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Rolling Resistance  proportional to speed? 
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#1
Feb213, 10:20 PM

P: 5

Hi all you physics people.... we are building a highspeed robotic camera dolly here in LA for a film, and are trying to make sure we calculate our torque requirements correctly.
The maximum torque required to propel a wheeled vehicle up an incline at a given acceleration is fairly easy to understand. But how in the heck do you figure the rolling resistance of the wheels into that basic equation? I do know the basic equations to calculate the rolling resistance force, based on a coefficient at 3 mph... but does this stay the same no matter what the speed? I've read conflicting accounts that the rolling resistance force is linearly proportional to speed... but then have also heard and seen in numerous bicycle charts, that it is a relative constant??? It makes a HUGE difference if is linearly proportional, and we will need huge motors. Really need to figure this out as we have a lot of wheels on the dolly that are guide wheels and drive wheels that do not support the load, but are spring loaded with lots of force. We are using this formula for our basic torque calculation : T = ( a + g (sinθ) ) × m × R Where: Many thanks to you all! 


#2
Feb313, 01:16 AM

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P: 7,049

It's possible that what you've read about rolling resistance is related to power. If rolling resistance remains about the same regardless of speed, then the required force or torque remains about the same, but the required power will increase linearly with speed.
What type of wheels are being used? Rubber tires will have more rolling resistance than metal wheels. To avoid issues at very slow speeds (you mentioned 3 mph), metal wheels may be a better choice, but you'll need a very smooth track and very smooth wheels. 


#3
Feb313, 01:47 AM

P: 5

The top wheels are polyurethane Rollerblade style wheels 52mm in diameter. There are 16 of them riding on an aluminum beam. Soft wheels like this are industry standard for us as the provide smooth, vibration free, and above all, quiet, dolly travel.
The drive wheels are 4.5" diameter also with polyurethane treads of around 78 durometer. They do not take the load of the dolly, but are mounted perpendicularly and are spring loaded into the web of the Ibeam. There are also side and bottom mounted guide wheels. I found a source that listed the coefficient of rolling friction for this durometer of poly wheels on a steel surface at .030 (inches at 3mph.) Along with the equation: F = (f*w/r) I then saw another source that said rolling resistance is proportional to speed so I modified the equation to be:Where: T= (f*w/r) * (s/3) * R I sincerely hope this last equation is incorrect, because it seems astronomically high, and like I said, I also saw other sources that show the rolling resistance force as constant.Where: 


#4
Feb313, 02:20 AM

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P: 7,049

Rolling Resistance  proportional to speed?
equation 6.2: P_{drag} = ρ A c_{d} v^{3} / 2 equation 6.3: P_{rolling} = c_{r} m g v 


#5
Feb313, 03:55 AM

P: 5

I'm not too clear on what solving for Power is, or if I even need to, but its seems then this would be a good thing then... meaning my last equation was incorrect for figuring torque? I should leave it as a constant force?
So I would just use this: T= (f*w/r) * R Instead of this: T= (f*w/r) * (s/3) * R And simply add this torque to the torque number I already got from calculating the mass going up the incline? 


#6
Feb313, 08:00 AM

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From this wiki article:
Rolling_resistance_coefficient.htm equation for force, C_{rr} is coefficient of rolling resistance, which has no units. F = C_{rr} m g equation for torque (R is radius of wheel) T = F R = C_{rr} m g R C_{rr} could be defined as a function of radius. Your first source includes a table that defines C_{rf} to represent the table values and an equation where C_{rf} is defined in unit of inches (so radius would need to be defined in inches), to end up with the wiki style equations: F = (C_{rf} / R) m g T = F R = (C_{rf}/R) m g R = C_{rf} m g or you could define C_{rr} as a function of radius, using units of inches for radius from that table: C_{rr} = C_{rf} / R F = C_{rr} m g T = F R = C_{rr} m g R 


#7
Feb313, 06:36 PM

P: 5

Thanks for your replies,
I have two radii to be concerned with. One is the radius of the drivewheel (R) that i am trying to determine the overall torque on. The other is the radius of any additional wheel (r) that I am trying to determine the rolling resistance of. So I can be very clear... should your equation T = F R = (C_{rf}/R) m g R actually read... T = F R = (C_{rf}/r) m g R That way I can play with the diameter of these extra wheels till the overall torque is within acceptable limits.Where:R=radius of the drive wheel I didn't see anything in the wiki article about speed, so I guess I just leave it constant force no matter what the speed. Lastly, I am confused why, if the coefficient is a dimensionless number... the first article I referenced expresses it in "inches@3mph"? 


#8
Feb313, 10:48 PM

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#9
Feb313, 10:51 PM

P: 5

Man... you guys are awesome.... Huge thanks RC Glider for all your help. I will try to post a pic here at some point for you to see... its a pretty cool looking rig.



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