I know I’m going to get hammered on this one…
BUT… is a 10% increase in power directly proportional to a x% increase in speed? I do recognize exponential wind resistance and climbs/descents can throw it off. So lets assume same rider, same course and wind resistance is not a factor.
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I think you answered your own question, because wind resistance is not linear.
and you can’t ride in a vacuum, so I’m not sure why you added that to the question. Why not get rid of gravity so the only losses are drivetrain friction. Heck, lets get rid of drivetrain friction… You see where this is going, I’d focus on how it works in the real world.
yes yes… but drivetrain friction and gravity are fairly constant. So OTHER than wind resistance, which actually could be factored in. And yes… real world is what I’m after. Have you ever looked at the numbers to see a correlation?
Isn‘t the real question: Is a 10% power increase enough to impress my riding buddies? 
(SO doesn‘t care 
)
Ok, I‘m out.
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At speeds that matter (18mph+) 80% or more of the overall resistance is aerodynamic drag.
That leaves 20% or less that come from tire rolling resistance, drivetrain losses (chain, pulleys, BB) and hub bearings for the most notable. I have no idea if rolling resistance is linear or not, and it likely varies between tires if nothing else, but it’s probably the largest contributor among them. The rest of those losses would seem to be so minor as to be negligible overall, not to mention in delta’s of power you mention.
I guess I don’t see the end goal in the question here, since the two big dawgs (wind & tires) are mostly known and dwarf the others for real world speeds.
I barely skimmed this, but it seems to head in the same direction as this rabbit hole:
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Answers like yours are my end goal. Thanks!
I will say this though… since I’m dealing with XCMTB, your speeds are not my speeds. Therefore less of a factor. Rolling resistance probably falls in the same camp, but apples to apples I wonder what the real world correlation is🤔
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Perfect… ty
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- This is key info that belongs in the OP of any discussion like this, to keep from heading off-trail for those of us trying to offer help
Considering that difference places this all in a very different light as you noticed.
Example from a 2.4 mile / 3.9km segment with a lot of efforts as its a favorite route back towards town.
Two weeks ago I was in a tailwind with a small amount of drafting (~10 in peloton):
solving for that speed with an online calculator, I used -8mph effective tailwind:
close enough. (calculator: An interactive model-based calculator of cycling power vs. speed)
My young friend has the KOM at 30.4mph and 334W:
similar tailwind. So what does the calculator say if I tried to match that speed:
About 344W for me, which is a little more than what he put out on that KOM while pulling 2 guys. And I’m a little bigger, a little less aero.
So in a solo effort, with similar wind conditions, to go from 27.6mph to 30.4mph for nearly 5 minutes I would need roughly ~350W effort. Looking at my power curve:
makes me think it unlikely!!!
Back to your question…
- 30.4mph happens to be 10% faster than 27.6mph (a coincidence, I didn’t go looking for that)
- power increase required is 344/248 = 39% more power required
so in this example, a 10% speed increase requires about 39% more power, in a tailwind, in the real world on rough pavement and a steady ~12mph tailwind.
Here are two efforts on the 1 mile segment just before the segment above, separated by a week, one in the peloton and the other I got dropped just before the segment so its solo:
similar wind conditions.
Thats why the bigger guys (about my size) with 350W FTPs can hammer at 28+mph for 40-50 minutes on Tue/Wed/Thur worlds in this area. And why I get dropped with a 270W ftp.
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I keep forgetting that road biking exists…
This is Beautiful @WindWarrior! Thank you 
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Unspoken (unwritten) assumptions are the bane of my existence. 
Easy to do, but I try to think about talking to someone who is NOT at all familiar with the topic when trying to cover details and premise. But I tend to be on the overload side which is not without it’s own set of issues.
The more modern example I see mentioned is “Explain Like I’m Five”.
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Totally get it… I should have included that. Let me edit.
Actually… I really like the roadie input. I think you guys really hammer these numbers in and look at all the data. I think I will keep the same.
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No sweat. I don’t mean to beat you up for it.
Just mentioning it more broadly because it’s overly common here. Most OP’s require one or more clarification questions to offer any really useful info. Just necessary steps in the process, but can add time or lead to incorrect or unrelated info as we saw.
Seems like you’re getting some good info, so all is good in the end 
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by the way, at higher speeds being more aero makes a big difference, not easy to see it on this similar segment because the three smaller-more-aero guys didn’t post power:
but you can clearly see who was pulling last Wed (Sept 20) at 395W vs my 249W (highlighted). The guy below typically posts 50-to-70-ish watts less, so I’d guess he was doing around 180-200W.
And the 395W guy posted this on Strava:
of course that means I spend a lot of time in daycare! 
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This is awesome…
Very broadly speaking…
Wind resistance is speed squared. A 10% increase in speed requires far more than 10% increase in power.
Everything else: scales pretty linearly. If you had a velodrome in outer space…I think a 10% increase in power would equal almost exactly a 10% increase in speed.
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I am pretty sure power is proportional to speed cubed (rather than squared) “in a vacuum” ( which would remove wind resistance lol!)
Edit: I’ll be damned, putting my aerospace degree to use today. Nice… aerodynamic drag causes power to be proportional to speed cubed; rolling resistance is roughly linear with speed. So the real-world answer is something slightly less than speed cubed.
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Wow! 
Elegant and simple.