4" vs. 6" vs. 8" wheels. Advantages?
 

I've searched and I really didn't find any discussions that directly answer these questions. If you know of a posting or white paper that addresses these questions, can you please post a link to it, otherwise, what are your thoughts, and why?
I've read through several white papers, but none seem to address these specific questions.

If gearing was appropriately matched, what are the advantages and disadvantages of the various diameters of wheels? Does the width of the wheel really matter that much?

EDIT: This is as much for general consumption as it is for my education.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

As a general thing, obstacle traversing is better with a larger wheel (larger wheel, larger obstacle). However, larger wheels can easily be more weight, and a smaller wheel can be made to climb as effectively as a large one. Pick your poison; I'm not quite sure whether there's enough difference between a 6" and 8" or between a 4" and a 6" to make it worthwhile. You only get about an extra inch of vertical climbing ability. 4" to 8", probably enough to make it worthwhile.

On width, ideal physics says no difference, while reality says wider is better. I'll let the idealists and the realists argue that one out, preferably by testing.

Gearing matched: Given that the gearing is matched to give the same robot speed, a smaller wheel will tend to need a smaller reduction (less weight) to go as fast as a larger wheel. (Smaller reduction = higher rotational speed, for those that might be confused.)

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Cost, tread life, ability to go over obstacles, ground clearance, room for sprockets/chains, and robot stability (you can have a longer wheelbase with smaller wheels), are a few of the considerations that I can think of.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

OK, so smaller wheels have a distinct advantage for lowering the CG of the robot and maybe reducing the weight a bit, but also reduce ground clearance if it is needed. Larger wheels allow you to traverse a larger step change in the driving surface, but not much advantage on a ramp change.

Good stuff. What else?

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

I think I can help you out a little. The width of a wheel does matter. A 1" wide wheel has half the contact patch of a 2" wide wheel. ex: You don't ever see dragsters with thin wheels. They always have very thick wheels giving them a higher normal force so they can take off faster. That said, with FIRST robots it is a pretty small difference. If you are looking to increase your traction, you should look for wheels with a higher coeffient of friction. As far as I know pneumatic wheels have the highest CoF (about 2.0). Other wheels have more but are not legal in FIRST because they destroy the carpet.

As to wheel size there are lots of pros and cons to each. Weight, speed, efficiency to name a few. It's really personal preference, do you need the weight? do you want low/high ground clearence?, ect.

As to whitepapers I think one team (234?) is working on testing various sized wheels for differences in preformance. However, I wouldn't expect it to be out any time soon.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Bryan, wider wheel does not give higher normal force because it is a wider wheel. Normal force is the same--object mass/# of object points of contact.

However, tires are rubber. Rubber, when warmed to a certain point, gets "stickier". In that case, more surface area contact at a contact point is better.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

If you're going to assert reality contradicts physics, please at least cite a source of test results or other evidence. Statements of fact without backing like this are how misconceptions are made.

Anyway, there are a lot of reasons to like smaller wheels. The wheels themselves weigh less, and less of a reduction is needed to achieve the same output properties as a larger wheel. The primary drawback is that smaller wheels require more effort to climb obstacles with - a smaller wheel inherently has lower potential ground clearance than a larger wheel. With proper design this can be worked around - many teams climbed the bump this year with 4" wheels and the bump was a rather aggressive obstacle.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

There is a team working on testing this. As such, there are no definitive results yet. It's quite possible that theory and reality agree. But there have been some CD discussions on this topic over the years, which taken together indicate that there is some disparity, due mostly to rubber interacting closely with carpet to give a slight but noticeable increase in traction on a wider wheel.

Remember: Ideal physics tend to take place on a surface with uniform friction (possibly no friction) and in a vacuum unless otherwise specified. There are very few places that have both. Because that sort of place is rare, especially when Murphy is around (or at a robotics competition), reality tends to win over physics by emphasizing those slight differences.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

"F= uN" is physics

"u = constant" is an engineering approximation... which may or may not be a good approximation depending on material properties.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

http://www.chiefdelphi.com/forums/sh...ht=tread+width I will point everyone to that thread. There are a couple others.

http://www.chiefdelphi.com/forums/sh...ht=tread+width

http://www.chiefdelphi.com/forums/sh...ht=tread+width

I also distinctly recall Andy Baker making some comments on this. Where they did some tests and found that a wider tread DOES have more grip on carpet.

Suffice to say this debate has been going on for as long as most of us have been around these boards.

I also want to point out an earlier thread on this http://www.chiefdelphi.com/forums/sh...ad.php?t=84980

(If I screwed up some of these links and made them point to the same place someone let me know, I'm sort of out of it today)

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Wider tread provides absolutely no benefit. When the surfaces are hard, uniform, and flat (Lunacy)

A wider tread does increase the amount of gripping ability when you are talking about carpet though. Think of carpet wheels kinda like Velcro, when you drive a carpet wheel over carpet, some amount of interweaving occurs, resulting in some amount of grip based on contact area.

Whether or not the amount of increased grip is usable is still up in the air, but I am betting that it would increase grip a small amount.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Unfortunately, in the case of polymers, this is not a misconception. On a microscopic level, polymer-based materials (such as the rubber on wheel treads) have "knobs" that protrude and grab on to the microscopic "hooks" of fibrous materials (such as carpet). For this reason, increasing the contact pad increases the number of "knob" to "hook" interactions, which in turn provides an increase of traction. Idealistic entry-level physics states that F=uN, and so as long as the normal force and coefficient of friction remain the same, (it is commonplace to assume that surface area has no affect on the coefficient for basic physics because the other equations are far to complex for classroom labs) no change in frictional force will occur, regardless of the surface area.

Think of it like Velcro. What's harder to pull straight off, one hook grabbing on to one loop, or one inch of hooks on one inch of loops.

To build on what Ether said, this is only a rough approximation of the resistant force felt by an object, and lumps together everything from microscopic surface roughness to how deep one object sinks into another (e.g. a marble on carpet). There are, however, many other equations that these factors into account.

Sorry if this repeats any of the information on the linked threads, it's just nice to have all the important information in one place.

EDIT:

big1boom got to it first :(

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Do any of you have measured data of how this phenomena applies to an FRC application? Anyone?

Do any of you whom are convinced about this fact with long explanations know how much surface area comes into play? Numbers and rates, not "a little" or "a lot".

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Chris, see the links that Andrew gave.

Wider wheels (or tank treads) = larger contact patch. Larger contact patch = more grip than smaller contact patch. More grip = more traction for the same surface. Therefore, more drivetrain contact patch = more traction, under carpet conditions.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

234 did some testing recently, I imagine they're planning on publishing the results.

My wager is the effect is larger than people would think.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

If wider wheels give more grip, would larger diameter wheels also, because they increase the length of the contact patch?

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Yes, I understand that more = more, that's not what I was asking at all.

My point was that accepting a statement as truth without understanding the magnitude of the effect, or knowing how much the effect applies, is not a good idea. Especially when "conventional wisdom" has all of those things.

It seems like a lot of people are parroting back stuff they heard from some guy instead of relying on observations and data. How is that good engineering?

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

For roughtop tread, I am going to make an assumption that smaller diameter wheels get more grip as they form more of a sharp cleat than larger diameter wheels do. This cleat is a better shape for interlocking with the rows of carpet fibers.

Making it wider still retains this shape, but increases the width of the cleat.

This is purely based on the anecdotal evidence of our 2008 krab drive running 2" wide wheels.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

You are correct of course, doing the experiment yourself/having well documented reports is the proper way. I will try to find the thread I recall reading it in, it was from a few years ago. (I want to say 2003)

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Maybe, when first-hand observations are scarce, you have to go by hearsay or not go at all. Have you ever actually observed that F=m*a? Have you ever measured the coefficient of friction without using F=u*N? How do you know, then, that what you've heard is correct? Maybe F=m*a^0.9999999999999993, or F=u^0.999999995*N measured experimentally. Every time that we as engineers use an equation we've learned, we're parroting back stuff we heard from some guy.

The only difference is that for these established equations, "some guy" is whoever wrote the textbook and whoever taught the classes. Sure, they've been backed up by decades or centuries of testing. But only a few tests have actually been run on wheel width vs. traction at the FRC level. I can only think of 2, and only 1 has actually been finished and put out there so far.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

On a smaller wheel, the tread will wear down faster than a larger wheel. If we compare a 4" and 8" wheel, we can see that if both wheels travel the same distance, a point on the 4" wheel experiences twice as much "wear" as a patch of tread on the 8" wheel. In the same vein, a wider wheel experiences less wear since the load is spread out more over the tread.

From team experience, we used 4" wheels in 08 to some success, but we did have to change the tread more often than I remember using 6" or 8" wheels. This might also be because 08 called for lots of movement around a track as well. The small wheels were great for lowering the CG of our robot, and that's one tangible benefit you'll see from using smaller wheels. Small wheels also weigh less (obviously) than others and are (I believe) less expensive.

Personally, I like the 6" IFI wheels that we used in 07. They were pretty easy to deal with and gave us pretty good results.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Ok, I continued my searches and reading and actually found some interesting threads.

http://www.chiefdelphi.com/forums/sh...traction+width was my starting point. It is quite a long thread discussing Friction as a function of area. This lead to a pair of white papers http://www.chiefdelphi.com/media/papers/1381 and http://www.chiefdelphi.com/media/papers/1382 which have some interesting conclusions.

I can keep searching or you could wait until you get into the shop and do some tests yourself. Whichever.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Quite right, my mistake. I believe the correct term would perhaps be contact patch? In reguard to my example the dragster has more tire contacting the ground thus interacting with the ground. Like someone else pointed out if the ground is slick (or otherwise does not allow the wheel tread to "lock" togeather with the ground) the added width is mostly useless.

As to theoretical happenings, I don't think those take into account the way tread (say roughtop) locks togeather with the carpet besides their CoF. Correct me if I'm wrong though.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

If anyone happens to have a strip of carpet, a couple of weights and a section of tread you can test this in two seconds.

Cut two sections of tread, lets say a 2x1 and 4x1 section. Attach the piece of carpet to the board. Put the weighted tread sections (weight them both equally!) on the carpet board (evenly distributing the weight would be best, like a 1/2" piece of steel flatbar on one and 1/4" thick piece of flatbar behind the other. Tilt the board. Which one slides first? Argument solved.

Okay, well not solved, but better than a lot of the "he-said she-said" arguing going on here. :)

I'm very curious to see the "real" answer, since Cyberblue seems to be puzzled by their data.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Those threads are a good starting point, but after reading the write-up it does not appear that the total weight was evenly distributed, which makes the results sketchy at best.

An interesting experiment (and one I'll do tomorrow at school if I have time) would be to keep pressure constant while changing the surface area.

The issue with a drag experiment is that the knobs on the tread are interacting with the hooks radially instead of linearly, so that could affect actual performance.

If I get a chance to run the experiment I'll have the results up by kickoff!

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

The fact that they are puzzled by their data leads me to infer that it's a puzzling subject. There's probably more to it than we've thought of.

btw the drag racing tire analog is probably not very good, because different things are going on (mainly involving temperature of the tire tread) that most likely don't directly translate to robot wheels on carpet. My drag radials "hook" a lot better when I spin them enough to make them smoke for a while first....

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Interaction of wheels and tread with carpet is a very complex subject. Coulomb friction (F=mu*N, with fixed mu) becomes a pretty poor model for the interaction when you get into macro-scale effects like roughtop digging into carpet fibers. Add in the fact that both tread and carpet are compliant (they compress under load), and I am not surprised that Cyberblue has made some "puzzling" findings.

Factors that I would expect to be involved in the final determination of maximum tractive force (traction-limited assumption):

* Tread material
* Tread pattern
* Tread wear
* Tread orientation relative to carpet grain (the carpet is not rotationally symmetric)
* Carpet wear
* Contact patch size
* Normal force (note: will not necessarily be uniform across all contact patches, such as in a drop center 6WD)
* Temperature (can affect the compliance of many types of rubber)
* The sides of the wheel (in our testing, with worn tread, the plastic sides of a Plaction wheel start making contact with the carpet)

This identifies 9 different independent variables. There might be more (or less...some of these may not turn out to be big factors). For any single team, doing a 9-dimensional study across all of these factors would be pretty daunting.

Would someone want to make a test bed to bring to Championships? Just a patch of carpet and a scale to measure pushing force (and robot weight) - along with a system to log the data - would go a long ways. Invite teams to come test their pushing capabilities, then roll up the data into a report on CD. Maybe someone could even make a trophy for the "Highest CoF in FRC 2011". :)

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

This wasn't entirely true. There were a few teams that I drove against that year (25 and 2753 come to mind) that had 12 wheels in their drive trains versus our 6 and they had noticeably more pushing power than we did, and could also out accelerate us. I'm not sure what caused this, I always theorized that the carpet under the Regolith may have had some effect on the amount of Friction, but never cared much to test it once the season was over.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

If you really enjoy the topic of CoF of wheels and tires, I would highly recommend:
Fundamentals of Vehicle Dynamics (R114) [Hardcover]
Thomas D. Gillespie

He has a lot of great documentation of test results from tire companies, and can explain some of the issues you guys are arguing over. The CoF of a rubber component on a surface is an extremely complex interaction. Contact pressure, temperature (both tire and surface), slip angle, slip ratio, and the tires ability to dissapate heat all play into this variable. These minor deltas usually are not necessary for engineering approximations where you only need to be within a few percent. However, they become a bigger deal when you are looking at performance applications.

As far as surface area effecting grip, probably within 10% (for the size differences we are discussing). Keep in mind that static versus dynamic friction can also often be on the order of 10% (or more). That means that if I had 10% more traction than you, and start pushing you and my wheels are close to the static grip level, and you are spinning yours, I may no have 20% more traction (all things being equal). This is a very frequent occurrence in FRC.

If someone did a truly down-town experiment on this, they really should document it well and enter it into a science fair. They could probably get some pretty big scholarship money.

*********************
One of the coolest projects I have worked on in my career dealt with the %slip vs. traction and its role in a phenomenon called Power-Hop or Wheel-hop. This problem also dealt heavily with a systems vibration issue. (Vibes and Physics are often looked at as two horibly boring classes, but put the two together and you get to do burnouts in muscle cars for a few months).:p

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

I'll pluralize that anecdote. 57 went with 4 slicks at our first Lunacy regional and driving performance was lackluster. I argued loudly that just doubling up the wheels was completely pointless, physics! etc. But we had a little weight and a lotta desperation, so we gave it a shot. I subsequently had to eat my words when 8 wheels DID perform better than 4. I still have no adequate explanation for it.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

We found that double-wheel sets in the rear of our 2009 robot did significantly improve "traction"; double-wheel sets in the front yielded negligible results.
We used a wide-style 2-ToughBox 4WD drive base (6 actual wheels in a 4wd configuration); our weight was evenly distributed front-to-back and side-to-side; the improved traction was amplified by the trailer.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

What I find interesting is, my biggest question for this thread was in regard to the diameter of wheels, thus the thread title. I knew that gearing could nominalize torque and speed differences so I believed there had to be other reasons for making a size selection. Asking the question about width was actually a side note, yet it has become the main topic of discussion, and I welcome that!

Please keep the conversation going, there has been a HUGE amount of good information presented.

I really would love to see some data that supports the anecdotal evidence because that is where there "appears" to be discrepancies with physics. My guess is that actual data will support the physics, when ALL variables are accounted for.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

The only explanation I can come up with is that the Regolith was not "Rigid".

In an ideal world, the Regolith would not have depressed or deformed at all when weight was put upon it, but at every competition I went to and drove it did. We spent build season practicing on field where the FRP Regolith was placed directly over a tile floor and found minimal if any difference between the number of wheels and traction - and the floor felt much more slippery than any Regional Field or The Curie Championship Field. I'd venture to say that the Deformation of the Regolith Playing Surface due to the Carpet Underneath was probably the cause for the strange friction differences - though not knowing enough about the physics behind it I can't really give a conclusive answer.

There was also the "breaking in" effect that I still don't completely understand. It seemed that Fresh Fields were more slippery than a field that had about 40 or so matches played on it. I'm not sure if the coating of the FRP began to break down dude to the heat of wheels spinning over it or if there was some other thing at play here.

...


On the topic of the original post, We prefer to use 6" wheels when the game allows. We've found that 6" wheels are a nice compromise between the Small-Low COG benefits of a 4" wheel and the Higher Speed and Obstacle climbing abilities of 8" wheels.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

So now for an odd addition to the question(s):

Since wider wheels do seem to improve traction so much, and smaller diameter wheels seem to have a decent advantage over larger diameter wheels, what happens if we go to extremes a bit? Say, a 3" wide X 3.5" dia. wheel with rough-top. Would there be enough variation in the speed of the wheel, from it's inner edge to it's outer edge, while turning the robot, to be a problem?

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

That's going to depend on the width of your wheelbase, but at first glance, I'm doubting it will matter. The narrower your wheelbase the worse it will be, but the narrower your wheel base, the worse problem you'll have simply scrubbing the wheels sideways when turning. So I think if you had things narrow enough for that differential velocity to matter, it'd still be dominated by the much larger force required to scrub your wheels. It's certainly an interesting problem to consider though. I might try throwing some physics at it tonight to help me sleep before kickoff.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Yeah, several labs in physics, and it's also a scientific law so I'm going to give it more credence than any other idea.

Yes. You can determine a coefficient of static friction by placing your traction material on the surface it's measured against (so a square of carpet), then rotating the surface with one side against the ground until the material slips. The tangent of the angle of your material is the coefficient of friction.

True, but "some guy" should generally be things determined by science that are easily verifiable!

This is the only reason they are given credence and you can't just brush that aside! It's the very basis of science as a whole

So a good general policy is if we don't know, don't state things as fact, which was my original point.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

So I got time to run the test, and the double width strip of tread had 20N of static friction force, and the single wide tread had 18 N of frictional force maximum. I videotaped the force gauge, and I'll get a formal report posted as a whitepaper soon.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Correct, as far as it goes.

But in the case here in front of us, there is data, widely observed. It's just not quantified. Because it's not quantified, all we really have is what has been generally observed. We know, but we don't know exactly, therefore we generalize.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Anecdotal evidence does NOT equal data. You're comparing apples to oranges half the time, and non-equal test cases ("oh that team had treads and could push anyone around!") are useless.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

As of right now I have empirical proof that surface area affects static friction. A video of this proof will be uploaded to YouTube within the week, but for now you just have to take my word for it.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

The double wide strip weighed twice as much - that's pretty important!

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

But, with that noted, it shouldn't be terribly hard to rerun the test with a few fishing weights duct-taped on top of the single-wide strip so the strips are equal within a few grams or so. Then, put up both videos.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

Actually, it didn't because I used two segments of 2x4 for the weight on the double wide strip and stacked two 2x4 segments of the same length for the weight on the single wide tread. The only weight difference is the weight of 3.5"x6" of rougtop tread and 3.5" of two-inch aluminum angle iron, the total of which could hardly combine to cause an additional 2N of frictional force.

This would be one of those "if you don't know, don't state something as fact" moments.

EDIT:
I had one of our animators edit the video, and I just got it sent to my email unfortunately, it's a download link so I am unable to view it on my iPod :(. However, I trust he did a good job and so here's the link: http://dl.dropbox.com/u/4749895/Comp.mp4

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

If that's 1/4" thick AL, that's a third of a pound of material. Assuming those 2x4s weigh about 3 pounds and your traction material is 1.0 CoF (rough guesses here), the third of a pound would indeed make the difference.

That being said, I think it's VERY cool that you tested that with demonstrable result. If doubling thickness does increases your traction by 11%, that could be something.

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

4 inch the smaller the better. For this game you also need a low center of gravity and their are no obstacles... h:yikes:

Re: 4" vs. 6" vs. 8" wheels. Advantages?
 

There are some small obstacles, there are metal plates under the carpet to support the towers, for example. Leave at least 1/2" ground clearance to be safe.