# When will POWER/MASS be replaced by FORCE/MASS or ACCELERATION in professional cycling?

#### marius-ciclistu

After some years of observations, research and calculations in the cycling and rally fields, I realised that because power is synonymous with force outside of physics terminology, it gained popularity after Jes Watt defined the power as "the ability to act" with the formula Power = Force * Speed. Later Joule introduced the ENERGY concept that better explained power as a RATE of ENERGY (Power = Energy / Time).

At the end I did some references also to cycling but I did not had the resources to dig deeper into it.

Bottom line is: I see that cyclists use power metters and power to weight ratios. Mass is measured in kg and weight in N (Newtons). Besides the fact that weight is used as mass, this is not the big issue, but power usage is. I'm not saying that this measurement is useless. I'm just saying that it is inaccurate in comparison with Force (and acceleration) when comparing the dynamics of a material body.

Force = Mass * Acceleration

Energy (or work) = Force * Distance

The power is just a calculation between energy and time (or force and rotational speed).

The cycling world would benefit if they would look at FORCE/MASS in a period of time rather than at POWER/MASS in a period of time, and by FORCE I mean propelling (pushing) force at the back wheel's circumpherence.

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#### Armchair Cyclist

Moderator
When? Never, because we are more interested in the speed that they can sustain rather than the rate of acceleration to reach that speed. Explosivity is a thing, most obviously at the finish or in creating a gap, but it is not the thing.

I don't think anyone makes an issue of whether we are describing the kg as mass or weight: weight is a casual inaccuracy of technical language, but given that neither the w/kg, nor a rider's mass, is usually given to more than 2 sig fig, and that even if we were to race on the top of Everest, the gravitational fluctuation would be less than 0.3%.

#### marius-ciclistu

When? Never, because we are more interested in the speed that they can sustain rather than the rate of acceleration to reach that speed. Explosivity is a thing, most obviously at the finish or in creating a gap, but it is not the thing.

I don't think anyone makes an issue of whether we are describing the kg as mass or weight: weight is a casual inaccuracy of technical language, but given that neither the w/kg, nor a rider's mass, is usually given to more than 2 sig fig, and that even if we were to race on the top of Everest, the gravitational fluctuation would be less than 0.3%.
We talk about different accelerations here.

Resulting force that acts on the cyclist-bike (as material body) = propelling force(that I talked about) - resistive force( air friction + gravity + etc).

This Resulting force divided by mass is the acceleration you talk about.

The acceleration I propose is the propelling force divided by mass during a period of time. This acceleration can be over 0 while your acceleration is 0( meaning constant speed).

#### marius-ciclistu

Needless to say that the torque or force graph on (for example) 50-150 crank rpm range for a profesional cyclist is not constant, so saying that power is directly proportional with force because of its formula Power=Force*Speed is nonsence.

#### JayKosta

Watts are understood by most people (in the US at least) because light bulbs, power tools, etc. all have a watt rating and people have gotten an approximate mental concept of watts as a measure of 'power' - whether it is the number of watts that a rider is capable of producing in a short sprint, or the number of watts that a rider is able to maintain for some duration - perhaps 30 minutes or several hours.
Also the range of watts makes it convenient for physical activities - typically about 20 - 1000 watts - nice whole numbers in an easy to understand range.

#### marius-ciclistu

@JayKosta My question is targetting mostly the pro area.

Most people don't understand power and they use improperly watts for all the measurements that contain W like WH ( 1 KWH =3.6 MJ which is the unit measure for energy). It took me several years (taking into account that my studies are in the physics field, but that did not help much) to see the link between power and reality (which is force), concluding that marketing is the only reason why it is still being used (after more than 200 years) to describe the dynamics of a material body...

But you have a point in what you are saying and I would complete your answer with the fact that if you use the word power in marketing, usually you have more success.

PS.
I received the same pushback feedback also from the petrolheads (automotive) and also from the colledge teachers since 2017. The difference being that the HORSE POWER is banned from official records as a power's unit of measure and it was replaced with watts, meaning a partial acknowledgement that power was just a tool of marketing the steam engines.

Also BIPM France replied to me that they are responsible with defining the units of measure but not with enforcing their proper usage.

#### Krzysztof_O

power/mass ratio is much easier to use when comparing climbing performances because on sufficiently steep climbs vertical speed (VAM) changes almost linearly with w/kg (due to gravity being the main resistive force) and we intuitively know how much climbing time changes with each 0.1 w/kg.

force/mass would be way more difficult to analyse. Increasing the ratio by 1 % would mean that the uphill speed will increase to some value v, for which total resistive force increases by 1% (due to increase of velocity related component, which isn't easy to calculate - part of it is linear and part quadratic function of speed).

marius-ciclistu

#### marius-ciclistu

@Krzysztof_O

force/mass you compare as raw values.

That is how I saw it is done now with power/mass, even by the famous by now, moe. His comments inspired me to ask this question here.

The force is the ponderate(weighted) average by time (in the time period) of: the force with which the rider pushes on the pedals multiplied by the transmission coefficient (to transform it into propelling force).

If you want to calculate the climbing time, then the calculations you wrote come into discussion.

The power meter manufacturers can expose this data if they want, because power can't be measured anyway, but just calculated from multiplying force (N) with rotational speed (radians per second).