The perfect power/kilogram point

[Derny Driver]

Not up a steep hill you won't.

If you are faster, by definition your rate of energy transfer per kg is higher.

What if I cut the corners and my opponent didn't?

I'm happy to go head to head with you up a long climb if you'd like?

Unfortunately I have retired from bike riding.
I am left with only 2 options:
1. I use my motor-pacing scooter
2. I deputise my son to fill in for me. He's 21, 6'1 and 68kg.
Either way you are in trouble

[GJM]

I'm in trouble against most people. But I have no doubt that your son would make mince-meat of me.

Unless of course I can bring in a deputy too

[Nobody]

Without knowing what the OP looked like as a teenager, personally I would be greatly concerned or would expect those around me to be greatly concerned if I was 48 and had just dropped enough weight to be 5kg's lighter than when I was 14. That is seriously disturbing.

https://cyclingtips.com/2011/11/the-pur ... -leanness/

I'm 48 and lighter than I ever remember being as a late teen anyway.
In a western society where everyone has a tendency to be slightly heavier, even when young, my comparative weight now may not be a problem. That is if my diet isn't taxing my bone density and I keep doing weight bearing exercises.

[trek52]

this is interesting. I am not much of a climber but the thing to note here iis is it a TT or a race. It seems in a race I can hang on to most climbs up to 2.5km but in a TT i would lose minutes.

At the state masters this year it finished on a steep 600m climb that came down to brute horsepower, not climbing power.

in saying all this I think the lighter guys climb better even at equal watts per kg.

[Alex Simmons/RST]

If you and I had the same watts per kilo I could still beat you up the hill

Not up a steep hill you won't.

If you are faster, by definition your rate of energy transfer per kg is higher.

What if I cut the corners and my opponent didn't?

It's vertical metres that matter on steep climbs, not line taken on the road.

[Alex Simmons/RST]

in saying all this I think the lighter guys climb better even at equal watts per kg.

If W/kg are the same then steep climbing speed is the same. If a lighter guy climbs faster then they have higher W/kg (ceteris paribus).

kg being that of the bike + rider

[cyclotaur]

Without knowing what the OP looked like as a teenager, personally I would be greatly concerned or would expect those around me to be greatly concerned if I was 48 and had just dropped enough weight to be 5kg's lighter than when I was 14. That is seriously disturbing.

haha. I matured early so by the time I was 14, I was at my adult weight.
I was/am 172 cms tall and at 14 I weighed 65 kgs.
Now I'm 60kgs. Or maybe 59.5 (or 60.5), depending on when I weigh myself
At my "peak" (i.e. pre cycling) I was 78kgs.

I am similar, attained my current height (175cm) by 14 but weighed <60kg.

Unfortunately my peak was 86kg, my optimum would be around 70, but I'm still about 77kg....
So apart from riding like a maniac I want to know your magic weight-loss secret !!

[Alex Simmons/RST]

Just to explain, on a steep climb (say 10% gradient), of the total the energy / power demand, about 90% is required to increase vertical height, while only ~3% goes to overcoming air resistance, ~4% rolling resistance and the balance is drivetrain friction, bearings etc.

[march83]

http://s220.photobucket.com/user/ASimmo ... 2.jpg.html

[Derny Driver]

Trust Alex to come on here and spoil all the fun ...

[cerb]

..conversely, thanks for coming with some actual numbers/science!

I like the chart March83 posted from Alex's photobucket. Who went to the effort of working all of this out?

[Alex Simmons/RST]

..conversely, thanks for coming with some actual numbers/science!

I like the chart March83 posted from Alex's photobucket. Who went to the effort of working all of this out?

I did.

It only requires one to solve this equation:



it's not as bad as it looks, although it's much trickier when dealing with dynamic scenarios involving accelerations*. Calculating power from speed is relatively easy (provided you have all the relevant inputs).

Calculating speed from power is somewhat harder as it requires having all the relevant inputs as well as solving a cubic equation and there is no a closed form solution (e.g. Cardano's method) that works for all scenarios. So I use the closed form solution when it works and revert to Newton's method when it doesn't (typically when assessing steep negative gradients).

* I've solved those as well using a method known as forward integration, e.g. when considering the impact of wheel rim mass on acceleration performance when the old weight v aero argument comes up.

[Alex Simmons/RST]

Trust Alex to come on here and spoil all the fun ...

can't help myself

[Calvin27]

Calculating speed from power is somewhat harder as it requires having all the relevant inputs as well as solving a cubic equation and there is no a closed form solution (e.g. Cardano's method) that works for all scenarios.

Can't you just brute force work it out with software without solveing mathematically?

I would have thought the various coefficients were the tricky part - I'd imagine in the real world they are also functions of velocity amongst other variables.

[cyclotaur]

^^
I'd say by the time that equation is solved, stating the traditional "QED" is manifestly insufficient.

It would probably be more appropriate to say "Houston ... the Eagle has landed!!"

[lock_]

I stuck those equations into a test app few years back, complete with some simple drafting models and rules dictating what riders should do when they catch a rider in front (pull out of draft, or break). Maths, it can be fun sometimes



All the riders are putting out constant power. The intention was to then start modelling the physiology of the riders, how long they could hold X power, how they fatigue, etc. Unfortunately the project then ended up on my stack of half done ideas.

Another set of equation implementations can be found at http://www.analyticcycling.com/Topics.html.

[Alex Simmons/RST]

Calculating speed from power is somewhat harder as it requires having all the relevant inputs as well as solving a cubic equation and there is no a closed form solution (e.g. Cardano's method) that works for all scenarios.

Can't you just brute force work it out with software without solveing mathematically?

I would have thought the various coefficients were the tricky part - I'd imagine in the real world they are also functions of velocity amongst other variables.

You can brute force it if you have such software. Most just have the ubiquitous spreadsheets.

As for the variables, most are pretty invariant with velocity (mass, gradient, coefficient of rolling resistance, air density), while there can be small variance in coefficient of drag with velocity, in particular the yaw angle. On some shapes (e.g. upper arms) there can be some Reynolds number effects under certain conditions.

[fat and old]

Ok so Day A I ride Mt Hotham in such and such a time. Its 27 degrees at the bottom and 10 at the top, wind SE at 32 knots. Ive trained 14 hours the previous week and had bacon and eggs for breakfast.
A month later Day B, I ride Hotham again. Its 29 degrees at the bottom and 7,5 degrees at the summit. Wind is Nor-Nor west at 12 knots. I had Coco-Pops for breakfast and trained 8 hours last week and had to take 2 days off for a work trip to Melbourne. I did the climb 2 minutes quicker than last time. Oh and I lost 10 kg last month too.
What do you conclude from this?

The first time you had a head wind and were tired. On top of that weak from starving yourself (or sickness) so pigged out on fatty crap that reared it's ugly head halfway up. Second time you were rested,normal weight or so, tail wind and nice and cool when it mattered.

?

[Derny Driver]

Ok so Day A I ride Mt Hotham in such and such a time. Its 27 degrees at the bottom and 10 at the top, wind SE at 32 knots. Ive trained 14 hours the previous week and had bacon and eggs for breakfast.
A month later Day B, I ride Hotham again. Its 29 degrees at the bottom and 7,5 degrees at the summit. Wind is Nor-Nor west at 12 knots. I had Coco-Pops for breakfast and trained 8 hours last week and had to take 2 days off for a work trip to Melbourne. I did the climb 2 minutes quicker than last time. Oh and I lost 10 kg last month too.
What do you conclude from this?

The first time you had a head wind and were tired. On top of that weak from starving yourself (or sickness) so pigged out on fatty crap that reared it's ugly head halfway up. Second time you were rested,normal weight or so, tail wind and nice and cool when it mattered.

?

What about my weight loss and the Coco-Pop factor?

[fat and old]

Ok so Day A I ride Mt Hotham in such and such a time. Its 27 degrees at the bottom and 10 at the top, wind SE at 32 knots. Ive trained 14 hours the previous week and had bacon and eggs for breakfast.
A month later Day B, I ride Hotham again. Its 29 degrees at the bottom and 7,5 degrees at the summit. Wind is Nor-Nor west at 12 knots. I had Coco-Pops for breakfast and trained 8 hours last week and had to take 2 days off for a work trip to Melbourne. I did the climb 2 minutes quicker than last time. Oh and I lost 10 kg last month too.
What do you conclude from this?

The first time you had a head wind and were tired. On top of that weak from starving yourself (or sickness) so pigged out on fatty crap that reared it's ugly head halfway up. Second time you were rested,normal weight or so, tail wind and nice and cool when it mattered.

?

What about my weight loss and the Coco-Pop factor?

I thought the weight loss was in month before 1st effort?

Coco pops go easier on me before a hard ride than bacon and eggs. All cereal does. Nutritional wise I haven't got a clue.

See, I'm basing my assumptions on what works for me. Everyone is different,

[kb]

...
Everyone is different,

Not me, I'm...
oh..

[Nobody]

Coco pops go easier on me before a hard ride than bacon and eggs. All cereal does. Nutritional wise I haven't got a clue.

You are correct. Coco Pops are better for you than bacon and eggs, especially before a hard ride and especially if you don't use milk. The reason is that animal products have been shown cripple the endothelial cells in the arteries for hours, which are responsible for dilation of those arteries.