Help! Cycling Physics Question...

This is a waste of brain power... principles of inertia mean the weight of your shoe is not really slowing you down at all ever ! your overall weight will, on a hill, aerodynamics is your real enemy, pushing wind is what really slows you down, oh yes the other thing, your legs !!!!!
The water in your bottle or pack weighs 1kg per litre.
The weight of your tires is far more relevant, But principles of inertia mean that a heavier wheel may mean a more stable bike !

Dear Edd,

Thanks for your reply on this.

Our interest is the fact that you have to actually pick up and put down /t move this extra weight on each revolution.

The 2 gram total is just for a baseline, we figure that it is not too difficult to take 100g off a pair of shoes & pedals...if our math is correct.

100g x 7,200 rotations = 720,000g moved and that is almost 3/4 of a Metric Ton extra that you have rotate per hour.

Track runners use ultralight shoes to increase their foot speed...we are wondering if the same principle holds true for cycling...

Tks again...heavy summer rain squalls in Tokyo...no lunchtime rides...to keep us busy.

you pick it up, gravity helps you put it down + principles of inertia = a body set in motions will etc. the thing is a cyclist = (3/4 of a Metric Ton extra that you have rotate per hour. ) key word "rotate" = inertia assisted. A runner has to swing back and forth a weight, his shoes = inertia encumbered.

😕

The moment of inertia is the physical measurement for the resistance of a rotating mass. As the moment increases, performance decreases.

Stuart Baird has an excellent book about science and cycling. It's called Performance Cycling.

Quoted post said:

Originally posted by TCG
Greetings...We have a discussion here and need some educated advice...

If you shave 1 gram off of each cycling shoe (total 2g), how much energy will you save based on 1 hour of riding at cadence of 60rpm using 172.5 or 175 crank arms...and how much less mass have you moved over that same hour.

I agree with the other guys: inertia will cause this to make no difference whatsoever...unless of course, you are cycling with an ankling technique (thus moving your ankle up or down depending on which part of your stroke you are). In this case you will be moving the mass of the heel part of your shoe up and down with regard to the axis of your pedal. This implies you are exerting a force on a mass, causing it to move (=work) over time (=power).

A quick calculation shows me this effect would be in the range of 0,03 watts, but probably less - I'm making some very rough approximations in integrating the torque associated with the weight of the shoe in relation to the axle of the pedal over the angle you ankle), depending on the weight distribution of your shoe. I'd say there must be better things to worry about, even if it is raining 🙂

(this must be my most geeky contribution to this forum...wonder if my peers will challenge my rusty physics)

ciao, pj

Have a surgeon implant a titanium plate in your foot that will enable you to use the cleat of your choice. You can also have him cut off any unneccesary foot parts that don't contribute to your cycling perfromance.

"toes are for sissies" has always been my motto.

Looks like the cranks, and the bits of your legs near them, obey the same principles as the wheels: they require slightly more energy than the rest of the bike to accelerate, but once at a constant speed, there is next to no energy required to keep them there because they have their own angular momentum. All mass uses up work only under acceleration (climbing is acceleration, according to Newton). Only mechanical inefficiencies (with pedalling, this would include your action) and wind resistance are slowing you down once you are at speed, not mass, rotating or otherwise.

I think someone once said,

"It's not about the bike."

---kp

Quoted post said:

Originally posted by ant evans
Looks like the cranks, and the bits of your legs near them, obey the same principles as the wheels: they require slightly more energy than the rest of the bike to accelerate, but once at a constant speed, there is next to no energy required to keep them there because they have their own angular momentum. All mass uses up work only under acceleration (climbing is acceleration, according to Newton). Only mechanical inefficiencies (with pedalling, this would include your action) and wind resistance are slowing you down once you are at speed, not mass, rotating or otherwise.

Though I won't do the calculations here, as a physics student and mechanical engineer I feel the need to set the record straight.
The rotational inertia of an object is dependant only on its mass and the relative position of its mass centre from the axis of rotation. I=mr^2 for a point mass.
The energy needed to accelerate such a body to a particular angular velocity w is E=0.5Iw^2.
Because the body is rotating, gravity is NEGLECTED. If you dont believe me take the chain off and see if the cranks will rotate by themselves, they don't!
If you remove weight from the shoe then you reduce the energy required to accelerate to a particular speed, by a greater amount than if the same mass was romoved from a non rotating part of the bike.
Obviously on a flat road once you are up to speed the difference will be negligible except for when changing gears. But it is important to realise that masses on th earth are ALWAYS accelerating downwards and when you go up hill, even at constant speed, you have to counteract the gravitaional acceleration with your legs, with a force proportional to the mass of the bike.

Quoted post said:

Originally posted by never_doped
Have a surgeon implant a titanium plate in your foot that will enable you to use the cleat of your choice. You can also have him cut off any unneccesary foot parts that don't contribute to your cycling perfromance.

"toes are for sissies" has always been my motto.

Hey, was this you???

Man eats own toes

An Austrian man cut off his toes, fried them up and ate them between two slices of bread after getting high sniffing butane gas.

When ambulance men arrived he offered to share his meal with them, passing over a toe and saying: "It tastes like chicken, do you want some, there's a few still left over."

Police said the 35-year-old suddenly became very hungry after sniffing the gas and had searched all his kitchen cupboards, but found nothing to eat.

Grabbing a kitchen knife he cut off his toes on his left foot and dropped them in the frying pan.

The man's sister called the police when she walked into the kitchen and saw him making the toe sandwich.

By the time ambulance men arrived there was little of the hacked-off toes left and a spokesman said: "What there was, was too badly burned to re-attach."

A police spokesman added: "He told the ambulance men that he had more toes than he needed and didn't think he would notice if he got rid of a few."

He was taken to a hospital in Steyr where he is recovering from his injuries.

Story filed: 08:54 Wednesday 18th June 2003

tafi

OH !
if your right and I'm wrong. Which is probably the case. The questions that begs an answer is; Is it going to really make any difference to the performance of the rider/bike ? And are we going to see people removing the lower parts of their legs ( from just below the knee ) to have super lightweight carbon fibre "pedalimbs" implanted ?

by-the-way

I have never really trusted engineers. Reason does not equal reality.
Our calculations are limited to our understanding, which is afforded to us by our perceptions and our ineptness. Deep down below all of our education lies the true F....wit that is us.

Pedal like it matters hopefully science will catch up.

edd,

what do you mean by u have never really trusted engineers. i hope you don't really mean that. In fact you do trust them. if you didn't you wouldn't go careening down hills at 70 odd k an hour with a contact patch of around 2 sq inch. that would be a good example in how much you do trust them.

afforded to us by our perceptions and our ineptness, wtf.

hopefully science will catch up? catch up to what.

Quoted post said:

Originally posted by edd
by-the-way

I have never really trusted engineers. Reason does not equal reality.
Our calculations are limited to our understanding, which is afforded to us by our perceptions and our ineptness. Deep down below all of our education lies the true F....wit that is us.

Pedal like it matters hopefully science will catch up.

Did you happen to see any footage or photos from the 1903 Tour de France? They were shown as part of the 100 year anniversary. I sincerely doubt you'd wish to regularly ride one of those old bikes.

You should thank the engineers for the efficient and comfortable ride we enjoy today. But those changes didn't come overnight - they come incrementally and very slowly. It's easy to scoff at any minor change, one needs to look at the big picture.

Quoted post said:

Originally posted by tafi
Though I won't do the calculations here, as a physics student and mechanical engineer I feel the need to set the record straight.
The rotational inertia of an object is dependant only on its mass and the relative position of its mass centre from the axis of rotation. I=mr^2 for a point mass.
The energy needed to accelerate such a body to a particular angular velocity w is E=0.5Iw^2.
Because the body is rotating, gravity is NEGLECTED. If you dont believe me take the chain off and see if the cranks will rotate by themselves, they don't!
If you remove weight from the shoe then you reduce the energy required to accelerate to a particular speed, by a greater amount than if the same mass was romoved from a non rotating part of the bike.
Obviously on a flat road once you are up to speed the difference will be negligible except for when changing gears. But it is important to realise that masses on th earth are ALWAYS accelerating downwards and when you go up hill, even at constant speed, you have to counteract the gravitaional acceleration with your legs, with a force proportional to the mass of the bike.

This is the best explanation, as far as it goes.

However, crank motion on a bike is not uniform. There are constant accelerations and decelerations. Then there’s the irregular road surface and friction. One might argue that this is one of those “angels on the head of a pin” discussions. When one considers how much just body weight varies from day to day, at what point is the bias on the noise significant?

Where the rubber meets the road shaving a gram or two everywhere one can think of does add up. Where it really matters though is when the competition is so fierce that small amounts of mass translate into the few tenths of seconds between winning and placing. When is this the case in cycling? After watching Armstrong winning his fifth, I would say conditioning and tactics play a larger role.

I noticed some anti-engineering sentiments in some of the other postings. I think both the engineering and lay public should keep in mind that engineering is only as good as the models that are applied to the problem. Then there’s the issue of testing to validate the design. It may work on paper or in simulation, but can people build it and make it work? I’ve seen instances where politics and ill-defined requirements have made a muddle of a project. Engineering is a human activity and consequently is as fallible as humans. In the end, hubris is the enemy.

M2cycler

You have elucidated my point exactly.