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#1 Zblj

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Posted 16 August 2010 - 04:49 PM

So I decided to check if speed of the truck does affeect its climbing abilites. In order to do so, the small 4x4 model was placed ona tilted plank and its speed was regulated. When the model was unpowered, it slipped down with a certain speed. In order to climb up, the speed on wheels had to be larger of its slipping speed. Here is a picture explaining that:

Posted Image

And a very short video:



You guys agree with my findings?

#2 efferman

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Posted 16 August 2010 - 05:50 PM

yes, i agree.
but works it at a obstacle like a rock?

#3 Ultimario

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Posted 16 August 2010 - 06:12 PM

This theory works but only up until a certain point. When you slip too much you end up losing traction again.

So yes, a little slip gives you better grip but when you step over the line you end up losing all the grip you just gained, balance is everything.

And physics apparently have problem addressing this rubber wheel slip thingy, at least that's what my university physics professior said, It's apparently a science of its own that you best describe by trial and error :P
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#4 rgbrown

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Posted 16 August 2010 - 09:46 PM

View PostUltimario, on 16 August 2010 - 06:12 PM, said:

And physics apparently have problem addressing this rubber wheel slip thingy, at least that's what my university physics professior said, It's apparently a science of its own that you best describe by trial and error :P

Your physics prof was fobbing you off, it's easy to come up with a simple model that explains this. Here goes:

Let w be the wheelspeed (linear speed at the outside of the wheel), and let v be the speed of the car, with positive v defined to be up the slope. Likewise, positive w means the wheels are rotating forwards. Then the relative wheel speed u, i.e. the speed at which the wheel surface passes the slope is

u = w - v

If there's full traction, then u = 0. Now consider the force balance in the following picture
Posted Image
N is just the normal force that counteracts the gravitational pull on the car. f(u) is the friction force from the wheels passing over the slope, and increases with increasing u (this is standard physics).

If the car is moving at constant velocity, or stationary, then all of the forces in the figure must balance. In particular

mg sinθ = f(u)

The speed u* that makes this equation balance is the relative wheelspeed that the car will stabilise at, as shown in this figure:
Posted Image
From our first equation, the speed of the car is then given by

v = w - u*


So if w > u*, the car goes forwards at speed w - u*.
If w < u*, the car goes backwards at speed u* - w, and
if w = u*, the car stays still.

Finally, if w = 0 (i.e. the wheels are locked), then v = -u*, so you can measure u* as the speed at which it slides down the slope.

So, yes, zblj, your theory is entirely reasonable  :tongue:

Edited by rgbrown, 16 August 2010 - 09:49 PM.


#5 Countdown

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Posted 16 August 2010 - 09:49 PM

View PostUltimario, on 16 August 2010 - 06:12 PM, said:

This theory works but only up until a certain point. When you slip too much you end up losing traction again.

So yes, a little slip gives you better grip but when you step over the line you end up losing all the grip you just gained, balance is everything.

And physics apparently have problem addressing this rubber wheel slip thingy, at least that's what my university physics professior said, It's apparently a science of its own that you best describe by trial and error :P

  Climbing up an incline mostly depends on the friction coefficient, angle of the plane, and location of the centre of gravity and mass of the vehicule. There's static friction which is higher than dynamic friction. The relation between friction of the tires and the surface at any given speed is not linear (meaning that the faster the wheels turn, the less friction you have, the less force is transmitted to the plane). But like ultimario said, it's a science of its own.

   Very nice demonstration nonetheless!
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#6 rgbrown

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Posted 16 August 2010 - 10:39 PM

View PostCountdown, on 16 August 2010 - 09:49 PM, said:

Climbing up an incline mostly depends on the friction coefficient, angle of the plane, and location of the centre of gravity and mass of the vehicule. There's static friction which is higher than dynamic friction. The relation between friction of the tires and the surface at any given speed is not linear (meaning that the faster the wheels turn, the less friction you have, the less force is transmitted to the plane). But like ultimario said, it's a science of its own.

   Very nice demonstration nonetheless!
OK, let me refine my argument. Let's not give up, we can include what you say too !

First, we'll assume we're not dealing with static friction here, all of the cases are dynamic (the wheel is rubbing the slope somehow or other).

Remember, u = v - w where u is the relative wheelspeed, v is the observed speed of the car up the slope, and w is the wheelspeed (linear speed at the outside of the wheel).

First, note that in the model I showed, if v is higher than the equilibrium speed (the car is moving faster than expected), then the relative speed u is lower, hence the friction is lower, and so the gravitational pull acts to slow the car down to equilibrium. And if v is lower than equilibrium speed (car is moving slower than expected), friction is higher, and the car speeds up towards its equilibrium. Therefore the equilibrium predicted by this model is dynamically stable. You can imagine arrows on the blue curve pointing towards the equilibrium, which would be how the operating conditions change with time, as follows:
Posted Image

Suppose now that friction was decreasing with increasing relative wheelspeed, so we have a graph like this:
Posted Image
In this case, if the car was moving faster than its equilibrium speed, u would be lower than equilibrium, friction would be higher, and the car would grip even better, making it go even faster up the slope. If the car was moving slower than its equilibrium speed, u would be higher than equilibrium, friction therefore be lower, and the car would start to slip even faster down the slope. If this type of equilibrium existed, it would be dynamically unstable (you couldn't observe it). You can imagine arrows on the curve pointing away from the equilibrium.

Since zblj has observed a kind of equilibrium of the first type, it's fair to conclude that the assumptions I made in the operating region he's working in are essentially correct (increasing friction with increasing speed).

However, we've all observed that if wheels spin too fast, you don't get enough grip, so there must be a region of the curve for high u where the friction is lower than the gravitational threshold. A continuity argument means that the shape of the friction vs relative speed curve must look like this:
Posted Image

I've added arrows this time.

Now's where it gets more interesting (I think). The second equilibrium on this graph is of the unstable type, so if you put the car down with a really high u (to the right of u2 (fast wheels, no "push-start"), it will start sliding downwards, u will increase even further, and you eventually crash at the bottom of the hill. However, if you set it going fast enough (give it a really good shove), then u will be low enough to be on the left-hand side of the unstable equilibrium u2, and you will effectively traverse the curve towards the stable equilibrium, speeding up even more, until the stable equilibrium is reached (lowish u). Cool huh?

Conclusion. Even at really high wheel speed, it is possible for the car to have upward traction on the hill if it was going fast enough to start with. So speed is everything.

We can explain it all! the power of mathematics (or something)

Edited by rgbrown, 16 August 2010 - 10:49 PM.


#7 Blakbird

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Posted 17 August 2010 - 12:40 AM

As long as we are going to make it really complicated, let's add a few more variables. First is that the tangential force between a rubber tire and a surface is not pure friction (F=mu*N), it is also adhesion. Unlike friction, adhesion is not necessarily a function of normal force. Then let's not forget that as a tire spins dynamically against a surface, it heats up. Both friction coefficient and adhesion change as a function of temperature.

From a physics standpoint, the static friction coefficient is always higher than the dynamic friction coefficient, so you always have better traction when NOT slipping your tires (considering only friction). Neglecting aerodynamic drag, the forces on your car are exactly the same no matter how fast you are going up the slope (or are stopped) as long as your speed is not changing. So speed shouldn't matter.

But clearly rotation does matter. What then, is happening? My colleagues and I have spent considerable time discussing this. Our consensus is that it is an effect of the shape of the tires. These tires are somewhat "knobby". When rotating, the irregular shape of the tire has a greater probability of striking and gripping the surface than a stopped tire. The vehicle therefore gets better traction when the wheels are turning quickly. This effect would be even more noticeable on an irregular surface like a gravel hill.
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#8 Zblj

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Posted 17 August 2010 - 05:54 AM

Ok guys you impressed me! Im gonna try the same with smooth wheels to see if knobby wheels really matter. This is getting really interesting  :tongue:

P.S. Rgbronw you are a phsysics teacher?

#9 rgbrown

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Posted 17 August 2010 - 07:05 AM

View PostBlakbird, on 17 August 2010 - 12:40 AM, said:

As long as we are going to make it really complicated, let's add a few more variables. First is that the tangential force between a rubber tire and a surface is not pure friction (F=mu*N), it is also adhesion. Unlike friction, adhesion is not necessarily a function of normal force. Then let's not forget that as a tire spins dynamically against a surface, it heats up. Both friction coefficient and adhesion change as a function of temperature.
OK, I'll take your word for it on the terminology. All I'm positing is some tangential force that varies with the slip speed when the wheels are slipping (limiting ourselves to the dynamic friction case) Because I'll keep forgetting, I'll continue referring to this as friction. But no, we don't need more variables! We have a minimal model here that explains the observations. Sure we'd need to do more if we wanted to actually estimate the exact shape of the curve. And yes, ignoring temperature changes is certainly a simplification that we could take into account if we really wanted to. Does friction increase or decrease with a rise in temperature?

Quote

From a physics standpoint, the static friction coefficient is always higher than the dynamic friction coefficient, so you always have better traction when NOT slipping your tires (considering only friction). Neglecting aerodynamic drag, the forces on your car are exactly the same no matter how fast you are going up the slope (or are stopped) as long as your speed is not changing. So speed shouldn't matter.
Sure, static friction is higher than dynamic, however in the scenario that Zblj posted, the wheels are slipping, no matter what you do. Only dynamic friction applies here. So the whole point is that the forces on the car are NOT exactly the same no matter what you do. Otherwise the car would slip down the hill no matter what you do. And I don't think it's to do with the irregularity of the tyre or the surface here, as the surface is smooth. Therefore, the dynamic friction/adhesion forces must vary with slip speed.

Quote

But clearly rotation does matter. What then, is happening? My colleagues and I have spent considerable time discussing this. Our consensus is that it is an effect of the shape of the tires. These tires are somewhat "knobby". When rotating, the irregular shape of the tire has a greater probability of striking and gripping the surface than a stopped tire. The vehicle therefore gets better traction when the wheels are turning quickly. This effect would be even more noticeable on an irregular surface like a gravel hill.
This is a different question, when we're dealing with irregular surfaces, and I agree that it's probably right that it's more to do with the shape of the tire than any pure friction argument. This argument doesn't apply to Zblj's example though. Doesn't mean that the friction is irrelevant though -- again, as soon as you're spinning your tyres you're into the realms of dynamic friction. The interesting thing about the above model in this case is that it implies that there is an optimal spinning speed that maximises the amount of traction you get from dynamic friction. If you must spin your tyres, it can't hurt to spin at that speed.

This is a fun little problem, by the way.

@Zblj, I'm not a physics teacher, I'm an applied mathematician. Basically, that means if reality is too hard I have the right to make it up. I would guess if you try smooth tyres you'll see the same thing, but the slip speed will be different, and you may need to go steeper to make it slip. I would guess that smooth tyres will work slightly better (more surface area in contact at any one time)

Edited by rgbrown, 17 August 2010 - 07:07 AM.


#10 Zblj

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Posted 17 August 2010 - 01:09 PM

I tryed smooth F1 wheels, and the result is the same  :tongue: At 3V the model skidded slowly down, but when i increased voltage to 9V it drove (bit jerky) up.

#11 Countdown

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Posted 17 August 2010 - 01:10 PM

BTW mr rgbrown, i think we posted at the same time, I didn't even see your marvelous demonstration.

With all these "serious" discussions, I think it's time to lighten up the mood with an old university joke.

  There's 3 students in a dormitory, an engineer, a physicist and a mathematician. In the middle of the night (let's assume there all sleeping...) there's a fire that breaks out.

  The engineer wakes up in a hurry, looks at the fire, rushes out to get the fire extinguisher and puts out the fire and goes back to sleep.

  The physicist wakes up, calmly looks at the fire, sees the fire extinguisher calculates the optimum angle to put out the fire, gets up and put it out with minimal usage of the extinguisher and goes back to sleep.

  The mathematician wakes up, sees the fire, looks at the fire extinguisher, looks back at the fire and the extinguisher. Whilst still in his bed, thinks about it, says to himself: "there's a solution" and goes back to sleep.

Anyway, there's way too much variables to consider to effectively calculate the tracction of the lego tyres. In my opinion if we could just get the "form factor" of each different tyres (radius, width, tread form, dynamic response) we could really simplify this problem.

BTW: there's 3 kinds of engineers: those who can count and those who can't.

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#12 rgbrown

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Posted 17 August 2010 - 01:25 PM

View PostCountdown, on 17 August 2010 - 01:10 PM, said:

With all these "serious" discussions, I think it's time to lighten up the mood with an old university joke.

  There's 3 students in a dormitory, an engineer, a physicist and a mathematician. In the middle of the night (let's assume there all sleeping...) there's a fire that breaks out.

  The engineer wakes up in a hurry, looks at the fire, rushes out to get the fire extinguisher and puts out the fire and goes back to sleep.

  The physicist wakes up, calmly looks at the fire, sees the fire extinguisher calculates the optimum angle to put out the fire, gets up and put it out with minimal usage of the extinguisher and goes back to sleep.

  The mathematician wakes up, sees the fire, looks at the fire extinguisher, looks back at the fire and the extinguisher. Whilst still in his bed, thinks about it, says to himself: "there's a solution" and goes back to sleep.
Nice!


Quote

Anyway, there's way too much variables to consider to effectively calculate the tracction of the lego tyres. In my opinion if we could just get the "form factor" of each different tyres (radius, width, tread form, dynamic response) we could really simplify this problem.
Impossible to calculate, but possible to measure. Imagine this experimental setup:
Posted Image
Set up the slope so that you can get the different kinds of behaviour we saw earlier. The idea is, you change the wheelspeed (by adjusting gear ratios, or using PWM speed control), and then add weights to either the top or bottom tray so that the car is stationary. You can then find the optimum wheelspeed for those conditions, by finding the speed that requires the most mass on the bottom tray to keep it still. You could sketch out the u vs f(u) profile curve from my previous post this way too ...

Anyone game to humour me and try this? :)

#13 Countdown

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Posted 17 August 2010 - 02:00 PM

Good thinking;

  Put the total mass of the vehicule in the upper tray (m vehicule* sin theta) including the tires. By keeping the vehicule mass and size constant, we could get the "form factor" as a ratio of the mass pulled from the bottom tray at a certain speed and the kind of tyres used. Then repeat the experiment for different theta values and try to fit a curve trhough the points with a RK4 algorithm or similar. BLAAAAHHHH, feels like i'm still in university...

-Nick

Edited by Countdown, 17 August 2010 - 02:02 PM.

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#14 Blakbird

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Posted 17 August 2010 - 06:42 PM

rgbrown said:

Does friction increase or decrease with a rise in temperature?
The friction coefficient (or total tangential behavior, if you prefer) generally increases with temperature. This is why dragsters do a "burnout" to heat their tires prior to a race.

rgbrown said:

And I don't think it's to do with the irregularity of the tyre or the surface here, as the surface is smooth.
Doesn't necessarily matter that the surface is smooth. The surface area of the tire which is in contact with the surface is still varying as the tire rotates, and therefore so is the total possible tangential force. However, since zblj also tried it with smooth tires and got the same result, we can conclude this is not the source of the behavior.

Another possibility is a resonant stick/slip condition. Because of the difference between static and dynamic friction coefficients, sticky surfaces tend to "chatter" when you drag them while in contact, bouncing between stopped and moving. When the frequency of the bouncing tire matches the natural vibration frequency of the vehicle, you'd get more consistent contact and better traction. This theory is pretty wacky, but it's a possibility.

Countdown said:

With all these "serious" discussions, I think it's time to lighten up the mood with an old university joke.
A Psychologist decides to do an experiment on an engineer and a scientist. He puts them both in a room and places a "prize" at the other end. In the original joke it is a beautiful woman, but to keep on topic we'll say it is a MISB 8868 Airtech Claw Rig. He then says, "If you can calculate the distance to the prize, you may then move half the distance closer to it. Whoever repeats this enough to get to the prize wins it." The engineer immediately builds a ranging device from a paper clip, a laser pointer, and some pocket lint. He calculates the distance to the prize, moves half the distance, and starts repeating. The scientist just stands with his arms crossed and does nothing. This continues for a while until the Psychologist says to the scientist, "Why are you not going for the prize? Is it not appealing to you?" The scientist replies, "It is a wonderful prize. But every good scientist knows that you have provided a halflife equation. The prize will never be reached even with infinite repetitions, so the exercise is useless." "Right", says the engineer, "but I'm going to get close enough for all practical pusposes!"

Countdown said:

BTW: there's 3 kinds of engineers: those who can count and those who can't.
There are 10 kinds of people in the world, those who understand binary and those who don't.
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#15 Jurgen Krooshoop

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Posted 17 August 2010 - 11:11 PM

View PostBlakbird, on 17 August 2010 - 06:42 PM, said:

There are 10 kinds of people in the world, those who understand binary and those who don't.
Hahaha :classic:  That is really funny !!




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