How increased mass and drag affect speed

[rc1234]

Hello. I read an article about aerodynamics.

http://www.cyclist.co.uk/in-depth/2873/fat-v-skinny-who-goes-downhill-faster

I'm a little bit confused with this statement regarding mass, drag, and velocity:

"When you increase the mass the speed increases by cubic function, whereas if you increase the aerodynamic drag the speed decreases by a square function. Hence why cyclists who are heavier can go faster"

I get the relationship between the aerodynamic drag and speed based on the Drag equation

Drag = 0.5 coefficient * rho * v^2 * A so v = sqrt(2mg/coefficient*rho*A)

However, I'm not sure where the cubic function for the mass and speed relationship was taken. Can someone tell explain this to me? Thank you.

 

[BvU]

I get the relationship between the aerodynamic drag and speed based on the Drag equation

Do you ? I find the wording in the link utterly confusing. Key is in

Terminal velocity is the speed at which aerodynamic drag counters the force of acceleration

Downhill acceleration force is $mg\sin\alpha$ if the slope angle is $\alpha$. So if you put a cylinder with mass $m$ and frontal area $A$ on a saddle and let it coast downhill, the contraption will reach some terminal velocity $v_t$. Make the radius 10% bigger and the area will increase by 10%. But the mass will increase by 20%, so the equilibrium "downhill force = drag force" allows an in crease of 5% in $v_t$ (if the coefficient doesn't change).

where the cubic function for the mass and speed relationship was taken

And right you are there: heavier folks generally are not lighter folks enlarged in three directions.

Further down the link is also confusing: the tandem bicycle has double the force and about the same air resistance on a horizontal road.