Energy input\losses for a cyclist accelerating from a standing start

[JasonFit]

I have been analysing the power that a cyclist puts out during a standing start and the numbers don't seem to match the effort that is going in!
Here's a real example:
Cyclist (93kg incl bike) moves 15m from standing start in 4secs (average velocity 3.75m/s).
Assuming a constant acceleration, of 1.875m/s², I calculate the power required for this acceleration to be 654W

I know there are other resistive forces to overcome for aero drag, gravity and rolling resistance but on the flat surface of the velodrome these only amount to less than 10w at this initial speed (see https://www.gribble.org/cycling/power_v_speed.html).

This cyclist continues to ride around the velodrome and actually holds an average power around 600w for a couple of laps but that initial effort was way harder than any other time afterwards (perhaps double) so what is happening to cause that apparent over-exertion?

 

[Lnewqban]

Welcome!
That cyclist must give the mass of the bike and his own mass enough energy to increase their speed from zero to the cruising speed, overcoming inertia.
After that is accomplished, his energy will be used to maintain that speed against rolling resistance and aerodynamic drag.

 

[willem2]

I suppose this was on a track bicycle that doesn't have gears? It's not really possible to exert a constant power. Acceleration is likely about constant, since there is little drag. The power produced will be proportional to the speed. At the start of the 4 seconds, the power produced will be very low, and the muscles will work inefficiently. To produce an average power of 634 W, much more power must be produced at the end of the period.
If you have gears, you can improve on this, but you probably can't change gears more than once in 4 seconds, and you will be limited by wheel spin, so the power will still be far from constant.

 

[berkeman]

Cyclist (93kg incl bike) moves 15m from standing start in 4secs (average velocity 3.75m/s).
Assuming a constant acceleration, of 1.875m/s², I calculate the power required for this acceleration to be 654W

I'm not sure what you mean by the "average velocity 3.75m/s", but whatever.

Don't forget to include the rotational Moment of Inertia (MoI) of the two wheels and drive sprockets in your calculation. On light velodrome racing bikes, it will be fairly low, but if you want to get better accuracy on the acceleration calculation, include the MoI effects.

 

[Lnewqban]

Yes, Moment of Inertia is a very important factor.
There is also some energy going into moving and rotating the legs (mainly thighs), accelerating and decelerating them in a cyclic way, especially at higher speeds.

 

[berkeman]

There is also some energy going into moving and rotating the legs (mainly thighs), accelerating and decelerating them in a cyclic way

Good point. And when I am standing and accerating or climbing a hill on my MTB, I do pull the bike side-to-side about 10-15 degrees to get extra power into my pedals. I guess that movement/rhythmic acceleration should be factored in as well...

https://ilovebicycling.com/wp-content/uploads/2018/01/cover.jpg

 

[jack action]

Cyclist (93kg incl bike) moves 15m from standing start in 4secs (average velocity 3.75m/s).
Assuming a constant acceleration, of 1.875m/s², I calculate the power required for this acceleration to be 654W

No, you calculated the average power over the 4-second period by using the average velocity.

So if the average velocity is 3.75 m/s, and the initial velocity is zero, then you can imagine that the velocity after 4 seconds would be twice as much as the average velocity (constant acceleration).

If the acceleration is assumed to be constant (i.e. the force), then the power will be proportional to the velocity, thus also twice as much as the average power at the end of the 4-second period.

 

[JasonFit]

I suppose this was on a track bicycle that doesn't have gears? It's not really possible to exert a constant power. Acceleration is likely about constant, since there is little drag. The power produced will be proportional to the speed. At the start of the 4 seconds, the power produced will be very low, and the muscles will work inefficiently. To produce an average power of 634 W, much more power must be produced at the end of the period.
If you have gears, you can improve on this, but you probably can't change gears more than once in 4 seconds, and you will be limited by wheel spin, so the power will still be far from constant.

Yes he was on a track bike (63:15 fixed gearing). I took another look at my video analysis and calculated the power for the first 1m (0.85secs) and you're correct, the calculated power is even lower (about 300W)! Which adds further to my original question which is why does the cyclist seem to be exerting the most effort during the first movement of the pedals but producing the least amount of power?

 

[JasonFit]

I'm not sure what you mean by the "average velocity 3.75m/s", but whatever.

Don't forget to include the rotational Moment of Inertia (MoI) of the two wheels and drive sprockets in your calculation. On light velodrome racing bikes, it will be fairly low, but if you want to get better accuracy on the acceleration calculation, include the MoI effects.

Average velocity id taken from moving 15m in 4secs (15 / 4 = 3.75).

I didn't include the rotational moment of inertia as I've seen this as pretty minor in previous calculations. Correct me if I'm wrong!

 

[JasonFit]

Yes, Moment of Inertia is a very important factor.
There is also some energy going into moving and rotating the legs (mainly thighs), accelerating and decelerating them in a cyclic way, especially at higher speeds.

I am only concerned about the initial few seconds or less, so the speed is very low.

 

[JasonFit]

Good point. And when I am standing and accerating or climbing a hill on my MTB, I do pull the bike side-to-side about 10-15 degrees to get extra power into my pedals. I guess that movement/rhythmic acceleration should be factored in as well...

View attachment 292767
https://ilovebicycling.com/wp-content/uploads/2018/01/cover.jpg

Yes these are all factors to take into consideration for other situations but I'm specifically trying to understand the first few seconds of acceleration and how the power doesn't seem to match the exertion (i.e. max effort but power numbers lower than later in the ride when pedalling at speed but with less perceived effort).
There was no such side to side movement with this rider during his start.

 

[berkeman]

my original question which is why does the cyclist seem to be exerting the most effort during the first movement of the pedals but producing the least amount of power?

Did you understand this comment by Jack?

If the acceleration is assumed to be constant (i.e. the force), then the power will be proportional to the velocity,

You can also think of it as Power = (Force * Distance)/Time, so at first when the cyclist is pedalling slowly, he can't develop much power since the Force is limited to his body weight and some leg strength. At speed, the legs and pedals are moving much faster and further, which allows more power input. Does that make sense?

 

[Lnewqban]

I am only concerned about the initial few seconds or less, so the speed is very low.

What was the speed at distance 15 m and time 4 seconds from start?

 

[JasonFit]

Did you understand this comment by Jack?

You can also think of it as Power = (Force * Distance)/Time, so at first when the cyclist is pedalling slowly, he can't develop much power since the Force is limited to his body weight and some leg strength. At speed, the legs and pedals are moving much faster and further, which allows more power input. Does that make sense?

Ah ok I think I'm seeing the light!
So this is more of a biomechanical issue with the body struggling to get the pedals turning.
Any ideas where that extra (inefficient) energy is going - heat?

 

[JasonFit]

What was the speed at distance 15 m and time 4 seconds from start?

6.25m/s - that's how I got to the 654W

 

[JasonFit]

6.25m/s - that's how I got to the 654W

Correction it was 7.5m/s in this example.

 

[A.T.]

Which adds further to my original question which is why does the cyclist seem to be exerting the most effort during the first movement of the pedals but producing the least amount of power?

When you are pushing against an immovable wall, the power you are putting into it is zero power, but your muscles still consume energy.

 

[JasonFit]

When you are pushing against an immovable wall, the power you are putting into it is zero, but your muscles still consume energy.

I realize that I’m now moving away from physics but can anyone explain how/what is consuming that energy when nothing moves?

 

[A.T.]

I realize that I’m now moving away from physics but can anyone explain how/what is consuming that energy when nothing moves?

On the microscopic level stuff might be moving in the muscle. The energy goes ultimately into heat.

 

[JasonFit]

On the microscopic level stuff might be moving in the muscle. The energy goes ultimately into heat.

Getting back to the physics - would the additional energy consumption simply be the force (torque) applied to the pedals?

 

[berkeman]

Getting back to the physics - would the additional energy consumption simply be the force (torque) applied to the pedals?

It's not so much that there is lots of wasted energy at the low speed, it's that you *cannot* put a lot of power into the pedals when they are moving slowly.

 

[Lnewqban]

Correction it was 7.5m/s in this example.

In order for a standing still mass (bike plus rider) of 93 kg to reach a speed of 7.5 m/s in a distance of 15 m, a constant forward force of 174.4 N must have been horizontally applied onto the axis of the rear wheel.
That means that 2616 useful Joules of energy or work reached that axis.
If all that also happened in a time of 4 seconds, we can say that the rate of energy delivery, or power, was of 654 Joules/sec or watts.

Your on-line calculator shows that in order to keep that forward speed of 7.5 m/s, the rider only had to use 119 watts.

The initial acceleration process could have used much less pedal force, if only the rider decides to increase the time in which that cruising speed would be reached.
There is a certain amount of food and oxygen accumulated in the muscles, which only last a few seconds, but that the spring runners use for explosive short efforts.
For a marathon, the runner only has the food and oxygen that the stream of blood can carry into the muscles.

 

[berkeman]

So this is more of a biomechanical issue with the body struggling to get the pedals turning.

Have you looked at pedal power meter data? That may be a good resource to help you see power profiles for starting up versus pedalling at speed. Here is a link to the product -- I didn't search for typical profiles...

https://stagescycling.com/en_us/pro...fQgu51B_-DtsB-lvbu6VORbBlTUPGyNwaAmg4EALw_wcB

 

[JasonFit]

It's not so much that there is lots of wasted energy at the low speed, it's that you *cannot* put a lot of power into the pedals when they are moving slowly.

Ok what I mean is that if the cyclist is held in the gate while he is applying all that force on the pedals (and handlebars) he would soon become exhausted having moved nowhere - that’s what I meant by wasted (to heat?).

I’m now trying to determine what amount of energy is being wasted by using this big gear as opposed to a smaller gear which would get that energy turned into power sooner.

 

[berkeman]

I’m now trying to determine what amount of energy is being wasted by using this big gear as opposed to a smaller gear which would get that energy turned into power sooner.

Not much. Why are you asking about different gear ratios for the start? That seems like such a trivial part of velodrome racing...

 

[JasonFit]

Not much. Why are you asking about different gear ratios for the start? That seems like such a trivial part of velodrome racing...

:) this is true but that is the role I have taken on - to analyse every aspect of the cyclists performance. First I want to make sure I’m accounting for all the energy expenditure correctly.

It would be good to be able to quantify the difference in those first seconds between a big gear and smaller gear. The power readings do not give the full story at this stage so I’m thinking that all I need are the torque readings instead until get the pedals get moving at a ‘reasonable’ speed (whatever that is)?

 

[JasonFit]

In order for a standing still mass (bike plus rider) of 93 kg to reach a speed of 7.5 m/s in a distance of 15 m, a constant forward force of 174.4 N must have been horizontally applied onto the axis of the rear wheel.
That means that 2616 useful Joules of energy or work reached that axis.
If all that also happened in a time of 4 seconds, we can say that the rate of energy delivery, or power, was of 654 Joules/sec or watts.

Your on-line calculator shows that in order to keep that forward speed of 7.5 m/s, the rider only had to use 119 watts.

The initial acceleration process could have used much less pedal force, if only the rider decides to increase the time in which that cruising speed would be reached.
There is a certain amount of food and oxygen accumulated in the muscles, which only last a few seconds, but that the spring runners use for explosive short efforts.
For a marathon, the runner only has the food and oxygen that the stream of blood can carry into the muscles.

Your calculations match mine for the power to accelerate (654W) but I think you have plugged in different values for the steady speed calculation. I’m using a CdA of 0.25 (0.5 for the coefficient and 0.5 for the area - this is a bit generous but not a big factor at the slow start). The rolling resistance is only 0.001 (wooden boarded velodrome) and the average speed during those 4secs is 3.75m/s (13.5kph). So the total power calculated is then only 12w (on average over first 4 secs)