What is "wobble" and "shimmy" of a bicycle?

The words (speed) wobble and shimmy are both interchangeably used in academic and popular literature without a unique or definitive definition. Both terms are used to describe higher frequency oscillations that single track vehicles (bicycles, motorcycles, and similar vehicles) sometimes exhibit [Wikipedia2020]. In this case, "higher frequencies" refers to being higher than the vehicle's weave oscillation frequency. Weave is the fundamental steer and roll oscillation that occurs in the 0 to 4 Hz bandwidth for bicycles traveling at speeds below 20 m/s (72 km/h, 45 mph). In addition to the frequency differences, at higher speeds this wobble/shimmy oscillation can grow in magnitude (unstable) whereas weave oscillations become more damped (stable) as the speed increases.

Wobble/shimmy oscillations are attributed to the effective flexibility of the bicycle frame between the contact patches of the two tires. This flexibility is primarily a combination of the flex in the tire carcass and structural stiffness of the frame and wheels. On the other hand, weave oscillations are present even if the bicycle and tires are infinitely stiff, i.e. weave is a function purely of the assembly of rigid bodies (wheels, fork, frame, ground) and the nature of their connections.

Advanced dynamics models of bicycles are able to predict the wobble/shimmy oscillation ([Plöchl2012], [Klinger2014]) and, at least in these papers, wobble is specifically defined. These models show that:

• at speeds > 13 m/s (45 km/h) the wobble frequency of oscillation is between 8 and 12 Hz
• the dominant motion during wobble is the oscillation of the handle bar and fork about the steering axis and this steer motion has an amplitude magnitude of 3-5X that of the roll motion
• there is a speed threshold (2-6 m/s) at which the oscillation will tend to be unstable and grow; above this threshold damping this oscillation is the responsibility of the rider
• slowing down will dampen the oscillations

This video shows a steer dominant high frequency oscillation that qualitatively matches the wobble/shimmy model predictions to give an idea of what these research papers are modeling:

Did Chloé Dygert experience wobble/shimmy?

After watching Dygert's crash frame-by-frame, we make some observations:

• She's likely traveling at a speed between 9 m/s (32 km/h, 20 mph) and 13 m/s (47 km/h, 29 mph)
• She is in a steady rightward turn, with a large roll angle of about 30 degrees or so.
• She is not pedaling during the event.
• She is initially bounced from her seat and the oscillation builds with her disconnecting more and more from the seat. This left her fully connected to the bicycle only at the time trial bars and at the pedals.
• The magnitudes of the steer and roll angles during oscillation are of similar magnitude.
• The frequency of oscillation is approximately 4.2 Hz.

The last two points would seem to indicate that this isn't wobble/shimmy; at least not by the definition espoused by the academic literature. The frequency is half what it should be and it isn't steer dominant. The video of Dygert shows clearly different oscillations than that shown in the "Bicycle Shimmy" video above. We aren't likely seeing wobble/shimmy in Dygert's crash but the initial jolt visible in the video surely excited an unstable oscillation. The large bump may have played a significant role in initiating the subsequent cascading effects. There is also the possibility of the rider effectively causing the instability. This is well documented in aircraft as "pilot induced oscillations", but seems less likely as it requires more activity on the rider's part.

Here is a video that has similarities to Dygert's oscillation. In this video, the rider's pelvis seems fairly firmly connected to the seat. The oscillations are similar in magnitude for steer and roll and a frame-by-frame analysis estimate gives a 2 Hz oscillation frequency, which also doesn't fit the bill to be wobble/shimmy. Interestingly, it occurs with the more solid seat-rider coupling and not at a hard roll angle.

Conclusion

One important assumption in the wobble/shimmy academic literature is that the rider's pelvis is firmly connected to the seat in the models. With Dygert's pelvis disconnected from the seat, that bicycle-rider system is thus different than these models. The interactions of the rider's flexible body with the bicycle in Dygert's riding position may very well destabilize the weave oscillation. For example, [Moore2012a] shows that simply adding the inertial effects of the rider's arms to the handlebars can have a destabilizing effect.

A second important assumption in the models in the academic literature is that the nominal roll angle of the bicycle is zero. At a roll angle of 30 degrees, the predicted frequencies of wobble/shimmy oscillation could be lower and the steer and roll amplitudes similar in magnitude. This would then better match what we observe with Dygert's crash. At large roll angles like this, the vehicle could also have an easily destabilized lower frequency weave oscillation. But there are no studies of these phenomena in hard steady turns for bicycles.

So, what caused Chloé Dygert's crash? Given the limited information and barring there were no mechanical failures, our best idea is that a bump excited an unstable weave-like oscillation during the descent. The high speed and large roll angle as well as Dygert's time trial body position and her disconnection from the seat may have all contributed to this instability.

Developing a predictive model of the rider being loosely coupled to the bicycle could help answer whether there are aspects of the bicycle's design or seating position which could minimize the chance of this happening. Studying perturbations around large roll angles could also offer more insight. And, lastly, a rider control model could help determine whether there is something the rider could actively do to stop this and regain control (besides slowing down). These types of analyses take more time and resources, but could likely pin down the cause more concretely.

Acknowledgements

We thank Jaap Meijaard for some helpful comments as well as the folks on the Single Track Vehicle Dynamics discussion list for providing food-for-thought. Yumiko Henneberry contributed copy editing.

References

Notes

• Women time trial-ers average about 45 km/h (12.5 m/s), so she should have been going faster than this going down hill (but she isn't pedaling).
• [Plöchl2012] shows wobble frequencies between 6 and 9 Hz for 0 to 20 m/s in Figure 4. Same figure shows the wobble mode unstable from about 4 to 20 m/s. This is for a model with rider lean and the but attached to the seat.
• [Klinger2014] shows wobble between 8 and 12 Hz for 0 to 20 m/s for leaned over hands on handlebars (no rider lean DOF).
• Figure 6.10 in [Moore2012b] shows that the weave frequency for a bicycle without a rider can get higher 10 rad/s (1.6 Hz) at 7 m/s, maybe it would be close to 4 Hz at 13 m/s?? But weave should be damped and stable at these speeds.

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import pandas as pd
df = pd.read_csv('dygert-oscillation-data.csv')
fps = 30
df['time'] = df['second'] + (df['frame'] - 1)/fps
period = 2*df['time'].diff().mean()
frequency_hz = 1/period
frequency_hz

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