Physics of T-boning

[brennonbrimhall]

Originally Posted by DampRobot

T bones occur when the usual dynamic of friction in FRC is switched. Usually, friction between the ground and the wheels is static, or rolling, and the friction between bumpers is dynamic (as robots slide off each other, etc). When the bumper-bumper friction becomes static, and the wheel friction of the robot being defended becomes dynamic, then theres a T bone pin going on.

The pinned robot can't escape because they can't move sideways relative to the defending robot (because the bumper friction outweighs the sliding friction on the tires) and it can't move forwards of backwards relative to the pinning robot because it's wheels don't move that way. Its wheels are in constant dynamic friction because it is being pushed from the side, so it's always sliding (whether or not it's wheels are rotating). As soon as the pinned robot stops getting pushed sideways, it can usually get out of the pin.

That implies that bumper construction and design would be critical in a T-bone situation.

How would

• Relative Bumper Height
• Bumper Material
• Robot Center of Gravity

theoretically play into a T-bone situation?

Originally Posted by brennonbrimhall

That implies that bumper construction and design would be critical in a T-bone situation.

How would

• Relative Bumper Height
• Bumper Material
• Robot Center of Gravity

theoretically play into a T-bone situation?

As you may have already seen, many teams are starting to shape their robots so that their bumpers assist with getting out of pins. 971 is a notable example with their octagonal frame this year, where the majority of their robot frame is angled so that they are more likely to be pinned from one of the angled parts where they can get out of instead of from the side or front where it's harder to get out of the pin.

The height of the bumper itself doesn't matter - it's the point of contact. Bumpers that contact each other more have more friction between each other. If both teams have their bumpers at the lowest possible point, then there is more friction between the bumpers. If one has their bumpers at the highest point, and another at the lowest point, there is less bumper friction and is therefore more difficult to pin solely due to bumper friction. What this also does is makes it easier for the robot with the lower bumpers to get under the bumpers of the robot with the higher bumpers, thereby lifting the pinned robot off the ground lessening their normal force (and their friction), and increasing their own normal force and friction, making their pinning strength a lot more powerful (and it's completely legal since it's not within the frame perimeter).

Bumper material definitely does play into the pin, since the coefficient of friction between two bumpers is dependent on the two materials. Teams have recently started making smooth leather bumpers to decrease this coefficient of friction and make slipping out of pins a lot easier.

A robot's center of mass will change where a robot rotates around when getting pinned, or if it will fall over when hit too hard. It is an option to put your center of mass off to one side making rotating out of pins through rotating that side a very viable option.

[brennonbrimhall]

Originally Posted by Andrew Lawrence

The height of the bumper itself doesn't matter - it's the point of contact. Bumpers that contact each other more have more friction between each other. If both teams have their bumpers at the lowest possible point, then there is more friction between the bumpers. If one has their bumpers at the highest point, and another at the lowest point, there is less bumper friction and is therefore more difficult to pin solely due to bumper friction.

I'm pretty sure that I'm misunderstanding something here. Ff = mu*Fn. While I could see that more bumper-bumper contact would make the t-bone more stable (greater chance of maintaining contact as Robot A wiggles and tries to escape Robot B), there should not necessarily be a frictional force increase as the bumper-bumper contact area increases.

Originally Posted by brennonbrimhall

I'm pretty sure that I'm misunderstanding something here. Ff = mu*Fn. While I could see that more bumper-bumper contact would make the t-bone more stable (greater chance of maintaining contact as Robot A wiggles and tries to escape Robot B), there should not necessarily be a frictional force increase as the bumper-bumper contact area increases.

The common force of friction model taught in most high schools isn't false....all the time. It's a good way of predicting generalities of friction, but it makes a lot of assumptions about the two materials in contact - mainly that each are perfectly flat and that there will be no catching on one another - the big difference here. We make the assumption that all materials just perfectly slide past each other, but this isn't true in many cases.

Have you ever heard of wider wheels having more friction? Like why would teams use any wheels larger than the smallest amount possible since surface area doesn't matter? The reasoning lies behind the nature of the two materials in this equation: competition carpet, and rubber tread on the wheel. The difference is these materials aren't perfectly flat - there are small bumps and ridges on each that catch on to the small bumps and ridges on the other. It's essentially how velcro works. This velcro under a microscope shows how the bumps and ridges of the materials get caught together. When the surfaces interlock, you get more grip on the wheel to push forward with, creating more traction. Of course the standard model doesn't account for this, because the math would be insane and extremely difficult to measure.

The same applies to two bumpers in contact. Bumpers aren't extremely hard materials, nor are they perfectly flat due to the pool noodles and the nature of the cloth. When two robots push against each other, the bumpers squish together and deform to take the impact and protect the robot from harm. But by deforming inwards, a ridge of sorts is made that the pushing robot can use to get extra grip from. The point of contact is important as well, especially with the shape of our bumpers. By using two cylindrical pool noodles, there is an open area between the cylinders that can be pushed inward upon impact if the contact point is right. If that happens another indented ridge is created that the pushing robot can use to interlock bumpers against (this is why I've always been a fan of square pool noodle). Remember a lot of this is on the small scale of contact, so you won't be able to see all of it with the naked eye (though you can see the bumpers deforming). Cloth material is equally important. Rough cloth like the cordura suggested by FIRST has lots of bumps and ridges in the design that can grasp onto the bumps and ridges on the opposing robot's bumper cloth. As Roger suggested above, some teams combat this by using smoother, flatter material in their bumpers that have less bumps and ridges that could interlock with the opposing robot's bumpers.

[EricH]

Originally Posted by brennonbrimhall

I'm pretty sure that I'm misunderstanding something here. Ff = mu*Fn. While I could see that more bumper-bumper contact would make the t-bone more stable (greater chance of maintaining contact as Robot A wiggles and tries to escape Robot B), there should not necessarily be a frictional force increase as the bumper-bumper contact area increases.

You also shouldn't see a frictional force increase as a robot's wheels get wider, but you do. (Cue angry theorists.) I'll do my best to explain why; I would think it's the same explanation for both.

In the case of the wheel, the rubber on the wheel interacts with the carpet on a microscopic scale, digging into the nooks and crannies like Velcro sticking together. The wider the wheel, the more rubber there is to do that (even if nothing else on the robot, including weight, changes). So mu appears to be higher by some amount.

Applying to the bumpers, there is some digging in fabric-to-fabric. If you've got fabrics that are really rough-ish, they'll dig in more than smoother fabrics (like sailcloth). Even a sailcloth bumper cover will see this, but it'll be less noticeable than a Cordura bumper cover will because the sailcloth already has a much lower mu.

The theoretical value of mu and the actual value of mu will almost certainly be different in such cases; not by much, but by enough to make a noticeable difference.


This also doesn't take into account the various variances in bumper mounting and configuration that can affect apparent mu, like bowed bumpers, corner-only bumpers, height of the bumpers, stuff like that.

[themccannman]

Originally Posted by EricH

You also shouldn't see a frictional force increase as a robot's wheels get wider, but you do.

Which is why the standard highschool model of friction is incredibly misleading. It's applicable in almost no real world situation. The only time that model really works is with two extremely hard, extremely smooth surfaces, which you rarely encounter. Soft, rough surfaces (e.g. a car tire) are much more common and behave entirely differently than that model predicts.

[thefro526]

There seems to be a bit of conflicting information in this thread, although most of it's on the right track...

In it's most traditional (Pure) sense, a T-Bone is a situation where a defensive robot it's pushing against another robot in such a way that the defended robot cannot actually pull away defending robot. This is most often due to the fact that the robot being defended has a high enough lateral CoF to keep itself from being moved laterally allowing a significant amount of pushing force to be transmitted through the contact surfaces making them appear to lock together. There are also a number of situations where it would seem like the robot being T-Boned should be able to 'spin' off of the pin, but more often than not, it's actually a physical impossibility.

Looking at the bumper to bumper contact first, you've got a fairly straightforward friction problem, where the amount of force required to make the two surfaces slip against one another is going to be proportional to the effective* CoF of the two surfaces and how hard they're being pushed together. I don't know the numbers off the top of my head for Cordura to Cordura interactions (Or any other fabrics for that matter) - but for the purpose of this discussion, lets just say it's somewhere in the neighborhood of .5. Now say the force between the two surfaces is somewhere around 150lbs (not an unreasonable amount) you'd need approximately 75lbs of force (really 'thrust' from the drive) to break the friction between the two surfaces and start pulling away. 75lbs doesn't sound like a lot, but remember that your drive wheels are also being loaded laterally during a t-bone as well, so it's very likely that putting an additional 75lbs of force through them would cause them to spin, meaning that it's very likely that your robot will start to spin it's wheels in place, rather than actually moving out of the T-Bone.

The other half of the T-Boning problem are the forces (mechanics?) that keep you from just 'spinning' out. Most FRC Drivetrains are skid steers of some kind, and have some sort of "Traction" (not omni) wheel - and these usually are going to pivot around some consistent point. In a 6WD, this point is usually approximately centered left and right on the robot, and somewhere between the middle and one of the outer wheel pairs, and in an 8WD robot, this point is usually centered left/right, and in between the two inner wheel pairs. When either a 6WD or 8WD robot attempts to 'spin' out of the T-Bone, you'll notice that one of the ends of the robot will appear to move 'away' from the Defender, while the opposite side will attempt to move towards the defender. Because of this, you'll find that it's nearly impossible to 'spin' out of the t-bone since the drive's maximum turning torque/force will be significantly lower than what is required to over come the lack of mechanical advantage.

Now in the case of Omni Drives, or even a robot that's 4WD with Omnis on one side and traction wheels on the other, you'll see that they're very rarely, if ever T-Boned. Part of this is because of their relatively low lateral CoF - they'll most often be pushed sideways, rather than locked in place - and another part of this is that their more likely to be able to turn out of a situation like this since their effective center of rotation is much less constrained than a traction drive. If you think about why a robot with omnis on one end can just do a cool 180 to turn, you'll see that it's point of rotation appears to be approximately centered between it's two traction wheels, and it's omni wheels appear to be moved laterally relative to those when turning.

Back to traditional drive setups for a bit - say you've got a 'regular' (no tricks) 6WD or 8WD and you need to get out of a T-Bone? One thing you can try is to 'spin' the defending robot quickly enough that their contact force appears to decrease, and you can eventually 'slip' out of the pin. All you have to do is apply force in one of your fore/aft directions and wait until the defending robot starts to turn, once they start to turn (you'll turn in an arc with them) you can either keep spinning them in that arc while gradually attempting to turn out of - or rock the defender back and forth in that arc and eventually you should have an opportunity to wiggle out. The other method is to apply force to the inner (closer to the defender) wheel set in some amount that's greater than the outer wheel set, which should result in your drive attempting to go in a smooth arc that's approximately tangent to the contact between the two machines, and will more than likely result in you slipping out of the pin - if I remember correctly, this is the method that our driver used to breakout of T-Bones this year, and I don't remember him getting caught up all that often.

Also, it's worth mentioning that bumper heights (relative to one another) can have a bigger effect on a contact scenario than some people think. In cases where the pushing robot has bumpers that are significantly lower than the 'pushed' robot, you may notice that the pushing robot gets under the robot being pushed, which results in a change in normal force in favor of the pushing robot. In scenarios like this, you may find that there is little hope that the robot being defended gets out without help, since their normal force has decreased to the point where they can't actually apply a significant force to counter the pin. (Our 2013 robot had the tendency to get under other robot's bumpers, and usually once it did, the pushing match almost always went in our favor, assuming that our breaker stayed closed....)

Anyway, some of these concepts are really hard to grasp without sketching out a few diagrams of different scenarios, so if you're trying to wrap your head around this, it might be a worthwhile exercise.

*As others have mentioned above, CoF and calculating Force of Friction are rarely as straightforward as is assumed when using the equation Ff = CoF x Fn. There are microscopic interactions between two surfaces - along with visible interactions between to surfaces (think about wearing cleats to play soccer) that will cause something to appear to have a higher CoF than what's published - in these cases, you may find that Ff increases with surface area, which is contrary to what is taught in most physics classes.

[Chris is me]

Originally Posted by brennonbrimhall

In a situation where Robot A (with, say, a standard four rubber wheel drivetrain) is getting T-boned by Robot B (but not pinned), is it appropriate to define the T-bone as a situation where Robot B's drivetrain is applying a force that causes Robot A to lose traction with the floor (therefore only having the benefits of the coefficient of kinetc friction) and therefore not being able to generate enough force to escape laterally?

This is most of it, but the friction generated between the bumpers is also important as others have said.

Does this imply that Robot A's drivetrain would be more resistant to T-boning if it had a higher coefficient of static friction?

The only way this would be true is if the wheels were so grippy, the defending robot could not push them sideways. In which case the pin is more escape-able.

In the real world, where our drives exert enough force that we can make most traction materials slip, a higher CoF wheel actually makes you *less* resistant to T-boning. The force the pushing robot exerts to slip the wheels becomes the normal force of the bumpers against each other. As a robot becomes harder to push, the normal force between bumpers becomes greater, resulting in more friction force between them.

Originally Posted by Andrew Lawrence

That is correct, but in most cases* an all-omni drive would just render you powerless against your opponents since you have almost no traction. A traction + omni mix, a butterfly drive, or drop down casters fixes this by adding an area of high friction to rotate around while the low friction spins out of the pin.

This is just straight up not true. "Omni tank" drives have far fewer problems with T-bones than you let on. The biggest reason is that by not resisting sideways motion at all, the normal force between the bumpers (and the compression of the pool noodles, etc) is much lower. In addition, omni wheels can be driven forward while pushed sideways without compromising traction as much. The sideways "traction" in an omni wheel comes from rolling resistance in the rollers, while the forwards traction comes from the rubber of the rollers which aren't slipping.

Finally, it is very hard to "square up" against an omni drive to begin the maneuver. This isn't driver dependent, but a good driver helps maximize the advantage in this situation.. Unless the pushing robot pushes an omni wheel robot normal to the exact center of rotation, it will just spin out rather than stay with the pusher. This gives the driver the opportunity to get away. A good driver will predict defender actions and position their robot to make each contact either incosequential or even beneficial by displacing the robot away from the defender with the contact.

Also, butterfly drives for the most part don't drop a set of traction wheels to spin out of T-bones. Usually they just stay in all omni mode and never get pinned in the first place. I think this was one of the design intents of the system but as the butterfly drive has been iterated people don't even gear traction and omni wheels for the same speed anymore. There are situations where 2 traction 2 omni becomes the better option, but strictly in terms of avoiding T-bones an all omni drive does just as well.

Originally Posted by Andrew Lawrence

That is only in the direction of rotation, assuming movement is all in a straight line. Problem is because omnis have rollers on the wheels which makes them slip and slide and rotate, which makes it extremely easy to move an omni bot sideways, or rotate it from head-on.

That's the point. Because the wheels are easy to move sideways, there is less grip between the bumpers. Being spun is the best possible outcome here for this specific situation.

Originally Posted by Andrew Lawrence

The height of the bumper itself doesn't matter - it's the point of contact. Bumpers that contact each other more have more friction between each other. If both teams have their bumpers at the lowest possible point, then there is more friction between the bumpers. If one has their bumpers at the highest point, and another at the lowest point, there is less bumper friction and is therefore more difficult to pin solely due to bumper friction. What this also does is makes it easier for the robot with the lower bumpers to get under the bumpers of the robot with the higher bumpers, thereby lifting the pinned robot off the ground lessening their normal force (and their friction), and increasing their own normal force and friction, making their pinning strength a lot more powerful (and it's completely legal since it's not within the frame perimeter).

The point of contact is determined by the height of the bumpers... And the height does matter. For both administering and avoiding T-bone pins you want your bumpers as close to the ground as possible. For administering T-bone pins, you'll be able to get under higher bumpers as you've already laid out. This reduces the robot's normal force which is what it uses to be able to drive away at all. Under the right circumstances you can almost completely disable a robot this way.

It's less intuitive why low bumpers would help with avoiding T-bone pins, when raising them reduces the contact patch of the bumper and thus (to a small extent, due to the deformability of the pool noodles) reduces friction between them. The main reason is that force being applied below the centroid of the bumper will almost always result in some part of the pinned robot being supported by the pinning robot. This changes the robot's normal force from the ground. Even if the pin isn't as dramatic enough to noticeably raise the robot off the ground, the higher bumper robot is at a slight disadvantage due to the lowered but non-zero normal force.

Originally Posted by Andrew Lawrence

Have you ever heard of wider wheels having more friction? Like why would teams use any wheels larger than the smallest amount possible since surface area doesn't matter? The reasoning lies behind the nature of the two materials in this equation: competition carpet, and rubber tread on the wheel. The difference is these materials aren't perfectly flat - there are small bumps and ridges on each that catch on to the small bumps and ridges on the other. It's essentially how velcro works. This velcro under a microscope shows how the bumps and ridges of the materials get caught together. When the surfaces interlock, you get more grip on the wheel to push forward with, creating more traction. Of course the standard model doesn't account for this, because the math would be insane and extremely difficult to measure.

There's a little bit more to it than that. Wider wheels wear less quickly, which means that at any given instant less of a wider wheel is being worn down - this wear decreases friction.

It's really important to note that this effect you're speaking of has only been observed in 4" wheels with roughtop tread. Larger wheels with roughtop tread tend to have about the same traction with width. Test it yourself some time if you wanna.

[ttldomination]

Originally Posted by brennonbrimhall

That implies that bumper construction and design would be critical in a T-bone situation.

How would

• Relative Bumper Height
• Bumper Material
• Robot Center of Gravity

theoretically play into a T-bone situation?

There's a famous quote out there that goes something like, "Now you're thinking with portals." Along those same lines, think in terms what each of those variables would do to the friction between the two bumpers. In other words, start thinking in terms of vectors.

Relatively Bumper Height won't play too big of a role in prevent t-bones. Friction is a function of the surface material and the force involves. Limiting the surface area wouldn't do anything. However, mounting your bumpers too high could let a particularly low defender get under your bumpers, which isn't good either.

Bumper Material is definitely an interesting idea, and something that immediately came to mind when this thread popped up. The going theory is that if your bumper cover reduces friction, then you're on the right track. However, in my opinion, you'd need to not only show that your material is (a) low-friction on most other bumper material used in FRC and (b) makes a significant enough difference to actually matter.

COG is another interesting point. If you look on the three axis, "up and down" positioning should not matter in a pin situation (aside from the obvious instability issues). When considering where on the base your COG lies, this could be a difference. You'd have to consider the moments involved, which include the moments caused by your pinner, your wheels, etc. Ultimately, there's two things to note about this; you have to balance your free performance with anti-pinning performance and if a defender pins you head on your COG, you're both gonna get to know each other well for a few seconds.

- Sunny G.