# Finding Pulley Sizes

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3952 Norman Road Clarkston, Georgia 30021

This is some information which I thought might be interesting and helpful to people who like to 'belt' their engines to various equipment. A friend of mine recently belted two of his engines to some hammermills he had acquired. When I asked him how fast he was turning the mills, he said, 'I don't know, I just found some pulleys that made them sound right.' That is one way and he has two nice hammermills. However, I proceeded to explain how to determine pulley sizes and RPM. With my shaft tachometer I checked the engine RPM (no center hole in mill shaft) and computed the mill speed at 1821 RPM using the pulley sizes. This procedure is explained on the attached sheet.

My interest comes from my experiences around my dad's sawmill and shop. There we had numerous occasions to use such equipment as the shaft tachometer. One application was checking such things as saw mandril RPM. As you may know, the circle saw has to be operated at the specified RPM for which it was 'hammered' and is rather critical. I remember on one occasion he had a power unit which ran 1800 RPM with a 14' drive pulley. It only took him a few minutes with his 4th grade education and a pencil to figure he needed a 48' pulley on the mandril to run the saw 525 RPM. He was well aware of dangers involved with flywheels, belts, pulleys, and etc., and always kept people clear of such equipment. The main drive belt was one of his major concerns besides the circle saw. This belt was 10' or 12' wide, probably 50' or 60' overall length, and I would guess weighed in excess of 100 lb. This belt could create a lot of havoc when it started fraying and coming apart. He probably never knew its actual travel speed so I thought it might be interesting to compute.

Pulley circumference = 14' x 3.1416 = 43.98'

Rim speed (per minute) = 43.98' x 1800 RPM = 79164'

Feet per minute = 79164'/12' = 6597' (App 110' per second)

Feet per hour = 6597' x 60 (min.) = 395820'

Miles per hour = 395820'/5280' = 74.96 MPH

Imagine strips of this belt lashing out at you at 75 MPH. I have seen it tear down the shade boards the men had constructed over the mill. It is a lot worse than the little keen peach limbs my dad used to enhance my education with.

One interesting project we became involved with was converting an old mule driven cane mill to electric power. Using a 90:1 gear box and a right angle drive, we selected pulleys to operate the mill at 9 RPM. This was 3 or 4 RPM faster than the mule but worked very nicely. I remember it made some fine cane juice.

I am a member of the Georgia Antique Engine Club and have a couple of engines, a blacksmith forge, wood cook stove, 'shine' jug, butter churn, an early 1900s Edison 'Amberola' (cylindrical) record player, along with a few other small items which I carry to the shows. Courteous and friendly are people you meet at these shows.

### FINDING PULLEY SIZES

PULLEY A DIAMETER X RPM = PULLEY B DIAMETER X RPM

WITH THE ABOVE STATEMENT IN MIND, IT BECOMES RELATIVELY SIMPLE TO COMPUTE DESIRED PULLEY SIZE, OR RPM PROVIDED THE 3 OTHER VALUES ARE KNOWN.

EXAMPLE: THIS WAS AN ANTIQUE ENGINE DRIVING A SMALL HAMMERMILL. I WAS ABLE TO CHECK ENGINE RPM WITH MY SHAFT TACHOMETER BUT HAD TO COMPUTE THE HAMMERMILL RPM.

8.5' x 750 RPM = 6375
6375 / 3.5'= 1821 RPM

SUPPOSE YOU DESIRE TO REDUCE THE HAMMERMILL TO 1600 RPM:

6375 / 1600 RPM = 3.98' CHANGE PULLEY B TO 4'
6375 / 4' = 1593.75 RPM

OR: CHANGE PULLEY A TO: 1600 RPM X 3.5' = 5600
PULLEY A DIAMETER BECOMES: 5600 / 750 RPM = 7.466'
USE 7' DRIVE PULLEY: 750 RPM X 7.5' = 5625 / 3.5' = 1607 RPM.
THIS COULD ALSO BE COMPUTED BY RATIO. DIVIDE THE DIAMETER OF THE LARGE PULLEY BY THAT OF THE SMALL PULLEY:
8.5' / 3.5' = 2.428:1 THEN 750 RPM X 2.428 = 1821 RPM.

BELTED PULLEYS COULD BE RELATED TO PULLEY CIRCUMFERENCE, BELT TRAVEL SPEED, ECT. HOWEVER, WHEN (3.1416) IS INSERTED INTO A DIVISION FORMULA, IT BECOMES A VALUE OF 1 AND DOES NOT AFFECT THE RESULT.

FOR AN INTERESTING PROBLEM, COMPUTE BELT TRAVEL SPEED.

FOR GEARS AND SPROCKETS, USE NUMBER OF TEETH RATHER THAN DIAMETER. TO FIND RATIO, DIVIDE THE NUMBER OF TEETH ON THE LARGE GEAR BY THAT OF THE SMALLER GEAR.

EXAMPLE: A 40 TOOTH GEAR MESHED WITH A 16 TOOTH GEAR WOULD HAVE A RATIO OF: 40 /16 = 2.5:1