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  1. #1
    Senior Member cyclezealot's Avatar
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    are their studies on weight factors per spoke as the wheel turns. ?

    Guess this is bordering on some kind of physics as related to the wheel.. Some how the weight must be distributed to other spokes as the wheel turns and not just the spoke contacting the ground.? That would be a lot of stress for just one spoke to take. Particularly as you were traveling over rough road.
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    Sir Fallalot wroomwroomoops's Avatar
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    Apparently, there are, but I myself cannot access the article itself:



    "Bicycle Wheel as Prestressed Structure

    J. Engrg. Mech. Volume 119, Issue 3, pp. 439-455 (March 1993)

    C. J. Burgoyne
    1 and R. Dilmaghanian2
    1Univ. Lect., Engrg. Dept., Univ. of Cambridge, Trumpington St., Cambridge CB2 1PZ, United Kingdom
    2Formerly, Steel Construction Inst.


    Issue Date: March 1993

    Bicycle wheels achieve their structural efficiency by making use of prestressing in three ways.
    Tests show that the bottom spokes carry virtually all the load by compressive forces, which reduce the tensile prestress set up in the spokes when the wheel was made. The test results are compared with an analysis that considers the spokes as a disk that can carry force in one direction only. This is shown to give good agreement, as does an analysis that considers the rim as a straight beam on an elastic foundation. The behavior of the wheel with an inflated tire is also considered, and it is shown that good comparisons with theory are obtained if the reaction from the road is assumed to be distributed over a specific length of the rim. Prestressing is shown to be important also in the mechanism by which the various forces are transmitted through the tire from the road to the rim.

    ©1993
    American Society of Civil Engineers"


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    On a properly tensioned wheel, all spokes are under tension at all times. Imagine the bike at rest, with a single spoke for each wheel, and the hub is suspended from the top of the rim by that single spoke. Those two spokes will be supporting the weight of the bike and rider. Now add the rest of the spokes and tighten them all up. As the wheels roll, the tension in the spokes in the upper half of the wheel increases to support the bike and rider and the tension in the bottom half of the wheel is reduced by the same amount. All of the spokes must be tight enough to stay in tension at all times. If the spokes are not tight enough, as the wheels turn, the spokes in the bottom half of the wheel can become loose or go into compression, which can lead to either the nipples loosening, or the spokes "flexing" and breaking, or both.
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    Sir Fallalot wroomwroomoops's Avatar
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    I wonder if anyone has taken a wheel (with a tire installed), measured the spoke tension, loaded the hub with say 100 Kg, then measured the spoke tension again. It would be a simple experiment, and would completely obviate *THIS WHOLE DISCUSSION!*

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    Jobst Brandt wrote a whole book on the subject. He did a bunch of finite element analysis, as well as actual laboratory experimentation. Go read it.

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    Senior Member cyclezealot's Avatar
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    Interesting . Thanks to all.. Just occurred to me. Say, Do 4 spokes as they hit the ground carry all that weight..?. That thought is sort of scary.
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    Senior Member DannoXYZ's Avatar
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    Quote Originally Posted by cyclezealot View Post
    Interesting . Thanks to all.. Just occurred to me. Say, Do 4 spokes as they hit the ground carry all that weight..?. That thought is sort of scary.
    Well, they carry the weight by REDUCING their TENSION. So if you've 4 spokes at 100kgf tension and you add 40kg of load, they will each get reduced tension of -10kgf each (assuming all four are loaded evenly). This reduction in tension is caused by the bottom of the rim being flattened and pushed towards the hub by the weight. So now you've got 4x spokes at 90kgf because the distance from the rim to hub as been reduced.

    There is debate as to what happens next, whether this missing 40kgf appears at the "hanging" spokes on top or is distributed amongst all of the upper spokes. So far from all the modeling and actual in-the-field measurements I've seen, the 40kgf that's lost from the 4 bottom spokes is distributed amongst most of the upper spokes. The spokes next to the loaded zone actually stay the same and the ones above increase tension. So it may look like this:

    4 bottom spokes -40kgf tension (-10kgf each)
    2 spokes adjustment to each side of those: zero change
    26 spokes above loaded area = +40kgf tension (+1.54 kgf each)

    Here's a graph showing the change in stress & strain on a spoke as the wheel turns. At the very bottom, the spoke shows the least amount of load. Notice also that lacing pattern makes minimal differences in the variations of total load.


  9. #9
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    the concept that folks that folks unfamiliar with wheels have trouble grasping is that it isn't the bottom spokes that hold the hub up, nor is it hanging from the top spokes. It's the failure of the lowest spokes to pull the hub down as hard that's the key.

    By analogy -- two evenly matched teams are playing tug o war and neither is winning as they both pull equally. What would happen to the middle of the rope if some big gorilla ran into the back of the last man on one of the teams?

    Can't visualize it, try this experiment. You need 4 people and a length of rope. Tie the rope (the spokes) around the waist of one person (the hub) and have two others (the rim) pull at the ends tiug o war style, but they shouldn't try to win. Now have the fourth person (the bump) body check one of the rim people from the back. The other two should instantly learn how wheels work. Change places and repeat until everybody understands.

    Likewise the unloaded wheel is in equilibrium with all spokes pulling on the hub. When a load is added it replaces some of the tension on the lower spokes, so the system remains in equilibrium. When the wheel hits a bump the tension on the spokes in the impact area is reduced momentarily upsetting the equilibrium so the hub is lifted.

    In trying to understand a wheel, don't think of added tension, but of the locally reduced tension and how it changes the equilibrium.
    Last edited by FBinNY; 05-10-10 at 05:23 PM.
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    Senior Member DannoXYZ's Avatar
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    Quote Originally Posted by FBinNY View Post
    By analogy -- two evenly matched teams are playing tug o war and neither is winning as they both pull equally. What would happen to the middle of the rope if some big gorilla ran into the back of the last man on one of the teams?

    Can't visualize it, try this experiment. You need 4 people and a length of rope. Tie the rope (the spokes) around the waist of one person (the hub) and have two others (the rim) pull at the ends tiug o war style, but they shouldn't try to win. Now have the fourth person (the bump) body check one of the rim people from the back. The other two should instantly learn how wheels work. Change places and repeat until everybody understands.

    Likewise the unloaded wheel is in equilibrium with all spokes pulling on the hub. When a load is added it replaces some of the tension on the lower spokes, so the system remains in equilibrium. When the wheel hits a bump the tension on the spokes in the impact area is reduced momentarily upsetting the equilibrium so the hub is lifted.

    In trying to understand a wheel, don't think of added tension, but of the locally reduced tension and how it changes the equilibrium.
    Good analogy. Brandt has a good picture in his book. The device that distributes the equilibrium in a wheel is the rim. The rim must maintain a constant circumference. In the flattened portion at the bottom on the ground reduces the radius of the wheel at that portion. The load is then transferred around the circumference of the rim and the rim tries to expand everywhere else in order to maintain the same circumference.

    This increases the radius of the rim a tiny amount everywhere else (imagine a ring of keystones, when you push one in, it pushes all the others out so that the circumference remains constant). The increased radius everywhere above the contact area then increases the spoke-tension of the spokes above the contact area.

  11. #11
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    "superposition of stresses" is an engineering principle that we use for lots of things. That in conjunction with prestress in the spokes when the wheel is built is the key to the wheel functioning. It can be a hard principle to grasp- whether you think of the spokes hanging from the top or carrying compression from the bottom or whatever, it all gets back to this same principle. The completed wheel is complex and applying load at one point on the rim can affect the stresses somewhat in all of the spokes.

    As for the "4 spokes at the bottom", this also depends on the particular rim section you are using. I.e. some deep rims are stiffer than some of the older thinner rims, and will distribute that load at the bottom to more of the spokes near the point of contact. It was mentioned above that the rim will try to oval-shape when it touches the ground, it will do this a little less if you have a deep v section rim.

    I'm not up on the latest wheel building technology. Now that we have spoke tension gauges, what tension range is typically used now? I would guess that a single spoke could be pretensioned to 150# or more, so "the 4 spokes at the bottom" would amount to a lot. As a structural engineer I would like to read Mr. Brandt's book, but it seems a bit expensive to me for a casual read. (Maybe I shouldn't be so cheap.)

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    Quote Originally Posted by bjtesch View Post
    "superposition of stresses" is an engineering principle that we use for lots of things. That in conjunction with prestress in the spokes when the wheel is built is the key to the wheel functioning. It can be a hard principle to grasp- whether you think of the spokes hanging from the top or carrying compression from the bottom or whatever, it all gets back to this same principle. The completed wheel is complex and applying load at one point on the rim can affect the stresses somewhat in all of the spokes.

    As for the "4 spokes at the bottom", this also depends on the particular rim section you are using. I.e. some deep rims are stiffer than some of the older thinner rims, and will distribute that load at the bottom to more of the spokes near the point of contact. It was mentioned above that the rim will try to oval-shape when it touches the ground, it will do this a little less if you have a deep v section rim.

    I'm not up on the latest wheel building technology. Now that we have spoke tension gauges, what tension range is typically used now? I would guess that a single spoke could be pretensioned to 150# or more, so "the 4 spokes at the bottom" would amount to a lot. As a structural engineer I would like to read Mr. Brandt's book, but it seems a bit expensive to me for a casual read. (Maybe I shouldn't be so cheap.)
    I think that this guy does a good job explaining how the bicycle wheel works: http://www.astounding.org.uk/ian/wheel/. It is pretty much in line with what Brandt says in his book and there is no need to get the Brandt book if that's what your interested in. There is a lot of other good stuff in the book, though, and it's worth looking at if you're interested in bicycle wheels. You can get the book used through Amazon for about $13 including shipping.

    I have the first edition (I think) of Brandt's book and I understand that there are some technical issues that are fixed in later editions. My opinion is that the book is pretty good on the technical issues though sometimes I have questions, particularly when Brandt is hyping the benefits of butted spokes as opposed to straight gauge spokes.

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    Quote Originally Posted by bjtesch View Post
    ..I'm not up on the latest wheel building technology. Now that we have spoke tension gauges, what tension range is typically used now?
    Highly dependent on spoke count, and somewhat of hub design/lace pattern. If you get down to a 20-spoke rear it can have a recommended range of 140-160 kg on the driveside. Designs that run the driveside radial (heads-in or straight-pull) tend to be at the lower end, as they can position all the spokes closer to the cassette.

    For 32-36 spoke wheels it's usually considered OK to run the driveside somewhat above 110 kg

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    Well, they carry the weight by REDUCING their TENSION.
    So, if I find a Ferrari on sale for $400,000 instead of $500,000, I'll be $100,000 richer if I buy it!

    It's all BS.

    Make a wheel with 4 spokes distributed evenly across 1/2 the circumference. Now see how much weight that wheel supports when the spokes are 1) on the top, 2) on the bottom.

    Now build a wheel using fishing line for "spokes." Try and tell people that it's supported by the "spokes" at the bottom.

    It should be perfectly clear to anyone with any common sense that the weight is supported by spokes in tension. Adding weight increases that tension. Anyone arguing that the spokes on the bottom somehow support that weight is playing fast and loose with terminology to make some nonsensical point.
    Last edited by mike_s; 05-11-10 at 06:39 AM.

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    Quote Originally Posted by DannoXYZ View Post
    Well, they carry the weight by REDUCING their TENSION. So if you've 4 spokes at 100kgf tension and you add 40kg of load, they will each get reduced tension of -10kgf each (assuming all four are loaded evenly). This reduction in tension is caused by the bottom of the rim being flattened and pushed towards the hub by the weight. So now you've got 4x spokes at 90kgf because the distance from the rim to hub as been reduced.

    There is debate as to what happens next, whether this missing 40kgf appears at the "hanging" spokes on top or is distributed amongst all of the upper spokes. So far from all the modeling and actual in-the-field measurements I've seen, the 40kgf that's lost from the 4 bottom spokes is distributed amongst most of the upper spokes. The spokes next to the loaded zone actually stay the same and the ones above increase tension. So it may look like this:

    4 bottom spokes -40kgf tension (-10kgf each)
    2 spokes adjustment to each side of those: zero change
    26 spokes above loaded area = +40kgf tension (+1.54 kgf each)
    If you add a 40 unit load to the hub shouldn't the sum of the vertical components of all the tensions change by 40 units? That is, shouldn't the sum of all the forces on the hub be zero?

    An interesting thing about the graph, if I am interpreting it correctly. There seems to be a large deformation of the rim at the bottom, as expected, but the deformation at the top (and therefore, the change in tension in the upper spokes) appears to be the lowest of all the spokes. The spokes from about 70 to about 110 degrees seem to elongate (and therfore increase in tension) more than the other spokes and yet changes in the tension of these spokes can do little to support the load because the vertical component of tension is small.

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    Quote Originally Posted by mike_s View Post
    S
    It should be perfectly clear to anyone with any common sense that the weight is supported by spokes in tension. Adding weight increases that tension. Anyone arguing that the spokes on the bottom somehow support that weight is playing fast and loose with terminology to make some nonsensical point.
    Your common sense is defective. Return it for a working model.

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    Quote Originally Posted by mike_s View Post
    So, if I find a Ferrari on sale for $400,000 instead of $500,000, I'll be $100,000 richer if I buy it!

    It's all BS.

    Make a wheel with 4 spokes distributed evenly across 1/2 the circumference. Now see how much weight that wheel supports when the spokes are 1) on the top, 2) on the bottom.

    Now build a wheel using fishing line for "spokes." Try and tell people that it's supported by the "spokes" at the bottom.

    It should be perfectly clear to anyone with any common sense that the weight is supported by spokes in tension. Adding weight increases that tension. Anyone arguing that the spokes on the bottom somehow support that weight is playing fast and loose with terminology to make some nonsensical point.
    Depends on how much the Ferrari is worth whether you are richer or poorer and by how much. For example, if you find yourself a really nice old Schwinn Paramount for $100 and buy it, you are probably richer as a result of the bargain.

    It's not correct to say that the load is supported by spokes which see an increase in tension. What is correct is that when a load is added to the hub it is supported by the net change in tension of all the spokes. It turns out that the sum of the changes in all the vertical components of tension in all the spokes will equal the weight added to the hub. If it did not, the hub would accelerate.

    Another way that you can look at this that might help is to consider that tension in the spokes has a direction up and down. That is, tension can be either a positive or a negative quantity. If you look at the change in tension of the various spokes without accounting for direction you will say that the bottom spokes decrease in tension while the upper spokes increase in tension. But, if you account for the fact that tension has a direction and if you call the up direction the positive direction, you will conclude that the tension in the bottom spokes increases too. The tension in the bottom spokes becomes less negative when the load is applied; that is, it increases.

  18. #18
    Type 1 Racer rydaddy's Avatar
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    Quote Originally Posted by mike_s View Post
    So, if I find a Ferrari on sale for $400,000 instead of $500,000, I'll be $100,000 richer if I buy it!

    It's all BS.

    Make a wheel with 4 spokes distributed evenly across 1/2 the circumference. Now see how much weight that wheel supports when the spokes are 1) on the top, 2) on the bottom.

    Now build a wheel using fishing line for "spokes." Try and tell people that it's supported by the "spokes" at the bottom.

    It should be perfectly clear to anyone with any common sense that the weight is supported by spokes in tension. Adding weight increases that tension. Anyone arguing that the spokes on the bottom somehow support that weight is playing fast and loose with terminology to make some nonsensical point.
    Major fail.

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    Quote Originally Posted by mike_s View Post
    So, if I find a Ferrari on sale for $400,000 instead of $500,000, I'll be $100,000 richer if I buy it!
    It depends. If you had a choice to buy it or not your logic would hold, and finding it on sale wouldn't effect your wealth.

    But if you had to buy a Ferrari, possibly because you had a contract to sell one at a set price, finding it for $100,000 less would make most definitely you richer by $100,000.

    ------------------

    Go back to my earlier tug of war strategy. A goat is tied in the middle of a rope with two people pulling at the opposite ends. As long as they both pull equally the goat won't feel a thing. If either suddenly gives a harder tug, the goat will be pulled in that direction. I'm sure you accept that. After all, as you said, it's common sense.

    Now if one person suddenly relaxes his pull what happens? The goat will be pulled in the opposite direction by a force exactly equal to that reduction in force by that person. it's a simple balancing process, reducing the force in one direction is functionally equal to increasing the force in the opposite.

    Kids learn this by experience because it works in tug of war, on seesaws, or others things they deal with. Then they become adults, learn a little bit and can no longer accept what doesn't fit into their narrowed view of how things work. But the physics doesn't change.
    Last edited by FBinNY; 05-11-10 at 10:32 AM.
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    Senior Member Road Fan's Avatar
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    This thread is 1000 times better than the current Road Forum thread on the same topic, not to mention about 4 times shorter!

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    Quote Originally Posted by FBinNY View Post
    Now if one person suddenly relaxes his pull what happens? The goat will be pulled in the opposite direction by a force exactly equal to that reduction in force by that person. it's a simple balancing process, reducing the force in one direction is functionally equal to increasing the force in the opposite.
    Yes, but then someone comes along and says that the people who reduced their force 'pushed the goat,' as though you can ignore the other forces. The outcome is the same (the goat moves) but it is misleading wordplay. Just like comments like 'the bottom spokes are exclusively what hold up the hub because of their reduction in tension' are misleading. One has to account for all the forces, thus:

    Quote Originally Posted by desconhecido View Post
    It's not correct to say that the load is supported by spokes which see an increase in tension. What is correct is that when a load is added to the hub it is supported by the net change in tension of all the spokes.
    And as you say,

    Quote Originally Posted by FBinNY View Post
    it isn't the bottom spokes that hold the hub up, nor is it hanging from the top spokes.

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    Senior Member DannoXYZ's Avatar
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    Quote Originally Posted by desconhecido View Post
    If you add a 40 unit load to the hub shouldn't the sum of the vertical components of all the tensions change by 40 units? That is, shouldn't the sum of all the forces on the hub be zero?
    yes. In the diagram I posted, if you do an integration between the graphs and the zero-line, it does appear that the surface-area above zero is roughly equal to surface-area below zero.

    Quote Originally Posted by desconhecido View Post
    An interesting thing about the graph, if I am interpreting it correctly. There seems to be a large deformation of the rim at the bottom, as expected, but the deformation at the top (and therefore, the change in tension in the upper spokes) appears to be the lowest of all the spokes. The spokes from about 70 to about 110 degrees seem to elongate (and therfore increase in tension) more than the other spokes and yet changes in the tension of these spokes can do little to support the load because the vertical component of tension is small.
    As mentioned before, the rim deforms to maintain constant circumference, but it doesn't deform uniformly. It actually deforms more into an oval shape. But the total tension-changes are balanced so that the amount of tension in the contact-area equals the tension changes amongst all the other spokes above.

    You can't separate the spoke-pull into vertical & horizontal components because the hub doesn't "hang" from the top-spokes, but rather it hangs "within" the rim. The rim is pulling outwards at all times and any change in the shape at one spot causes a change everywhere else.

    It's more like how a pneumatic tyre works. The skin of the tyre is what holds the car up, but you'll notice that none of the tyre-casing is stretched vertically. it's stretched outwards all around. At the bottom, the casing is actually unstretched and the deformation causes an increase in air-pressure due to the decreased volume. This increase air-pressure acts on ALL parts of the tyre ABOVE the load zone. It's this increased air-pressure pushing on the tyre casing that holds the car up on the tyre.

    Same thing with a wheel, the increased tension on the non-loaded spokes is what keeps the hub from moving down and the total sum of increased tension balances the load at the hub.
    Last edited by DannoXYZ; 05-11-10 at 03:26 PM.

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    Sir Fallalot wroomwroomoops's Avatar
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    ^^Why only "roughly"?

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    Consider a 28 spoke wheel, which can easily support 140 pounds, or 5 lbs per spoke.

    For those who think that the spokes on the bottom support the weight, try supporting a 5 lb weight on the top of one spoke, and let us know how that works out for you. I can easily hang a 5 lb weight from a spoke.

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    Are we trying to come up with a simple analogy that people can understand? Try this one-

    tie 2 rubber bands to your keyring, one on each side of the ring
    hold one rubber band in one hand
    with the other hand pull upwards on the other rubber band, enough that the keys are picked up and the lower rubber band is stretched a little bit
    now you have the keys suspended in the middle, one rubber band above stretched by your hand, one rubber band below stretched by your other hand
    there is less tension in the bottom rubber band than the top rubber band, but there is tension in both rubber bands
    the differences in the tensions is equal to the weight of the keys
    that makes sense so far

    now if you took a board and put 2 nails in it, the same distance apart as your hands were at the end of the above exercise
    lay the board on a table, stretch the rubber bands and hook them onto the 2 nails
    laying flat the 2 rubber bands should have the same tension and aren't affected by the keys because the keys are laying on the board
    now turn the board so it is going up and down
    you should have the keys suspended in the middle, one rubber band stretched above, one rubber band stretched below the keys
    the keys are held up by BOTH rubber bands
    rubber bands are not perfectly linearly elastic but lets assume they are for this discussion- the upper rubber band stretches a little bit more due to it picking up additional force equal to HALF of the weight of the keys, the lower rubber band relaxes a little bit due to its tension relieved by an amount equal to HALF of the weight of the keys, half plus half equals the weight of the keys and they are suspended in the middle as if by magic

    And YES it would work if you stretched the keys between monofilament fishing line

    (paraphrasing Mythbusters:
    don't try to explain this at home, I'm a professional engineer, I do this for a living)

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