[Closed] Watt / kg and hills

Are you on a conveyor belt?

i think the big issue here is drag which is a factor of surface area

I reckon the lighter person gets up quicker than the fatter person who comes down quicker so that overall the two combined were the same time.

I await the physicists/mathematicians to see if I am correct.

Yes you should climb at very similar speeds.

On the flat the heavier, more powerful person should have an advantage.

Yes by dividing the power by kg you've corrected for your extra mass

Assuming both of your bikes weigh a similar amount, yours would represent a smaller promotion of bodyweight thus give a slight advantage.

The weight of the bike is a smaller percentage of the heavier person, which would drop the overall weight/kg, however I would argue that it depends on temperature - if it's hot a larger person generally will suffer more.

Yes by dividing the power by kg you've corrected for your extra mass but not taken account of aero drag. ie if they both have the same power to weight the least draggy one [ stop me if my terms get to scientific] will go faster.

Also, on the flat it's more about air resistance versus power, and the larger surface area would be negated by the additional power - so larger should go faster.

Or the fella who'd pumped his tyres up a bit harder............

There's more to it as well. Are you both as good at each other at making power on that grade of slope? Some are better than others. Also you're assuming you're both riding precisely at your thresholds, which is rarely the real world case. So depends on length of the hill, how much variance in power there is and how well you each deal with this, how different your power profiles are... I could go on 🙂

Are the power to weight ratios measured before or after the pre-ride poo?

This type of question needs a simulator: http://www.gribble.org/cycling/power_v_speed.html

If two riders each produce 4w/kg whilst cycling up a 10% hill they arrive at the top at the same time.

Thats not a cycling question it's mathmatics.

Surely it would depend on other factors as well such as wind resistance. The power needed to overcome drag would benefit the heavier, stronger rider.

Not on a 10% incline, speed wouldn't be sufficient for drag/wind resistance to be a factor.

I suppose there could be an increased gravitational pull on the heavier rider, certainly helps me downhill :). We may need a gravitationalist to quantify that though.

You need to take into account the bike weight, effect of heat on fatigue (smaller guys generally cool quicker) and that's if we assume both riders are riding at threshold on a steady climb.

Depends if he likes looking at your arse

They're riding at a constant 4w/kg.

w/kg wins on a hill, watts wins on the flat. Sir Bradley has put on 11kg since he won the TdF and started training for the track.

AS above as a maths question would both arrive at the same time. In reality it is more complex. Your ability to sustain those watts over the length of the hill would matter. Also your motivation. To go fast up hill on your limit is uncomfortable - I can never get close to my competition times in training. While that number adds a few grams it provides a lot of motivation. I've never had to sit down mid training ride because I've gone to hard up a hill.

Not on a 10% incline, speed wouldn't be sufficient for drag/wind resistance to be a factor.

It will be, just a small factor.

If you're really interested then shove all the data in here...

http://www.cyclingpowerlab.com/PowerSpeedScenarios.aspx

... and you can tweak parameters for weight, power, CdA, grade, etc and see what difference small changes make.

pretty marginal- 10kph x slightly bigger frontal area = not a lot. 🙂

Didn't say anything to the contrary, it's still a factor, just a small one. Like rolling resistance and what not.

For the purpose of answering the question I agree with you. Maths question, not cycling!

Is the hill exactly one hour long?

One rider might be capable of 4.5 w/kg for 30min and 3.5 w/kg for the second 30 minutes, the other rider more consistent.
OK, very general example - but you get the point.

It isn't an accurate method of comparison between riders, but good to compare yourself and gauge performance gains.

There won't be much aero on that sort of slope. If you had a tailwind the lighter guy would go faster, headwind or no wind the heavier guy, and if both bikes weigh the same the heavier guy plus bike has a better pwr.
Another factor is that on the flat and downhills before the climb the big guy will have an aero advantage so will be less tired at the bottom of the hill- although conversely if you've been riding together the smaller guy will have had more of a hole punched in the air when he's been on the back.
The moral is always act tired and get on your mate's wheel until you get to the climb you want to beat him up.

Maths question, not cycling!

Plugging in some numbers....

[img] [/img]

Assuming one rider is 70kg and the other 80kg, they both are riding at 4 w/kg, both bikes and kit weigh 10kg, up a 10% grade, with same CdA.

Heavier rider with more power will be going 11.87kph, lighter rider will be going 11.66kph. This is because of the lower w/kg when you add in the bike weight. The smaller rider would need to put out an extra 6 watts to match the pace of the heavier rider (or lose ~1.5kg from bike and kit weight.)

Aero doesn't make a huge amount of difference at that speed. Going from a typical tops to drops CdA only gets you about .1 kph.

On the flat, riding in the drops, the heavier more powerful guy will be almost 2kph faster...

[img] [/img]

That's assuming both have a CdA of .31 (typical drops). The lighter guy would need to reduce his CdA to about .27 to keep up (and that's a good optimised aerobar type of figure.)