> My intuitive feeling is that you should increase effort above average into the
> wind and uphill, then recover when the wind and gradient are helping you.
I have had a go at some predictions of cycle effort adjustment in the face of oncoming wind to maximise average speed. I don't necessarily believe them at the moment as they are not verified, but for for a first stab - here they are.
I will not be able to revisit these for about three weeks, maybe some other people can respond with their thoughts in the interim.
First I had to tune up an aero and tyre friction model, just quickly using five data conditions I have (unfortunately at a mix of altitudes and on different bikes). There are other unknowns in this model, since my estimates of relative effort for powered conditions are the best guesses I can make. However the qualitative rather than quantitative results are what I want to see.
The friction model has tyre friction proportional to weight-on-wheels normal to road, and the aerodynamic models have v¹ and v² terms.
I tuned the three friction coefficients using a steepest descent algorithm searching for a least squares solution, final model RMS force error is about 5% of peak friction and gravitational forces.
The friction model characteristics are
v¹ and tyre friction crossover at 36 km/h
v² and tyre friction crossover at 24 km/h
v² and v¹ friction crossover at 18 km/h
I have run two scenarios thus far - will want to verify these before I do more runs and predict the optimum effort profile (also for gradients).
The first case (well actually I ran it second as a sanity check) has no wind. For given physical effort conditions the average road speed on a there and back course is
38.6 km/h .
The "there" was into a 0km/h wind, with gearing 16/52, and the "back" was with a 0km/h wind with gearing 13/52, so not actually realistic, but it means the next case only has wind variation.
Then I considered an increase in propulsive force of 20% "into" the 0km/h wind. I setup a conservation condition that (effort x time) must be preserved, using this and an interating condition on the interaction between speed and effort, I calculate what the effort level on the "with" wind direction should be. [I did consider an energy conservation condition, but suspect that time integral of exerted force is more indicative of fatigue than energy expended].
This effort profile my model predicted an increase of average speed to
42.9 km/h .
This does not make intuitive sense at the moment, I would expect the average speed to go down if the effort profile in still air deviates from flat, but all the cross-checks I looked at quickly are correct.
The second case is with a 16 km/h wind, first a leg into the wind, then the return. With a flat profile and the same effort as without wind, the average speed predicted was
36.1 km/h ,
while with a 20% effort increase into the wind the predicted average speed is
39.9 km/h .
Once again, my intuition tells me that the speed should drop more than around 3 km/h, but I will have to go through the individual calcs to see whether I believe these results.
Finally, the following are the headwind /tailwind speeds that make up the 39.9km/h average speed with effort profiling :
34.4 & 47.4 km/h .
