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.

4 thoughts on “Wheels – Vertical Compliance, Lateral Flexibility”

  1. Killa,
    The 15 lbf lateral force load the wheel and the wheel support which could be the bike frame and then the stand. So measuring the wheel support deflection, possibly in a repeated test if one has only one dial gauge, will let us know with more confidence that the data is relevant.

    Thank you for the interesting article.

    Pierre

    1. Pierre,
      Fair challenge. I’ll set up my test rig to isolate and measure the deflection in the arms of my truing stand relative to the base when I laterally load the wheel. I’ll report back later today. I’m also setting up a test of rear triangle and front fork lateral flexibility for my next post.
      Killa

  2. Update on test rig flexibility – At Pierre’s recommendation, I set up my dial indicator to isolate and measure the flex of the truing stand arm while applying my 15 lb lateral load at the wheel rim. I read a deflection of 0.007″. This leaves 0.093″, or 93%, of my total measured deflection attributed to the wheel. Thanks Pierre, for encouraging me to upgrade my experimental method. Given the cavalier design of my test rig and measurement techniques, I don’t think this correction changes my conclusions. 7% of something less than 0.5% is a very small change.

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