# How much time can I save in a bike race

1. Dec 10, 2014

### Renton

1. The problem statement, all variables and given/known data
Hi all,

I race bikes in my spare time and someone asked this on a cycling forum:
How much time could you save on a 40km race on a flat course, riding at 40km/h if your bike was one pound lighter. Let's say the weight of the rider and bike together is 80kg.

There was a time when I was younger when this would be trivial but right now I can't figure it out.

2. Relevant equations
v = d / t
a = v - v0 / t
F = m * a

3. The attempt at a solution
So I know I have to figure out how much time it takes to do the course in both cases.
And I know I have to factor in mass somehow.

t = (v-v0)/a = (v - v0) *m / F

And this is where I get stuck. I don't know what force is required to move the bike.
Thank you in advance and sorry about my English, it's not my first language :)

2. Dec 10, 2014

### Bystander

Zero.

3. Dec 10, 2014

### Doug Huffman

I agree. There will be no time saved on a flat course. As speed increases aerodynamic drag goes up proportional to the square.

Look to the HPVA Battle Mountain results of streamliners which first concern is aero and then weight.

4. Dec 10, 2014

### CWatters

You might expect that a lighter bike would be faster on hills however it looks like several people have done the experiment and found that lighter bikes aren't always any faster even on hills..

This one suggests that riding a heavy bike up a hill is no slower than riding a lighter bike. Seems that humans can't exploit the lighter weight....
http://davesbikeblog.squarespace.com/blog/2013/2/21/lighter-is-not-necessarily-faster.html
This one reports on a trial of over 1500 miles..
http://blogs.reuters.com/felix-salmon/2011/08/22/why-a-lighter-bike-doesnt-make-you-faster/

5. Dec 10, 2014

### Doug Huffman

I rode fully loaded touring at over 300 lbm all up, me near 250#, HD recumbent Vanguard by Longbikes, and loaded BOB trailer. I was nicknamed 'The Republican' for all the cyclists passing me "On yur left!" up hill. Then I had a realio-trulio air horn to clear them out of the way as I converted my huge potential energy back to kinetic energy. I tested the rig at 55 mph when the bike and trailer started to feedback too much.

6. Dec 10, 2014

### Renton

Instinctively I know weight on flats is a very small factor, I was just hoping to see how much exactly.

7. Dec 10, 2014

### Bystander

How much energy does it take to get the extra mass to the same speed?

8. Dec 10, 2014

### Doug Huffman

It's more subtle than that. Heavy at speed is momentum conserved through small obstacles.

9. Dec 10, 2014

### Bystander

Also more energy dissipated in small obstacles.

10. Dec 10, 2014

### Doug Huffman

During my nap I realized that riding rolling hills is a good example of maintenance of momentum. Nobody rides rollers better than I do.

11. Dec 10, 2014

### haruspex

Interesting. Both articles suggest psychological explanations, that on a lighter bike the rider did not work as hard. The first article also implies that a stiffer frame somehow allows the rider to work harder, but no explanation is offered. The 1500 miles was made up of many short journeys. It would be interesting to have a comparison over a single long ride.
I certainly don't find any other explanations offered in this thread so far in the least persuasive:
Sure, but that does not in itself imply any greater acceleration. The acceleration would be greater because of the reduced significance of drag, but the total energy demand over the hills is increased. To minimise energy cost, the ideal is to maintain a constant airspeed - work at getting up the hills and rest coming down.
Again, it's momentum per unit mass (oh, velocity!) that matters.