Technical FAQ: Factoring tire weight into modeling energy consumption, and understanding the physics of front-end shimmy

Have a question for Lennard? Please email him at veloqna@comcast.net to be included in Technical FAQ.

Dear Lennard,
With the advent of very precise ways to measure rolling resistance across a broad range of tires, I'm curious as to how the actual tire weight factors into the total energy required. I get that lower rolling resistance is an obvious benefit (all other things considered equally) but what about the actual weight of the tire?! Particularly for gravel tires, there is a significant difference in tire weights across manufacturers. As an example, if “tire A” has a modest advantage in rolling resistance but is 70 grams heavier than “tire B,” what is the upshot of that, or can it even be quantified?
-- Jeffrey

Dear Jeffrey,
Weight comes into play in a number of ways. First, it tends to be baked into the rolling-resistance lab results. A lighter tire will have less mass in the casing and tread. It will tend to absorb less energy hitting bumps when rolling along because there is less mass being moved with each compression into the tire. If two tires have identical materials, casing construction, and tread compound and pattern, the lighter one will roll faster.

Secondly, a lighter tire will take less energy to lift it up a hill, which will be an advantage in the mountains. On undulating terrain, you get the energy back on the downhill, but only at low speeds; it is lost to extra aerodynamic drag at high speeds.

Thirdly, a lighter tire will take less energy to accelerate. Once it is up to the same speed as a heavier tire, their relative weights are irrelevant on flat ground until the rider applies the brakes. If brakes are not used, weight is not a factor once the tire is up to speed, since, while it takes more energy to accelerate it and get it up to speed, that energy is returned when the rider eases off and takes advantage of its higher translational and rotational momentum.

To quantify the benefit of a lighter tire, it is necessary to clearly define the terrain it is being ridden on and the style of riding (if brakes are applied or not). In cyclocross, for instance, low weight is a big advantage, and rotating weight even more so, because each of the multiple laps contested contains numerous very sharp corners, requiring hard braking followed by accelerating. It also requires lifting the bike over obstacles and running uphill with it, and lighter weight is obviously an advantage for that. In that instance, 70 grams saved in each tire could lead to an advantage in a race over a set of tires with modestly less rolling resistance. On a straight, flat, gravel road at steady-state riding, however, the heavier, faster-rolling tire will have the advantage.
-- Lennard

Dear Lennard,
Recently, front-end shimmy came under discussion again. This topic has created lots of interest in your column through the years. I’ve seen good advice to stop it: stiffer frames, unloading the front wheel, etc., but might have missed an explanation why it actually happens? Or have you kept yourself from opening this Pandora’s box?

Also, from other sources, it is hard to find conclusive info regarding its cause, but there is certainly more to read about its complex nature. What seems obvious is there has to be in contact with the ground, and there has to be a resonator.

A firm and reasonably even ground support seem to be needed, it is not likely to happen on grass or gravel. It will not happen if the bike is airborne. So where is the cause of the phenomenon, and where is this resonator?

I’ve a theory that this phenomenon could be initiated and withheld by an oscillation in the self-balancing action of the bike?

If a free-rolling bike falls slightly to one side, the front wheel and fork will steer to that side but in reality actually overcompensate, soon making it steer to the opposite direction. After which this repeats itself. This way the bike repeatedly straightens itself, and most bikes can thus balance themselves even without a rider, as long as the bike is being propelled.

This "self-balancing" should happen with a certain frequency and more or less dampened return force depending on, among other things: the load, speed, geometry of the fork, as well as the size, shape, and hysteresis of the tire and its contact patch. One can easily observe that the return force is higher when fork angle is slacker as well as when tire pressure is low, for example on a fat bike.

What in reality constitutes this self-stability of bicycles has been discussed in scientific terms, and to my knowledge, it is still much of an enigma. Here is one interesting report, for example, it shows balance is still possible without both trail or gyroscopic forces.

Anyway, if my amateurish assumption is correct, this often unnoticeable steering undulation may then under some circumstances may become augmented, specifically if its frequency is mirrored and equaled somewhere else in the vehicle.

A marriage just waiting to happen when frequencies happen to coincide.

Even more so if there is a lack of damping and support of that structure. It could among other things be flexing of the fork, a loaded rack, the frame, or even the musculoskeletal properties of the rider. Or maybe gyroscopic counterforce, really not sure of this one.

The gyroscopic counterforce might at least be part of the equation and will certainly influence how the wheel itself steers or wobbles. In experiments I made on the driveway hitting a free-running, naked bike wheel sideways with a stick, I had to jerk the wheel almost completely down to the ground in order to make it lose control, or else it catches momentum again and in a few revolutions stabilizes as if nothing had happened. It's really amazing to observe! So, it would surprise me a bit if gyro forces per se in the bare wheel are actually ruining the ride. Rather, it seems these are important for both return force and dampening when trying to save it to the bitter end. But I lack the proper knowledge of physics to know if this stabilizing force has a frequency that could also pose a problem. Maybe this is a most central part?

Shimmy may often seem spontaneous but is sometimes observed to be started by a short jerk, the phenomenon soon in full bloom when bike or driver, or maybe then gyro is soon trying to compensate. If there is play somewhere I would imagine things could start up more easily.

In the motorcycle world, they differ between shimmy and weave. Shimmy happens at the front end at a somewhat higher frequency and comparatively lower speed, weave at higher speeds, the whole motorcycle undulating together with the driver. To me these look like expressions of the same thing, the difference being what structure is in resonance with the steering action of the wheel against the tarmac. If the driver is brave enough to make a wheelie, the phenomenon stops and tends to start again when the front wheel lands.

Here is a video of a related example, the front wheel of a small aircraft. Shimmy is a well-known problem with aircraft landing gear, and often there is a specific damper applied. Interestingly in the video, this effect only happens when the tire is compressed - not just touching the ground and in full rotation at a certain necessary speed. One could speculate if there is something uneven in the structure of the tire that shows itself under load, or if the load itself changes self-steering properties, like the fat bike example. As soon as the wheel is lifted just a bit the phenomenon stops, so lack of wheel imbalance per se is unlikely as an explanation. The at the same time, increased fork angle should decrease return force and stability but at the same time make the system less sensitive to any sideways leaning of the pavement. It seems obvious watching the footage that the wobble goes from the ground up.

And in the video below, you can see it happen on a monowheel motorcycle. I’m not sure what resonates with the undulating wheel here; maybe it's the gyroscopic counterforce combined with a softness in the wheel itself, or maybe how the engine is suspended, but could even be the mass of the driver? There is no fork (or trail) present in the system. According to my observations on a naked wheel, this vehicle should have no problems whatsoever quickly saving itself if left alone without a swinging mass "destroying" its ride.

Probably a valid presumption would be that the shimmy phenomenon takes a swinging mass or swinging return force somewhere. But for it to bloom, this needs to come into interaction with the wheel oscillating in its steering grip to the ground. One could discuss which is the hen or the egg, as both are clearly necessary. My guess is the driving force, the whip if you like, is in the contact patch. Remove that, and stabilization should occur regardless of the frequency of the resonating compensator.

But identifying and taking measures against the resonator in each specific case should give a good chance for it not to happen again.

If this ever happens to me, I would make a turn by leaning the bike sideways and at the same time put the load on the rear instead of the front wheel. That is somewhat similar to what every downhill skier would do when a wobbler starts when going straight out at high speed, and in that situation, it is a most effective measure.
-- Kai

From the math professor who explained the principle of Hopf bifurcation in bicycle front-end shimmy:

Hi Lennard,
I am sort of confused by this email. It discusses shimmy, what stabilizes a bike to stay upright (gyroscope or not), and then resonance all in one blur. I see those all as three separate things to discuss.

Shimmy is a hopf phenomenon and not a linear resonance phenomenon. There is a simple "normal form" which in polar coordinates form is rdot=r(a-r^2) and thetadot=w theta that as a passes through zero you get a stable limit cycle. It shows up in many areas in physics and in nature. It can't be reasoned or rationalized by stories that compare it to resonance and I am not sure why people want to throw away math and make everything analogies.

The work he notes regarding how bikes can be stable -- not requiring the gyroscopic force that is usually referred to -- refers to a paper from Andy Ruina's lab at Cornell. I know Andy and I respect him tremendously. He really knows what he is doing. BTW - have you ever seen Andy's mechanical, no-motors walking robot? It's fantastic work!

-- Erik M. Bollt, W. Jon Harrington Professor of Mathematics and Electrical and Computer Engineering, Clarkson University

Lennard Zinn, our longtime technical writer, joined VeloNews in 1987. He is also a custom frame builder (www.zinncycles.com) and purveyor of non-custom huge bikes (bikeclydesdale.com), a former U.S. national team rider, co-author of “The Haywire Heart,” and author of many bicycle books including “Zinn and the Art of Road Bike Maintenance,” “DVD, as well as “Zinn and the Art of Triathlon Bikes” and “Zinn’s Cycling Primer: Maintenance Tips and Skill Building for Cyclists.” He holds a bachelor's in physics from Colorado College.

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