## [Bike] How Fast Before Walking More Efficient Than Cycling?

From: andrew cooke <andrew@...>

Date: Thu, 21 Jan 2021 22:52:02 -0300

Cycling is generally more efficient, per km travelled, than walking.  However,
someone just pointed out to me that if you go fast enough this is not the case
(since losses to air resistance increase rapidly with velocity).

So what velocities are we talking about?

A typical walking speed is 3.5 mph.  That's roughly 1.5 m/s.  Looking at
http://sprott.physics.wisc.edu/technote/walkrun.htm that correponds to roughly
300 W.

So walking burns 300 / 1.5 J/m = 200 J/m.

Now let's consider cycling.  A typical CdA on a road bike is 0.3.  Force is
CdA x p x v^2 where p is air density (1.2kg/m^3).  So F = 0.36 v^2 N.  The
energy required to travel 1m is then 0.36 v^2 J (force x distance).  Setting
this equal to 200 (above) we can find the break-even velocity: 200 = 0.36 v^2
so v = 23 m/s (50 mph).

I may have made a mistake, but that ties in with my intuition, so I'll go with
that for now.

Andrew

### Better Walking Data

From: andrew cooke <andrew@...>

Date: Fri, 22 Jan 2021 19:14:03 -0300

Re-reading the above I am suspicious of the 300W used for walking.  That's one
hell of a lot.

Googling turns up
https://www.verywellfit.com/walking-calories-burned-by-miles-3887154 which
says that 100 calories are burned per mile.

That's roughly 25 calories expended (25% efficient metabolism) per mile.
Converting to useful units, that's 100kJ per 1500m or 66 J/m.  Which is a
factor of 3 lower than what I had above.

That leads to a break-even speed of 14 m/s or 30 mph.

Andrew

PS On yet more reflection I think both sources are consistent, but both are
energy consumption, while it's normal in cycling to look at energy output.
And despite me using "burns" in the first calculation I was basing things
around output energy.