Chain Saw Math

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Philbert

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I was trying to figure out how to explain why it is so important to take care of chains
for a training session, and did some simple calculations (no scary math) below.
Please let me know if these are correct, if they make sense, and if they might be helpful.

Thanks.

Philbert



Assume:

- chainsaw motor turning at 12,000 RPM
- 3/8 inch (0.375) pitch, full comp/standard chain
- 18” bar with 70 drive links
- 7 tooth sprocket

1) How fast is the motor really turning?

- 12,000 revolutions per minute / 60 seconds per minute = 200 revolutions per second!
The piston travels up 200 times and down 200 times in the time it takes to say “One Husqvarna, . . .”,


2) How fast is the chain actually moving?

- 7 tooth sprocket will move 7 drive links of chain past a given spot per rotation
- 12,000 RPM x 7 drive links = 84,000 drive links per minute of chain movement
- .375 chain has drive links spaced 3 rivets apart (.375 + .375) or every 0.75 inches
- 84,000 drive links per minute X .75 inches per drive link = 63,000 inches per minute
- 63,000 inches per minute X 60 minutes per hour = 3,780,000 inches per hour
- 3,780,000 inches per hour / 12 inches per foot = 315,000 feet per hour
- 315,000 feet per hour / 5,280 feet per mile = 59.6590909 miles per hour
Almost 60 miles per hour!

Note that .325 pitch chain would only be traveling at 51.7 MPH. Traveling slower,
and taking smaller bites, but taking more of those slower,
smaller bites because of the closer spaced cutters.


3) So what if my chain touches a rock (dirt, embedded metal, etc.) but only for a split-second?

- From #1, the chain saw sprocket rotates 200 times per second.
- Each 7 tooth sprocket rotation moves 7 drive links of chain.
- A 70 drive link loop of chain will make a complete pass around the bar every 70 / 7 = 10 revolutions of the sprocket.
- 200 / 10 = 20 times per second that each drive link (or cutter) will pass any specific point on the bar.
if your chain touches a rock for just one second, every tooth on that loop will have hit the rock 20 times.
If the chain touches the rock for only a split second, each tooth might only have hit the rock 10 times.

(Note: I corrected an error in my original post - it doesn't matter what type of chain it is, since the entire loop will pass around the bar 20 times per second, each tooth will as well, despite whether it is full comp, skip-tooth, etc. Only the number of teeth per second would change. - Philbert)
 
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Philbert,

You remember your mom telling you to do your math studies because you would need it one day? You remember ignoring her advice and making 2 cycle noises with your mouth and then drawing cars, trucks and chainsaws on your paper?

Let the haunting begin,

ole joat
 
I was trying to figure out how to explain why it is so important to take care of chains
for a training session, and did some simple calculations (no scary math) below.
Please let me know if these are correct, if they make sense, and if they might be helpful.

Thanks.

Philbert



Assume:

- chainsaw motor turning at 12,000 RPM
- 3/8 inch (0.375) pitch, full comp/standard chain
- 18” bar with 70 drive links
- 7 tooth sprocket

1) How fast is the motor really turning?

- 12,000 revolutions per minute / 60 seconds per minute = 200 revolutions per second!
The piston travels up 200 times and down 200 times in the time it takes to say “One Husqvarna, . . .”,


2) How fast is the chain actually moving?

- 7 tooth sprocket will move 7 drive links of chain past a given spot per rotation
- 12,000 RPM x 7 drive links = 84,000 drive links per minute of chain movement
- .375 chain has drive links spaced 3 rivets apart (.375 + .375) or every 0.75 inches
- 84,000 drive links per minute X .75 inches per drive link = 63,000 inches per minute
- 63,000 inches per minute X 60 minutes per hour = 3,780,000 inches per hour
- 3,780,000 inches per hour / 12 inches per foot = 315,000 feet per hour
- 315,000 feet per hour / 5,280 feet per mile = 59.6590909 miles per hour
Almost 60 miles per hour!

Note that .325 pitch chain would only be traveling at 51.7 MPH. Traveling slower,
and taking smaller bites, but taking more of those slower,
smaller bites because of the closer spaced cutters.


3) So what if my chain touches a rock (dirt, embedded metal, etc.) but only for a split-second?

- From #1, the chain saw sprocket rotates 200 times per second.
- Each 7 tooth sprocket rotation moves 7 drive links of chain.
- A 70 drive loop of chain will make a complete pass around the bar every 70 / 7 = 10 revolutions of the sprocket.
- 200 / 10 = 20 times per second that each drive link will pass any specific point on the bar.
- Since standard chain has approximately one cutter for every 2 drive links, this means that
if your chain touches a rock for just one second, every tooth on that loop will have hit the rock 10 times.
If the chain touches the rock for only a split second, each tooth might only have hit the rock 5 times.

Interesting.

The numbers on hitting a rock might open someone's eyes when I talk about how fast an obstruction can dull a chain. I will have to keep those numbers in mind.

:cheers:
 
I was trying to figure out how to explain why it is so important to take care of chains
for a training session, and did some simple calculations (no scary math) below.
Phil,

Good post. I had just mentioned about some of this a couple days ago, when a chain was run into the dirt in a video, in this post.
 
excellent thread! Thanks for the eye opener Philbert!

Now where were my chaps!

7
 
Now try a Hotsaw, with a 14 pin sprocket, running .404 chain, and turning 12K:cheers:

Easy to substitute:

2) How fast is the chain actually moving?

- 12,000 RPM x 14 drive links = 168,000 drive links per minute of chain movement
- .404 chain has drive links spaced 3 rivets apart (.404 + .404) or every 0.808 inches
- 168,000 drive links per minute X .808 inches per drive link = 135,744 inches per minute
- 135,744 inches per minute X 60 minutes per hour = 8,144,640 inches per hour
- 8,144,640 inches per hour / 12 inches per foot = 678,720 feet per hour
- 678720 feet per hour / 5,280 feet per mile = 128.5 miles per hour

Or, simply divide and multiply:

(59.6590909/7) X 14, then divide by 0.75 and multiply by .808 = 128.545454 MPH

Philbert
 
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