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.

Here 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 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 wheel 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 when 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 down 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.