Mazian on 7/10/2007 at 19:36
Quote Posted by heywood
Arguing harder isn't going to help you.
And repeating yourself without anything to back it up isn't doing much for your case. You just simply keep saying the bottom of the tire is moving 60 mph (among other assumptions) without adequately explaining how this is possible when both vehicles are traveling at the same speed. So if they were both traveling 45 mph, the outside edge of the tire would be going 45 mph? How about at 30 mph?, or 100? This is the first I've heard of a 1:1 correlation between a tire's rotational speed and the speed of the vehicle to which it's attached.
Quote Posted by heywood
Which is wrong because we don't need to worry about the distance of the fragment from the center or the rpm to figure out the max speed. We already know the speed of the bottom of the tire relative to the go-kart. It's 60 mph.
No, since the 60 mph speeds cancel out, it's the rotational speed of the tire. You're telling me that a 10 in. tire on a car is going to rotate at the same speed as a 20 in. tire? That's just patently ridiculous.
Quote Posted by heywood
I'd love to see you explain how to calculate the speed based on the weight of the truck and the radius of the tire.
I mis-typed, you can use the weight and radius to calculate the maximum deliverable force to a piece of debris, and just the radius and rpm's to calculate the speed. For calculating the speed you find out the rpm's, convert it to radians per hour, convert the radians to feet (using the circumference of the tire), then convert this to mph.
Quote Posted by heywood
You may not have noticed, but what we're discussing now is whether a tire that runs over an object can propel it backwards (relative to its previous state) so that the impact velocity with the kart would be greater than 60 mph.
What I've noticed is that you'd prefer to preemptively declare victory for your baseless assumptions.
Whatever, here's what I think the speeds would be. If the tire disintegrates (and assuming a perfect transfer of energy to the fragment) the impact speed on the go-kart will be equal to the speed of the fragment and nothing more (since the two 60 mph speeds cancel out). If it's a piece of stationary debris on the road way, the impact speed will be 60 mph (the speed of the kart) plus the speed of the fragment (the rotational speed of the tire at the moment of launch).
heywood on 7/10/2007 at 20:33
Quote Posted by Subjective Effect
But if both cars are going 40mph then the collision is equivalent to hitting a tree at 80mph. Doubling the velocity does something horrible to the forces involved, I'm sure.
Actually, I assumed the closing velocity in the head on collision was 40 mph (e.g. two cars traveling at eachother at 20 mph each). My bad. If we're talking about a closing speed of 80 mph, that's a different story, and a harder question to answer because it's vehicle dependent. I believe what it comes down to is the amount of kinetic energy involved and how it can be absorbed by the vehicles.
Quote Posted by Mazian
And repeating yourself without anything to back it up isn't doing much for your case. You just simply keep saying the bottom of the tire is moving 60 mph (among other assumptions) without adequately explaining how this is possible when both vehicles are traveling at the same speed. So if they were both traveling 45 mph, the outside edge of the tire would be going 45 mph? How about at 30 mph?, or 100? This is the first I've heard of a 1:1 correlation between a tire's rotational speed and the speed of the vehicle to which it's attached.
No, since the 60 mph speeds cancel out, it's the rotational speed of the tire. You're telling me that a 10 in. tire on a car is going to rotate at the same speed as a 20 in. tire? That's just patently ridiculous.
The 10 inch tire will rotate at twice the rpm, but since the radius is half that of the 20 inch tire, the speed at the outer edge of the tire will be the same.
The speed at the outer edge of the tire HAS to be the same no matter the radius, because the tire has to roll the same distance the car moves no matter the radius.
Start with a circle formula: Circumference = 2 * PI * radius.
Now, as the tire rolls, it traces out a path on the ground that is the same length as the distance the car traveled. So, car speed = circumference * rpm, or rpm = car speed / circumference.
And using another circle formula, the speed at the outer edge of the tire = 2 * PI * radius * rpm.
So, speed at the outer edge of the tire = 2 * PI * radius * (car speed / circumference). Or just speed at the outer edge of the tire = car speed.
DaveW on 7/10/2007 at 20:45
Quote Posted by Taffer_Boy_Elvis
(
http://en.wikipedia.org/wiki/Kart_racing) I beg to differ ;)
The tire would still be going forward like the truck's momentum, 60 mph. It would have been slowing, so say about 40 mph. The gokart is going forward at 60 mph. I'd say the best case scenario is the kart hit the tire at 20 mph in my physics universe.
The truck's momentum is gained from the wheels creating friction on the road. To do this, the wheels rotate backwards towards the car, so if they came off they would go in that direction (i.e away from the truck) pretty much at the same speed, I'd imagine.
But yes, 120 does seem wrong. I can see where your friend is coming from, though.
hopper on 7/10/2007 at 20:47
Quote:
If it's a piece of stationary debris on the road way, the impact speed will be 60 mph (the speed of the kart)
This is what I meant. You are bringing the road into the equation without realising it, since the 60 mph is relative to the road.
Quote:
plus the speed of the fragment (the rotational speed of the tire at the moment of launch)
And then you leave the road out, arguing only with the rotational speed of the wheel, which is fine if you leave the road out of the equation. But you can't add both values up like that, because they are the same thing, only with different frames of reference.
Shug on 8/10/2007 at 00:19
csi, more like bsi am i correct gentlemen
Pyrian on 8/10/2007 at 02:08
I think CSI's science-to-bs ratio is still better than this thread's. :D
rachel on 8/10/2007 at 03:51
Quote Posted by heywood
The OP said...
I don't need the OP, I watched the episode. They never mentioned the truck's tire blowing, only that he rolled on a piece of debris. There was even a discussion about how common tire debris are on the side of US roads.
theBlackman on 8/10/2007 at 11:12
Quote Posted by heywood
The OP said:
And for the last time, tires that are
rolling forward don't throw stuff backwards. :mad:
Have you ever seen a "wheel" (circle of material attached to an axle) spinning and disintegrate? The pieces radiate outward from center on line with the degree of direction (portion of a 360 circle) that they are facing at the time of seperation from the "wheel".
Ignoring the roadbed, if the tire/wheel whatever comes apart while rotating the pieces will fly off of the object in all directions.
In the case of a tire exploding (and I've seen it at drag races and other circumstances), the fragments go in all directions. Granted in the case of a tire it does not completely shred, but those portions that do come off go in the direction they were pointed at when the tire exploded.
Up, down, forward, backward. When portions of the tread seperate from recapped tires, (and they sometimes do in "chunks" of tread), they can and do fly "backward" relative to the forward motion of the vehicle. Due to the rotation they usually have a rearward, upward combined line of travel, but they are thrown out/off with force caused by the rotational speed of the tire. With all the attendant energy generated by the rotational speed of the "wheel".
heywood on 8/10/2007 at 19:35
OK, I'm going to try one last time, this time with pictures. Worth a thousand words? I hope so.
First a picture of all the velocities from an observer's point of view (somebody standing on the side of the road watching this happen):
Inline Image:
http://home.comcast.net/~dave.kingsland/misc_pics/observer_frame.jpgFrom this point of view, the road is stationary, the debris on the road is stationary, and the wheel axle and vehicles are traveling at 60 mph to the left. The portion of the tire touching the road at any given instant has zero velocity. That's because the tire is rolling, the vehicle is not skidding or doing a burnout.
The first important thing to note in the picture above is that from the observer's point of view,
no part of the tire is ever moving backwards. So if the tire disintegrates at this moment, the maximum velocity that any part of the tire has relative to the go-kart is 60 mph. The next important thing to note is that as the tire rolls over the piece of debris, the portion of it that contacts the debris is not moving relative to it. So it can't throw the debris backward like a baseball launcher.
Next, lets look at the same scenario, but from the point of view of the vehicle (ie. the treadmill analogy, which is suitably equivalent neglecting air drag):
Inline Image:
http://home.comcast.net/~dave.kingsland/misc_pics/vehicle_frame.jpgThe velocities in the second picture differ from the velocities in the first only by a fixed 60 mph backwards component. From this point of view, the wheel axle and vehicles are stationary and the rest of the world is moving backwards relative to them.
Just like in the observer's perspective, you can see that pieces from a disintegrating tire would hit the go-kart at no more than 60 mph. Also, as the debris rolls under the tire, the portion of the tire that contacts the debris is moving at the same speed as the debris, so the tire cannot accelerate the debris backwards.
With the aid of the first picture, you can see what actually happens when a tire rolls over something in the road. When the leading edge of the tire's contact path first touches the debris/gravel/water/whatever, it pushes forward and down. As the tire rolls directly over, it pushes straight down. And as it rolls past, the trailing edge of the tire's contact patch lifts forward and up. If the thing in the road is water, some of it sticks to the tire due to surface tension and then gets thrown up and around. If the thing in the road is dust or gravel, some of it also sticks to the tire and is thrown up. None of it is thrown backwards because none of the tire is moving backwards. If the thing in the road is elastic, like a piece of tire, it will compress as it gets run over and then rebound up.
If none of this is convincing, do a simple experiment. Find a tire; a car tire, motorcycle tire, bicycle tire, whatever as long as it's decent size. Place your hand palm down on the pavement. Have somebody roll the tire down the pavement and over your hand, the faster, the better. Does your hand get thrown backward as the tire rolls over it?
theBlackman on 8/10/2007 at 20:07
Good visuals. :thumb: :thumb:
