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Yes, clearly the answer is going to be different in different scenarios.
So for the purposes of my original question, I'm talking all things equal, straight line speed on a smooth surface, a straight tarmac road for example. Same size tyre, same bike, wheels, rider, position.Obviously a 24c turbo cotton is not going to be faster than a 1kg knobbly DH tyre down a world cup trail or faster than a 42c gravel tyre on singletrack and less grip of a harder tyre will clearly mean needing to slow down more for corners so I'm talking in terms of velocity rather than lap times.
Likewise for acceleration, real world use case, softer is better for grip and acceleration
But I wanna know about speeeeeed
PhilDAS-
a straight tarmac road for example
Tarmac isn't that smooth, if you look closely at it. Softer compound tyre could conform better to the very small but constant variations in the surface. At a guess.
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Straight line speed on a perfectly flat surface the harder compound will go faster, just take longer to accelerate due to less grip. I can't remember where it was but ages ago I was reading about how bikes actually go faster when the ground is wet
Howard
Sumo
some bro science below, but...
Presumably grip is needed for acceleration.
At one end you'd have an almost solid tyre that hardly deforms as it bounces over the imperfections on the road surface. For something like an indoor velodrome track then this works pretty well as you lose very little energy bumping over things. But you'd waste plenty by bouncing around on a gravel path, not to mention sliding out as the tyre fails to hold on.
Then as you get a wider tyre and a lower pressure then you can deform around/deal with the imperfections of the road surface. And the ideal tyre depends on the road surface.
And the added reassurance of a tyre feeling more sure footed will lead to a rider pushing a bit more than they might on a rock solid tyre on sketchy ground. So there'll be a crossover where a technically faster tyre probably ends up slower in the hands of 99% of riders/drivers who value the confidence inspired by the marginally slower tyre.