[hpv] Re: hpv-digest V7 #1051

[F.A. Karelse]

Scott wrote:
> I will note this one caveat. I've never understood why a hillier ride,
> that's a closed loop, is always slower than a flat ride of the same distance
> and under the same conditions. Somehow you invest energy on the uphill that
> you fail to recapture on the downhill. Perhaps it's just a matter of
> maintaining a safe speed so that by braking you are deliberately throwing
> away energy rather than spending it. Does this mean that if you kept the
> downhills shallow enough so that you didn't need to brake you'd achieve the
> same average speed as on a flat ride? Gosh, I wish I could store that
> braking energy somewhere...
>
> - -Scott

Take this example:
You ride a flat road of 20 km (don't know how many miles that is -
sorry)
at 20 km/h. It costs you one hour.
Now you meet a hill which goes up for ten km and down again for ten km.
You keep good pace: 10 km/h.
You see what happens: The rise will cost you one hour and no matter how
fast you 'sink' the hill will cost more time than the flat road.

Further:
Suppose you spend as much power on the flat as during the climb, so the
difference in speed is your potential energy rise.

flat: energy = force * distance = C * 20^2 * 10 km= C*4000 kJ
where C is the aero-dragcoefficient. (Air resistance force is C* v^2,
where v is the velocity)
hill: E = C*1000kJ
So you won C*3000 kJ potential energy, which will be released down-hill
Suppose you don't break, and your speed reaches a constant value
quickly.
Then your speed downwards will be v=square root(700)= 26.5 km/h.
That is not very much, is it!

You lose a factor two in speed on the way up, but on the way down this
effort leaves you with a tiny factor 1.3 speed increase. Air resistance
is not fair.

For the same reason a ride in windy conditions will cost you more time
(or effort ;-) )

Frank -no hills around here, but a lot of wind though- Karelse