How do you calculate energy to go differnet speeds.



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Bill Smith

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Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18 mph
vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more energy
to hold the pace at 20 or 22 mph.
 
Bill Smith wrote:
> Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18
> mph vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
> energy to hold the pace at 20 or 22 mph.

From a physics point of view you are interested in how much *power* it takes to maintain that speed
- the rate of energy use per second.

Ignoring second-order effects and whatnot most of your power when peddling at constant speed on
level ground goes into overcoming wind resistance - and assuming a constant windspeed relative to
the ground your power output increases with the square of your speed. It's four times as hard to go
twice as fast, and going from 18-22mph is an increase of (22/18)^2 or about 1.5 times as much power.

It might *feel* like even more if this level of exertion causes your muscles to switch from aerobic
exertion to anaerobic - it's pretty subjective and dependant on your body.

Others may disagree.

Adam
 
Jacobe Hazzard wrote:
> Ignoring second-order effects and whatnot most of your power when peddling at constant speed on
> level ground goes into overcoming wind resistance - and assuming a constant windspeed relative
> to the ground your power output increases with the square of your speed. It's four times as hard
> to go twice as fast, and going from 18-22mph is an increase of (22/18)^2 or about 1.5 times as
> much power.

Actually it's the cube
--
Ron Hardin [email protected]

On the internet, nobody knows you're a jerk.
 
Bill Smith wrote:
> Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18
> mph vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
> energy to hold the pace at 20 or 22 mph.

http://www.kreuzotter.de/english/espeed.htm
 
Ron Hardin wrote:
> Jacobe Hazzard wrote:
>> Ignoring second-order effects and whatnot most of your power when peddling at constant speed on
>> level ground goes into overcoming wind resistance - and assuming a constant windspeed relative
>> to the ground your power output increases with the square of your speed. It's four times as hard
>> to go twice as fast, and going from 18-22mph is an increase of (22/18)^2 or about 1.5 times as
>> much power.
>
> Actually it's the cube

How is that? I would have thought that the drag force is proportional to the speed so...
 
Jacobe Hazzard wrote:
> How is that? I would have thought that the drag force is proportional to the speed so...

You're right, but the power is the force times the speed.
--
Ron Hardin [email protected]

On the internet, nobody knows you're a jerk.
 
Ron Hardin wrote:
>
> Jacobe Hazzard wrote:
> > How is that? I would have thought that the drag force is proportional to the speed so...
>
> You're right, but the power is the force times the speed.

Sorry, I misread your ``would have thought'' - the drag force is the square of the speed; you hit
twice as much air twice as hard.

and then the speed multiplies force again to get power.
--
Ron Hardin [email protected]

On the internet, nobody knows you're a jerk.
 
Ron Hardin wrote:
> Ron Hardin wrote:
>>
>> Jacobe Hazzard wrote:
>>> How is that? I would have thought that the drag force is proportional to the speed so...
>>
>> You're right, but the power is the force times the speed.
>
> Sorry, I misread your ``would have thought'' - the drag force is the square of the speed; you hit
> twice as much air twice as hard.
>
> and then the speed multiplies force again to get power.

Yeah you're right of course. My assumptions were wrong.

Adam
 
Bill Smith wrote:
> Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18
> mph vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
> energy to hold the pace at 20 or 22 mph.

From: http://www.analyticcycling.com/ForcesPower_Page.html

you can find the answer to your questions.

18mph = 103.5W 20mph = 135.8W 22mph = 174.7W

These use the default assumptions about weight, wind, etc.
 
So are you guys saying that to go from 18 mph to 22 mph it would be
(22/18)^3 or 1.8 times more energy. It feel like that but I would not have thought theoretically
it would be.
 
"Jacobe Hazzard" <[email protected]> writes:

[snip]
>
> Ignoring second-order effects and whatnot most of your power when peddling at constant speed on
> level ground goes into overcoming wind resistance

Agreed so far.

> - and assuming a constant windspeed relative to the ground your power output increases with the
> square of your speed.

The wind resistance _force_ increases with the square of the speed, hence the _power_ needed to
overcome it increases whith the cube of the speed.

> It's four times as hard to go twice as fast,

Eight times as hard.

> and going from 18-22mph is an increase of (22/18)^2 or about 1.5 times as much power.

By doubling your power output you can increase your speed by approximatly 1/4.

>
> It might *feel* like even more

Indeed, trust your feelings, in this case they coincide with classic physics.

> if this level of exertion causes your muscles to switch from aerobic exertion to anaerobic - it's
> pretty subjective and dependant on your body.
>
> Others may disagree.

Yes.

>
> Adam
>
>

--
__o | Øyvind Røtvold _`\(, | http://www.darkside.no/olr/index.html (_)/(_) | ... biciclare
necesse est ...
 
[email protected] (Bill Smith):

>Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18 mph
>vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
>energy to hold the pace at 20 or 22 mph.

Well, there's bikepwr.c by Ken Roberts, see http://www.mystrobl.de/ws/fahrrad/bikepwr.htm,
for example.

A year a go, I ported this to Python for better readability
http://www.mystrobl.de/ws/fahrrad/PyBikePower/bike_pow.py and made a portable graphical version
using wxWindows/wxPython: http://www.mystrobl.de/ws/fahrrad/PyBikePower/pybikepwr.html (sorry, this
page is German language only - the program itself has English messages). For MS Windows there is a
.msi package available at http://www.mystrobl.de/ws/fahrrad/PyBikePower/bike_pow.msi

--
Wir danken für die Beachtung aller Sicherheitsbestimmungen
 
On Wed, 28 May 2003 20:36:19 GMT, [email protected] (Bill Smith) wrote:

>Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18 mph
>vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
>energy to hold the pace at 20 or 22 mph.

www.analyticcycling.com
 
There is an article in the Rivendell reader (RR27) entitled "Force, Horsepower, Speed, Math, and
Climbing" by Michael Barnes. Mr. Barnes' primary focus is how much more energy is required to climb
per extra pound carried. However, he provides a link to a really nifty spreadsheet of his own
creation. With this spreadsheet, you can build your own scenarios to model the effects of weight and
wind on your output:

http://www.ucop.edu/~mbarnes/bike.xls

Trevor

"Bill Smith" <[email protected]> wrote in message
news:[email protected]...
> Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18
> mph vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
> energy to hold the pace at 20 or 22 mph.
 
I was unable to find this article or go to this web site. Could you provide me with some additional
information?

Bill Smith

On Sat, 31 May 2003 02:29:59 GMT, "Trevor Taylor" <[email protected]> wrote:

>There is an article in the Rivendell reader (RR27) entitled "Force, Horsepower, Speed, Math, and
>Climbing" by Michael Barnes. Mr. Barnes' primary focus is how much more energy is required to climb
>per extra pound carried. However, he provides a link to a really nifty spreadsheet of his own
>creation. With this spreadsheet, you can build your own scenarios to model the effects of weight
>and wind on your output:
>
>http://www.ucop.edu/~mbarnes/bike.xls
>
>Trevor
>
>"Bill Smith" <[email protected]> wrote in message
>news:[email protected]...
>> Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18
>> mph vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
>> energy to hold the pace at 20 or 22 mph.
 
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