Dabeer
26th April 2008 - 03:34 AM
QUOTE
The second would require much less torque, but would not move the load nearly as much.
Exactly. This is why heavy haulers, like diesel trains, have small wheels. The amount of power (torque) required from the engines is much lower, allowing the same engine to haul a much heavier load. The smaller distance moved is less important than the ability to move the load in the first place.
I see your point about the purpose of the large wheels on racing skates being to minimize the impact of terrain irregularities, but I still think that the larger wheel also allows a higher maximum speed (traveling the same distance requires less rotations of the wheel, thus less friction being overcome for the same distance).
Either way, this isn't really answering the cart question, I think.
The question would boil down to inertia and friction, and the amount of force required to overcome that inertia. Would the weight difference in the wheels be significant?
I did a few google searches, as I'm too tired to do the math tonight, and I found this statement (here: h**p://howthingswork.virginia.edu/print.php?title=Rockets&startdate=0&enddate=99999999&topic=rockets):
QUOTE (->
| QUOTE |
| The second would require much less torque, but would not move the load nearly as much. |
Exactly. This is why heavy haulers, like diesel trains, have small wheels. The amount of power (torque) required from the engines is much lower, allowing the same engine to haul a much heavier load. The smaller distance moved is less important than the ability to move the load in the first place.
I see your point about the purpose of the large wheels on racing skates being to minimize the impact of terrain irregularities, but I still think that the larger wheel also allows a higher maximum speed (traveling the same distance requires less rotations of the wheel, thus less friction being overcome for the same distance).
Either way, this isn't really answering the cart question, I think.
The question would boil down to inertia and friction, and the amount of force required to overcome that inertia. Would the weight difference in the wheels be significant?
I did a few google searches, as I'm too tired to do the math tonight, and I found this statement (here: h**p://howthingswork.virginia.edu/print.php?title=Rockets&startdate=0&enddate=99999999&topic=rockets):
The cart with the small wheels will be easiest to move. That's because, as the cart starts moving, each kilogram of mass in the wheels acquires twice as much energy as each kilogram of mass in the cart itself. Keeping the mass of the wheels low by making the wheels small reduces the energy in the overall cart and makes it easier to start or stop.
So I will concede that if we are ignoring the friction in the axle, the smaller wheels will make the cart easier to get moving from a standstill, or to bring it to a stop, but I maintain that the larger wheels will make it easier to keep pushing it once the cart is moving.
Once the friction in the bearing is re-introduced into the problem, and if that friction is significant (obviously not overwhelming, just a noticeable resistance to the wheel spinning), then I maintain that the larger wheels will be a significant advantage in all cases.
mr_homm
26th April 2008 - 11:39 PM
This question is really very vague, which is what is generating most of the discussion. Define "easy." Define "push." Define "flat." Define "large wheel."
Flat does not mean level, only that the surface is not curved. It also does not mean smooth, so the surface may be a hill on an asphalt roadway. The question PROBABLY meant level as well as flat. It may or may not have meant to imply smooth. Smooth certainly does not mean frictionless in this case, since then the wheels would be completely irrelevant.
Push doesn't mean horizontal push. It may be that it is slightly easier to push the cart while lifting it slightly, because it reduces the bearing friction and rolling friction of the wheels. The problem PROBABLY means a horizontal push, or perhaps a push in whichever direction is easiest.
Easy might mean that a low amount of work is required to move the cart a given distance, or that a low amount of force is required to produce a given initial acceleration to get it moving. Because the work done must replace the energy lost to friction and vibration, the work interpretation is relevant if the surface is either rough or sticky. The force interpretation is more relevant if the surface is smooth and not sticky, since then there is no energy loss and so the net work to move the cart is essentially zero. The problem PROBABLY means that the surface is smooth and not sticky.
Large wheels may or may not be heavier than small wheels, so the word large may refer to the mass of the wheels, or it may just mean that the radius is larger but the mass is the same (as in an experiment where you wish to isolate just one effect). The problem PROBABLY means that the large and small wheels are the same mass, because I suspect that the question is really trying to get at the effect of rotating a large versus a small wheel, independent of the wheel's mass.
Taking all the most probably interpretations gives the following clarified version of the problem:
Four carts of identical mass have the four sets of wheels described. The large and small wheels are the same mass, the ground is level, smooth, not sticky, and has enough friction to force the wheels to turn. There is no bearing friction in the wheels. In order to give each cart the same initial acceleration, which cart would require the largest horizontal force?
In that case, the answer is clear: Since the larger wheels will have a larger rotational inertia, even with the same mass, but a lower rotational velocity, they will have exactly the same kinetic energy when rotating as the small wheels. Therefore, the kinetic energy of the cart is identical in all four cases when it is going at the same speed, so the work required to start it moving is the same, and therefore the force is the same also.
The second most likely case is that the mass of the large wheels really is more than the mass of the small wheels. In that case, the large wheels will have more kinetic energy than the small ones when the cart moves at the same speed, so it is obviously harder to accelerate the large wheeled cart. But this interpretation is TOO obvious, because it really has nothing to do with the wheels. Since the total object (cart + wheels) is more massive, OF COURSE it requires more force to accelerate it. That would be true even if the extra mass was just in the form of a brick sitting on top of it.
It is possible that they problem intended that the total mass of cart + wheels was the same in all four cases. Then you have a problem that requires actual physics understanding to solve, because you have to know that the rotation of the wheels causes them to have more kinetic energy than just the energy of their forward motion. So again, the cart with the big wheels is hardest to accelerate, because a greater fraction of its mass is rotating and therefore requires more kinetic energy to move at the same forward speed.
The third most likely case is that the ground is actually rough and that the word easy refers to the total work done in pushing the cart a fixed distance. In that case, since small wheels transmit more vibration to the cart than large wheels on a surface of the same roughness, the small wheeled cart would have less energy loss due to vibration. It would therefore require less work to make up for losses, and so it would be easier to push.
So, a complete analysis of the problem reveals at least three interpretations which produce three different answers.
Hope that helps to confuse the issue totally!
--Stuart Anderson
BigDumbWeirdo
27th April 2008 - 03:18 AM
QUOTE (mr_homm+Apr 26 2008, 06:39 PM)
Hope that helps to confuse the issue totally!
Oh, you have gone above and beyond in that regards!
Your post was still a wonderful read, as always.
Dabeer, check your feedback. I left you a response there, and I would like to add to it here:
Welcome to physorg! I think you will do well, here.
Dabeer
27th April 2008 - 09:53 PM
QUOTE
Then you have yet to explain why the designers chose to put small wheels on those devices.
Probably because movement of the devices is a secondary concern, and the smaller wheels were less expensive than larger wheels. In the case of office chairs, the smaller wheels also provide less impediment to foot movement.
QUOTE (->
| QUOTE |
Then you have yet to explain why the designers chose to put small wheels on those devices.
|
Probably because movement of the devices is a secondary concern, and the smaller wheels were less expensive than larger wheels. In the case of office chairs, the smaller wheels also provide less impediment to foot movement.
Welcome to physorg! I think you will do well, here.
Thanks! I found this site while involved in an intense discussion of the Plane on a Treadmill issue, and have since decided that this might be a fun place to hang out. So far, so good
Precursor562
27th April 2008 - 10:27 PM
Since the buggy/cart is being pushed and not driven then there is no need to go into torque, wheel diameter and what not.
Also a bigger wheel does not mean a larger bearing to connect said wheel to the axle.
It's a simple matter of mass. Giving the cart larger wheels will give the cart more mass and therefore more weight. It will then require more force to push the setup. Larger wheels will also have a greater frictional contact with the flat surface.
That makes small wheels both front and back your best answer.
Dabeer
27th April 2008 - 11:45 PM
QUOTE
Since the buggy/cart is being pushed and not driven then there is no need to go into torque, wheel diameter and what not.
I was referring to the torque generated by pushing the cart acting on the axle. Given identical axles with identical friction, the large wheel will turn the axle more easily than the smaller wheel.
QUOTE (->
| QUOTE |
| Since the buggy/cart is being pushed and not driven then there is no need to go into torque, wheel diameter and what not. |
I was referring to the torque generated by pushing the cart acting on the axle. Given identical axles with identical friction, the large wheel will turn the axle more easily than the smaller wheel.
Also a bigger wheel does not mean a larger bearing to connect said wheel to the axle.
I never said that, I only said that there would be friction in the axle bearing. Again, given identical bearings, and enough friction to be significant, a large wheel will turn the axle more easily than a small wheel.
QUOTE
It's a simple matter of mass. Giving the cart larger wheels will give the cart more mass and therefore more weight. It will then require more force to push the setup. Larger wheels will also have a greater frictional contact with the flat surface.
But it's never that simple. Friction exists in the axle bearing, like it or not, and a large wheel will overcome that friction more easily than a small. The surface can never be perfectly smooth or flat, and a larger wheel will overcome irregularities more easily than a small.
I've already conceded that, ignoring friction in the bearing and assuming a perfectly smooth flat surface, the mass and inertia of a smaller wheel will make it easier to start and stop the cart in question. However, once the cart is in motion, keeping it at the same speed should still be easier with large wheels, due to the same inertia argument.
The question would really need to be better defined before an answer we can all agree on can be found.
Precursor562
28th April 2008 - 12:29 AM
Aw see you're thinking of wheels fixed to the axle with bearing connecting the axle to the cart. I was thinking a fixed axle with bearings that connected the wheels to the axle.
The size of the bearing would have a greater influence on the amount of force to overcome any frictional resistance than a mechanical advantage due to leverage. The resistance of the bearings would be so small to begin with that a mechanical leverage wouldn't really make any noticeable difference.
Now having the wheels fixed to an axle that spins with the wheels would have the mechanical advantage make more of a difference since the axle would have noticeable mass. The leverage isn't to just spins the wheels but to spin the whole axle.
Dabeer
28th April 2008 - 01:38 AM
QUOTE
Aw see you're thinking of wheels fixed to the axle with bearing connecting the axle to the cart. I was thinking a fixed axle with bearings that connected the wheels to the axle.
The size of the bearing would have a greater influence on the amount of force to overcome any frictional resistance than a mechanical advantage due to leverage. The resistance of the bearings would be so small to begin with that a mechanical leverage wouldn't really make any noticeable difference.
You're right, I was. I was envisioning some old soap-box-derby-style bearing which is just a loop of sheet metal holding the axle to the cart. This would have significant friction, which a larger wheel would definitely have an advantage in overcoming.
That being said, the bearings in casters, such as those on the bottom of the rolling filing cabinets in my office, for example, while being much more advanced than a simple loop of sheet metal, are frequently quite imperfect and have a significant amount of friction. Whether this bearing attaches the axle to the cart or the wheel to the axle, there is still a significant amount of friction to be overcome.
QUOTE (->
| QUOTE |
Aw see you're thinking of wheels fixed to the axle with bearing connecting the axle to the cart. I was thinking a fixed axle with bearings that connected the wheels to the axle.
The size of the bearing would have a greater influence on the amount of force to overcome any frictional resistance than a mechanical advantage due to leverage. The resistance of the bearings would be so small to begin with that a mechanical leverage wouldn't really make any noticeable difference.
|
You're right, I was. I was envisioning some old soap-box-derby-style bearing which is just a loop of sheet metal holding the axle to the cart. This would have significant friction, which a larger wheel would definitely have an advantage in overcoming.
That being said, the bearings in casters, such as those on the bottom of the rolling filing cabinets in my office, for example, while being much more advanced than a simple loop of sheet metal, are frequently quite imperfect and have a significant amount of friction. Whether this bearing attaches the axle to the cart or the wheel to the axle, there is still a significant amount of friction to be overcome.
Now having the wheels fixed to an axle that spins with the wheels would have the mechanical advantage make more of a difference since the axle would have noticeable mass. The leverage isn't to just spins the wheels but to spin the whole axle.
Playing devil's advocate for a second here - I'd think the small diameter of such an axle (relative to whichever size wheel you use) would prevent it from being a significant load. However, since we are arguing the minutiae of the inertia in the wheels, I guess you're right that such an arrangement would make a significant difference.
For the sake of argument, I'll accept that the axle is mounted to the cart, and the bearing is between the wheel and the axle. Given my example of the caster bearings above, I still feel there could be significant friction, which would make it easier with a larger wheel.
Precursor562
30th April 2008 - 12:22 AM
Although the larger diameter wheels would offer better leverage in the case of the wheels attached to a fixed axle through bearings, if we are talking a well designed and assembled hub assembly then the added leverage to overcome the resistance of the bearing with the larger wheel (where both the large and small wheel would be using the same bearing) wouldn't be necessary and the added weight/mass would do more harm than good.
Now the kind of wheel assemblies found on a filing cabinet (I agree) would indeed benefit from having larger wheels but I believe there is a limit to this. Eventually you would get to a point where making the diameter of the wheel larger would do more harm than good. You can never make the resistance go away completely and you will get to a point where having larger wheels would simply add to the mass without giving any noticeable difference to the leverage advantage.
So I guess, starting at really small wheels, it would get easier as the diameter increases to a maximum advantage then it would get harder and harder until finally the size of the wheels would be so huge that the mass/weight they add to the item they are fitted to would be too high and would make it physically impossible for any person to move it by pushing.
Dabeer
30th April 2008 - 12:24 AM
QUOTE (Precursor562+Apr 30 2008, 12:22 AM)
Although the larger diameter wheels would offer better leverage in the case of the wheels attached to a fixed axle through bearings, if we are talking a well designed and assembled hub assembly then the added leverage to overcome the resistance of the bearing with the larger wheel (where both the large and small wheel would be using the same bearing) wouldn't be necessary and the added weight/mass would do more harm than good.
Now the kind of wheel assemblies found on a filing cabinet (I agree) would indeed benefit from having larger wheels but I believe there is a limit to this. Eventually you would get to a point where making the diameter of the wheel larger would do more harm than good. You can never make the resistance go away completely and you will get to a point where having larger wheels would simply add to the mass without giving any noticeable difference to the leverage advantage.
So I guess, starting at really small wheels, it would get easier as the diameter increases to a maximum advantage then it would get harder and harder until finally the size of the wheels would be so huge that the mass/weight they add to the item they are fitted to would be too high and would make it physically impossible for any person to move it by pushing.
Thus leading back to needing the question to be better defined.
Precursor562
30th April 2008 - 12:29 AM
Absolutely.
Although, if it were better defined like describing how the wheels are attached, what the buggy/cart is made of and defining the size of the wheels, I don't think that it would be as simple as picking large wheels or small wheels.
photojack
30th April 2008 - 03:06 PM
How about PROPELLING this hypothetical cart with compressed air? Have you seen anything connected with cars driven from compressed air? On the Science channel a few days ago, they showed European research on a vehicle with three carbon fiber tanks that when charged with compressed air only, would drive the car for nearly 3,000 miles before needing to be re-pressurized! The tanks used that material to avoid metallic shrapnel in case of an accident. They would only split and release the air if ruptured. They already have a car, a mini-van and a mini-truck operational. The "engine" runs so cool, you can only feel slight warmth from minimal friction. No wasted heat, only air as exhaust and very simple mechanical components. Sounds almost to good to be true. I think it was on the show called, "Beyond Tomorrow". The vehicles were very aerodynamic, lightweight and modern looking. With mass production and the simple mechanics involved, the price would be minimal. What a deal for us and the environment, and to get us completely away from fossil fuel use and OPEC!
Fynlcut
2nd May 2008 - 10:00 AM
If we are rolling over a hard smooth surface, I'd go with small hard wheels, with a thin profile. Otherwise it will depend on the surface and the cart design.
Bloy
2nd May 2008 - 08:54 PM
QUOTE (photojack+Apr 30 2008, 09:06 AM)
How about PROPELLING this hypothetical cart with compressed air? Have you seen anything connected with cars driven from compressed air? On the Science channel a few days ago, they showed European research on a vehicle with three carbon fiber tanks that when charged with compressed air only, would drive the car for nearly 3,000 miles before needing to be re-pressurized! The tanks used that material to avoid metallic shrapnel in case of an accident. They would only split and release the air if ruptured. They already have a car, a mini-van and a mini-truck operational. The "engine" runs so cool, you can only feel slight warmth from minimal friction. No wasted heat, only air as exhaust and very simple mechanical components. Sounds almost to good to be true. I think it was on the show called, "Beyond Tomorrow". The vehicles were very aerodynamic, lightweight and modern looking. With mass production and the simple mechanics involved, the price would be minimal. What a deal for us and the environment, and to get us completely away from fossil fuel use and OPEC!
I missed that show. What was the acceleration and cruising speed?
Corvidae
14th May 2008 - 07:47 PM
QUOTE (Fynlcut+May 2 2008, 10:00 AM)
If we are rolling over a hard smooth surface, I'd go with small hard wheels, with a thin profile. Otherwise it will depend on the surface and the cart design.
Ding ding ding! We have a winner!
Without defining the surface the cart is rolling on (or meant to roll on), it's really pointless to decide what size wheels to put on a cart. The mass difference can be engineered to the point of insignificance. So it all depends on what kind of friction the surface is going to create.
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Hello, I thought I would post this question we had on an aptitude test. My friends and I all put different answers, so we have no idea which one is the "correct" answer.