how hard am i working?

ARob
ARob Posts: 143
edited August 2007 in Road beginners
i started riding a few months ago and have got my average speed up from 17mph to around 19-20.

i heard somewhere that wind resistance is proportional to speed squared and therefore the power needed to overcome this is proportional to speed cubed.

does anyone know if this is right? that would mean the power needed at 20mph is 63% more than at 17 mph. can this be right?

Comments

  • Big Red S
    Big Red S Posts: 26,890
    The force created by the viscous drag at low speeds is approximately proportional to the velocity. So the power increaces as a square.
    At high velocities it is proportional to the square and the cube, respectively.

    But this is a measure of the power at the rear wheel, not neccesarily the power you're producing (presumably you're now more efficient at using your energy to make you go), and it's only of the power used to overcome viscous drag, not any other form of resistance (like hills and bad bearings).
  • Garybee
    Garybee Posts: 815
    Drag (wind resistance) increases by the square of the speed. So if you double your speed you quadrouple your drag. This is true at any speed, there is no switch to cubing.

    At low speeds much of the resistance you have to overcome is rolling resistance. As you increase speed the proportion of the total resistance that is made up by the total resistance is less. This is due to rolling resistance increasind linearly.

    At high speeds the majority of the resistance is made up by wind resistance.

    In the example you used the power required would be about 38% greater to sustain the increased speed.

    Hypocrisy is only a bad thing in other people.
  • ARob, you've got it correct. Drag (air resistance) is proportional to your speed squared, or more precisely, your relative speed squared (i.e. the difference in speed between you and the air, which may be blowing in a wind either against you or with you). So by doubling your speed (in still air) you quadruple your wind resistance, as Garybee said. However, by doubling your speed you also double the work done per unit of time. In cycling, you can think of it like this: by doubling your speed, you double your gearing so that your cadence is the same, and by doing that, you double the resistance of the pedals against the drag force that you're fighting (which has quadrupled as I mentioned). So overall, doubling your speed requires 8x more power, i.e. the power required is cubed.

    Air resistance forms the vast majority of your resistance to motion while cycling. At 20 mph we're already talking upwards of 80%. At 25 mph it would be closer to 90%. As a rough guide, while cycling at speed on the flat, your power output is dissipated as follows:

    65% body drag (in a good position on the drops)
    10% wheel drag (with well over half of this from the front wheel)
    10% frame drag
    12% rolling resistance

    ...with the remaining couple of percent accounted for by frictional losses in the geartrain and wheel bearings.

    But as Garybee mentioned, rolling resistance increases proportionally with speed, so the overall resistance to motion doesn't quite cube with speed. But it's pretty close. Doubling speed from 12 mph to 24 mph perhaps requires 7x more power.

    Your result of 63% more power from 17 to 20 mph (i.e. (20 / 17) ^ 3) is correct if we ignore the losses that increase linearly. Including those will lower the figure a little, perhaps to a bit more than 50% at a rough guess.

    This doesn't necessarily mean that you are producing 50% more power, or that your body is burning 50% more calories per unit time. Some of the speed improvement may be due to a better, more aerodynamic position on the bike. Some may be down to fine-tuning saddle height, etc., thereby reducing the extra power required. Of course you are producing more power, and that comes from two things: your body processing more oxygen (burning more calories) and your body being able to produce more power from a given amount of energy, due to improvements in your cardiovascular and muscle efficiency.

    I'll stop blathering on now. :) But good job on getting to 20 mph. Imagine now how much power a Tour de France cyclist puts out in a time trial with an average speed over 30 mph! :shock: (Of course they spend huge effort reducing their air resistance for this very reason.)
  • Garybee is right, there is no 'cubed' involved.
    Perhaps you're thinking of how hard it is to accelerate. The power needed would be the wind resistance squared PLUS the power needed to provide the force needed to accelerate. But the force needed to accelerate isn't proportional to your speed (and even if it was it wouldn't make the total power needed the speed cubed), it's proportional to your mass.
  • jonesy124
    jonesy124 Posts: 205
    eat sugar cubes, then you will go faster :)
  • daniel_b
    daniel_b Posts: 11,569
    jonesy124 wrote:
    eat sugar cubes, then you will go faster :)

    Possibly for a horse yes, but I don't think they make bikes for them do they? :wink:

    How do you guys all calculate your average speed, a cycle computer I guess?

    Hopefully I will be getting our 3 cycling computers back at the end of the month, all wireless, but never yet fitted, going to put one on my Marin, one on the Felt, and the other one on the gf's Trek.

    Are they generally pretty accurate - I guess you just need to measure a full rotation of the wheel, and input that, and it works out the rest?

    Cheers

    Dan
    Felt F70 05 (Turbo)
    Marin Palisades Trail 91 and 06
    Scott CR1 SL 12
    Cannondale Synapse Adventure 15 & 16 Di2
    Scott Foil 18
  • Garybee
    Garybee Posts: 815
    Daniel B wrote:
    jonesy124 wrote:
    eat sugar cubes, then you will go faster :)

    Possibly for a horse yes, but I don't think they make bikes for them do they? :wink:

    How do you guys all calculate your average speed, a cycle computer I guess?

    Hopefully I will be getting our 3 cycling computers back at the end of the month, all wireless, but never yet fitted, going to put one on my Marin, one on the Felt, and the other one on the gf's Trek.

    Are they generally pretty accurate - I guess you just need to measure a full rotation of the wheel, and input that, and it works out the rest?

    Cheers

    Dan

    You're correct in how a cycle computer works. They are very accurate, i have compared speeds/distances between a wheel sensing cycle computer and a GPS based one and they both come out near enough as to make no real difference.

    Gaz

    Hypocrisy is only a bad thing in other people.
  • jonesy124
    jonesy124 Posts: 205
    Daniel B wrote:
    jonesy124 wrote:
    eat sugar cubes, then you will go faster :)

    Possibly for a horse yes, but I don't think they make bikes for them do they? :wink:

    Cheers

    Dan

    What do you mean? I often see the odd horse pedalling away. For example I took this picture just this morning http://www.dreamco.com/eotbh/images/cha ... rse_sm.gif
  • daniel_b
    daniel_b Posts: 11,569
    jonesy124 wrote:
    Daniel B wrote:
    jonesy124 wrote:
    eat sugar cubes, then you will go faster :)

    Possibly for a horse yes, but I don't think they make bikes for them do they? :wink:

    Cheers

    Dan

    What do you mean? I often see the odd horse pedalling away. For example I took this picture just this morning http://www.dreamco.com/eotbh/images/cha ... rse_sm.gif

    me thinks you took that picture in your hungover state......

    there's a lot of BRIGHT colours in there :D
    Felt F70 05 (Turbo)
    Marin Palisades Trail 91 and 06
    Scott CR1 SL 12
    Cannondale Synapse Adventure 15 & 16 Di2
    Scott Foil 18
  • daniel_b
    daniel_b Posts: 11,569
    How many fingers am I holding up?

    Hand-03-june.gif
    Felt F70 05 (Turbo)
    Marin Palisades Trail 91 and 06
    Scott CR1 SL 12
    Cannondale Synapse Adventure 15 & 16 Di2
    Scott Foil 18
  • Garybee
    Garybee Posts: 815
    jonesy124 wrote:
    Daniel B wrote:
    jonesy124 wrote:
    eat sugar cubes, then you will go faster :)

    Possibly for a horse yes, but I don't think they make bikes for them do they? :wink:

    Cheers

    Dan

    What do you mean? I often see the odd horse pedalling away. For example I took this picture just this morning http://www.dreamco.com/eotbh/images/cha ... rse_sm.gif

    Now that picture's just silly. Bikes for horses have pedals on the axle of each wheel.

    Hypocrisy is only a bad thing in other people.
  • daniel_b
    daniel_b Posts: 11,569
    Daniel B wrote:
    How many fingers am I holding up?

    Hand-03-june.gif

    The Jonester still hasn't answered this, so I think that tells us all we need to know :lol:
    Are you sure it was 'just' a bottle of wine, anything you need to share with the group?

    I've just been down to a lovely pub by the canal for a few jars, and don't really want to work now, and I'm here til 6 :cry:

    Dan
    Felt F70 05 (Turbo)
    Marin Palisades Trail 91 and 06
    Scott CR1 SL 12
    Cannondale Synapse Adventure 15 & 16 Di2
    Scott Foil 18
  • ricadus
    ricadus Posts: 2,379
    Work? It's Friday afternoon. :roll:
  • daniel_b
    daniel_b Posts: 11,569
    Well ok, sat at my desk appearing to work.
    Felt F70 05 (Turbo)
    Marin Palisades Trail 91 and 06
    Scott CR1 SL 12
    Cannondale Synapse Adventure 15 & 16 Di2
    Scott Foil 18
  • ricadus
    ricadus Posts: 2,379
    Speaking of "appearing to work", I am reminded of another forum I used to frequent that had a "boss" button next to the "reply" and "new topic" buttons that, when clicked on, would open a full screen pop-up of an innocuous-looking Excel spreadsheet that hid the forum page from view.

    A very handy feature. 8)
  • Garybee is right, there is no 'cubed' involved.
    Perhaps you're thinking of how hard it is to accelerate. The power needed would be the wind resistance squared PLUS the power needed to provide the force needed to accelerate. But the force needed to accelerate isn't proportional to your speed (and even if it was it wouldn't make the total power needed the speed cubed), it's proportional to your mass.
    Not sure why you insist on saying this when I carefully explained why it is cubed. It's undeniable physics I'm afraid. Power = force x velocity. The force in cycling approximately squares with the speed because air resistance squares with speed, and if the velocity doubles then you can see from that equation that power must also double due to that.

    The real world is full of examples to back this up. Consider a Renault Clio Campus with a 60 horsepower engine and a top speed of 98 mph (I got these specs from their website just now, by the way, so they're exact). If the power requirement cubes with speed, then to double that top speed we would expect a requirement of about 60 x 8 = 480 horsepower. Well surprise, surprise: a Ferrari Scaglietti has 532 horsepower and a top speed of 199 mph. This is very close to what we expected, with the difference easily accounted for by the difference in aerodynamics of the two cars. But if power squared with velocity we would expect ~200 mph to be possible on ~240 horsepower, which is clearly nowhere near the case in real life. A car with approximately 240 horsepower is the BMW 325i with 218 horsepower. It has a top speed of 152 mph, which is very close to what we would expect if power cubed with speed. (152 mph / 98 mph) ^ 3 = 3.73. And 60 horsepower x 3.73 = 224 horsepower, which is very close to the actual 218 horsepower of the BMW.

    Acceleration forces are something else entirely, and while doing a TT type of ride on a course where you don't brake much, they account for very little of your total energy expenditure.
  • Garybee
    Garybee Posts: 815
    Dorian,

    I should of replied to this sooner to save confusion. You are quite right, i didn't take into account anything other that aerodynamic drag when i responded. Was initially trying to explain that aerodynamic drag increases by the square regardless of speed and doesn't switch to cubing at higher speeds as somebody else had written. Nice example you have found there by the way.

    Gaz

    Hypocrisy is only a bad thing in other people.