Talk:Rolling resistance

Consistency between text and figures
The definition of the "rolling resistance coefficient" refers to some "Figure 1", in which "F is the rolling resistance force". But in the Figure 1 (http://en.wikipedia.org/wiki/File:Rolling_Resistance_2.png) F is "some towing force applied to the axle". It is no clear if it is some force pulling the wheel that compensates the effect of the rolling resistance, of it is the force that provokes the wheel to loss energy and eventually stop. — Preceding unsigned comment added by 186.135.53.190 (talk) 00:44, 11 October 2014 (UTC)

Additions

 * I don't that thats right either, the smoother a surface, the lower the rolling resistance. Think about the difference between riding a bike on smooth concrete vs rough asphalt - or even riding a bike on a bed mattress. The bed mattress would have the highest rolling resistance because its "squishy". Fresheneesz 20:17, 27 May 2006 (UTC)


 * ...Right, the mattress has a high rolling resistance because it's squishy, not because its surface is rough. It doesn't matter how smooth it is for rolling resistance. Even if you put the smoothest silk sheets on that mattress, it would still be hard to ride your bike on it, because most of your energy goes into compressing the mattress and heating it up. —Keenan Pepper 21:07, 27 May 2006 (UTC)

g vs normal force
I'm going to change "g" in that equation to $$ F_N $$ for normal force. I think that would be more general. Fresheneesz 20:17, 27 May 2006 (UTC)

Shouldn't there be slope or angle mentioned in the formulas? Friction[kinetic] = u[k] * N = u[k] m g cos(theta) and Energy = u[k] m g d cos(theta) I thought. Victor (talk) 07:08, 17 August 2010 (UTC)[User:Victory2006]

Temperature
That external link at the bottom is very interesting, is Crr's relationship with temperature not well documented? This would be something that should be on this page. Fresheneesz 23:05, 27 May 2006 (UTC)

It is well documented. see for example SAE paper 800090. Reading off the graph .025 at -20 deg C, .012 at 30 deg c, .009 at 80 deg C Greglocock 22:44, 23 September 2006 (UTC)

Definition of 'slip'
The term 'slip', referred to road vehicles, is equivalent to 'creep' of railway wheels (see adhesion railway), it appears that automotive engineers don't talk to railway engineers.

It is a misnomer because the region of contact is not subjected to actual sliding, but elastic distortion, the figure of 11% is indicative of the condition where the tyre forces arising from the shear stress in the region of contact are sufficient for gross slippage to occur. Wheel forces arise from the elastic distortion of both the wheel and supporting surface at the region of contact.

This cyclic distortion results in energy loss, particularly in materials which have high internal friction such as rubber, so rubber tyres on asphalt have higher rolling loss than iron tyres on steel rails, because the internal losses are higher, and a much larger volume of material is affected by the distortion.

There is some partial slippage at the edges of the region of contact, which adds further to the losses, but the region is effectively stationary, so that adhesion is governed by static friction, which is usually greater than sliding friction.

I think what is meant in the article is the fundamental kinematic property of the wheel to transfer the motion of the vehicle relative to the surface from the region of contact to the hub, where greater control of the friction loss is achievable, hence roller bearings and lubrication.

Despite its superficial simplicity, the humble wheel is quite a sophisticated machine when studied to any depth. Gordon Vigurs 10:46, 4 June 2006 (UTC)

Table of Rolling Friction Coefficients
This table does not cite an original source. If it is known where the values originated, please cite.

I was able to get a copy of the source for the passenger rail car coefficient, written by Astakhov. I'm entirely new to Wikipedia but I've uploaded it to the Wikipedia commons and allowing someone much more familiar with Wiki standards to include it in the references section. https://commons.wikimedia.org/wiki/File:Pages_from_397774.pdf — Preceding unsigned comment added by Ironchief (talk • contribs) 14:47, 21 November 2017 (UTC)

Rolling resistance independent of speed?
From the formula given it seems that the rolling resistance is independent of the speed of the rolling object. Is that correct?--129.70.14.127 12:07, 11 May 2007 (UTC)Quixy

Yes, pretty much. At very high speeds things get more complicated, but to within the normal sort of testing accuracy it doesn't change significantly with vehicle speed. That is, in a fuel economy model they don't normally have a speed sensitive contribution to rolling resistance. Anything small would be masked by the aerodynamic drag from the wheel, which is quite significant above 80 mph. Greglocock 07:25, 12 May 2007 (UTC)

Note that it's the rolling resistance FORCE that's independent of speed. The energy used is the force times the distance moved, and that's also independent of speed. If you go faster, though, you're moving more distance in a given time, and you need more energy in a given time, and energy per unit time is power. So you do need a bigger engine as you go faster... but it doesn't run as long. —Preceding unsigned comment added by 123.2.171.243 (talk) 09:19, 20 April 2009 (UTC)

'If you go faster, though, you're moving more distance in a given time, and you need more energy in a given time, and energy per unit time is power. So you do need a bigger engine as you go faster... but it doesn't run as long. '''

Thats not necessarily true, of you modify the gear ratio (if the application is geared) you can achieve a higher speed with the same or less energy. — Preceding unsigned comment added by 209.127.10.18 (talk) 01:41, 2 October 2011 (UTC)

- Rolling resistance of rubber tyres is speed dependent! Tyre is polymer, every polymer has creep behavior. Therefore young modulus of polymer depends on bending frequency! — Preceding unsigned comment added by 188.120.195.255 (talk) 21:48, 11 February 2015 (UTC)

Rename to "Rolling friction"
Shouldn't this article be renamed to "Rolling friction". That s what its called in physics. Also the rename is needed to be consistent with Friction article. Firestonetireguy 17:22, 9 September 2007 (UTC)


 * 'Opoose'Since it is mainly concerned with vehicles, rolling resistance is the usual term. Why not add a redirect if you want to cover both in the same article? Alternatively start a physics based page rather than an engineering one. Greglocock 23:09, 9 September 2007 (UTC)

Totally incorrect statement regarding static vs sliding friction
The person who said kinetic/sliding friction is greater than rolling/static friction is totally wrong. The coefficient of sliding friction is much less than static/rolling friction. That is why good car brakes doesn't skid to a stop when you hit the brakes. Furthermore, sliding is much more efficient on a lubricated surface, hence rocket sleds use sliding sleds, and not wheels. Edited and fixed this portion by adding this:

"Rolling friction/static friction is much greater than sliding friction. The coefficient of rolling/static friction is greater than that of sliding/kinetic friction. Static friction prevents motion. This is why car wheels roll to a stop instead of skidding in order to stop as soon as possible. Also, rocket sleds using sliding sleds instead of wheels since sliding friction is much less. ...However, rolling/static friction does not create heat, since it prevents motion.

"Rolling friction depends on the coefficient of rolling friction between the two materials (µr) and the normal force (N) of the object. The force of kinetic friction depends on the coefficient of kinetic friction between the object and the surface on which it is moving (µk) and the normal force (N) of the object. For any pair of objects, the coefficient of kinetic friction is usually less than the coefficient of static friction." -MSN Encarta"

Edit it if you want to make it more concise.

Intranetusa 05:13, 9 October 2007 (UTC)


 * (Note: moved from top of page to bottom of page, per convention.) Intranetusa, I'm fairly sure you think "static friction" is another term for "rolling friction." They mean very different things. The confusion seems to permeate all of your changes. If you want a more detailed explanation, I can provide it, but I would suggest checking your understanding of the terms with other sources. For anyone else trying to follow this, note that Intranetusa's quotation from MSN Encarta took sentences from different paragraphs and reordered them.


 * Your fundamental dispute seems to be over the sentence that says rolling friction "is much lower than sliding friction...." It may not be the best wording, but the essence of its meaning seems indisputable; as the MSN Encarta source you cited put it, "Wheels and other round objects will roll along the ground much more easily than they will slide along it." Ice skating being an obvious general counter-example.


 * I'm going to revert your recent edits, for reasons above. I will also add a citation for the statement that rolling friction "is much smaller than sliding friction...", since that seems to be a point you're challenging. A quick google search finds hundreds of reliable sources that could be cited. Examples:


 * "Rolling friction is much lower than sliding friction." Bharat Bhushan (2002.) Introduction to Tribology.


 * "Rolling friction is produced by objects such as wheels or ball bearings and is less than sliding friction." NASAexplores 5-8 Lesson: (Teacher Sheets) (Admittedly dumbed down.)


 * "The coefficient, or unit, of rolling friction is equal to the quotient obtained by dividing the entire force of friction by the normal pressure. This coefficient is much less than the coefficient of sliding friction." William Guy Peck (1859.) "Elements of Mechanics: For the Use of Colleges, Academies, and High Schools"


 * "...the average rolling friction utilized by vehicles is generally less than the sliding friction coefficient." Douglas W. Harwood (2003.) "Review of Truck Characteristics as Factors in Roadway Design"


 * "...the magnitude of the resistance due to rolling friction is much less than that of sliding friction." Frank Bell (1998.) "Principles of Mechanics and Biomechanics"


 * "For a given load, rolling friction is significantly less than sliding friction." Robert C. Rosaler (2002.) "Standard Handbook of Plant Engineering"


 * -Agyle 11:24, 9 October 2007 (UTC)

"in braking"
The section "in braking" seems to me a tangent at best, more appropriate for an article on the physics of braking. I think it should be at least moved later in the article if not moved to the brake article (which is rather thin at the moment). Any thoughts?Ccrrccrr (talk) 03:50, 14 December 2007 (UTC)

Rolling resistance value for steel.
What sources do you have for the steel wheel/steel rail values?

I have found specific ranges in between 0.0002 and 0.0005 for c. 30" diameter wheels. That's 2e-4 to 5e-4, mainly from the following two sources:

-Gordon, David W. Bicycling Science. Cambridge, Mass. : MIT Press, c. 2004. (They computed a range of 0.0002-0.0005)

-Williams, John A. Engineering Tribology. New York : Cambridge University Press, 2005. (This one has a value of 0.0004, but doesn't specify a size but it strongly implies a regular-size railroad wheel)

It is my belief that the latter value in the first source, 0.0005, is often rounded to 0.001. Just my two cents, hope it's correct.


 * I finally fixed the problem by "pure rolling resistance". The total rolling resistance is much higher (up to 0.0025).  I'll explain it, when I find time, in the article.  — Preceding unsigned comment added by 66.81.198.151 (talk) 02:54, 8 March 2012 (UTC)

Additionally, how does Fatigue Cracking relate to Rolling Resistance in rail applications? — Preceding unsigned comment added by 209.127.10.18 (talk) 01:27, 2 October 2011 (UTC)

Bicycle tire hopping due to inflation
""Over inflating tires (such a bicycle tires) may not lower the overall rolling resistance as the tire may skip and hop over the road surface. Traction is sacrificed, and overall rolling friction may not be reduced as the wheel rotational speed changes and slippage increases."" Reasonable men might conclude that if a tire is hopping and skipping, those moments would be marked with ZERO rolling resistance (yes, zero traction, as well--but this isn't a safety article now, is it?). —Preceding unsigned comment added by 75.37.224.235 (talk) 16:29, 13 September 2009 (UTC)


 * Yes, momentarily zero rolling resistances, but the energy loss when it hits after a hop could exceed the gain from zero RR during the flight. Maybe some clarification needed, but I don't think there's an error.  --Ccrrccrr (talk) 19:44, 13 September 2009 (UTC)


 * Yup, plus extra energy is pumped into any damping or shock absorbers in the suspension, the energy for which has to come from somewhere. I used to have a nice graph from Michelin showing this for our solar car.Greglocock (talk) 01:47, 14 September 2009 (UTC)

The effect of rough surfaces transferring forward momentum to vertical momentum - which gives rise to vibrations that are eventually dissipated in various ways - may not be the same as 'rolling friction', but it is part of what is considered 'rolling resistance'. One reference I could find about this on the internet is this: http://janheine.wordpress.com/2010/10/18/science-and-bicycles-1-tires-and-pressure/, which is written by an author of an article in Bicycle Quarterly, I have not seen that article directly but it should contain the numbers as well. It is also generally considered the cause for the lower rolling resistance of mountain bike tires with lower inflation pressures on rough surfaces, which is mentioned in the Schwalbe article already referenced in the wiki, but much more clear in the full report that appeared in the German Mountainbike magazine and of which an English translation can be found here http://www.mtbonline.co.za/downloads/Rolling_Resistance_Eng_illustrated.pdf. This report also provides strong evidence for the claim that wider tires have lower rolling resistance. — Preceding unsigned comment added by 145.94.178.86 (talk) 14:31, 19 June 2014 (UTC)

Pneumatic tires, effect of diameter
How do you know this ins't due to better aero rather than Crr? Greglocock (talk) 01:43, 12 January 2012 (UTC)


 * I agree that the overall result in the races have been in part due to using wheels with better aero properties and reduced energy stored within the wheels in the form of rotational energy. However, prior to bringing the wheels to the track, I developed a test method and ran fairly exhaustive tests for rolling resistance on a series of wheels that had similar characteristics (tire materials, tire geometry,smooth tread) but differing diameters ( 7 inches) .  The tests are repeatable and have been the core of our success in the race.  Our wheel and tire development path led to circumstances where the same tire design and material could be tested at different diameters.  These tests were conducted in a manner that allowed aero effects to be removed from the results.  I did eventually find a diameter below which rolling resistance increased markedly for a particular load and surface.  However, for the rest of the diameters tested, rolling resistance was not a function of diameter.  While diameter was not a factor, tire geometry and tire  material properties have a significant role in determining the rolling resistance for a given load on a given surface.  This aligns with much of the discussion on pneumatic tire sidewall deflection and skinny bike tires not really having the lowest rolling resistance.  -Mark c estes (talk) 01:12, 4 April 2012 (UTC)


 * We'd love to see where these results are published. -AndrewDressel (talk) 12:44, 4 April 2012 (UTC)


 * These results are not published as the method and detailed findings are central to our current success in the race. Given that these are offered as a counter to an unsubstanciated statement, that will have to suffice. I would not freak if you deleted them as they are not well referenced. -Mark c estes (talk) 04:34, 5 April 2012 (UTC)


 * There have been a lot of changes lately, and I should check it against my references. -AndrewDressel (talk) 15:23, 5 April 2012 (UTC)


 * Where would a layman publish such results?  Mark c estes (talk) 04:34, 5 April 2012 (UTC)


 * Lennard Zinn wrote about rolling resistance in VeloNews on Oct. 11, 2010 and discussed tires again on Mar. 27, 2012. He may be interested in your results. Bicycle Quarterly has also written about the subject. Otherwise, I know of no restrictions against "laymen" publishing results in journals such as Vehicle System Dynamics, etc. -AndrewDressel (talk) 15:23, 5 April 2012 (UTC)

Moved from deleteed section "Small wheel size?"

The LGV-Est world speed record ini 2007 (the one which achieved 357 mph) was done specifically under special conditions, and one of those conditions was that they used, in fact, larger-diameter wheelsets for the train than usual. —Preceding unsigned comment added by Facial (talk • contribs) 06:57, 2 March 2008 (UTC)

Large drive wheels reduce the rotational speed of all mechanical components, surely a desirable design feature. The consideration of rolling resistance might be nominal as all other train set wheels remained much smaller than the driven wheels. 75.37.224.235 (talk) 16:33, 13 September 2009 (UTC)homebuilding

Being a successful competitor in the ultimate speed challenge soap box derby races mentioned in the article (wins in 2010 and 2011) and having developed a system for evaluating the rolling resistance of such wheels, I can attest from direct experience to the following:

Wheels with solid polymer tires of similar construction and identical tire materials and cross sections were tested at diameters varying from less than 4 to greater than 7 inches. Over a significant part of this range the rolling resistance was not a function of diameter. There is a point where rolling resistance appears to increase with decreasing diameter but for much of that range the rolling resistance was constant with diameter which is counter to the unsupported broad assertion the smaller wheels have higher rolling resistance. Mark c estes (talk) 00:49, 4 April 2012 (UTC) -- Moved from deleted section"Rolling friction depends on the wheel radius!!!": Incorrect statements have been deleted such as support for the discredited "Coulomb's law" or claims that rolling resistance doesn't depend on the wheel radius (which is only approximately true for pneumatic tires on a hard surface over a limited range of radii).

The American equation [Coulomb's law] is obviously not a physically based formula but a nonsense-formula of the type that is so common in the US (just think of SEER, for instance, comparing BTU per hour with watts instead of just giving a non-dimensional efficiency number). The equaiton given by Andrew is obviously invalid outside the US, and thus does not belong in Wikipedia except for US consumption. Also, the article should consider that narrower wheels are more efficient (as anybody having used bikes with different tire widths has noticed). I don't know exactly why, that is why I went here, but it is not explained. I guess it is because a smaller surface of rubber is being deformed per time. Could someone take care of this? —Preceding unsigned comment added by 67.191.4.25 (talk) 01:41, 22 December 2009 (UTC)


 * "the article should consider that narrower wheels are more efficient ", um, no, not always. If you are interested in bike tires I'd have thought a book on bike tires is the place to look. The most efficient solar car tires are quite wide, and have lower Crr than silks. Greglocock (talk) 01:57, 22 December 2009 (UTC)


 * "The equaiton[sic] given by Andrew is obviously invalid outside the US, and thus does not belong in Wikipedia except for US consumption." That is so weird because when I checked my copy of Tyre and Vehicle Dynamics by Hans B. Pacejka, Professor Emeritus at Delft University of Technology, the Netherlands, he states on page 465:
 * Experiments show that rolling the resistance force Fr (pointing backwards) is proportional to the tyre normal load FN.
 * We have: Ff = frFN   (9.230)
 * I wonder why Elsevier, headquartered in Amsterdam, would publish something "obviously invalid outside the US?" It cannot simply be in order to sell in the US market because they also have a US-specific version with the American English spelling of tire in the title. Perhaps international experts in the field find some value in characterizing rolling resistance with a dimensionless coefficient after all. -AndrewDressel (talk) 16:15, 23 December 2009 (UTC)

Note by David Lawyer (May 2012): The debate (much of which I removed) had 2 sides and both were wrong. One side thought that rolling resistance is independent of radius (correct for pneumatic tires on hard pavement) while the other thought is was inversely proportional to the radius. See written by me, which resolves the debate, using literature on the subject that the people in the debate didn't know about.

Issues
In particular, the diagram, the formulae and the statement "The above equations don't include variation of rolling resistance with speed. This is a reasonable simplification but measurements at different speeds show some variation"


 * 1) The force diagram of rolling resistance on a soft surface has the reaction force passing through the axle. This cannot slow the wheel as it exhibits no torque about the axle. -JBel (talk) 00:50, 31 January 2012 (UTC)
 * Since the horizontal driving force and the vertical load, as depicted, also exhibit no torque about the axle, then the wheel may be assumed to be rolling at a constant velocity. In reality, there must be some small friction with the ground which generates a torque to overcome the friction of the bearing, but these usually are much smaller than the other three forces and so neglected in this analysis. -AndrewDressel (talk) 07:17, 31 January 2012 (UTC)
 * So in an article about Rolling Resistance, we have a diagram of a wheel in which there is no rolling resistance? -JBel (talk)
 * Not at all. If there were no rolling resistance in the situation pictured, the reaction force would be vertical, and the wheel would accelerate. -AndrewDressel (talk) 12:35, 31 January 2012 (UTC)
 * OK. I see a bit better now. I had been ignoring the thing marked 'F' because it hasn't been labelled. F is some driving force, and it is being applied at the axle (elsewhere in the article F is the rolling friction) so the wheel is rotating anticlockwise. However, to have any effect on the wheel, there has to be an *external* torque present. You have sort of answered this yourself by saying that if the reaction were vertical, there would be an acceleration... we require it to provide -ve acceleration (which is why a wheel slows on a run down test). It can do this by passing slightly to the left of the axle, so either we can treat R as the total reaction and make it pass to the left of the axle, or we treat R as the normal force, and add in a tangential frictional force at the ground.JBel (talk) —Preceding undated comment added 14:02, 31 January 2012 (UTC).


 * I have added more detail to the caption describing all the labels in the image. -AndrewDressel (talk) 06:57, 1 February 2012 (UTC)
 * It is peculiar that a diagram is provided for the case of a rigid wheel on a deformable surface, but not for a deformable wheel on a rigid surface. Or combine the two? -JBel (talk) 00:50, 31 January 2012 (UTC)
 * You are welcome to create additional or replacement images and add them to the article. -AndrewDressel (talk) 07:17, 31 January 2012 (UTC)


 * 2) The formula and the text indicate that rolling resistance is more or less independent of speed. If this were true, there would be a resistive torque when not moving. Symmetry considerations tell you it must have a value of zero when not moving. I'd say that goes beyond showing "some variation". -JBel (talk) 00:50, 31 January 2012 (UTC)
 * Never-the-less, these are the models of rolling resistance given in the provided sources. If you have sources with a velocity-based model, please feel free to add them to the article. -AndrewDressel (talk) 07:17, 31 January 2012 (UTC)
 * Yes, this is one of the difficulties, not a lot of work is published. The formula Crr=b/r implicitly has a velocity dependence since b (the centre of reaction pressure) varies with velocity and hysteresis, and obviously goes to zero for a static wheel. -JBel (talk)


 * 3) Crr=sqrt(z/d) It needs to be explained that this is valid on a plastic surface. All surfaces deform under a wheel to some extent. If the material is perfectly elastic with no hysteresis, the deformation can't slow the wheel. -JBel (talk) 00:50, 31 January 2012 (UTC)
 * See the second section of the article. It states "the primary cause of rolling resistance is hysteresis." Perhaps since perfectly elastic materials do not exist, they are not mentioned explicitly. -AndrewDressel (talk) 07:17, 31 January 2012 (UTC)
 * But the formula is not true in general...only for a material like sand that doesn't return any energy whatsoever.JBel (talk)
 * Please, if you have access to a relevant source, make the changes necessary. -AndrewDressel (talk) 12:35, 31 January 2012 (UTC)

I plan on removing the following formula (and text): The force of rolling resistance can also be calculated by[1]: F=(Nb)/r where F is the rolling resistance force (shown in figure 1), r is the wheel radius, b is the rolling resistance coefficient or coefficient of rolling friction with dimension of length, and N is the normal force (equal to W, not R, as shown in figure 1). Equating the above two equations, and solving for b, gives b = Crr·r. Therefore, if a source gives rolling resistance coefficient (Crr) as a dimensionless coefficient, it can be converted to b, having units of length, by multiplying Crr by wheel radius r.

The above formula is based on the disgraced "Coulombs law" impling that rolling resistance is inversely proportional to the wheel diameter (in this case the radius r). It's been shown to be wrong (see the section I wrote on diameter). Someone later showed that b = Crr x r which is correct but it's just a tautology. So I plan to delete it all. One of the previous formulas correctly shows it to be inversely proportional to the square root of the radius. 99.135.20.235 (talk) 01:48, 8 March 2012 (UTC)

Use ‰ for specific rolling resistance ?
‰ is something like % only it means parts per thousand. Although it's not on keyboards it's a Unicode symbol and can be copied and pasted. Then one can say that automobile rolling resistance with ordinary tires is about 10‰ while in the 1950's it was 20‰ and that for a loaded rail freight car it's only 1‰. We could show both Crr (as a ratio) and Crr as parts per thousand (‰) in the table, but I would like to avoid using the direct ratio entirely and state that to get the Crr coefficient, one just moves the decimal point of the ‰ by 3 places to the left (multiplies by 0.001). This unit is sometimes called pounds per thousand pounds or kilograms-force per metric ton. 66.81.123.252 (talk) 21:49, 22 March 2012 (UTC)

An alternate proposal would be to use Newtons/tonne (metric ton). But conversion of this back to the coefficient is not so simple since one has to divide by gravity g. — Preceding unsigned comment added by 99.135.20.235 (talk) 02:46, 21 March 2012 (UTC)


 * I completely and utterly oppose this. I understand it, but it is ridiculous. There is nothing wrong with the dimensionless units currently employed, ie 1%=0.01 Greglocock (talk) 03:06, 21 March 2012 (UTC)


 * I can see the argument for it, but Wikipedia is not the place for making such a change. Also, the symbol is too easy to interpret a % in a quick glance.  Ccrrccrr (talk) 11:48, 21 March 2012 (UTC)


 * This symbol ‰ is defined in Wikipedia but I don't know how much it's used in the US. I tried Googling on it but Google (and other search engines will not look for it).  This symbol was used in the Soviet Union (and I think also in Europe) for train resistance (in parts per thousand).  So it wouldn't be anything new to use it if one considers world usage.


 * I've found that parts per thousand is widely used in the literature on rolling resistance. Roberts paper on tires used pounds per thousand pound.  The Russian book on train resistance used kilograms (force) per metric ton (also parts per thousand) and Hersey used 1000f where f is the same as Crr.  To find a common symbol for all these would use ‰.  Using pounds or kg for force can be objected to as not being SI units which are currently used in physics.  But such an objection doesn't apply to ‰ since it's not a unit (it's a dimensionless ratio).  So I still think we should use it here.


 * PS: Greglocock undid an edit I made to the section defining Crr where I defined ‰ but didn't use it. But my original edit to define ‰ also did more than that (which should not be undone).  So after I undid his undo, I deleted all ‰ symbols which I hope should satisfy him.


 * I've always thought about rolling resistance in terms of ‰ (or parts per thousand) while others may have thought about it in terms of Crr. I strongly think using Crr is not good since using larger numbers for specific resistance is a lot easier to comprehend and it's what is used in the majority of articles I've seen about this topic.  If ‰ is not to be used in this article, what is to be used?  Pounds per 1000 pounds?  or kgf per metric ton?  Newtons per metric ton?  I think any of these would be better than Crr. - David Lawyer


 * Crr vs. pounds per 1000 pounds is an apples and oranges comparison. That would be like, on a page about mass, debating whether to talk about m or kg.  Crr and m are variable names.   Pounds per 1000 pounds, % and ‰ are units.  The question is what units should we use for discussion of Crr.  If Crr is 0.7% = 0.007 = 7‰, we could also describe that as 7 pounds per 1000 pounds, but that's silly, because it's also 7 N/kN, 1 millidyne per dyne, etc.  The three options of 0.7% = 0.007 = 7‰ better represent the true dimensionless nature of the quantity.


 * So then we are simply down to the question of 0.7% vs 0.007 vs 7‰. I think 0.7% is sufficiently common that we aren't doing WP:OR by promoting it here, and it avoids the possible confusion with  7‰, and the annoyance of counting decimal places with 0.007.  Is there a problem with that?  Ccrrccrr (talk) 14:40, 24 March 2012 (UTC)


 * The problem with using % is that no one else uses either % or parts per hundred. The most common "unit" used in the literature on the topic is parts per thousand but they don't call it "parts per thousand".  While this is actually ‰, its usually expressed as "pounds per thousand pounds" or kgf/tonne etc.  So if we use parts per thousand, wouldn't it be best to abbreviate this as ‰, since the definition of ‰ is found in Wikipedia.  Also ‰ would be also defined at the start of the article, since most readers wouldn't know what it means.  So I think that using ‰ is the lesser evil of all the other possible solutions.  Wikipedia articles are supposed to represent and international point of view.  So using pounds per thousand pounds would mainly be a US point of view and thus should be rejected.  Using ‰, which is used much more in Europe than the US, represents more of an international point of

view, although most people in the US don't know what it means. 16 April 2012 (UTC) -David Lawyer


 * Another reason for not -using % is that some components of rolling resistance are very small.  For example, under ideal conditions total railroad rolling resistance is only 1‰ so obviously its components are all less than 1‰.  The component representing the loss due to oscillation of the railroad car (including energy absorbed by the suspension such as shock absorbers) might be only 0.05‰ = 0.005% = 0.00005 as a ratio (provided the track is nearly straight with no dips).  Thus using ‱ for one part in 10,000 might be even better than ‰, except that no one else uses this.  But the Russians today use N/tonne which is quite close to ‱ since a tonne force = 9,800 Newtons.  I'm somewhat opposed to using ‱, mainly because no one else uses it for rolling resistance.  -David Lawyer 66.81.29.73 (talk) 17:22, 18 April 2012 (UTC)

I quote from above: "no one else uses either % or parts per hundred". If that were true, it would be a problem. But it's not true. Examples:,  (last paragraph in first column),  slide 8, , question 10, , , p. 8,  on pages ~23, 25-28.
 * I stand corrected. But all your examples seem to be for rubber tires and not railroad wheels.  So I'm still strongly in favor of using parts per thousand or ‰.  If this article were for only highway vehicles, then I would go along with %.  I've got a lot more info to add for rail and I've hesitated in doing this when I have to put in values like 0.00005. David S. Lawyer 00:04, 4 November 2013 (UTC)

Suggestion for restructuring
I just added a picture illustrating the hysteresis effect. Further I would like add another picture showing plastic deformation (e.g. a wheel on soil, leaving behind permanent depression), if I can find the time. Besides that I would like to suggest some restructuring of the article. In my opinion we could do more to separate the different effects. Therefore the section "Rolling resistance can mean different things" could be moved up: directly after "primary causes"? The section on physical formulas could be moved down? It should be clearer about the phenomena that are incorporated here, instead of just quoting the external sources. Finally I suggest to remove sub-headers such as "Wheel bearing resistance", making slightly bigger paragraphs. Okay? Edwinv1970 (talk) 15:45, 2 June 2012 (UTC)

Don't remove the sub-header which I created "Wheel bearing resistance". Other subheadings I was going to add were: Pure rolling resistance, Energy lost due to shaking the earth, Energy lost due to shaking the vehicle, Losses due to sliding of the wheel on the rail (mostly due to hunting). While automobiles have such losses, I don't think anyone has estimated them. So this section will be only for trains since the Russians did it for railroads during the Soviet era. I stopped because I want to use units of parts per thousand. Writing Crr= 0.0003 is not as easy to comprehend as Crr=0.3‰. David S. Lawyer 07:22, 4 July 2013 (UTC)

Should this article belong to Wiki projects: physics?, civil engineering?
Most of the work on rolling resistance is experimental and not theoretical, often resulting in empirical formulas. Thus I think the topic of rolling resistance belongs to the "Transport engineering" wiki category and is part of the wiki project of "Civil engineering" both of which I've added to the talk page. However, it started out under the physics heading. Should it be removed from the Physics project? I added a link to it from the "Railway engineering" article, which is just a bunch of links to other articles. I think it's fine to continue to cover rolling resistance here for all types of vehicles since it facilitates comparisons. David S. Lawyer 00:38, 4 November 2013 (UTC) — Preceding unsigned comment added by Dlawyer (talk • contribs)

-I would think automotive or mechnical engineering would be the best home for this article. AresLiam (talk) 01:10, 4 November 2013 (UTC)

- Absolutely... Mechanical Engineering. That's what they do. Civil engineers deal with things that are static. — Preceding unsigned comment added by 2600:100D:B02B:A80B:8DE3:D324:81CA:8A06 (talk) 02:20, 22 December 2015 (UTC)

Everything about "Coulomb's Law" should be in one section.
Assuming "Coulomb's Law" is widespread, I suppose it is notable enough to be here. It does not, however, need to be scattered all over the article. Any mention of it should be prefaced by a note that it is incorrect. — Preceding unsigned comment added by SllipsLacimech (talk • contribs) 21:13, 28 January 2014 (UTC)

Dead link
http://indiatransportportal.com/wp-content/uploads/2016/02/india-rolling-resistance-itp-feb-2016.pdf is dead. I found something similar at https://www.slideshare.net/ArnaudRenard3/india-rolling-resistance-and-fuel-saving-2016 but I don't know whether it is the same and whether this is a canonical link. — Preceding unsigned comment added by TN (talk • contribs) 12:21, 14 November 2017 (UTC)

External links modified (January 2018)
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Rolling resistance in bicycle tires
I cannot find support for these claims in the cited source:


 * However, rolling resistance increases with increasing side deflection, for example while cornering or during the normal and constant precesssion associated with bicycle riding. (Hence wider tires grip better while cornering.)  This precession is not present in vehicles having intrinsic lateral stability such as  automobiles.  The decreased rolling resistance due to increased tire cross-section diameter is more than offset by the increase in lateral rolling resistance due to the constant precessional motion in bicycling.  Hence, For bicycles (and less so for motorcycles) the total rolling resistance increases with increasing tire cross-section diameter.  Rolling resistance measurements made on bicycle tires using test equipment not taking into account natural lateral/precessing motion do not accurately measure the rolling resistance of bicycle tires.

Guiggniani doesn't seem to devote much space to rolling resistance or bicycles. Also, I am unfamiliar with this use of the word "precession", and I can't find where Guiggniani uses the word at all. -AndrewDressel (talk) 13:03, 23 May 2018 (UTC)


 * My guess is that by precession he means camber change. Greglocock (talk) 22:54, 23 May 2018 (UTC)


 * Yes, that is my guess also, maybe just the result of a poor translation, but it would be great to find the source that is making all these claims to be sure, and as far as I can tell, Guiggniani isn't it. -AndrewDressel (talk) 13:00, 24 May 2018 (UTC)