# Rolling Resistance - proportional to speed?

• Kuklish
In summary, a group of people are discussing how to calculate the torque requirements for a high-speed robotic camera dolly being built in LA. They are trying to understand how to factor in the rolling resistance of the wheels into the basic equation for torque. There is some confusion about whether rolling resistance is proportional to speed or a constant force. They are using a formula that includes acceleration, gravity, incline, mass, and radius of the drive wheel. They also discuss the type of wheels being used and their coefficients of rolling friction. One person suggests using equations for power instead of torque and another suggests using a function of radius for the coefficient of rolling resistance. In the end, they are still unsure about the correct equation to use and how to factor
Kuklish
Hi all you physics people... we are building a high-speed 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:
T= torque at the drivewheel
a=desired acceleration
g=acceleration of gravity
θ= incline of ramp
m=mass of vehicle

Many thanks to you all!

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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.

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 I-beam.

There are also side and bottom mounted guide wheels.

I found a http://www.csemag.com/single-article/calculating-proper-rolling-resistance-a-safer-move-for-material-handling/82fa156f91ea516c6b08be3bc595db65.htmlthat 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)​

Where:
F=the force required to overcome the rolling friction
f=the coefficient of rolling friction (units must match same units as r
r=radius of the wheels with friction​

I then saw another source that said rolling resistance is proportional to speed so I modified the equation to be:

T= (f*w/r) * (s/3) * R​

Where:
T= torque at the drivewheel (just from the rr of course)
s=speed of vehicle in mph

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.

Kuklish said:
I then saw another source ... that said rolling resistance is proportional to speed
I looked at that source. Those equations are for power:

equation 6.2:

Pdrag = ρ A cd v3 / 2

equation 6.3:

Prolling = cr m g v

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​

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?

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From this wiki article:

Rolling_resistance_coefficient.htm

equation for force, Crr is coefficient of rolling resistance, which has no units.

F = Crr m g

equation for torque (R is radius of wheel)

T = F R = Crr m g R

Crr could be defined as a function of radius. Your first source includes a table that defines Crf to represent the table values and an equation where Crf is defined in unit of inches (so radius would need to be defined in inches), to end up with the wiki style equations:

F = (Crf / R) m g
T = F R = (Crf/R) m g R = Crf m g

or you could define Crr as a function of radius, using units of inches for radius from that table:

Crr = Crf / R
F = Crr m g
T = F R = Crr m g R

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 = (Crf/R) m g R​

T = F R = (Crf/r) m g R​

Where:
r=radius of extra wheel that is contributing to the rolling resistance force​

That way I can play with the diameter of these extra wheels till the overall torque is within acceptable limits.

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... http://www.csemag.com/single-article/calculating-proper-rolling-resistance-a-safer-move-for-material-handling/82fa156f91ea516c6b08be3bc595db65.html expresses it in "inches@3mph"?

Kuklish said:
Lastly, I am confused why, if the coefficient is a dimensionless number... the first article I referenced[/URL] expresses it in "inches@3mph"?
The wiki article uses a dimensionless coefficient for rolling resistance, where the effect of the radius of a wheel is already taken into account. The first article you referenced has a table of coefficients based on the materials, but where the radius is not already taken into account. The coefficients in that table are stated in units of inches, and need to be divided by the radius of a wheel, also in units of inches, to end up with the dimensionless coefficient that the wiki article uses.

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.

## 1. What is rolling resistance?

Rolling resistance is the force that opposes the motion of a rolling object, such as a wheel or tire, on a surface. It is caused by the deformation of the object and the friction between the object and the surface.

## 2. How does rolling resistance affect speed?

Rolling resistance is directly proportional to speed, meaning that as the speed of a rolling object increases, the force of rolling resistance also increases. This means that a higher speed will require more energy to overcome the force of rolling resistance.

## 3. What factors affect rolling resistance?

Several factors can affect rolling resistance, including the type of surface the object is rolling on, the weight of the object, and the design and materials of the object's wheels or tires. The inflation pressure of the tires also plays a significant role in determining the level of rolling resistance.

## 4. How can rolling resistance be reduced?

There are a few ways to reduce rolling resistance, such as using tires with low rolling resistance, maintaining proper tire inflation pressure, and using smoother and flatter surfaces for rolling objects. Additionally, reducing the weight of the object can also help decrease rolling resistance.

## 5. Why is understanding rolling resistance important?

Understanding rolling resistance is essential because it can impact the performance and efficiency of various machines and vehicles that rely on rolling motion. For example, reducing rolling resistance in cars can improve fuel efficiency, while minimizing rolling resistance in industrial equipment can increase productivity and reduce energy consumption.

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