Symox

Got a copy of Jobst Brandt's classic "The Bicycle Wheel" - great book but some sections I've reread several times to understand.

One section that I still cannot understand is the following:

" As the chain turns the rear wheel sprocket it exerts torque on the hub. Torque is expressed in terms of a force and the length of the lever on which it acts. In the bicycle the force and lever are the tension in the chain and the radius of the sprocket. Spokes are flexible and cannot transmit torque by acting as levers, so they transmit torque from the hub to the rim by becoming tighter and looser. The lever arm is the distance by which the line of the spoke misses intersecting the centerline of the rear axle. The force is the total change in tension among the spokes, some of which become tighter, and some looser. "

The main concept I cannot understand is in this sentence: "Spokes are flexible and cannot transmit torque by acting as levers, so they transmit torque from the hub to the rim by becoming tighter and looser." I get it that the spokes will compress or stretch based on torque and that they cannot transmit torque by acting as levers since they are flexible. What I don't get is how the change in spoke tension transmitting to the rim causes the wheel to turn.

The reason I even care about this is I'm trying to understand the effect of flange diameter on torque transmission and if a more tangent spoke with a larger diameter flange leads to more efficient transfer of power.

My head hurts now
Thanks for the help

oldbobcat

When you apply forward pressure to the cranks, the chainring pulls the chain. The chain pulls the rear wheel cog. The cog pulls the hub flange. The hub flange pulls on the spoke. The spoke pulls on the rim and the bike moves forward. Something as narrow and flexible as a spoke can't push a rim forward, it can only pull. Under power only the pulling spokes are tensioned. But don't confuse this with supporting the bicycle. The weight of the bike plus rider is supported by the spokes at the top of the rim. The hub is literally hanging. Of course, the rest of the spokes prevent the hub from swinging like a pendulum. And under power, the trailing spokes keep the hub from winding up. The hub always rotates at the same speed as the rim.

Likewise, a disc brake decelerates the hub, so the pull is in the opposite direction.

As for flange height and cross pattern, within normal parameters you're probably splitting hairs. Generally, the stiffer and lighter the wheel, the more quickly it accelerates. Larger flanges, shorter spokes, and more spokes make a wheel stiffer. Larger flanges and longer spokes also make the wheel heavier. And longer spokes make the wheel less stiff. As for the cross-pattern, you have to consider the angle of pull from the flange and the spoke count. Two-cross on a 24-spoke wheel is like 3-cross on a 36-spoke wheel. And there's flange height. The spoke length on a low-flange 3-cross wheel is more equivalent to spoke length on a high-flange 4-cross wheel.

I once built 4-cross rear wheel around a 36-hole high flange hub. It felt more sluggish than 3-cross. My bet is any efficiency of the more direct tangential pull was lost in the weight and flexibility of longer spokes.

Andrew R Stewart 

Spoke are springs in a manor of speaking. A thinner spoke will have more stretch then a thick one (and this is why butted spoked wheel tend to suffer from less broken spokes over time)

I wouldn't be too wrapped up in "efficient transfer of power" as it relates to a tangentally laced rear wheel. Now a radially laced one is a really poor application. Basically the more a spoke is at a 90* angle to the lever arm that the hub acts as, WRT the axle, the more efficient the spoke will be at passing along the force to the rim. However the differences are rather minor between, say, a 4x and a 3x lace pattern. Both provide a geometry that has been proven to be adequate for millions of bikes over many decades. This is why i say don't fret the tiny details of proven designs too much.

Now there's far greater factors that affect wheel performance like spoke tension, spoke gage, spoke count, rim stiffness and spoke bed strength, aero slipperiness, tire/rim matching, tire pressures. And all these pale in comparison to the rider's conditioning and fit let alone fitness.

Jobst has had rather strong opinions and not all are worth too much energy. His book does lay a good foundation for thought but one can get lost in the engineering claims. Just because one can measure a thousandth of an inch easily does not mean it has great value in real life. Andy

WizardOfBoz

Imagine lying on a prone bike holding a spoke. You can reach out to the front wheel. You want the bike to move. Do you hold the spoke near the center of the hub and try to use the stiffness of the spoke to push the rim around? Of course not, because the spoke is not a very stiff lever.

Spokes exert force on the wheel in one way only: by tension. Not by acting as a lever. Put another way, there are spokes that work just fine that are made of ultra high strength fiber. They look like a string. When installed, they transmit torque just fine.

Trakhak

I wonder how Brandt would have explained the forces at work in a rear wheel composed entirely of radially oriented spokes, where the only practical constraint is the strength of the hub with respect to resisting the tendency of the spoke heads to rip out of its flanges.

Symox

Thanks for the excellent explanations!

Symox

but the spokes pull on the rim at close to a 90 degree angle, wouldn’t that just compress the rim not rotate it?

im almost getting it

oldbobcat

Mavic, Zipp, Enve, Bontrager, etc., have engineers and computer programs to figure all this stuff out. If the rear bicycle wheel is a problem to be solved, they will solve it, not a hobbyist wheel builder or bike shop mechanic. If it is indeed a problem to be solved.

oldbobcat

Yes, but the rim, being rigid, doesn't compress, so the force is vectored. Another reason not to overthink it.

Andrew R Stewart 

Solving something that the basic engineering work was published in 1896 is not what I would call a study to get worked up about. Oh, there's the millions of millions of wheels built with that 1896 work by AR Sharp that have proven the tangentally and tensioned spoked wheel works in real life too. Sorry but I have better things to get all tangled up in then what has been proven over and over. Andy

Andrew R Stewart 

I'll add one more opinion- Today's wheel engineers are working on the materials, manufacturing, not the foundational engineering. And that big aspect of any product meant to be purchased, the marketing needs (which can be greater then that thousandth of an inch I referenced). Now I'm 3 and out. Andy

davidad

The wheel stands on the spokes.

davidad

He wouldn't because it is not practical.

Symox

Thanks everyone. I’m not trying to solve anything just understand the physics behind it to help make choices in hobbyist wheel building.

Trakhak

The practicality is limited only by the strength (resistance to cracking) of the hub flange. (A young mechanic at a shop where I worked forgot to take into consideration the need to calculate the lengths for crossed spokes for the rear wheel for the first set he built, so he went ahead and built the rear wheel radial on both sides. Last I heard, he had a couple of thousand miles on that wheelset.)

Ten years earlier, I worked in a shop with an engineer who amused himself by building wheels with all clockwise (pulling) spokes on one flange and all counterclockwise spokes on the other. He used hubs with large-diameter bodies (Phil or Durham or Weyless) to avoid twisting the hub body, barber-pole style.

cyccommute 

What does a spoke stand on? It’s not attached to the rim other by tension. The wheel is a tensegrity structure that hangs from the spokes just like this toy.



The upper platform isn’t “standing” on the two gray chains. Those only serve to stabilize the structure. The upper platform is hanging from the short black chain.

Similarly, the spokes of a wheel aren’t standing on the rim. The rim is free to slide up and down the spokes. There’s no compressive forces on the spokes from the rim. Let’s reduce the rim and spokes to (almost) their simplest form. Just a spoke (well 2 spokes), a hub, and a bit of rim. You can see in the picture below that the rim hangs from the hub through the spokes.



If you turn the system over, the hub can hang from the rim by the spokes.



However, if you put the hub on a hook and try to make it hold up the rim, the rim won’t stay up. It slides down the spokes to the hub. In a system where the wheel stands on the spokes, the rim should move in either configuration.




And, in fact, you can push the rim up off the spokes (if you hold it in position) when the hub is held in position.



Brandt has said that the wheel stands on the spokes because compression increases as tension decreases. But he is wrong in his analysis. However, while tension and compression are opposing forces in terms of direction of force, they aren’t the opposite of each other. Drive a stake into the ground, i.e. compress it. Now pull it out of the ground, i.e. put tension on it. You can push it but you can’t pull on it at the same time. If compression is removed, the object isn’t in tension. Compression has to go to zero before tension can start to ramp up.

On a bicycle wheel, just because the tension decreases due to compression of the rim, that doesn’t mean that the spoke is compressing. The whole system is still under tension and like the tensegrity toy, the wheel hangs from the top spokes. The bottom ones only stabilize the upper spokes.

oldbobcat

Probably why they spend more talk and energy on aerodynamics and weight than the brilliance of the tangential pull of their spoke patterns.

Andrew R Stewart 

I have to break my rule here due to a new aspect of this thread...

IIRC Brandt's book uses this model to make the math easier to deal with. My understanding is that we hang from the rim's upper section, like two hammocks. I really like this model as it fits with my feeling the flow of rolling over the road. Andy

Kimmo 

Given that you occasionally see a full radial rear (admittedly they usually have like 96 spokes), it's not a huge consideration, unless maybe the wheel in question is going to experience an unusual degree of torque. It doesn't take much tangentiality to provide an adequate lever on the spoke, since even the lightest spokes are often heavier than necessary for tensile loads (except perhaps in very low spoke count wheels) - there's a minimum size dictated by the need to withstand the twist of tensioning.

So the smaller the flange diameter, the more any torque applied to the hub stretches and loosens the spokes, but the effect is almost negligible. If you want to ensure durability, as Brandt has no doubt impressed upon you, paradoxically enough, you want lighter spokes with more elasticity, helping to ensure that any give in the system is confined to the stretching and slackening of spokes, rather than elbows flexing or what have you.

Troul 

In a general way of explaining: One section of spokes in the wheel give-way, bound tension; while the other section of spokes in the wheel go as straight as they can, achieving as much tension they're capable of. The "round" rim shape you see is going "egg" shaped from the spokes exchanging energy levels.

Kimmo 

Regarding whether a wheel stands or hangs, what about Brandt's measurements? No detectable increase in tension of any spokes in a loaded wheel, only a decrease in tension in the bottom spokes. If you accept that as fact, how can you possibly say it hangs?

IMO this counterintuitive conclusion serves to illustrate that most of us fail to understand just how clever this tensegrity structure is, almost entirely failing to appreciate that the tension is a structural component.

I'd be interested to see if Brandt's results would be mirrored in the tensions of leading and trailing spokes in a torqued wheel... No increase in tension of trailing spokes would thoroughly confirm Brandt's view, although I'm not sure the opposite would necessarily invalidate it.

Anyway, I reckon it's pretty safe to say that it's a lot more complicated than many folks imagine. A wheel stands on its lower spokes in the sense that these are the only ones experiencing a change in tension. Go figure.

cjenrick

some folks use bigger spokes for the pulling spokes in order to do something,

i have a wheel like that out in the garage, Mavis SSC 280 gram sewup rim, tied and soldered also, don't know how to get solder to stick to stainless, it must just cling to the wore used for the tie.

is it to give you more snap?

if that is what the mind thinks, then mission accomplished.

can you see the different gauge spokes? who cares, the only thing of interest here is the Mavic titanium freewheel which they made for maybe three weeks, you don't see those growing on trees, good for that, who wants a frewheel that wears out in two weeks and has slop develop in the bearings that go click click while you go up the hill? not to mention the stripped mangled Ti when you try to remove it, so there is stays.

Andrew R Stewart 

I'm not sure I can explain my thoughts well enough for some to understand. My thoughts are just those, not some engineering treatise. But here goes. The rim has for all intent a fixed circumference so when the rim deforms from the loads that gravity produces, and the bottom spokes lessen their tension, the rim wants to also deform elsewhere away from the hub. Other spokes see increased tension. If the overall spoke tensions are high enough this deformation is within the elasticity of the rim and the rim returns to it's previous shape. The spokes that see increased tensions are not the bottom ones but some are the spokes above the hub. I have played with a spoke tension gage and seen this when pressing the wheel against the ground while another person gaged the spoke tensions. No I didn't record the differences between the bottom and upper spokes but we did see the tension changes.

I believe it's well known that if the spokes are not fully tensioned they will relax as they pass through the bottom, enough to have nipples loosen. If a hub stands on the bottom spokes how can this relaxing of tension happen, as many have said how can you push on a rope? Now a old time wagon wheel with non compressible spokes does stand on the bottom spokes, or maybe better said the spokes are not under tension so the hub can't hang from above.

As I also mentioned I have read others smarter then I who say for the math purposes it is awkward to have a negative tension so Brandt's equations "pretend" the bottom spokes support the hub.

Regardless of my thoughts or other's too I still feel that the tangental and tensioned wheel is pretty well proven a design and pretty much most all the later "engineering" has more to do with product differentialization (sp?) which is a marketing aspect, not a basic first principle engineering one.

I've just about used up my ability to write about this. Andy

cyccommute 

Because the tension change is spread out over many spokes. A decrease in tension of the bottom spokes is what would be expected in a system that is under tension and one where the spokes aren’t attached to the rim. That change in tension may be present in the upper spokes but the magnitude of the tension change is small so that it quickly becomes unmeasurable.

The idea that the wheel stands on the spokes isn’t counterintuitive. We are used to seeing wheels where the vehicle stands on the wheels. Nearly every car wheel, buggy wheel, wagon wheel, and ox cart wheel stands on the wheel. The wheel is under compression. The real counterintuitive part is the idea that the weight hangs from the spokes. Tensegrity structures mess with your head because we see so few examples of them. Many people, looking at that Lego tensegrity structure assume that the long chains are the structural units. However, they aren’t. If weight is put on the structure, the long chains slacken and the structure becomes unstable. The long chains are important but they aren’t the most important element. Just like the bottom spokes are important as well but they don’t carry the load.

The problem is that Brandt made some wrong assumptions and was too stubborn to admit it. Here’s what he said in The Wheel

First, the spokes of a wire wheel don’t get shorter. The rim rides up on the spoke. The rim deforms and becomes oblate. Yes, the spokes undergo decreased tension. The real problem is that he assumes that the opposite of compression is tension and vice versa. But they aren’t. They work in opposite directions but aren’t opposing forces. A lack of tension doesn’t mean a increase in compression. That’s somewhat counterintuitive as well.


I agree that the spokes on the bottom of the wheel undergo a change in tension. But that’s because the rim is deforming not because the spoke is being shortened through compression. The spoke remains the same length. Nothing is pushing on it to shorten it’s length. Here’s another thought experiment. Remove all the spokes on 1/2 of the wheel. Put the wheel in the bike with the spokes above the hub. The bike can be balanced (but not ridden) in this configuration. You could probably even get on the bike and load the wheel.

Now spin the wheel so that the spoke are on the bottom. The bike won’t stand up. The spokes would poke through the bottom of the rim putting the spokes in compression and they will just bend. They could hold no weight. Maybe I’ll do the experiment sometimes.

davidad

Gerd Schraner in his book "The Art of Wheel Building" he states that the wheel stands on the spokes.
It doesn't mater weather the spokes are wood, or steel rods or steel wire under tension the load on the axle pushes down on the spokes and loads they by compression.