The science of efficient cycling

The A group

Well - some of the science.  I went to the Royal Institution's Summer Science Fair last week, and Bristol University had a stand explaining how they had brought a 1.5% efficiency gain to the GB cycling team at the Rio Olympics.  There are some possible ideas for us all.  But first: the science bit:

How hard you have to pedal for a given speed, v

There are three main parts to this equation:

1. Air resistance (at the top left), which goes up extremely fast as your speed increases, and quickly becomes the most important thing trying to slow you down above about 10mph.  At 20mph, air resistance makes up about 80% of the work you have to do.  To reduce air resistance, you need to have a small surface area (skinny bike, skinny rider, no panniers, tucked low on the bars), and wear skin-tight, aerodynamic clothes.   Or cycle slower.    And of course, cycling into the wind makes makes your effective speed higher, so it's even more important - this is why cycling behind someone else makes it easier, since it reduces the effective headwind.
2. Rolling resistance (top right) is resistance between your tyres and the road.  The GB team use high pressure kevlar tyres - and a very smooth track surface - but recent articles in Cycle magazine, and Mark's investigations, seem to suggest that wider, lower pressure tyres may be just as good on real road surfaces.  So - take your pick.  And - rolling resistance varies in proportion to your weight and speed.
3. Transmission efficiency (bottom of the equation) is how much effort gets from your legs through the chain and gears to drive the back wheel.  This is where the Bristol University research found 1.5% efficiency gains.  Chains are quite efficient - only about  5% of your effort is lost in the drive chain) - but this can be improved by using a bigger cog, front and back, as it reduces chain friction, and careful lubrication.  Team GB had a secret lubricant fomula that even the Bristol researchers don't know.   Cross-chaining is also said to be bad for transmission efficiency (see here).   I doubt this is a major factor for most of us.
4. Something is missing: hill-climbing effort.  The Bristol researchers had not heard of the Surrey Hills when they did their research, and so only took account of flat cycling.   They live a sheltered life.   So a fourth term has to be added: mgvSin(s) - your mass, times gravity, times your speed, times the sine of the steepness of the hill you're climbing.   This is by far the biggest factor (as we all know!).  If you're climbing even a 1% hill at 10 mph, more than half your hard work is going into climbing, rather than air resistance etc.   So - best to avoid hills!

So what did we learn?   Probably not much of use - but in summary: going uphill, most of your work is going into climbing;  on the flat, most is going against wind resistance;  and downhill - enjoy!

There is an online model here, if you want to put your own numbers in and see where your hard work is going on Box Hill or similar.