In athletics, the closest the women’s world record is to the men’s is actually in the 100m at +8.67%. All other events have a larger margin, typically between 10 and 11%.
Mike
I’m sorry you’re an engineer too, based on that explanation.
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Haha…but seriously, play the ball not the man, eh? 
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Fair enough, but when you follow up you explanation with “I’m an engineer”, it had better be right.
Mike
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Maybe they were an engineer helping to design the 2018 line of Kickrs? 
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You guys should listen to the Trainerroad podcast sometime
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Original question:
“if a small person were to race someone larger, of the same power to weight ratio, would there be a difference in speed?”
Of course the bigger guy will also climb faster 
- Power to weight ratio will be better for a bigger rider when you add rider and bike, kit or other stuff weight.
- We have three types of resistance: rolling resistance, air resistance and gravity.
So, if power to weight ratio is the same there is no difference in fighting against the gravity. I mean each of those riders must for example use [something] W/kg of what they have to climb up the same speed. And actually when you add bike weight the smaller rider has to use more of he has.
Then the rest can be disposed against rolling resistance and air resistance. And the bigger rider has much more pure watts left. So he will definitely be quicker.
Example: 50kg 250W rider VS 75kg 375W rider - both 5W/kg.
To climb up and resist gravity force we can use, let’s say 2W/kg - it desn’t matter how much actually, proportions could be different but results always the same. So for the smaller 100W, for the bigger 150W.
And now it is equal like on the flat road, no more gravity to consider. But the smaller guy has only 150W more to use and the bigger one 225W. Bigger wins. It’s sad, I am 51kg myself 
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Here are the two scenarios on gribble for riding up a 10% gradient (larger rider’s frontal area increased by the cube root of the increase in mass to keep that fair):
75kg rider using 375 Watts = 14.72 km/h:
50kg rider using 250 Watts = 13.99 km/h:
Mike
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hmmm…that surprises me…
Wind resistence is just so much of what we have to overcome. But we’re looking at 5 % in the above example, that’s not a lot, especially since we’re talking 125 watts absolute difference.
You only have to look at the Strava leaderboards, or the build of riders in the peleton. There’s a reason that Marcel Kittel, Andre Griepel etc etc are in the grupetto in the mountains. They are heavier. In the real world, the heavier rider does not go up hill more quickly.
They will IF they have same watt/kg…however much harder for a larger rider to achieve this hence lighter riders rule on climbs
But bigger riders* go down hills much quicker 
Surely a rule of thumb is Big v Small (lighter v heavier)…
FLAT relatively equal depending on riding position (I expect bigger people will likely be able to produce more power)
UP always the lighter/smaller person
DOWN heavier/bigger
But the list of variables beyond the basics is enormous.
*handling skills dependent
I had some spare time and did some digging on my strava. Looked at our chaingang rides that have a climb 0.8mile long near the end. Always into a prevailing wind. One of the lads (92kg) best time is 3mins 14s, 417W at 4.5w/kg. He’s around 70W over threshold. My closest time is 3mins 15sec, 335W, 4.4W/kg. I was 76kg at the time and was 15W over threshold. My PB on the hill is 2mins 58sec at 399W. There I was almost 80W over threshold. All those times were is similar conditions on a hill we’ve all ridden over 200 times each. When we hit the flat, the bigger guys had expended so much on the hill they were done, assuming they weren’t dropped (which often happens there).
What is the take away from this? From the figures you’ve given, you have a higher power to weight ratio, so would expect to be quicker and/or less spent when you reach the top of the hill, no?
Two riders at 5W/Kg: A 75Kg rider at 375W on a 5% grade, 0.004 Crr, seal level air density, same CdA, will climb at 7.96m/s. Same conditions a 60Kg rider at 300W will climb at 7.45m/s.
Check it out here: https://analyticcycling.com/ForcesSpeed_Page.html
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It’s not a power problem it’s an energy problem. Bigger guys have to put out more energy to work at the same W/kg. That will cause them to fatigue faster.
Yes, I have a higher W/kg figure at FTP, but we were climbing the same hill at almost the same w/kg in a similar time. He was burst at the top, I wasn’t. You can plug the numbers into as many calculators as you like, but in the real world, it’s more efficient to be lighter if you want to climb well.
You just explained the point of the thread. Other factors such as the likelihood of a heavier rider achieving the same w/kg as a smaller rider, or the extra energy expenditure of a heavier rider etc. are beyond the scope of what was being discussed. The question was, if power to weight was constant would both riders climb at the same speed, and within a margin of error due to other variables the answer is yes.
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Only if the rider is kilojoule limited to be fair. In an elite road race this is less likely to make a difference, that being said, in that context it is less likely that heavier riders will be at an equal power to weight of smaller riders as everyone is closer to their physiological limits.