Chainsaw Tooth Velocity

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MolaKule

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If a chainsaw sprocket of 1.5" Radius is rotating at 4300 rpm, how many feet will any one chain tooth travel in 1 second?

Recall that Tangential velocity Vt = w*R, where omega w is the velocity of the sprocket in radians per second and R is radius of the sprocket.

Of course, we're going to lube the chain with a tacky 30 grade oil called, "Bar and Chain oil."
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35.83repeating?(I forgot the repeating symbol and an to lazy to look it up.)

Edit that would be the linear speed though not the tip speed around the sprocket.

Edit 2 I did it the dumb way not the formula way.

Edit 3 I didn't do it right at all. 3377 ft per second.
 
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so 3" is the diameter *pi *4300(rpm) / 12 (inches in feet)

seems way off but 3377ft?
 
The velocity of the chain is approximately equal to the tangential velocity of the sprocket.

Hint: First convert RPM to radians/s.

So in one second the tooth will have traveled X feet????
 
Originally Posted By: IndyIan
Makes you think saw pants are a good idea!


Ha ha, for sure.
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4300 RPM/60 seconds per minute = 71.66 revolutions per second.

The circumference of a circle = pi X Diameter or pi X 2 X Radius

Circumference of a 3 inch diameter circle is 3 X 3.14 = 9.42 inches

71.66 revolutions X 9.42 inches circumference = 675.0372 inches per second.

Divide by 12 to get feet per second.

675.0372/12 = 56.2531 feet per second
 
Originally Posted By: cpayne5
~56.3'?


In what units?

Originally Posted By: A_Harmon
4300 rev/min x 2*pi radians/rev x 1 min/60 sec x 1.5 in x 1 ft/12 in = 56.28 ft/sec, or about 38 mph.


So any one tooth will travel how many feet in one second?


Originally Posted By: JiminPA
675.0372/12 = 56.2531 feet per second


So any one tooth will travel how many feet in one second?
 
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Originally Posted By: MolaKule
Originally Posted By: cpayne5
~56.3'?


In what units?


Feet, as indicated by the apostrophe (lazy man's prime).
smile.gif
 
Originally Posted By: MolaKule
Originally Posted By: cpayne5
~56.3'?


In what units?

Originally Posted By: A_Harmon
4300 rev/min x 2*pi radians/rev x 1 min/60 sec x 1.5 in x 1 ft/12 in = 56.28 ft/sec, or about 38 mph.


So any one tooth will travel how many feet in one second?


Originally Posted By: JiminPA
675.0372/12 = 56.2531 feet per second


So any one tooth will travel how many feet in one second?


Answer 56.28 Feet per second
 
Originally Posted By: cpayne5
Originally Posted By: MolaKule
Originally Posted By: cpayne5
~56.3'?


In what units?


Feet, as indicated by the apostrophe (lazy man's prime).
smile.gif



Sorry, didn't see the apostrophe, but yes you and Mr. Harmon and Jim were all correct, just trying to get everyone to answer the question of "how many feet of travel in 1 second?"

Any one tooth or chain link will travel 56.25 feet in any 1 second if the chain's linear velocity is 56.25 ft./sec.
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What's the trick here? Are you going to nitpick about how tall the teeth are, which would change the tangential velocity.
How long is the bar? What is the radius of the drive sprocket?

Am I biting on your hook?
 
(2*pi*1.5)x(4300/60)

first part is circumference
second is revolutions per second

full revolutions x circumference = inches traveled per second
divide by 12 to get feet
 
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Originally Posted By: jhellwig


Edit 3 I didn't do it right at all. 3377 ft per second.


3,300 feet per second is way faster than the speed of sound

that's high velocity rifle bullet speed
 
Originally Posted By: A_Harman
What's the trick here? Are you going to nitpick about how tall the teeth are, which would change the tangential velocity.
How long is the bar? What is the radius of the drive sprocket?

Am I biting on your hook?


No trick just simple calcs and units conversions to get to: How far will anyone tooth travel in one second?

Sprocket radius was given as R = 1.5" and I stated that the tooth velocity (for all practical purposes) is approximately equal to the tangential velocity of the sprocket.

Bar length is immaterial.

The linear velocity of the chain, which carries the teeth and links, is the key.
 
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A_Harmon and JimPghPA showed the correct calculations so we're going to give each a set of virtual BITOG Piston Cup Cufflinks.
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Mr cpayne5 will receive a virtual BITOG coffee stirrer.
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