I am having a disagreement with a friend. It stems around the scenario of 2 identical bikes on the same gear ratio side by side. If the rate of pedaling is same for both do both bikes travel at the same speed? Or does the rider's weight play a factor?
Speed is determined only by gearing, of which crank, cassette, wheel, and tire are components
Any 2 bikes using, say, 42t cranks with a rear 32t cog and 25c tires on 700c wheels at 90rpm will be going the same speed. Bike type and size, rider/bike weight, and even front wheel/tire size and crank length don’t matter. These other factors only effect how much power it will take to keep up that cadence with that gear combination.
The mechanical factors which translate pedaling rate to overall speed are:
- Gear ratio
- Size of wheels
The weight of the rider is not relevant for this question.
The weight of the rider would be relevant if you were asking about the power needed to keep the bike going, especially up any kind of hill.
There would likely be a small difference. If you have, eg, a bike with a rear tire that has a 68cm diameter, the effective tire diameter is reduced by the amount it compresses when the bike is carrying a rider.
Let's say that the heavier rider is heaver by 80kg, and this causes the tire to compress an additional 1cm vs the diameter with the lighter rider. The effective radius is 33cm vs 34cm, and the effective circumference is 207.34cm vs 213.63cm.
So he heavier rider would travel about 207.34/213.63 or 0.97 kilometer for each kilometer the lighter rider travels.
(In practice the difference would likely be somewhat less due to the dynamics of the tire. The lateral stiffness of the tread would tend to make the heavier bike "scoot ahead" relative to the above numbers, perhaps halving the disadvantage. This would depend on the specific tire/tread/pressure.)
If the weight difference is significant and the mountain bike tyres are inflated to low pressure, yes the ligther biker can be slightly faster than the heavier one.
The cadence (same) is directly bound via gear ratio (same) to the wheel's angular speed (rad per second). The velocity is proportional to wheel's angular speed (same) and the radius, which must be measured in the point of contact.
If you want to quantify the difference, sit on the bike and masure the distance of the rear wheel axis to the ground for both riders. Divide those numbers and you'll get the ratio how much faster/slower the other bike will ride.