I think I read somewhere that the relationship between power and mph is not linear. Do any of you scientists/mathematicians out there know the relationship???

If all other variables are constant, how much increase in power (in %) would one need to increase speed by 10%.

It depends on how fast you already ride. To increase from 10mph to 11mph (10%) requires far less improvement than from 20mph to 22mph (also 10%), mainly due to increased drag / wind resistance.

Use a calculator such as this one, and you can figure it out: https://bikecalculator.com/

At slow speeds about 20-25% more power, increasing to more than 50% at higher speeds (like around 20 mph). It's not linear, keeps increasing.

https://www.kreuzotter.de/english/espeed.htm

In theory it's asymptotic to 33.1%. The calculator you posted agrees.

I find going to 25mph from 20 mph to be quite harder than going from 15 to 20 mph. The relationship I think varies with the square of the speed.

As per the post above yours, it's asymptotic to the cube of the speed because aerodynamic drag increases as the square of the speed. The drag exerts a ******ant force, the power required to overcome that force therefore rises as the cube (because power is force x velocity).

Above about 40 kmh aerodynamic drag dominates all other forces.

power = (more or less) K * (1.1V)^3=1.331 KV^3 = 1.331 times initial power, so I'd say that's pretty close. I was just gestimating.

A 10% increase in speed requires approximately a 33% increase in that component of Power related to aerodynamic drag (flat ground, no wind,no change in position ...). At low speeds I'm sure the models reflect the components of power required to overcome drive train losses, losses related to tire deformation, etc., The faster the initial speed the greater the absolute power increase required to increase speed by 10%.

Plug the friggin numbers in kruezotter.


10 to 11 mph, not much much more than 10%

30 to 33mph way more than 10%

Also depends on aeroness, prevailing wind conditions, and elevation change on the course being tested.

Just get the watts higher.

This is a plot of a strava print segment I have ridden through at various levels of effort, it is flat and I average about 50kph on the harder efforts. Power is recorded by my powertap. I will need about an extra 100 watts to knock off 10% of my seconds.

Hope that helps answer your question

Variability is due to wind and the fact that some efforts were done in the drops and other on the hoods. I can maintain 600 watts for that time period but have yet to do so on that segment to fill in another data point. Also, in order to do that I would have to stand up which would alter drag so it may not give quite the expected time.

The important thing is, the gradient of the line gets significantly steeper as time reduces

Thanks for all of the replies as this really helps & is what I was looking for.

I plugged my current real life data & the numbers agreed to what was calculated.

It looks like my future gains are going to require more effort/time.

If it's up hill and dominated by overcoming gravity, it's linear with speed. If air drag dominates, it goes as the cube of the speed.

So 10% faster up hill will take 10% more power. 10% faster on the flat will take 33% more power.

does this even matter? regarding an average speed, isn't it unlikely to be able to increase your average by that much? seems like a lot to me