Calgarypuck Forums - The Unofficial Calgary Flames Fan Community - View Single Post - Mathematics finally learns how to ride a bike

tkflames · 06-07-2007, 11:01 AM

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.

06-07-2007, 11:01 AM	#8
tkflames First Line Centre Join Date: Feb 2006 Exp:	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.