
• $D = 80"$
• $D = 42.33\text{ mm - O scale}$
• $\textbf{Pulley Circumference = C}$
• $C=20.94'$
• $\textbf{80.65 RPM}$
• $\textbf{Pulley Circumferential Velocity}$ $v_{m}$ (Pulley Circumference in Feet x RPM)
• $v_{m}=C_f*RPM$
• $v_{m}=1689 \text{ FPM}$
• $\textbf{Pulley Power = P}$
• $P = 33000H/v_m$
• $P = 33000*45/1689$
• $P = 879$
• $\textbf{Shaft Diameter = d}$
• $d = 3"$
• $d = 1.6\text{ mm - O scale}$
• $\textbf{Belt width = b}$
• $b=10"$
• $b=5.29"\text{ mm - O scale}$
• $\textbf{Face Width = B}$
• $B = \frac{5}{4}b$
• $B = 12\frac{1}{2}"$
• $B=6.61\text{ mm - O scale}$
• $\textbf{Rounding of Pulley Face = s}$
• $s=\frac{1}{20}*b$
• $s=\frac{1}{20}*10$
• $s=1.05"$
• $s=.56\text{ mm - O scale}$
• $\textbf{Rim Edge Thickness = k}$
• $k = 0.08 + \frac{B}{100}$
• $k = 0.08 + \frac{12.5}{100}$
• $k=.205"$
• $k=.11 \text{ mm - O scale}$
• $\textbf{Pulley Nave Width = w}$
• $w = 0.4 + \frac{d}{6} + \frac{R}{50}$
• $w = 0.4 + \frac{3}{6} + \frac{32}{50}$
• $w = 1.7"$
• $w=.9 \text{ mm - O scale}$
• $\textbf{Pulley Nave Length = L}$
• $L = 2.5w$
• $L = 4.25"$
• $L=2.25 \text{ mm - O scale}$
• $\textbf{Number of Arms = N}$
• $N = \frac{1}{2} (5+\frac{R}{b})$
• $N = \frac{1}{2} (5+\frac{32}{10})$
• $N = 4.5$
• $N=\text{5 - Rounding up}$
• $\textbf{Arm Width at Nave = h}$
• $h=0.24+\frac{b}{4}+\frac{R}{10*N}$
• $h=0.24+\frac{10}{4}+\frac{40}{10*5}$
• $h=0.24+2.5+.8$
• $h=3.54"$
• $h=1.87 \text{ mm - O scale}$
• $\textbf{Arm Width at Rim = }h_1$
• $h_1=\frac{2}{3}*h$
• $h_1=\frac{2}{3}*3.38$
• $h_1=2.36"$
• $h_1=1.25 \text{ mm - O scale}$