Why bicycles are so stable?

Why bicycles are so stable?

Summary: For almost 150 years now, mathematicians have tried to understand why a bicycle could be so stable. Now, researchers of the Delft University of Technology (TU Delft), working with colleagues from Cornell University and the University of Nottingham, UK, say they've build a model which unravels how a bicycle works. As said a bicycle maker, when designing a bike, only three parameters are used: the general geometry, the distance between the axles, and the angle at which the fork points downwards. The new mathematical model includes 25 parameters and will permit to build bicycles aimed directly at special target groups. Already, a Dutch bicycle manufacturing company is hoping to design better bikes using this model.

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For almost 150 years now, mathematicians have tried to understand why a bicycle could be so stable. Now, researchers of the Delft University of Technology (TU Delft), working with colleagues from Cornell University and the University of Nottingham, UK, say they've build a model which unravels how a bicycle works. As said a bicycle maker, when designing a bike, only three parameters are used: the general geometry, the distance between the axles, and the angle at which the fork points downwards. The new mathematical model includes 25 parameters and will permit to build bicycles aimed directly at special target groups. Already, a Dutch bicycle manufacturing company is hoping to design better bikes using this model.

The TU Delft bicycle

This research was led by Arend Schwab, an assistant professor in applied mechanics at TU Delft working on Bicycle Dynamics. he's also leading the Delft Bicycle Dynamics Lab where he's working with his former student Jodi Kooijman. You can see above the bicycle built by Kooijman to valid the the 3 degree of freedom model. "He measured the steering angle (potentiometer), lean rate and yaw rate (angular rate gyros) and the angular rotation of the rear wheel (Avocet 50 bicycle computer). During 76 runs the bicycle was laterally perterbed and allowed to coast freely at a number of different speeds mostly between 2.5 m/s and 6 m/s." (Credit: Experimental Validation)

"Bicycle manufacturers have never been able to say precisely how a bicycle works," explains Schwab of the Faculty of Mechanical, Maritime and Materials Engineering (3mE). "They have always had to refine their designs purely through experimentation. In our model, they can enter into the computer all of the various factors that influence the stability and handling of their bicycle. The model then calculates how the bicycle will react at specific speeds."

This research work has been commented in Delft Outlook under the name "Bicycles made to measure" (written by Tomas van Dijk). Here are some comments about the stability of a bicycle. "The bike’s speed must be between fourteen and twenty seven kilometres per hour," Kooijman says. "At those speeds, the bicycle is inherently stable. If it goes faster, it will wobble less, but if you then push it sideways it will lean over to one side until it topples. The data match our model predictions exactly." You can see images and videos confirming this on thias page about Treadmill Measurements showing a bicycle's stability at various speeds.

The above article is also available in PDF format (4 pages, 364 KB). This version shows on the last page why we need to briefly steer on the right to make a left hand turn. "We all know intuitively the main combination of forces that ensure we stay upright when riding a bicycle. They involve leaning over and steering and they explain why, when we wish to turn to the right, we have to first turn the front wheel slightly to the left. The action, known as counter steer, results in a force that causes the bicycle to lean over to the other side, which is the direction in which we wanted to go. This also explains why we fall over if we pass too close to a kerb. We just can't manage to get away from it without hitting it."

This is why this new mathematical model is using as much as 25 parameters. "All of them are relate to the two connected motion equations, one for leaning over and one for steering. 'It remains unclear how exactly all these parameters affect the stability,' Schwab says. 'In the final model these parameters appear in fairly complex forms as coefficients to the motion equations. For practical purposes most researchers used to simplify the equations by disregarding certain parameters, but the results tended to be far from ideal. And scientists who failed to make the connection between leaning and steering certainly were on the wrong track altogether.'"

So will we ride better bicycles? Probably soon according to Rob van Regenmortel, product development manager of bicycle manufacturer Batavus. "Van Regenmortel would like to collaborate with Schwab and Kooijman on a future project that will also look at the riding behaviour of the cyclist. The ultimate goal of the bicycle research effort is to include the cyclist's riding behaviour in the model so as to be able to investigate the combination of the bicycle and its rider. 'We could then actually make a ‘tailor-made’ bicycle for everyone,' Van Regenmortel says. 'People who find it difficult to maintain their balance would no longer have to ride a tricycle.'"

Sources: Delft University of Technology (TU Delft) news release, September 18, 2007; and various websites

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8 comments
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  • Hmm... did I miss something here???

    I didn't see anything specifically intertwining the human brain in this? Fact is that the human brain is generously probably 50% of the formula because the brain, ears, etc., are what help the human body maintain balance, and this includes riding a bike. Even someone who is impaired somewhat by brain and head injuries manage to still ride a bike because if they could stand and walk, they can ride--the balancing circuits in their bodies are working. They just compensate on balance different than someone who is considered normal. Simple combination of balance, forward motion, "G's", gravity all play a part.
    jskline0@...
    • click

      You missed the links to the press releases and videos. "Ever
      since the invention of the pedal-driven bicycle around 1860,
      researchers have been trying to determine what makes a bike
      fairly stable [i]of its own accord[/i]."
      In the videos, you'll see a bike without rider so that factor
      doesn't balance the bike. The human brain in the vids actually
      tries to destabilize the bike. ;-)
      Caesar Tjalbo
  • RE: Why bicycles are so stable?

    About a year ago there was a program on one of the Science or History channels that covered this topic.

    A team of researchers experimented on a bicycle and determined that while the human rider did offer some control in keeping the bike upright, the wheels acted as gyroscopes. To demonstrate this, they had a rider take a short. As expected, the rider encountered no problems with the bike.

    The team then mounted weights beside the front and rear wheels. The weights were circular and spun like flywheels. The weight of these "flywheels" were equal to the weight of the bike's tires.

    When the flywheels were spun in the same direction as the bikes tires, the rider was able to keep the bike upright at slower speeds, and encountered difficulty when attempting to lean the bike to one side of the other.

    When the flywheels were spun in the opposite direction of the bikes tires, the rider was unable to keep the bike upright and failed to get it traveling in a controlled manner.
    ShoreLeave
  • The wheels are gyroscopes . . .

    "For almost 150 years now, mathematicians have tried to understand why a bicycle could be so stable."

    Which mathematicians? Obviously not the ones who played with gyroscopes when they were young. The mathematics were - and are - well known. They derive from the physics of centripetal and centrifugal motion.

    Maybe if the mathematicians got together with physics experts, they'd figure it out better.

    "Bicycle manufacturers have never been able to say precisely how a bicycle works"

    Basically this only really tells me they've never studied physics beyond high school. Gyroscopic motion is taught in physics classes.
    CobraA1
    • A myth, alas

      The gyroscopic effects of the bike wheels are very, very small - your high school probably didn't make you calculate it or experiment with it like <a href="http://www2.eng.cam.ac.uk/~hemh/gyrobike.htm">This guy</a> who computes "gyroscopic effect will only help me if I don't tilt more than 2 mm"
      htroup
  • RE: Why bicycles are so stable?

    Is there a reason the front fork is on backwards? This will change the geometry of the frame and might make all data gathered suspect.
    osub5
  • bike stability

    Is there a reason the front fork is backward? This will alter the bikes frame geometry making all data suspect.
    osub5
  • RE: Why bicycles are so stable?

    The most comfortable and stable bike I have ever had was my late sixtys paperboy bike. A Schwinn heavy duty with the front spring fork. They should study that with a full load of Sunday papers on it. That design (which you can still buy today) is by far the most stable.
    d11andrew@...