Bicycle Mechanics - 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.

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 (http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASCERL&possible1=Burgoyne%2C+C.+J.&possible1zone=author&maxdisp=25&smode=strresults&aqs=true) 1 and R. Dilmaghanian (http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASCERL&possible1=Dilmaghanian%2C+R.&possible1zone=author&maxdisp=25&smode=strresults&aqs=true)2
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"

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.

Here's the link to the article. (http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000119000003000439000001&idtype=cvips&gifs=yes&ref=no)

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!*

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.

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.

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.

http://i42.photobucket.com/albums/e346/DannoXYZ/Cycling/WheelStrainRotation.gif

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.

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.

"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.)

"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/ (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.

..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

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.

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.

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.

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.

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.

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.

This thread is 1000 times better than the current Road Forum thread on the same topic, not to mention about 4 times shorter!

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:


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,


it isn't the bottom spokes that hold the hub up, nor is it hanging from the top spokes.

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.


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.

^^Why only "roughly"?

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.

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)

I think that this guy does a good job explaining how the bicycle wheel works: http://www.astounding.org.uk/ian/wheel/ (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.

Cheapest on Amazon right now is $21 + shipping. I might buy a new one anyway just for grins.

I did a quick glance at Ian's analysis and it looks pretty good from an engineering standpoint. I'll have to study it later.

particularly when Brandt is hyping the benefits of butted spokes as opposed to straight gauge spokes

I think I could explain this even without having read the book. Of course there is the matter of weight but I don't know if this is significant or not. The other is the matter of elasticity. I've read that there is a limit to how much tension you can get into a spoke due to the limits of the strength of the nipples, friction, etc. So (I'll pull some numbers out of the air) if you have a straight gauge spoke, lets say 2.0mm x 300mm long, and you manage to get 200 pounds tension in that spoke, it will stretch about 0.017". Now if you tighten a double butted spoke, 2.0/1.8/2.0 to the same tension it will stretch more because you actually have higher stress in the thinner center section, spproximately 15% or 20% more. You can see that this amount of stretch isn't very much in either case. If you put load on the wheel, hit a bump, whatever that tends to add load to the spokes on the bottom, if they shorten close to 0.017" then their tension goes to zero. If they are double butted then they maintain their tension better through the same amount of shortening. If your wheels aren't laced tightly enough then there is less lengthening in the spokes but again the double butted spokes lengthen more than the straight gauge spokes and still give you some advantage. Does Brandt say anything similar to this?

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.

It's apparent that you never bothered to read any of this.

I think I could explain this even without having read the book. Of course there is the matter of weight but I don't know if this is significant or not. The other is the matter of elasticity. I've read that there is a limit to how much tension you can get into a spoke due to the limits of the strength of the nipples, friction, etc. So (I'll pull some numbers out of the air) if you have a straight gauge spoke, lets say 2.0mm x 300mm long, and you manage to get 200 pounds tension in that spoke, it will stretch about 0.017". Now if you tighten a double butted spoke, 2.0/1.8/2.0 to the same tension it will stretch more because you actually have higher stress in the thinner center section, spproximately 15% or 20% more. You can see that this amount of stretch isn't very much in either case. If you put load on the wheel, hit a bump, whatever that tends to add load to the spokes on the bottom, if they shorten close to 0.017" then their tension goes to zero. If they are double butted then they maintain their tension better through the same amount of shortening. If your wheels aren't laced tightly enough then there is less lengthening in the spokes but again the double butted spokes lengthen more than the straight gauge spokes and still give you some advantage. Does Brandt say anything similar to this?

More or less (I don't own a copy of the book, though I've read it.). If I remember right, he claims hat swaged[1] spokes (he's pedantical that way) don't increase the absolute strength of the wheel (what load it can support before the bottom spokes come out of tension and collapse), but greatly improve the fatigue resistance of a spoke by putting the strain in the swaged section, and not at the elbow.

[1] what everyone calls butted spokes are really swaged. Butted would mean that the thick sections are made thicker, when they're actually the nominal diameter of the spoke, and the thin section is formed by reducing its diamter. This makes little difference to anyone who isn't an engineer.

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.

Again, we're not really talking about the static compression of one or several spokes. Due to the spoke tension when assembled, we're talking about the bike and rider load reducing the tension of the bottom few spokes, while the tension of the remainder of the spokes increases a small amount. The bottom spokes do not ever go into actual compression in a well-built wheel. You are correct that in that case they would buckle.

I think I could explain this even without having read the book. Of course there is the matter of weight but I don't know if this is significant or not. The other is the matter of elasticity. I've read that there is a limit to how much tension you can get into a spoke due to the limits of the strength of the nipples, friction, etc. So (I'll pull some numbers out of the air) if you have a straight gauge spoke, lets say 2.0mm x 300mm long, and you manage to get 200 pounds tension in that spoke, it will stretch about 0.017". Now if you tighten a double butted spoke, 2.0/1.8/2.0 to the same tension it will stretch more because you actually have higher stress in the thinner center section, spproximately 15% or 20% more. You can see that this amount of stretch isn't very much in either case. If you put load on the wheel, hit a bump, whatever that tends to add load to the spokes on the bottom, if they shorten close to 0.017" then their tension goes to zero. If they are double butted then they maintain their tension better through the same amount of shortening. If your wheels aren't laced tightly enough then there is less lengthening in the spokes but again the double butted spokes lengthen more than the straight gauge spokes and still give you some advantage. Does Brandt say anything similar to this?

Yes.

I think I could explain this even without having read the book. Of course there is the matter of weight but I don't know if this is significant or not. The other is the matter of elasticity. I've read that there is a limit to how much tension you can get into a spoke due to the limits of the strength of the nipples, friction, etc. So (I'll pull some numbers out of the air) if you have a straight gauge spoke, lets say 2.0mm x 300mm long, and you manage to get 200 pounds tension in that spoke, it will stretch about 0.017". Now if you tighten a double butted spoke, 2.0/1.8/2.0 to the same tension it will stretch more because you actually have higher stress in the thinner center section, spproximately 15% or 20% more. You can see that this amount of stretch isn't very much in either case. If you put load on the wheel, hit a bump, whatever that tends to add load to the spokes on the bottom, if they shorten close to 0.017" then their tension goes to zero. If they are double butted then they maintain their tension better through the same amount of shortening. If your wheels aren't laced tightly enough then there is less lengthening in the spokes but again the double butted spokes lengthen more than the straight gauge spokes and still give you some advantage. Does Brandt say anything similar to this?

Yes.

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 magicIt's important to note that with two pre-stretched rubber-bands, when you turn the board into the vertical orientation, the amount of sag that occurs is less than what would occur if you had a single rubber-band carrying all the weight. Note the title in article wroomwroomoops post#2 - Bicycle Wheel as Prestressed Structure (http://www.bikeforums.net/showthread.php?644022-are-their-studies-on-weight-factors-per-spoke-as-the-wheel-turns.&p=10791137&viewfull=1#post10791137). The mechanical effects are VERY different than un-stretched compression-only wagon-wheels. A spoke and nipple is in effect a bolt and nut. Tension is what makes it all work. Check out this site for some basics on bolted-joints: http://www.boltscience.com.

^^Why only "roughly"?I believe it has to do with beam-bending chords. The rim has bending forces propagating in two opposite directions. All the loads actually go through the rim and depending upon how the rim is mis-shaped away from perfectly round, the spokes then respond. There are also compression-forces along the circumference as well and the models I've seen doesn't take that into account.

They calculate spoke-stress as if the spokes are hanging from the rim and pulling it inwards and they start the loads at the hub. But it's actually more accurate to model it from the rim's contact patch first. If you take the space between two nipples and flatten it from a curve, you'll see that the distance between the two nipples actually increase. This pushes outwards and tries to increase the rim's circumference and the rim will expand outwards above to maintain the same circumference. The models actually need to do their calculations based upon the rim expanding in response to load, rather than the hub moving donw.

Cheapest on Amazon right now is $21 + shipping. I might buy a new one anyway just for grins.

I did a quick glance at Ian's analysis and it looks pretty good from an engineering standpoint. I'll have to study it later.


See this link for $13:http://www.amazon.com/gp/offer-listing/0960723641/ref=dp_olp_used?ie=UTF8&condition=used

It's apparent that you never bothered to read any of this.It's apparent you don't know squat about physics.

See this link for $13

Thanks. I don't know why this didn't come up in my search.

It's apparent you don't know squat about physics.

This may be the funniest thing I've read on BF.

http://www.bikeforums.net/../images/misc/quote_icon.png Originally Posted by wroomwroomoops http://www.bikeforums.net/../images/buttons/viewpost-right.png (http://www.bikeforums.net/../showthread.php?p=10796488#post10796488)
^^Why only "roughly"?
I believe it has to do with beam-bending chords. The rim has bending forces propagating in two opposite directions. All the loads actually go through the rim and depending upon how the rim is mis-shaped away from perfectly round, the spokes then respond. There are also compression-forces along the circumference as well and the models I've seen doesn't take that into account.

I don't have "the book" but I've looked at what Ian has on his page. He doesn't go into much detail about his FE program or what elements he used but since he talks about the rim properties he used I'm sure he used beam and axial elements for the rim, which would consider the bending and the axial loads along the circumference. These are pretty basic elements for this type of analysis, I wrote software back in 1977 that would perform this same type of analysis.

There are engineers that graduate at the top of their class and there are engineers that graduate at the bottom of their class and guess what? They all think they know what they are talking about. There is no possible way for the bottom spokes to carry any compressive load because the nipples are simply not attached to the rim. If you remove the rim tape and cut a bottom spoke at the hub the spoke would fall on the floor. It cannot support any compressive load at all because if it did it would be pushed right through the tube. You can use all the superposition finite element mumbo jumbo you want but if the constraints are not put into the computer properly the results are nonsence. Lets assume for a moment that the nipples are attached at the rim. Even then the spoke is too long and slender to support any real weight and would simply buckle. The rider is supported by the top group of spokes. The weight distribution on the top spokes is a function of the angle difference from vertical. The more virtical the spoke the higher percentage of load it takes. The spokes from 3 to 9 o-clock do practically nothing except help keep the rim round and are under tension the whole time they are doing that. Yes the tension on the bottom spokes decreases when the wheel is loaded but in no way are they ever put into compression. Half of you get it. The rest of you?

Greg

Thanks. I don't know why this didn't come up in my search.

Amazon is a little weird in how it "sorts" used books. When you search for the Brandt book, it gives you a list of available choices one of which is to view "other formats." That's where the lesser priced ones appear. In this case, I assume that the original list is for a particular printing of a particular edition and the other formats are other editions. Sometimes when looking for a book on Amazon that is currently in print only in paperback, you can find almost new or remaindered hardcover editions of the book for a lower price by looking for "other formats." Sometimes the other editions will show very low priced hardcovers that are ex-library books. Of course, condition can be an issue with the former library books.

There are engineers that graduate at the top of their class and there are engineers that graduate at the bottom of their class and guess what? They all think they know what they are talking about. There is no possible way for the bottom spokes to carry any compressive load because the nipples are simply not attached to the rim. If you remove the rim tape and cut a bottom spoke at the hub the spoke would fall on the floor. It cannot support any compressive load at all because if it did it would be pushed right through the tube. You can use all the superposition finite element mumbo jumbo you want but if the constraints are not put into the computer properly the results are nonsence. Lets assume for a moment that the nipples are attached at the rim. Even then the spoke is too long and slender to support any real weight and would simply buckle. The rider is supported by the top group of spokes. The weight distribution on the top spokes is a function of the angle difference from vertical. The more virtical the spoke the higher percentage of load it takes. The spokes from 3 to 9 o-clock do practically nothing except help keep the rim round and are under tension the whole time they are doing that. Yes the tension on the bottom spokes decreases when the wheel is loaded but in no way are they ever put into compression. Half of you get it. The rest of you?

Greg

Jeez, just when you think it's safe, another one of them shows up. This is like whack-a-mole, Groundhog Day, and "deja vu all over again" all rolled into one.

Look at this site: http://www.astounding.org.uk/ian/wheel/ (http://www.astounding.org.uk/ian/wheel/)

Or read this abstract: http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000119000003000439000001&idtype=cvips&gifs=yes&ref=no

Or read this paper:http://www.duke.edu/~hpgavin/papers/...heel-Paper.pdf (http://www.duke.edu/%7Ehpgavin/papers/...heel-Paper.pdf)

or read the Brandt book. There is no debate about this among people who have actually studied the question.

There are engineers that graduate at the top of their class and there are engineers that graduate at the bottom of their class

I graduated summa *** laude. Where does that rate?



My daughter and I used to love that "whack a mole" game at Chuck E Cheese.

There are engineers that graduate at the top of their class and there are engineers that graduate at the bottom of their class and guess what? They all think they know what they are talking about. There is no possible way for the bottom spokes to carry any compressive load because the nipples are simply not attached to the rim. If you remove the rim tape and cut a bottom spoke at the hub the spoke would fall on the floor. It cannot support any compressive load at all because if it did it would be pushed right through the tube. You can use all the superposition finite element mumbo jumbo you want but if the constraints are not put into the computer properly the results are nonsence. Lets assume for a moment that the nipples are attached at the rim. Even then the spoke is too long and slender to support any real weight and would simply buckle. The rider is supported by the top group of spokes. The weight distribution on the top spokes is a function of the angle difference from vertical. The more virtical the spoke the higher percentage of load it takes. The spokes from 3 to 9 o-clock do practically nothing except help keep the rim round and are under tension the whole time they are doing that. Yes the tension on the bottom spokes decreases when the wheel is loaded but in no way are they ever put into compression. Half of you get it. The rest of you?

Greg

:facepalm:

Well, I guess that the only thing we've proved is that you can lead a horse to water, but that won't get him to taste the Kool-Aid.

At this point it might be time to give this horse the last rites ---.:deadhorse:

Ooooh, what fun! Here we go again. This is a fun game. Interestingly, and as intimated by Danno, the spokes with the highest load are those to either side of the contact patch, which makes total sense.

But back to the OP's question . . . or what I think he was getting at . . . my low spoke count Rolf's have a lower spoke tension than my 28H, 32H, and 36H wheels. Why? Because the rim is so stiff. The rim above the contact patch doesn't deform much, so the spokes don't get much shorter, hence they don't need to be stretched as much to avoid fatigue. Also, the tension on the spokes at the top of any wheel doesn't increase much in the loaded state over the unloaded. Also, butted (swaged) spokes make a longer lasting wheel than straight gauge, because you stretch them more in the initial build.

So it's not the number of spokes that makes a strong wheel. It's the design of the wheel as a whole, hub, flanges, spokes, rim. My Rolfs require fewer adjustments than my conventional wheels, though I still like conventional wheels because I can build them myself.

There is no possible way for the bottom spokes to carry any compressive load because the nipples are simply not attached to the rim. Very true.

Those claiming the spokes on the bottom support the weight are exactly like politicians who claim that because they only raised your taxes $50, instead of the $100 they wanted to, you're getting a $50 "tax cut."

If you redefine your terms enough, you can claim anything, however nonsensical, to be true. They're like Humpty Dumpty:


'There's glory for you!'

`I don't know what you mean by "glory",' Alice said.

Humpty Dumpty smiled contemptuously. `Of course you don't -- till I tell you. I meant "there's a nice knock-down argument for you!"'
rephrased:

'The spokes on the bottom support the wheel!'

`I don't know what you mean by "support",' Alice said.

Humpty Dumpty smiled contemptuously. `Of course you don't -- till I tell you. "Support" means "whatever it is that the bottom spokes do!"'

The answer is the wheel needs all the spokes. There is no dispute among people who understand pre-stressed structures that all the spokes are needed to maintain the pre-load tension, and there is no dispute that the greatest change in tension, the only change large enough to lead to eventual failure, and the change in tension that provides the greatest lift at the hub is the decrease that occurs as the spoke rolls through the bottom. Calling that change "compression" makes perfect sense to me and is commonly accepted among engineers. If you prefer to call that change "reduction in tension", that is a dispute about language, not about physics.

The graph in post #8 above is consistent with what's in Brandt's book, and with the conclusions every peer-reviewed study I have ever seen. If you believe it is not an accurate description of the change in tension as a wheel rolls, you need to back up that belief with something better than your own intuition.

em, p.e.

The answer is the wheel needs all the spokes. Nope (at least not for a static wheel subject to only vertical load). Load your wheel, then use wire cutters to cut out the 2 (or 4) at the bottom. If they're supporting the load, the wheel will collapse. I await claims of how the wheel is now being supported by non-existent virtual spokes.

Load your wheel, then use wire cutters to cut out the 2 (or 4) at the bottom. If they're supporting the load, the wheel will collapse. I await claims of how the wheel is now being supported by non-existent virtual spokes.

This has gotten worse than a chain lube debate, but mike S proposed an interesting experiment, and it warrants some thought. He's absolutely right that the wheel won't collapse because of the loss of support from the bottom spokes, but if done carefully on a conventional properly tensioned wheel with typical axle loads, he's in for a surprise. Not only won't the hub drop a bit as the lower spokes are cut, in fact it'll rise, as the tension below is relieved by the loss of those spokes.

The opposite of this has been experienced be everyone who's ever broken 2 or more adjacent spokes, a hop in the rim, not a low spot but a high spot.

Unfortunately the debate here has been compromised by sloppy language such as the use of the term compression when reduced tension is meant, but its a simple fact that wheels are tension structures and the the balance of tension forces (only) changes within the wheel to offset external forces on the hub and rim.

Simply put for a stationary loaded wheel there will be an area of higher tension above and lower tension below. The exact distribution of the tension changes depends on the rigidity of the wheel. With a very rigid rim the distribution will be more or less symmetrical above and below, but with a more flexible rim the changes in tension will be like the graph shown above with a large reduction in tension for the few lowest spokes, and a slight increase in tension distributed among the others.


BTW- if mike s's experiment is repeated with a few cut spokes cut at the top he wheel won't collapse either. We don't need to do the experiment because it's been done. Folks have ridden wheels missing spokes for years, and they go round and round with the missing spokes at the top, bottom and sides and manage to stay together despite they're lack of training in physics.