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I assume this has been studied to no end for e.g. UCI governed bicycle racing, and probably by others as well.

Simply:

How do you ride the most efficiently, in the context of putting down power?

I'm ignoring aerodynamics and bicycle attributes here entirely. Assume a generic road bicycle on any road course. Before anyone screams that it depends on the road you're bicycling, let me just state that I'm looking for a generic answer that can be applied to any stretch of road. A set of simple guidelines, or "rule of thumb" for how to bicycle the most efficiently.

How do you distribute your power budget? Should the rider put down extra power when going uphill? On the level surface? When going downhill? I think I've seen riders often rest when going downhill, is this due to such a rule of thumb -- that this is considered to be optimal, or is it due to personal preference?

Surely there must be a sweet spot in the graph for any inclination -- where efficiency is given as a function of a few parameters, the inclination, the power put down, and the wind resistance? Something like that?

If this is indeed subjective, and cannot be answered on a general basis, then I accept that as an answer. The simple fact that there is no guidelines to be given and nothing to be said on the matter would at least give me some peace of mind.

Whenever I bicycle, I'm always questioning myself, if I'm doing it wrong in terms of how I put down power. If someone could point me to a study that explains how and when to put down power that would be great, or a study that explains why such a thing is impossible.

closed as too broad by Daniel R Hicks, David Richerby, R. Chung, Klaster_1, Criggie Mar 10 at 7:05

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    Broadly speaking, putting more power uphill will always be better since you lose less of the power to wind resistance. – kevins Mar 6 at 21:45
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    Depends what you mean by 'efficient'. Strictly speaking that means using the least energy, but, the 'best' way to ride might mean to avoid getting overly fatigued early in the journey. – Argenti Apparatus Mar 6 at 23:21
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    Just to clarify, are you asking a question specifically about pacing during a ride, either to minimize time for a given amount of work, or to minimize work for a given time target? – R. Chung Mar 7 at 6:23
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    "I'm ignoring aerodynamics" Then you're wasting your time, because air resistance is the single biggest force you have to overcome, unless you're riding slowly and/or up a steepish hill. – David Richerby Mar 7 at 11:38
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    @DavidRicherby on reflection I think that the "ignoring aerodynamics" that OP refers to means "ignoring changes you could make by changing your riding position or equipment," rather than "ignoring drag due to air resistance" – kevins Mar 7 at 21:27
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The first answer is: you bike most efficiently inside a peloton (where air resistance is lowest)
The second answer (in a GCN video of a sprinter): you do a lot or close to no effort in order to stay at a certain speed (stay on the average). Any increase of speed means you lose a lot more to aerodynamic effect. This usually means you give everything on uphills and recover on downhills (assuming sprint-type uphills and downhills, i.e. 5% or so).

The general idea is that the average speed is much more affected by slow segments than by fast segments, so you want to increase as much as possible the speed on the slow segments, even with a significant decrease on the fast segments (if you drive 99km at 99 km/h and 1km at 1 km/h, the average speed over those 100km is about 50 km/h - one percent of the length at a very low speed just about halves the average on the rest)

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General Rule of Thumb: Go harder on "slow" parts (especially uphills), go easier on "fast" parts.

This rule of thumb has two separate justifications:

(1) Uphills or on slow surfaces (rough pavement or dirt) your air-speed is lower so a marginal increase in speed costs much less power since less force is being lost to wind resistance. This is because the power required to overcome air-resistance is cubic with speed while the power required to overcome the hill or the rough surface are linear with speed.

As evidence for item (1) I used a spreadsheet to numerically find an optimal distribution of power on a hypothetical course of 1 mile flat and 1 mile 8% gradient uphill with an "energy budget" of 164kJ and some reasonable values for aerodynamics and bike/rider weight. There is a rather flat minimum in time when applying less power on the flat, with huge penalties if applying more power on the flat: enter image description here

Accounting for physical limitations, something around 200-250W average on the flat and 574-444W on the hill seems actually optimal.

enter image description here

(2) On slower sections, the same absolute increase in speed "matters more" because it results in a greater %-increase in speed and decreases the time spent in the "slow section"

What's interesting in item (2) is independent of why the section is slow (even if it's slow because of a headwind). The maths are a little tricky and I'll work on optimizing in general, but here's a quick anecdotal calculation that shows this:

Imagine you are riding 5km out and back on a section with a 10km/hr wind. If we have enough power to ride for the entire distance at 20 km/hr relative to the wind, then with an even effort we would go at a ground speed of 10km/hr in the headwind and 30km/hr in the tailwind (all the time 20km/hr relative to the air), resulting in a trip taking 30 minutes in the headwind and 10 minutes in the tailwind for a total of 40 minutes.

Now suppose we found some extra energy. We now have the ability to add go 7.5km/hr faster (relative wind speed) for a single 8-minute period. (If you are curious, at an air-speed of 20km/hr it costs about 140W to go 7.5km/hr faster, so in this example we have an extra (140W)*(8minutes) = 67kJ to spend) Should we apply it in the headwind or tailwind section?

These numbers were chosen purposely because if we travel 37.5km/hr (27.5 relative to the air) for 8 minutes we can do the entire tailwind section in that 8 minutes. Keeping the headwind section the same results in a total time of 38 minutes.

Alternatively, we could travel the first 8 minutes of the headwind at a ground speed of 17.5km/hr (27.5 relative to the air). Doing this for 8 minutes covers 2.33km. The remaining 2.67km at our original 10km/hr will take another 16 minutes. So the total trip time in this scenario is 8 + 16 + 10 (tailwind at 30km/hr) = 34 minutes

(Note that in the above, I am neglecting types of mechanical resistance that increase with ground speed so, in actuality, it's even worse than it appears to apply extra energy in the tailwind)

So even if your extra energy is going into the wind, it's better to apply it when you are going slowly.

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    I have to question your thinking behind this "Now suppose we found some extra energy. We now have the ability to add 7.5km/hr (relative wind speed) for a single 8-minute period." Any extra energy you might find will not add an absolute amount of speed, it would add an absolute wattage, and the marginal speed you get out of those watts will diminish with increased aerodynamic drag. – Adam Rice Mar 7 at 18:27
  • @AdamRice I agree that the energy increase will add an absolute amount of wattage for time (definition of energy). Neglecting rolling/mechanical resitances (as I mention I do), this equates to an equal increase in air speed (speed relative to the air), which then equates to an equal increase in the (different) ground speed. In both cases our air-speed changes from 20km/hr to 27.5 km/hr for 8 minutes (but groundspeed is dependent on which way the air is going). – kevins Mar 7 at 21:31
  • I see what you mean. That makes sense. – Adam Rice Mar 7 at 23:39

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