The Physics of Cycling

Welcome to my website


During the past 2 years I've been rediscovering cycling, not as a sport, but rather as an utilitarian and leisure activity. As a consequence, I have spent quite some time reading blogs with advice on the subject, websites with technical information about bicycles, but I find that there is not much information about the physics approach to cycling. I also find that some bicycle specs (for example: the Pashley Roadster Sovereign's) do not indicate the gearing range which is something to consider when chosing a bicycle. In some forums I come across discussions like, how in some european hilly cities a considerable percentage of citizens use the bicycle as their principal mean of trasportation (and in everyday clothes) vs some north american lycra commuters on cities that aren't that hilly, or that the bicycle's weight isn't really that important...

Without wanting to dispute any of these statements, with this website I'll try to put the philosophy aside and look at cycling from a physics perspective so that the reader has a way of quantifying what really is at stake. Some of the information posted here may also be helpful for the purpose of selecting the bicycle's gear ratios that better meet the reader's needs, or, when chosing a certain bicycle, to determine if its gearing is adequate for the intended use without needing to test ride the bicycle up that one hill.


Note: Of course, before chosing a bicycle it's always a good idea to test ride it, see how well it fits and how comfortabe it feels, but in some cases, travelling 50 kms back to where you live, loading the bicycle with all the stuff you need to take to your destination and riding up that 8% sloped hill on km 8 of your commute to see if the bicycle's gearing will allow you to climb it comfortably is not a feasible test-riding option. There is a way to calculate that if you know the bicycle's weight and gear ratios.


My focus will be on the power to overcome gravity on hills, how is it affected by weight and what gear ratio will be needed depending on the power the rider is willing to output.

LIMITATIONS: Please note that the power needed to overcome air resistance and rolling resistance is not considered, as well as power losses in the bicycle (the bicycle is assumed to be 100% efficient). However this won't be an important factor if you calculate the power you can steadilly output (see random notes) by climbing a hill on your bicycle, as then, all these factors will be taken into account. This means your're producing power not only to overcome gravity but also to provide for all the power losses. 


cycling physics.xls 


This sheet has some formulas that give an idea of the power requirements for different scenarios selected by the user.

To use this file, input your values on cells A5 to G5 (note: for the value on B5 (mass)  input the total weight of the set bicycle+rider+cargo), and check the results on column B  (B11 to B16), then you can make some changes to an input, for example C5 (cadence) and see how it will affect the results.

If you are using an internal gear hub, you can calculate an equivalent rear sprocket if you know the gear ratios of your hub.

You will find the gear ratios of your hub in the Sheldon Brown's website. It has invaluable technical information and has helped me a lot with some of my projects (like lacing wheels for my bicycle).

Having the gear ratio for the speed you want to consider (when climbing hills you may want to consider the 1st speed), you can enter it on line 18, along with your drivetrain data and it will show the equivalent rear sprocket size on E22. The predifined ratio of 0.527 is for the 1st speed of the Shimano Nexus/Alfine 8 hub. Note that when in direct speed (hub ratio =1) the equivalent rear sprocket size is the same as the existing one.