Watts vs. Speed

chris_gr said:

Hi All,
I was trying to figure out the relationship between power output and speed. I assume it is not linear (i.e. 10% more speed needs much more than 10% more power). I think it is a squared relationship:

Power= Speed * Resistance
Resistance = Cd * Speed
-> Watts = Cd * Speed^2

So to go from 30kph to 33kph would require about 21% more power
30 to 36 requires 44% and so on...

Is this right?

I'm not exactly sure what you meant by "Cd", but by the looks of it, I think you meant cadance.
Power = cadence * torque (i.e.: time * force)
Once you bring speed into the equation, you have to account for rolling resistance, wind resistance and a few other variables. Check out www.analyticcycling.com for a more detailed look.

This is what I have gathered from my powertap pro:
(flat ground, no wind, normal seated riding position on standard road bike, I am 6'2" 175lbs)

20mph - 190watts
25mph - 320watts
30mph - 520watts
35mph - 820watts
40mph - 1200watts

I tend to get in a more lower, aerodynamic position the faster I go. Using this data at www.analyticcycling.com my frontal area is about .65m squared
That is the power after the acceleration up to that speed.

Smartt/RST said:

I'm not exactly sure what you meant by "Cd", but by the looks of it, I think you meant cadance.
Power = cadence * torque (i.e.: time * force)
Once you bring speed into the equation, you have to account for rolling resistance, wind resistance and a few other variables. Check out www.analyticcycling.com for a more detailed look.

Cd = coefficent of drag. Usually Drag = Cd * (frontal area) * Velocity * (some other stuff related to density of air or water etc...)

chris_gr said:

Cd = coefficent of drag. Usually Drag = Cd * (frontal area) * Velocity * (some other stuff related to density of air or water etc...)

That's what I thought at first, but the way you wrote the equations, I wasn't sure. Cd is very hard to measure, but the link I sent has the best suggestions.

chris_gr said:

Hi All,
I was trying to figure out the relationship between power output and speed. I assume it is not linear (i.e. 10% more speed needs much more than 10% more power). I think it is a squared relationship:

Power= Speed * Resistance
Resistance = Cd * Speed
-> Watts = Cd * Speed^2

So to go from 30kph to 33kph would require about 21% more power
30 to 36 requires 44% and so on...

Is this right?

It's an almost cubic relationship, generally described as ^2.7. Cd is generally written as CdA (coefficient of aero drag).

ric

velomanct said:

This is what I have gathered from my powertap pro:
(flat ground, no wind, normal seated riding position on standard road bike, I am 6'2" 175lbs)

20mph - 190watts
25mph - 320watts
30mph - 520watts
35mph - 820watts
40mph - 1200watts

I tend to get in a more lower, aerodynamic position the faster I go. Using this data at www.analyticcycling.com my frontal area is about .65m squared
That is the power after the acceleration up to that speed.

Interesting. If watts were proportional to the speed^2 than your watts at 40mph would be around 800. So it must be more like speed^2.7 or 3.0 to compensate for getting lower as you speed up. Powertaps seem like they are pretty cool.

velomanct said:

This is what I have gathered from my powertap pro:
(flat ground, no wind, normal seated riding position on standard road bike, I am 6'2" 175lbs)

20mph - 190watts
25mph - 320watts
30mph - 520watts
35mph - 820watts
40mph - 1200watts

I tend to get in a more lower, aerodynamic position the faster I go. Using this data at www.analyticcycling.com my frontal area is about .65m squared
That is the power after the acceleration up to that speed.

I'd just like to know how long you can hold that 40mph figure! It's not easy getting to 40.... at least it isn't for me. (with no help from wind or gravity)

John

Mansmind said:

I'd just like to know how long you can hold that 40mph figure! It's not easy getting to 40.... at least it isn't for me. (with no help from wind or gravity)

John

the 40mph figure is after a downhill leading on to a flat. It surely is not easy getting up to that speed on a flat road.

i used analyticcycling.com to help align the numbers.

chris_gr said:

Interesting. If watts were proportional to the speed^2 than your watts at 40mph would be around 800. So it must be more like speed^2.7 or 3.0 to compensate for getting lower as you speed up. Powertaps seem like they are pretty cool.

I really wish wind resistence was linear. Imagine that, 1000watts would get you up to around 100mph. Damn physics!

Just for comparison, Petacchi was known to produce 1600watts over the last 200meters(10seconds) of some his wins this year in the Giro. He was clocked in the 43mph range on some occasions.

velomanct said:

Just for comparison, Petacchi was known to produce 1600watts over the last 200meters(10seconds) of some his wins this year in the Giro. He was clocked in the 43mph range on some occasions.

that's.. well. that's I don't even know what to say... quite amazing

velomanct said:

Just for comparison, Petacchi was known to produce 1600watts over the last 200meters(10seconds) of some his wins this year in the Giro. He was clocked in the 43mph range on some occasions.

I would have thought he'd do abit more than that! Apparently chipo used to lay-down 2000+ watts at the end of a stage, altho he's abit bigger so maybe that makes up for it?

cheers

steve said:

I would have thought he'd do abit more than that! Apparently chipo used to lay-down 2000+ watts at the end of a stage, altho he's abit bigger so maybe that makes up for it?

cheers

my impression is that this is wrong, or was measured on inaccurate equipment. as the world's best track sprinters do this plus a bit more but have considerably more mass, and specialise at this (and maybe other sprint events) it wouldn't seem possible.

ric

steve said:

I would have thought he'd do abit more than that! Apparently chipo used to lay-down 2000+ watts at the end of a stage, altho he's abit bigger so maybe that makes up for it?

cheers

Cipo never sustained over 2000watts for more than a couple seconds at the most. He once stated he hits 2000 when jumping out from behind his team's smart car when they do motorpacing. His 10 second power was probally in the 1600-1700 range.
Petacchi is certainly very fast, but he is not far and above that much faster than any of your top local sprinters. I am a cat 3 and and about the same size as Cipo, my 10 second power is about 1450. But you have to remember that Petacchi is a superb endurance athlete, unlike me. His threshold is 400watts.

I local top amatuer sprinter (cat 1) says he has gotten close to 2000watts peak during sprints a few years back. He is a smaller guy at around 67-70kgs.

I know another local racer who is just as powerful or more than Petacchi. He is not a track racer, just road. When he is on, he demolishes everyone else in the sprint. (I still haven't been able to get him to ride my powertap. It would be interesting) Comparing him to myself and my peak readings, his peak must be over 2200.

velomanct said:

Cipo never sustained over 2000watts for more than a couple seconds at the most. He once stated he hits 2000 when jumping out from behind his team's smart car when they do motorpacing. His 10 second power was probally in the 1600-1700 range.

as i said before it's highly doubtful that he recorded 2000+ W or even close to it, unless he's considerably heavier than i think he is. As i work with world class track sprinters, i see what they can do. Road "sprint" pros aren't comparable

Quoted post said:

I local top amatuer sprinter (cat 1) says he has gotten close to 2000watts peak during sprints a few years back. He is a smaller guy at around 67-70kgs.

I know another local racer who is just as powerful or more than Petacchi. He is not a track racer, just road. When he is on, he demolishes everyone else in the sprint.

if someone that size had peaked at ~ 2000 W, they'd win the world/olympic/whatever sprint championships somewhat easily! My guess is that either the equipment was faulty, or the rider suffered with the same problem that most people do (overinflated imaginary figures!)

ric

ric_stern/RST said:

as i said before it's highly doubtful that he recorded 2000+ W or even close to it, unless he's considerably heavier than i think he is. As i work with world class track sprinters, i see what they can do. Road "sprint" pros aren't comparable

if someone that size had peaked at ~ 2000 W, they'd win the world/olympic/whatever sprint championships somewhat easily! My guess is that either the equipment was faulty, or the rider suffered with the same problem that most people do (overinflated imaginary figures!)

ric

Here is the interview from racelistings.com
http://www.racelistings.com/rzone/rzone.htm (go to <Riders to watch> archives, under 2002.)
Joe Papp is one of the best amatuer sprinters in the eastern US.
Peak power doesn't mean a whole lot, 10 and 20 second power is much more important for sprint finishes, and especially the 200 meter on the track.

Just curious, what is the highest peak power you have ever seen with these match sprinters?

velomanct said:

Here is the interview from racelistings.com
http://www.racelistings.com/rzone/rzone.htm (go to <Riders to watch> archives, under 2002.)
Joe Papp is one of the best amatuer sprinters in the eastern US.
Peak power doesn't mean a whole lot, 10 and 20 second power is much more important for sprint finishes, and especially the 200 meter on the track.

The rider uses an SRM. It's well known (in the power meter field) that they require careful calibration with either known certified masses or using dynamometry. often they don't come from the factory very well calibrated. It's definitely a mistake to think that all SRMs are spot on.

I've no idea why 20-sec power would be a good indicator for a ~10-sec sprint! Personally, and many others too look at peak power (although, obviously, 10-sec power is important to).

My guess is either an incorrectly calibrated SRM or over inflation, or he's some sort of alien! His peak power to mass ratio is way in excess of Olympic Champions...

Quoted post said:

Just curious, what is the highest peak power you have ever seen with these match sprinters?

highest i've seen is ~2300 W. we know that world champions are ~ 24 W/kg (i.e., a 96 kg rider would put out ~ 2300 W). if Papp is correct then he has a power to mass ratio of 29.4 W/kg..... i'm not saying he's not a good sprinter, but the figures don't stack up.

ric

ric_stern/RST said:

The rider uses an SRM. It's well known (in the power meter field) that they require careful calibration with either known certified masses or using dynamometry. often they don't come from the factory very well calibrated. It's definitely a mistake to think that all SRMs are spot on.

I've no idea why 20-sec power would be a good indicator for a ~10-sec sprint! Personally, and many others too look at peak power (although, obviously, 10-sec power is important to).

My guess is either an incorrectly calibrated SRM or over inflation, or he's some sort of alien! His peak power to mass ratio is way in excess of Olympic Champions...

highest i've seen is ~2300 W. we know that world champions are ~ 24 W/kg (i.e., a 96 kg rider would put out ~ 2300 W). if Papp is correct then he has a power to mass ratio of 29.4 W/kg..... i'm not saying he's not a good sprinter, but the figures don't stack up.

ric

I agree that there could certainly be an error with Papp's peak power being close to 2000. I have ridden with him a few times and he is relatively small (big legs though!) compared to most any other sprinter.

How can 20 second power not be important for the 200 meter time trial???
They need to accelerate up to ~43mph and then maintain that speed for the next 10 seconds. take a look at the power profile of a 200 meter time trial, and you will see that it is MUCH more than a 10 second effort. It takes at least 10 seconds to go from ~25 to the 40mph range. I am surprise you are unaware of this acceleration period.

About that 5 second column. If the top is 24w/kg and Nothstein (Sydney gold condition) was 98kg, that would mean his 5 second power is 2350watts. His absolute peak (1 second) would have to be around 2600watts.
(my 1 second peak is 200watts above my 5 second power)

How come we NEVER heard of ANY match sprinter capable of hitting 2600watts? In the cyclingnews.com interview with Nothstein 4 years ago, he stated he was rated at 2200watts.
What gives?

velomanct said:

How can 20 second power not be important for the 200 meter time trial???
They need to accelerate up to ~43mph and then maintain that speed for the next 10 seconds. take a look at the power profile of a 200 meter time trial, and you will see that it is MUCH more than a 10 second effort. It takes at least 10 seconds to go from ~25 to the 40mph range. I am surprise you are unaware of this acceleration period.

sorry, it was a bit of a lame attempt at humour, which on reflection didn't work. don't worry, i won't give up my day job to become a comedian!

ric