Warning, math related discussion follows:
F=ma
Gravitational acceleration is constant, yes. Gravitational force is dependent on mass. Drag force is dependent on cross-sectional area. Mass increases as the cube of the length while area increases as the square of the length so as riders get larger, the force acting on them due to gravity increases more than the force acting on them due to drag.
If you want to go back to talking acceleration and insist that acceleration due to gravity is constant (a true enough statement) then to be equivalent you have to compare acceleration due to gravity and acceleration due to drag (which is negative, or deceleration). (gravity of course depends on whether you’re going up or down)
Drag force F(drag)=1/2ρ*v^2*A*Cd
or at constant velocity and air conditions
F(drag)=C*A
where C is a combined constant and A is cross-sectional area of rider/bike.
Back to acceleration.
F=ma
or
a=F/m
therefore
a(drag)=F(drag)/m = C*(A/m)
A being the crosssectional area of rider plus bike and m being mass.(C is still constant with constant velocity and air conditions)
Mass still increases as the cube of the length while area increases as the square of the length so as riders get larger, the acceleration (remember, this is negative acceleration or deceleration) due to aerodynamic drag gets smaller= larger riders are slowed down less by drag. This is assuming height/width/depth all increase in equal proportions which is obviously not true in all cases, but is reasonable for a first approximation. Tall skinny riders with lots of frontal area will not do as well as same-weight short stocky riders with lots of mass added in the “depth” dimension. Keep in mind also this was at a constant velocity >>>drag actually increases with the square of velocity, so the faster you are going, the greater benefit larger riders have and this benefit increases pretty quickly with speed. Going downhill, one would presume a reasonable speed.
This explains nicely why I (115lbs) can’t ride in a headwind alongside my daily ride partner (190lb). I haven’t yet found the math to explain why I can’t climb.:rolleyes:
