How to calculate how fast something fires off your belt

Chiro75

Chiro75

Joined
Feb 4, 1999
Messages
5,786
I'm not 100% this is correct, but the numbers seemed about right for me. I'm not much of a math genius. Anyway, I was curious how fast something that gets grabbed by a belt is moving, and I found this calculation for converting RPM into MPH. The formula is 60x(rpm of your machine)x(diameter of your wheel)x pi/5280x12 = MPH.

So, when that belt grabbed my knife and stuck it in the concrete floor, according to this calculation it was moving around 104.12 MPH:

60 x 3500RPM (motor speed) x 10 (inche wheel) x pi= 6597344.6
5280x12= 63360

6597344.6/63360=104.12 MPH.

Sound about right?
 
Thats only right if you have a 1-1 ratio on pulleys. The rpms have to be the speed of the drive wheel, not the motor.
For it to have been moving 104 miles an hour your belt speed would be 9152 fpm :eek: Thats about 3 times the recommended speed!

Otherwise the math is correct.

Pi X wheel diameter =circumference or the distance traveled per revolution. (dividing by 12 gives you feet rather than inches)
So you have 10Pi/12 = 2.62 ft/revolution

Multiply that by rpms of the contact wheel itself to get ft/minute

Multiply ft/minute by 60 to get ft/hour

Divide ft/hour by 5280 ft/mile and you get miles/hour

For the coote with a 10" wheel, and step pulleys from Norm you ought to have these speeds with a 3450 rpm motor.

1-5/16" ( 4" ( 1131 rpm 2940 fpm
min.
2-9/16" ( on motor 5" ( on grinder 1766 " 4592 fpm
"
3-3/8" ( 6" ( 1939 " 5041 fpm

So on your highest speed you'd be doing around 57 mph. Still movin damn fast :eek:
 
I use step pulleys, so that's the speed of the fastest arrangement. According to Rob Frink's website, a 1725RPM motor with the fastest step pulley setup will run the belt at 3500RPM. That makes the equation okay, no?
 
Who did you buy your pulleys from?
If you bought them from Norm, those I posted are the numbers I got from him.
Rob's machine runs the belt off a smaller wheel, as oppposed to the contact wheel. So he can run his drive wheel at a higher rpm and have a lower belt speed. If you ran the 10 inch wheel at 3500 rpm you would have a belt speed of 9162 fpm......which is ridiculously fast.
 
Plus you need to take into account the dynamics of the situtaion. The amount of time that the belt is in contact with the knife when it grabs it is not enough time to overcome inertia and get the blade upto the same speed of the belt.

One thing for sure is that they are going fast enough to hurt you. Now just wait until the belt lets go and slaps you at 100+ MPH. :eek:

The fastest I ever run anymore is about 1500 SFPM with a 60 grit belt.
 
I would think Rob's info was for the smallest step would run the belt at 3500 SFPM not 3500 RPM.
 
steve
spending more time making and not figuring, works out to be one more knife faster then the alternative. :confused: :D
 
Dan, it was one of those "I wonder..." things. Now I know my math is all messed up (figures), plus I didn't account for acceleration of gravity over the 3.5 feet the blade traveled before hitting the floor! :D Oh well. A valiant effort. I'm trying to find things to occupy my time becuase I have three sheaths to make (boring, tedious work for me) and my finger and knuckles are still a little ouchy, so I don't want to hit the grinder again just yet.
 
Along the lines of what Sean said above, you have to figure in the coefficient of friction between the belt and the blade and how much of that is translated into kinetic energy as velocity of the blade in the direction of the belt. I think your formula considered it to be 1, which would be way too high.

Anyway Dan is right.
 
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Dan, I'm a super cheater. I have a Mac with about 7 trillion fonts on it. TOns of what they call "dingbats" which are fonts that are little pictures. I use Adobe Illustrator, which I can blow a font up to any size without losing any quality, and it makes the little font pictures bit. Then I use a font that looks like handwriting for the cartoon/comic book lettering. So, it's really easy, but fun. And for someone who has creative ideas but no artistic talent like me, it's great! I have some really funny sexual position fonts if you want to jump over to the Cove to have a look! :D
 
Personally, that's one of those calculations that one would hope they never have to figure out :)

If 60 mph is 88fps ...then at 60mph the blade would travel the 3 ft to the ground in approx 0.034090909 seconds, which means you could repeat that roughly 29.3 times per second ...which seems awful fast to me.

I'd say something like 20mph is more probable ....29.3fps, which is 0.102272727 seconds, or roughly 9.7 repeat performances per second. Seems more feasible.

Just a guesstimate, but probably not far off.

I suppose the way to really tell is to calculate the energy at impact for different speeds, then recreate the damage said energy would cause at different speeds, then gauge the damage caused at different speeds to the damage actually caused in the incident. That'd be the only way to know for sure.
 
I think time travel is already involved!

The blade LEAVES your hand and TRAVELS across the shop ...INSTANTLY! :eek:
 
also it depends on if it was spinning end for end or rotating and how many times
per min. per foot x by KE , did you have a fan on at the time?
you'll have to figure the velocity of it too, what the direction it was pointed in. and what the humidity was at the time,,
thick air will slow it down too you know :D I think it was going about
20.9229 miles per hour. if pointed to the south 95% of the time
or 1.2 boot knives.. :D
 
lso it depends on if it was spinning end for end or rotating and how many times
Click to expand...
It fired straight like a bullet, although the skin on my pinky that it dragged off as it slid between the belt and the workrest certainly would've slowed it down a bit.

I didn't have a fan on, but there's a good chance the heat may have kicked on as the knife was flying through the air, and the earth is also rotating pretty fast throughout this whole process...:D
 
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