Spoke Tension and Vertical Wheel Stiffness

The spoked bicycle wheel is a marvelous work of engineering. Spoke tension gives a bicycle wheel its amazing strength. Spoke tension is also responsible for wheel stiffness, and that is what I want to address in this post.

I hope to illustrate that even under severe load conditions, vertical wheel flex is measured in thousandths of an inch. And I will use spoke tension to try to prove my point. This is why I was trying to calibrate my Park TM-1 Spoke Tension Meter when I got off track in my last post.

When you apply tension to a spoke it stretches – a very small amount. The more tension you apply, the more the spoke stretches. In textbooks the tension is called stress and the stretch is called strain. The relationship between stress and strain is called the modulus of elasticity, or Young’s Modulus. Young’s Modulus for steel is ~29 million pounds/inch squared, provided you do not exceed the elastic limit.

All the spokes in a bicycle wheel are under tension. In a perfect front wheel all the spokes are under an identical amount of tension. In a perfect rear wheel all the left side spokes are under an identical amount of tension, and all the right side spokes are under a different identical amount of tension (except for some wheels laced in strange crow’s foot patterns or something.)

I’ll consider a radially laced front wheel for the rest of this post, because the geometry is easier to draw, but it won’t change my conclusions much. I will also assume the spokes are in a plane with the wheel, which they obviously aren’t. They angle out to the left or right, but this makes less than a 2% difference.

What I hope to do is use the amount of tension on an unloaded wheel and on a highly stressed wheel to show that the rim and hub stay at the same distance from each other within thousandths of an inch.

Back to my stressed spoke. A well tensioned steel spoke would be under a tension of about 200 lbs force, more or less. We can calculate the stress by knowing the cross-section of the spoke, and then calculate the strain by knowing the length. A 2mm round spoke tensioned to 200 lbs would be under a stress of ~41,000 lbs/inch squared. A 280mm (11″) long spoke undergoing this stress of 41,000 lbs/inch squared will lengthen (strain) about 0.016″. If we release all the tension in this spoke, it will shorten back to its original length.

Picture each spoke as a very stiff spring connecting the rim to the hub. In an earlier post I defined spring rate and its inverse, compliance, in relation to a tire. I calculated that a tire has a compliance of about 0.0025 inches per pound. If we make the same calculation for the spoke above we arrive at a compliance of 0.00000038 inches per pound. This is about 6500 times stiffer or less compliant than a tire.

Picture1

Here comes the trick – I am only concerned with the spoke that is pointing straight down at any time. It doesn’t matter what all the other spokes are doing. Yes, all the other spokes are responding to the applied forces, but their tension changes do not affect this analysis. By knowing the change in length of the downward pointing spoke, we know the change in distance between the hub and the rim.

If you hit a bump that pushes the rim toward the hub hard enough to completely relax the downward pointing spoke (And it takes a really, really nasty bump to do that. It will never happen in normal riding.) the rim will have moved relative to the hub 0.016″ (The thickness of three to four sheets of paper). Meanwhile the tire has compressed about a half inch! So don’t worry about vertical stiffness of your rims. They are plenty stiff enough.

Quick aside: Have you ever heard a loud snapping or cracking sound when you hit a sharp pothole or railroad track? It sounds like a spoke popped or the rim broke, but inspection reveals no damage. That is the sound of a spoke that has gone slack, snapping back into tension.

Why do we think we can feel that some rims are stiffer, some more comfortable, or more lively, or whatever? Maybe it is as Jobst Brandt described it over thirty years ago in his book The Bicycle Wheel:

“Stiffness, in its various forms, is a subject often discussed by bicyclists with a regard to components as well as frames. Stiff wheels are often mentioned with approval. However, it should be noted that a bicycle wheel is so rigid that its elasticity is not discernible because the tires, handlebar, stem, frame and saddle have a much greater combined elasticity. Therefore, the differences between well constructed wheels are imperceptible to a rider. The “liveliness” attributed to “stiff” wheels is an acoustic phenomenon caused largely by lightweight tires at high pressure and tight spokes with a high resonant frequency. This mechanical resonance can be heard, and possibly felt in the handlebars, but it is not related to the wheel stiffness.”

Now I ‘m heading out to the garage to take some tension measurements in support of the above. I plan to use resonant frequency to measure spoke tension, as recommended by my good friend Candyman. Wish me luck.

Killa

Vertical Wheel Flexibi – Oh, Look, a Squirrel!

Ya’ know how whenever you start to do something, you have to do something else first, and then you forget what it is you were going to do? Happened to me.

In this week’s post, I was going to use spoke tension, and specifically change in spoke tension, to prove that vertical flexibility of bicycle wheels is for all intents and purposes a non-issue. My plan involved measuring spoke tension on a loaded and unloaded wheel with my Park TM-1 Spoke Tension Meter.

So I figured it would be fun to calibrate my tension meter before I started, and that’s where I got sidetracked. I hung a spoke from the ceiling, with a bucket full of dumbbells below it. I knew the weight hanging from the spoke – the tension – was 118 lbs, because I weighed each dumbbell, and the bucket, with my Park DS-1 Digital Scale. My dumbbells, by the way, were all bang on their stated weight within an ounce.

Spoke Tension JigHere is my tension measuring jig – a spoke hanging on a cord from the ceiling with a bucket full of dumbbells suspended a few inches off the floor. My spoke tension meter is the Park Blue thingie mid-picture.

I proceeded to measure the tension in my hanging spoke, and instead of 118 lbs, I measured 167 lbs! Wow, could my calibration be more than 40% off?

A distraction within a distraction here: I checked the diameter of my 2mm nominal round spoke. It was 2.01mm, a 1% difference in cross-sectional area.

Time to read the TM-1 instructions: “Return to Park Tool for recalibration.” Really? I have a spoke with a known tension. I can calibrate this thing. It’s a very simple device, right?

It turns out measuring tension in a spoke is not that simple, and it’s been driving me nuts. The TM-1 spoke tension meter measures tension by displacing the spoke laterally a small amount (a few millimeters) between two points 100 millimeters apart. A spring provides a (fairly) constant force, so the amount of displacement is inversely proportional to the tension in the spoke. But it’s not a linear relationship, and it depends a lot on how the tension grows with the lateral displacement.

In my test rig, the bucket of weights is lifted a small amount due to the geometry imposed by the lateral displacement. The angles involved are miniscule (less than 2 degrees). So it seems to me that the tension in my test spoke remains essentially constant throughout the measurement (unless friction at the TM-1 contact points isolates the mid-section of the spoke during the measurement – hhmmm?)

A spoke installed in a bicycle wheel is constrained within a complex system comprised of the rim, the hub, and all the other spokes. It’s not at all clear to me how spoke tension responds to lateral displacement during measurement. I can’t help but think it grows faster than it does in my test rig. This is what has been baffling me about the 40% error in my calibration. I would have expected the error to be in the other direction.

Be that as it may, tool calibration must take tension growth response into account. Below is a graph of the Park TM-1 Spoke Tension Meter response curve for a 2mm round spoke.

Tension Graph.jpgTension in Kg on vertical axis.

TM-1 reading on horizontal axis. (Smaller numbers = larger displacement.)

 

The very competent people at Park, with a bigger research budget than I, have surely applied some experimentally derived calibration factors into their response curves. Did I mention that there are different response curves for spokes of different dimensions and materials.

Should I worry if my spoke tensions are off because of a mis-calibrated tension meter? If I were building wheels from scratch, definitely. If I am truing wheels and trying to maintain uniform relative spoke tension, not so much. In the latter case, resolution is more important than accuracy. If I measure five spokes that all really have the same tension, I better get near the same answer on every spoke. A spoke with 20% more tension had better read about 20% higher on the TM-1.

Now I’ve blown another Saturday afternoon and I still haven’t addressed vertical wheel flexibility. Maybe next week – unless I decide to send in my TM-1 for calibration.

Killa

 

 

 

 

 

 

 

Wheels – Vertical Compliance, Lateral Flexibility

 

Flexibility or compliance? Which would you rather have in a wheel? Or a whole bicycle for that matter? Deep down inside you know that flexibility and compliance are the same thing, but compliance just rings with goodness, and flexibility sounds bad.

Desirable characteristics in a bicycle wheel include a bit of vertical… let’s call it “cush”, or “resilience”, and absolute lateral (side to side) rigidity. Unfortunately we get the opposite. You can engineer it all you want, but tall thin structures are going to be stiffer vertically than they are laterally. Skyscrapers sway a lot, but they don’t bounce up and down all that much.

I’ve been out in the garage playing around with my Park Tools spoke tension meter and digital scale, and a new dial gauge I rationalized buying in support of this conversation. My measurements and calculations show that a common bicycle wheel can flex laterally a few tenths of an inch under hard pedaling loads, but only a few percent of that amount vertically under the most severe shock loads. Wheel manufacturers certainly know this. It shouldn’t surprise you either. You can grab your wheel near the brake and push it side to side with your finger. All I’ve done is quantify what you already know.

For the rest of today’s post I’ll be considering lateral flexibility only. It’s interesting that I am unconsciously using the negative term “flexibility” because I’m of the opinion that it’s a bad thing, instead of using the more positive term “compliance”, which I will reserve for my next post, where I will consider vertical wheel stiffness.

I fixed a Zipp 303 front wheel in my Park Tools professional wFlexMeasurementheel truing stand. This stand is about as rigid as they come. I then applied a side load of 15 lbs and measured a lateral deflection of 0.1″.  Remember these numbers – 15 lbs and 0.1″. We’ll see them later. (Yes, I tested a few other wheels; some were as much as 30% laterally stiffer than my Zipp 303.)

Lateral flex is really only a problem under hard pedaling loads, and then only while standing. It will remain as an exercise for the reader to deduce why lateral wheel flex is not an issue for seated pedaling.

Go out in the street and pedal standing up while thinking about what you are doing. When you push down on the right pedal with the bike upright, the bike will try to topple to the right because you are pushing down off-center. This is an unsustainable situation, and you have to do something to offset the overturning force.

One method of pedaling while standing is to lean the bike back and forth so that your pedal force is in a line going through the wheel track. This is how you ride wBike leanhen you are standing and lightly gripping the handlebars, rocking the bike from side to side, say, on a long climb.

I will not put the equations in this post because it’s been proven that for every equation in a publication, the readership is halved. I”ll just say that using the math associated with the picture to the left, it can be calculated that you can easily apply a side-load of ~30 lbs. My garage measurements show that 15 lbs will flex one wheel 0.1″, but you are flexing two wheels when you rock your bike.

There is another pedaling technique that offsets the toppling tendency without putting side-loads on the wheels. Pull up or to the left on the right side of the handlebar while pressing doOffset torquewn on the right pedal and keeping the bicycle vertical. This avoids lateral loading on the wheel, but it does it by generating torque loads in the frame/stem/handlebars instead. It also requires engagement of your core muscles and upper body. This is how you pedal in a hard sprint, or topping out an extremely steep hill when your gear is too high.

In practice, we all use a combination of these methods. Just riding a bike at all is a marvelous bit of mental physics. No wonder new riders feel uncomfortable pedaling while standing.

OK, there is a third way to avoid toppling over, but it sucks. Steer to the right when you push down on the right pedal, then to the left when you push down on the left pedal. We’ve all seen inexperienced riders do this. I do a little of this while getting clipped in when starting from a dead stop, if I need to steer with only one hand. I also probably did quite a bit of this in my college days, late at night…

What we really want to know is how much energy we waste flexing our wheels back and forth. If I generate 30 lbs of lateral load (15 lbs per wheel) and move my wheels laterally 0.1 inches, I’ve done 0.25 ft lbs of work. Say I’m pedaling at 60 RPM, I’m doing 0.25 ft lbs of work twice a second, or 0.5 ft lbs per second.

1 watt equals 0.74 ft lbs per second (I looked it up; isn’t the internet amazing). So I am wasting about 0.67 watts on lateral wheel flex.

I told you I’m not putting the equations in my post. Calculate it yourself if you want to check my work.

Power is power, but I’m not going to lose sleep over wasting two-thirds of a watt during hard pedaling efforts where my total output is several hundred watts.

In my next post, I hope to be able to convince you that your wheels are vertically rigid, for all practical purposes. But to do that I have to go out to the garage and take some measurements.

24% Stiffer, More Compliant, Able to Leap Tall Buildings

Hi! Welcome back to Killa’s Garage!

Today’s post starts with a few definitions shamelessly pulled off the internet:

Stiffnessthe rigidity of an object — the extent to which it resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.

Compliance – a property of a material undergoing elastic deformation or (of a gas) change in volume when subjected to an applied force. It is equal to the reciprocal of stiffness.

Compliance and stiffness are opposites!

softrideThe SoftRide people certainly knew about compliance, but that was years ago.

A current manufacturer makes the following (very typical) claim:

“[Their new frame] uses a 27.2mm seatpost, which is designed to both shave weight and increase vertical compliance. Of course stiffness and efficiency remain important, as one can see by the large downtube, tapered headtube, bulbous chainstays, and wide PF86 bottom bracket shell. The net effect is a bike that is 24 percent stiffer…”

Wait a minute. Stiffer and more compliant? It’s one or the other isn’t it?  Not necessarily. Read it again. Maybe the greater compliance is all in the seatpost. I assume the old design used a larger OD seatpost that was stiffer than the new one. Maybe there is nothing more compliant about the new frame at all. The large downtube, tapered headtube, bulbous chainstays, and wide PF86 bottom bracket shell certainly all scream stiffness, not compliance.

The claims actually may both be true – more compliance while seated, achieved with a more flexible seatpost, and greater stiffness when that’s important (sprinting, climbing off the saddle) due to a stiffer frame.

There is another whole discussion around vertical vs lateral stiffness. But for the rest of today’s post I am going to consider only vertical stiffness and compliance.

BTW, the frame is also claimed to be 20% lighter, but that’s also for another day.

Time for a little physics, but don’t run away. It’s all about springs.

A bicycle and rider can be modeled as a system of weights (where the rider is by far the most significant weight) and springs. The seat is a spring. The seatpost is a spring. The frame, the cranks, the wheels, the tires – all springs.

The stiffness of a spring, also known as the spring rate, is defined as the force required to deflect the spring a given amount.

For instance, consider a tire as a spring. Suppose we apply a load of 100 pounds on a tire and it deflects 1/4″. The tire’s spring rate is calculated as 100/0.25 = 400 lbs/inch.

A spring’s compliance is the inverse of the spring rate. So the tire in the example above has a compliance of 1/400 = .0025 inches per lb.

This sounds like a very small number, but it is huge compared to the compliance of other parts of a modern bicycle system.

The neat thing about using compliance instead of spring rate for a series of springs is you can add up the compliances of all the elements to arrive at the compliance of the whole load path. Because the tire has the largest compliance, it dominates the compliance of the system. But still, the compliance of each component contributes to the total compliance.

A rider can be viewed (simplistically) as resting on two stacks, or series, of springs. One series leads down from his/her butt through the rear wheel to the ground. The other leads down from his/her hands through the front wheel to the ground.

What about the series of springs that lead from the rider’s feet through the pedals/cranks/bottom bracket/frame, etc. For now, discussing compliance, let’s ignore that one. When you judge a bicycle’s comfort (compliance), do you think of your feet? I think of my butt and my hands. Later when we consider stiffness and efficiency, that one becomes critical.

I hope this introduction has gotten you interested. In coming posts I will wax esoteric on each load-bearing element of the bicycle system from the rider to the ground. I think I’ll start with wheels.

Until next time,

Killa

 

 

Nails and Tires

My friend Bryan “Doc” Dotson gets around by bicycle – a lot. This is a guy that takes stray cats to the vet in an infant trailer. So, when he makes an esoteric observation on bicycles and cycling, I listen. From Doc:

Flat tires. You would think that they would universally be regarded in the same category as say, fire ants or presidential candidates, but that’s not true. My youngest daughter, when she was about 3 years old, got really excited every time I had a flat tire on the bike. It’s her thing now.

One type of flat intrigues me. I just had my fourth “nail” puncture:

Nail in Tire

I’ve had three on my 2” tire mountain bike; this is the first I’ve had with my 34 mm tires (which, by the way, I ride much more). All have been the rear tire.

This is now more than a fluke.

My best guess is the front tire picks up the nail, which then tumbles in the wheel track. The rear tire arrives when the nail is ideally positioned to drive straight in.

I’m interested in how many others have observed this phenomenon. Anyone ever had a nail in the front [tire]?

An old article by Jobst Brandt describes this phenomenon. So Doc, you are not alone in your observation. I’ve only ever picked up one large nail in a bike tire, and it too was in the rear tire.

Another thing I’ve noticed – at almost any intersection while I am stopped waiting for a light, I can find a nail or screw lying in the street. I usually pick these up, not so much for for fear of flatting my bike tire, but because as a cyclist and a motorist, the car tire that picks up that nail later in the day may be my own.

Video – A Better Way to Remove and Re-install Your Front Wheel

In my most recent post, I described an alternative method to remove and re-install your front wheel that does not involve reaching down to the axle with both hands while trying to balance the bike with your chin. Recall the steps:

1. Stand directly in front of the bike.
2. Hold the handlebars with your left hand.
3. Place your left foot next to the right side of the front wheel.
4. Reach down with your right hand to operate the lever.
5. Press the inside of your left calf against the quick-release nut to hold it still while you turn the lever with your right hand to loosen or tighten.
6. When you are ready to flip the lever closed, release your calf pressure so that the fork can settle down evenly over the axle.

Here’s a video demonstration of the technique for the visual learners among you.

https://youtu.be/naVoZDnj_VM

If you like video and want to see something specific, let me know.

Thanks for watching!

Killa

Not-So-Quick-Release Skewers

I promise to move on to other topics next post, but I want to talk about the relationship between your front quick-release and your fork. And I will show you a trick to make wheel removal and installation easier – and a lot more elegant.

The quick-release mechanism was patented in 1930 by Tullio Campagnolo, then a frustrated bicycle racer. Blah, blah, blah. Read all about it here: Wikipedia Quick release skewers.

Fast forward some sixty years to the introduction of secondary retention methods, AKA lawyer tabs. These tabs on the fork dropouts prevent the wheel from bouncing out of the fork, even if you forget to tighten the quick-release. See Sheldon Brown’s article on quick-releases for some good photos of various prior designs. I think you’ll agree that lawyer tabs are the best of the lot.

Am I the only person that finds it interesting that no-one is concerned about the rear wheel falling out of the dropouts? I guess that would cause a less spectacular crash. Continue reading “Not-So-Quick-Release Skewers”

Skewer Spring Reprise

Amazing! Within 72 hours of my post on quick-release skewer springs, this tri-bike sBackwards springhows up in the garage.

Who can tell us what the problem is here?

That’s right, the spring is installed backwards. I did not stage this photo. I removed the skewer and there it was. Fortunately it didn’t jam the wheel in the dropout and all ended well. One more rider who will never make that mistake again.

 

 

 

 

Thinking About Quick-Release Skewer Springs

Do you have recurring nightmares about quick-release skewer springs? Me neither. But sometimes on a long ride I think about them.

Bicycles are made up of lots of parts. Quick-release skewer springs are among the smallest, right down there with bottle cage bolts. Such simple devices, yet so often misunderstood. I am talking about the small cone-shaped springs that go bouncing off into the grass if you unscrew your quick-release all the way. As you know (which means “You may not know this”), the pointy end of the spring goes towards the middle. It matters. This is how it should look.

FullSizeRender

If you just like to ride your bike without understanding it on a deeper personal level you can stop reading now and go look up a video on how to operate a quick-release. Otherwise, read on.

What do these springs do anyway? They exert a centering force on the quick-release skewer, equalizing the gap on both ends of the axle. This, in theory, makes it easier to insert the wheel into the dropouts. Then when you clamp the lever down, the springs compress to get out of the way.

Are they necessary? No, not really. If you lose one, remSpringWeightove the other one and ride without them. None is better than one. In fact, on bikes with rear-facing dropouts, many riders remove the skewer to remove the rear wheel. If you change your wheel this way, the springs are completely extraneous – and think of the weight you’ll save by leaving them out. Almost a gram!

There are several ways to get quick-release skewer springs right and wrong. Here they are, from best to worst, in my opinion:

  • Two springs, pointy ends inward – Correct!
  • No springs -You may have to jiggle the wheel to get it in place, which you sometimes have to do even with the springs.
  • One spring, pointy end inward – This pushes the skewer to one side, making it more difficult to insert the wheel into the dropouts.
  • Two springs on one side, nested, pointy ends inward – I just came in from the garage and added this ingenious method of getting it wrong after seeing it on a bike I am working on, really!
  • One or two springs, wide end(s) inward – This is bad. The wide part of the spring will ride over the axle. Several undesirable results can occur when you force the axle into the dropout with a spring over it.
    • The axle (plus spring) won’t seat fully into the dropout, causing the wheel to be misaligned. If you’re following someone and you notice their wheel is way off-center, but not wobbly, it is probably because one spring is on backwards.
    • The spring can get mashed and deformed as you jam it into the dropout. Throw that puppy away. Deformed springs will not compress cleanly and may prevent you engaging the dropout firmly the next time.
    • The wheel can get stuck in the frame. I had a friend text me – including pictures – with exactly this situation, wondering how a piece of wire had gotten jammed around his axle. The spring was so mangled it was unrecognizable. It took him an hour or so with needle-nosed pliers and assorted other implements of destruction to remove the culprit and get his wheel off. That’s one rider that will never get it wrong again!

Just remember, pointy ends to the middle.

In my next post, I’ll stay on the quick-release theme and discuss the relationship between your front quick-release and “secondary retention devices”, aka lawyer tabs. I’ll show you a trick to ease wheel removal and installation. And no, I am not going to suggest that you grind off the lawyer tabs.

 

 

Why do they call me Killa?

Why do they call me Killa? That’s a good question. As is common in social circles, especially of cyclists, everyone has a nickname – Cheetah, Harpoon, Patron, Ironman, Smoke, etc. And there is always one guy that is “giver of nicknames”. In our case, it’s Patron. He named me and it stuck. I think it had something to do with our relative speed on our daily commute. You’ll have to ask Patron.