# Problem of wheeled suitcases wobbling explained

(Phys.org)—A team of researchers at Universite Paris-Diderot has uncovered the reason for wobbling of wheeled suitcases. In their paper published in Proceedings of the Royal Society A, the group explains the physics behind suitcase wobbling and offer some suggestions to overcome the problem.

Most people who travel these days use a suitcase with wheels that allow for pulling it around rather than carrying it. While the new approach does make it easier to lug a suitcase, it has become clear such luggage suffers from a serious problem—wobble. Sometimes, while a suitcase is being wheeled, it starts to wobble back and forth—and in some cases, it progresses to actually tipping over. As the researchers with this new effort note, the natural reaction is to slow down—but that is actually not the best option, they report after conducting experiments with model suitcases in their lab. The suitcase problem is a reminder that not all physics are complicated.

To learn more about what happens with wheeled suitcases, the researchers placed a model suitcase on a treadmill and watched what happened. They discovered that if one of the wheels encountered an obstacle such as a small bump, it jumped into the air for just a moment and then banged back down to the ground. That second action caused the opposite wheel to lift off the ground and then to bang back down, causing the first to lift again and so on. This increases, the researchers found, as the suitcase is pulled forward. Eventually, it overturns. It happens, the group found, because the two wheels are on a fixed rod and because of the force exerted by the person pulling.

The researchers also found that the best way to slow the oscillations is to increase the speed at which the suitcase is being pulled—this gives the suitcase less time between each rising and falling, preventing the oscillations from growing stronger. Reducing the angle of the suitcase can help too, they note, which means lowering the handle toward the ground, though it seems that attempting to apply both remedies simultaneously would require some degree of athleticism.

Explore further

Context and distraction skew what we predict and remember

More information: The rolling suitcase instability: a coupling between translation and rotation, Proceedings of the Royal Society A (2017). rspa.royalsocietypublishing.or … .1098/rspa.2017.0076

Abstract
A two-wheel suitcase or trolley can exhibit undamped rocking oscillations from one wheel to the other when pulled fast enough. We study this instability both experimentally—with a toy model of a suitcase rolling on a treadmill—and theoretically. The suitcase oscillates only if a finite perturbation is applied. This is because intrinsic dissipation occurs when the supporting wheel switches. When unstable, the suitcase either increasingly rocks until overturning or reaches a stable limit cycle. The friction force at the rolling wheels constrains wheels to roll without slipping. This constraint imposes a coupling between the translational motion and the three-dimensional rotational motion of the suitcase that drives the rocking instability. The same behaviours are observed in the experiments and in the simulations. The asymptotic scaling laws we observe in the simulations are explained by means of a simplified model where the coupling force is explicit.

Feedback to editors

Jun 21, 2017
The thing that exacerbates the "wobble" is a top heavy load. Place the heaviest items at the bottom where the distance from the axle to the load is the shortest distance possible to the heaviest part of the load.

Jun 21, 2017
The thing that exacerbates the "wobble" is a top heavy load. Place the heaviest items at the bottom where the distance from the axle to the load is the shortest distance possible to the heaviest part of the load.

Yep, top-heavy load = more torque.

Jun 21, 2017
This is amazing.

Jun 21, 2017
Bigger wheels, wider wheel base, independent suspension...
And.. get to the airport sooner so you don't have to run from counter to gate...

Jun 21, 2017
Vehicle trailers are infamous for this, hence the care required for load weight & distribution, suspension damping and draw-bar design.

FWIW, the same wobble can be used to shift a very heavy, but 'leggy' table. An offset push or pull to break 'stiction' and torque the frame may let you quickly 'walk' it across a room when a steady effort fails...

Jun 21, 2017
"The researchers also found that the best way to slow the oscillations is to increase the speed at which the suitcase is being pulled—"
These researchers would have recommended that the Tacoma Narrows winds should be blown at different velocities so that the Galloping Gertie bridge wouldn't fall down. It's the job of designers to match their constructions to nature and human users, not the other way around.

Jun 22, 2017
Would it have anything to do with the shape of the wheels?

In the videos they seem to have square wall wheels, instead of rounded edges. It may be the wheel geometry that's causing some sort of screw action to happen with the treadmill belt.

Vehicle trailers are infamous for this

I think that's quite a different phenomenon, and it involves the pulling vehicle as well because it forms a two-mass system where the pivot in the middle is transferring angular momentum between the car and the trailer.

Jun 22, 2017
You can see the trailer wobble effect in this video:

https://www.youtu...kOVHAC8Q

It clearly involves some dynamics with the pulling vechicle, instead of the wheel-lifting effect demonstrated in this article.

https://www.youtu...rWHTG5e8

Jun 22, 2017
In all those caravan scale model videos, what they're doing is increasing the distance of the mass from the point of support, which is increasing the moment of inertia of the mass around the support. In other words, it's making the caravan heavier to turn. That lowers the resonant frequency of the car-caravan system.

When the car is driving along the road, bumps and dips in the road excite harmonic oscillations in the system. When you're going at a speed under the resonant frequency, the system is said to be underdamped. Disturbances are amplified, but don't grow without a limit. When you're running above the resonant frequency, the system is overdamped - oscillations actually decrease. The dangerous spot is in between, transitioning from under- to overdamping. Hitting the resonant frequency makes the wobbles grow without limit.

Increasing the moment of inertia of the trailer brings down the speed where you hit the system resonance to normal road speeds.

Jun 22, 2017
The above explaination is also the reason why the article says to increase speed: it takes the frequency of disturbances like floor tiles hitting the wheels above the resonant frequency and the effect is damped.

Jun 22, 2017
A closer and sometimes fatal analogue is ground looping in tail dragger aircraft. In both cases the side thrust of the wheels when tipped amplifies the swing. Outward inclined wheels were sometimes used to eliminate this effect. Narrow track relative to CG height adversely affects both Samsonite and Spitfire! (ME-109 was particularly treacherous with ground losses exceeding air combat)

The inclined wheels and larger diameter would seem to be adaptable to luggage. Packing wisely and reducing handle inclination as noted helps. Balls do not exhibit this side thrust but they may risk clipping your Designer heels! Narrows Bridge classic case of extrapolation --record slenderness resulted in discovery of coupled span/ wind resonance. Ok back to my drawing board to work on my topple resistant valices!

Jun 22, 2017
The equations for dual-wheel shimmy of aircraft landing gears will produce the same result. Applying a linear criterion for stability is all that one needs to properly understand what is happening.

Jun 22, 2017
Useful data. Speed up and lower the handle.

Now, who was whining that science never provides any benefits?

Next up, redesign suitcases to not wobble. Or convince people to put the heavy stuff on the bottom. Duh.

Jun 22, 2017
Now, who was whining that science never provides any benefits?

I don't know, but I do know of someone who likes to downvote people for explaining the science because of some petty personal feud.

Jun 22, 2017
The solution to this problem is an easy one. Simply push the case in front of you instead. of pulling it behind you.

Jun 24, 2017
This comment has been removed by a moderator.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more