One for the math Guru's, show me your stuff!

[Marc Lublin]

One for the math Guru\'s, show me your stuff!

I'm trying to determine what size belt I will need if I change the diameter of my crank pulley. I'm sure it must be a simple calculation, but I never studied!

Here's the deal:
Currently I'm using a 7.25" diameter crank pulley and a 2.75" SC pulley. Not sure about the length of my belt right now, but lets say it is 50"

I want to change the crank pulley diameter to 8.00" and leave the SC pulley as it is.
What change in length would the belt need to be?

Thanks in advance!

 

[Tom F&L GoR]

Re: One for the math Guru\'s, show me your stuff!

You need to know the angle of wrap (the arc length) to find the new belt length.

If it's 50%, then the change in wrap is the change in 1/2 of the circumference from a 7.25 to 8" pulley. Circumference = pi* dia, or 3.14159*7.25 vs. 3.14159*8.

22.78" vs. 25.13, or 2.35 larger circumference; wrap is 1.17" longer. I think it should be as simple as this.

This assumes the angle change as the belt approaches the pulley creates a negligible change in belt length.

 

[AviP]

Re: One for the math Guru\'s, show me your stuff!

Assuming the belt only engages about half (50%) the circumference of a pulley, the answer would :

= (percentage of pulley circumference engaged to belt) *
(new circumference - old circumference)
= 50% * ((pi * new diameter) - (pi * old diameter))
= .50 * ((3.14 * 8) - (3.14 * 7.25))
= 1.18"

This would be the additional length needed on the belt. You should visually check out the percentage of the existing pulley being engaged to arrive at a correct answer. This equation does not take into account the percentage of pulley being engaged by the new pulley but it should not matter. Note that existing belt length is not used in the calculation. I'm not sure if 1.18" is within the limits of the pulley tensioner.

 

[Jim Baughman]

Re: One for the math Guru\'s, show me your stuff!

Take the easy way out...use an on-line calculator. Here is one I found:

http://www.csgnetwork.com/pulleybeltcalc.html

 

[AviP]

Re: One for the math Guru\'s, show me your stuff!

You need to know the angle of wrap (the arc length) to find the new belt length.

If it's 50%, then the change in wrap is the change in 1/2 of the circumference from a 7.25 to 8" pulley. Circumference = pi* dia, or 3.14159*7.25 vs. 3.14159*8.

22.78" vs. 25.13, or 2.35 larger circumference; wrap is 1.17" longer. I think it should be as simple as this.

This assumes the angle change as the belt approaches the pulley creates a negligible change in belt length.

Damn it nerd, you beat me to it.

 

[98viperGTS]

Re: One for the math Guru\'s, show me your stuff!

I know understand everything and its telling me to get my Taco out of the oven.

WHAT?

 

[IEATVETS]

Re: One for the math Guru\'s, show me your stuff!

Speak english please!!

 

[AviP]

Re: One for the math Guru\'s, show me your stuff!

I know understand everything and its telling me to get my Taco out of the oven.

WHAT?

I'm sure that must be a typo. You must mean PI not Taco.

 

[Marc Lublin]

Re: One for the math Guru\'s, show me your stuff!

Thanks for the responses guys, I knew I should have studied in college. Tom and Avi, does the calculator that Jim posted work for you. If it's correct, it seems like a no brainer!

 

[Jim Baughman]

Re: One for the math Guru\'s, show me your stuff!

The problem I see with the assumption that more than 1/2 of the larger pulley is wrapped with the belt. Run the calculator & you will get a slightly larger increase. Going to the larger pulley also increases the % of circumference the belt is in contact with.

 

[Marc Lublin]

Re: One for the math Guru\'s, show me your stuff!

I guess the best way to test the calculator is to check it against what I have in the car right now and see if it's accurate. If so, I'm sure it will be accurate for the larger pulley. I will let you all know.

 

[Qualitywires.com]

Re: One for the math Guru\'s, show me your stuff!

I use some string and measure it...works for me...but I do that since I am no math guy.

 

[AviP]

Re: One for the math Guru\'s, show me your stuff!

Thanks for the responses guys, I knew I should have studied in college. Tom and Avi, does the calculator that Jim posted work for you. If it's correct, it seems like a no brainer!

The calculator assumes only 2 pulleys and does not allow me to set the "Minimum Belt Wrap Angle". So it returns a higher number and is useless. But our serpentine belt goes over more than 2 pulleys. As Tom and I suggested, all you need to figure out is the approx percentage of the circumference of the crank pulley currently in contact with the belt. You don't have to be spot on since I think the tensioner can absorb some of the play. Put in that percentage as a decimal in either Tom or my formula.

 

[joe117]

Re: One for the math Guru\'s, show me your stuff!

"I use some string and measure it...works for me..."

High level math, string theory.

 

[Marc Lublin]

Re: One for the math Guru\'s, show me your stuff!

I would use a piece of string, but I don't have the new pulley in yet. I wanted to have a belt here when I installed the new pulley. As it is, there is going to have to be a little fabrication to get this size crank pulley to fit. Anyway, the calculator can't be spot on, since I didn't realize until I looked under the hood that the tensioner pulley is not only tensioning, but also acting to redirect the belt, so it's considerably longer than the calculator would show if I measured the distance between pulleys. However, knowing the belts size, I can plug the numbers in backwards and get a pretty close estimate of what the new belt size should be. I think I will just purchase one a little shorter that I think I need, calculated size and longer and I should be OK.