Mathematics finally learns how to ride a bike

[Cowperson]

An odd story today . . . . . it took more than 100 years for mathematicians to finally describe why it is that you can ride a bike.

http://www.telegraph.co.uk/earth/mai.../scibike06.xml

Cowperson

[GoinAllTheWay]

That is really freakin weird how long it takes to get an equation figured out for that kind of thing, it is taking for granted by pretty much everyone who rides a bike what physics are in play. Didn't they have a tough time figuring out exactly how the physics of a curve ball in baseball works?

[4X4]

Anybody else have Webster flashbacks while reading that article?

[Maritime Q-Scout]

hrmmm I didn't understand the physics back in high school, I don't understand the physics now . . . amazing how things change over time

[Locke]

Originally Posted by GoinAllTheWay

That is really freakin weird how long it takes to get an equation figured out for that kind of thing, it is taking for granted by pretty much everyone who rides a bike what physics are in play. Didn't they have a tough time figuring out exactly how the physics of a curve ball in baseball works?

And this is the problem. They now know all the math behind riding a bike. I bet you half of them cant do it and the other half dont care......

[Bobblehead]

Now you are going to see some bike get really altered for spead and handling. With the mathematic models now known, designers can find the sweet spots for all the variables to make bikes more stable/ faster, whatever they want.

I had a physics teacher say once that everybody can do physics, they just can't explain it. People generally have no problem driving cars (bad driver jokes aside) but the physics of acceleration, momentum, centripetal forces and so on that come into play are staggering if you were to break it all down. Most people can do this with very little thought.

[Burninator]

Originally Posted by GoinAllTheWay

That is really freakin weird how long it takes to get an equation figured out for that kind of thing, it is taking for granted by pretty much everyone who rides a bike what physics are in play. Didn't they have a tough time figuring out exactly how the physics of a curve ball in baseball works?

I remember a study that was conducted, and I think posted on this site, that did the math on cow tipping. I believe the conclusion was that the only physical way to tip a cow is with four fully grown men. I am sure people who have actually gone cow tipping would disagree, but it was a funny study none the less. One thinks they should have actually gone and tried to tip a cow instead of sitting in front of a pad of paper and a calculator.

[tkflames]

From an engineering standpoint perhaps I can shed some light on the complexity of the mathematics.

The underlying equations used to derive these formulas are likely the same as those you learned in your highschool physics course namely F=mass* acceleration (the second derivative of position) etc. However since this is a mutlidimensional problem (namely that there are up to 18 different variables according to the article) these all need to be considered. Most of these variables will impact others (ie you cannot just consider the motion of the bike in the forward direction if there are forces pushing it left and right). Another way to understand this concept is think of how easy it is to push a shopping cart straight forward but how difficult it is to turn it left or right. When travelling diagonally (turning and driving at the same time) you cannot consider only the force required to turn or the force required to push forward. Both of these need to be modelled. BACK TO THE BIKE: For the bike imagine there are 18 of these dimensions to travel in all potentially affecting the balance of the bike and each other (eg. if the bike leans to one side, this may cause the handlebar to turn).

Included in these equations is also feedback and nonlinearity. Neither of which I will get into (as this is already enough for most) except to say that linearity issues force the mathematician to make restrictions (eg the bike must travel less than 40km/h for this model to be accurate or must travel on a straight road etc). The concept of feedback is required to ensure the model keeps your bike upright.

I hope that makes sense...please feel free to ask any questions but I meant for this to serve merely as an illustration of the complexity vs and analysis of the mathematics required for modelling a bicycle.