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I'm trying to work out how hard I should push myself when riding up or down a hill. Similarly, how hard should I push myself when riding into, or away from, or perpendicular to wind?

My aim is to arrive at a location in the shortest amount of time possible. I would assume that if I output more power going up a hill, then I would have to compensate by outputting less power going down the other side (let me know if you disagree). So, what is the most efficient way to achieve this aim? Is it better to work harder (and save time) up hills, or work harder (and save time) down hills. Similarly, how does wind affect this, both on the flat and concurrently? For the purposes of this question, assume I am riding by myself and hence ignore slipstreaming

Extra points for justification of your answer with links and/or physics. (N.B. there are no extra points.)

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Why the negative votes? At least leave a comment? Besides the interest to myself, I would have thought that this would be something that would be of interest and studied at a professional level (e.g. for time trials). –  Sparhawk Feb 16 '13 at 22:57
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I think that people tend to downvote questions they perceive as "bad" because they're obviously (to them) difficult or impossible to answer. This is pretty dumb, though - your question is clear and well-defined, and the explanation of why it's still pretty much impossible to answer is itself the answer. (+1) –  Jefromi Feb 17 '13 at 4:24
    
Thanks for the comments and vote @Jefromi. I was a bit surprised, as it's something that I've been dwelling on for weeks during my longer rides. :) –  Sparhawk Feb 18 '13 at 11:10
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6 Answers 6

up vote 8 down vote accepted

Basically whatever works.

If you're trying to conserve energy it's foolish to push yourself going downhill, since energy lost per mile to wind resistance increases with the square of speed -- just take advantage of the "free ride" on a reasonably steep hill.

Going uphill depends a lot on your physical condition and how steep the hill. You first need to ration your short-term energy availability so you don't run out of steam halfway up. Beyond that, though, there is a complex relationship between cadence and muscle efficiency, and the "sweet spot" in terms of force vs cadence is highly individualized, and also depends on the length of the hill.

On the flat it's a little clearer that maintaining a moderately high cadence is optimal in terms of preserving stamina, though "moderately high" again varies with the individual.

Running into the wind it's generally better to slow down, again because the higher your relative wind speed the more energy you "waste" per mile.

Running with the wind you can take advantage of it, of course. (But we all know that a tailwind is a fiction -- it never happens in real life.)

Whatever works.

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Some good ideas here. I originally thought my question might be a simple maths/physics problem, with a "pool" of energy that was constant. Then, I could use various "energy-usage" formulae, such as energy/distance = k*speed^2 that you mention. With these assumptions we could calculate (e.g.) whether the time saved in a headwind would be worth it. However, it seems clear that it's quite a bit more complicated than this, since one has to account for short-term energy stocks. I hadn't thought that cadence would be relevant to the question, but perhaps it is, in light of short-term energy. –  Sparhawk Feb 16 '13 at 5:16
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Whenever I have a tail wind, I always, even now, interpret it as "wow, I'm feeling good today!". Its a lesson I never seem to learn. –  PeteH Feb 16 '13 at 9:34
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@Sparhawk I think that "whatever works" does in this context really mean, that it will depend on individual factors and that you will have to figure out yourself what works best for you. Just take a look at the tour de france peloton. There are several types of riders: climbers, time trialists, allrounders, sprinters, guys that can escape from the peloton for have a race day... they all will have different physiology and different ways to deal with their own difficulties and benefits. Believe me, you will develop a feeling over time how to behave best in which situation. –  Benedikt Bauer Feb 16 '13 at 20:01
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Okay, that makes sense to me. I guess it's more likely that the optimal way to ride is empirically determined, based on individual riders, rather than calculated from theory. Thanks for the answer. –  Sparhawk Feb 16 '13 at 23:01
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One more reason uphill is complex: none of the real hills you ride up are going to be constant grade. You're going to have tougher spots and easier spots messing with your speed and short-term energy reserves, so it gets even harder to optimize. –  Jefromi Feb 17 '13 at 4:29
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The only thing that will work for everyone in all situations is to wear a heart rate monitor and ride right at your aerobic threshold. Otherwise, it will be mostly personal preference, for loose meanings of "shortest amount of time possible".

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To summarise, are you proposing a constant heart-rate, and hence constant power output? This seems counter-intuitive to me (for reasons that I find hard to describe). –  Sparhawk Feb 16 '13 at 5:11
    
@Sparhawk: Basically. Any faster, you will tire yourself out, any slower, and you are not using your entire biological energy output. –  whatsisname Feb 16 '13 at 6:02
    
This might not actually be optimal - your legs do work too, not just your heart, and under some circumstances (sufficiently steep hills or strong headwinds) they're going to become the limiting factor. At that point you have to figure out where to ease up in order to be able to make it the whole way, and you're back to the difficult optimization problem. –  Jefromi Feb 17 '13 at 4:26
    
@Jefromi: every joule your body burns, the heart has to supply oxygen for. If you use your legs too much on an incline, your heart rate will increase because your legs will be demanding more oxygen. –  whatsisname Feb 17 '13 at 6:09
    
@whatsisname Uh, yes, but that's beside the point. Your legs care about force, not just power, so if you're struggling up a hill, sometimes your legs become the limiting factor, and it doesn't matter if your heart rate increases. Unless you're a really, really strong cyclist, you can easily get to where remaining at threshold heart rate will tire your legs out too much, and you subsequently your legs won't be able to exert enough to keep you at threshold. –  Jefromi Feb 17 '13 at 6:25
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IF my hills are in the 4% or greater category, it is always going to take me longer to get up than to come back down. Example, a hill I ride frequently is about 4 - 5% and I ride it at about 7-8 mph and it takes me ~7 minutes to get up there. If I ride back down the same hill, I easily maintain 23-24 MPH and it takes me about 3-4 minutes to get down. If I work harder at coming down, I save maybe a minute at most. But if I could ride up at 10 mph, I'd get up the hill about 2-3 minutes faster. Unfortunately the limiting factor for me is my aerobic and physical ability. As I get in better shape and loose more weight, I'll go up faster. Two days ago, we had 15 mph winds gusting to 34 mph. Those winds were blowing up hill, I could not believe how fast I went up the hill, averaging about 11 - 13 MPH all the way up. Coming down, I had to WORK to stay above 15 mph. So the wind gave me an approximate 30% advantage going up and cost about 50% coming back down. Maybe someday I'll be able to ride up that hill like I had that tail wind, until then, I'll huff and puff my way to the top! I think hills make the man. (or woman).

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I realise it'll take longer to go up hills than down, but my question is whether the net advantage comes from pushing harder up or down. e.g. is that 10 mph speed uphill (and 2–3—minute saving) equivalent energy-wise to the one-minute downhill savings. –  Sparhawk Feb 16 '13 at 5:20
    
@Sparhawk I was rather focused on your statement My aim is to arrive at a location in the shortest amount of time possible. The biggest time expense is on the hill, therefore that is where the biggest gains can be made. And as others have pointed out, going faster downhill has diminishing returns because the wind resistance goes up by the square, at lease that's the way I understood them. Personally, I live for the day when hills are a breeze like they are for so many riders 1/2 my size, which by the way is where my obstacle lies. I hope all your commutes are safe and fun! Joe –  Joe Feb 17 '13 at 15:35
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It depends on the hills and your fitness. Assuming that your fitness is excellent and the hills mild, you would want to put out constant effort at your maximum that you could sustain without tiring out. You would maintain constant cadence and torque by shifting gears up and down as needed.

On the other hand, If the hill is steep and long relative to your fitness level you may have to work harder. In that case you may need to reduce effort or even coast down the hill to recover.

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It's also important to consider whether you're riding a relatively short fixed distance, something you can complete in maybe a couple of hours, or doing a day-long tour, where "saving some for later" is important. –  Daniel R Hicks Feb 17 '13 at 3:55
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I guess you may be working on the assumption that you have a total amount of energy for your ride and you choose which parts of the ride to use it on, or when to use it most quickly. Perhaps you suspect that, due to the lower wind resistance, you're better off spending more energy going uphill at the cost of needing to relax on the downhill?

Consider the simplest case of going up a hill and back down the same way, with no true wind (only what you induce by moving). My thinking used to be that I should go as hard as I possibly could up the hill, so that I had to coast down the other side. When climbing, I thought, very little of my effort would be lost to wind resistance. I'd be slower on the descent, but this would mean a smaller proportion of my work would be spent on overcoming (induced) wind resistance. I've read that at 20kph you are using 50% of your effort to overcome wind resistance and, as pointed out by Daniel R Hicks, wind resistance increases with the square of speed, so this strategy seems intuitively sensible.

However, my experience doesn't bear it out. I think the problem is pacing. I can't actually work hard enough on the climb to make this work. If I pedal flat out, then I need more than the same distance downhill to recover for the next hill or to keep me going on the flat. But working at, say, 40-80% of maximum is more sustainable for anything longer than a ten minute up and down. Extreme effort actually costs more than slightly above-average effort. (Also see a question about standing up to pedal).

Lately I've been concentrating more on my target average speed. Any time I'm below it I work a little harder and when I'm over my target I relax a bit. I don't have a heart rate monitor or power meter, but these might help too.

I'm afraid I don't know all the equations, but I think they'd have to take into account aspects of your body's performance, not just power and aerodynamics, so would be pretty complicated.

For me, working out through practice the best times to put the effort in on a 1-hour route is part of the fun of racing against my previous times.

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Part of the problem is that a cyclist's performance is generally optimized when he's right "on the edge" between fully aerobic muscle action and at least partially anaerobic action. When you go over a certain point in effort the muscles begin burning fuel without oxygen (which is less efficient) and, more importantly, begin burning glycogen stored in the muscles rather than sugar from the bloodstream. This depletes your body's limited store of glycogen and also produces large amounts of ketones that can build up to toxic levels (resulting in "bonk"). –  Daniel R Hicks Feb 17 '13 at 14:00
    
Good answer. All answers do seem to suggest that a cyclist has to work it out empirically! –  Sparhawk Feb 18 '13 at 11:18
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As you have guessed, it is better to work harder on the uphill and rest on the downhill. And as others have mentioned, whatever works for you on the uphill in terms of balancing high cadence and mashing is best. However, there are a few guidelines that you can follow to approach each situation in the most efficient manner possible.

  1. Downhill: Since wind resistance is the biggest factor in reducing your speed in this situation, you simply want to be as aerodynamic as possible. Tuck yourself into an aero position. Basically, you want your upper body as low and horizontal as possible. Check out pro riders on the downhill of a mountain for visual aids. Use this opportunity to rest and only pedal in short bursts coming out of corners that you've had to brake for.

  2. Headwind: You want to maintain a somewhat aero position, so keep low. However, a complete aero tuck compresses your lungs in your abdomen and you can't breathe as fully as if you were sitting straight up. This means you'll need to find a balance between aerodynamics and being able to breathe efficiently while keeping up a constant cadence and pedal force. You'll also want to keep your arms farther apart because tucking them into the center also compresses your lungs within your chest. Most likely, you'll want to either be in your drops or hunched over a bit with your hands on the hoods.

  3. Uphill and/or tailwind: You can pretty much treat these two the same way since wind resistance is less of a concern than your own aerobic fitness. Just sit up and keep your hands wide to keep your lungs as open as possible and pedal with whatever force and cadence works best for you. Studies confirm our everyday experience that standing while you pedal will increase your speed but is not sustainable for very long. You'll only want to stand up to maintain speed over short sections where the road rises steeply (or more steeply if you're already on a hill), when a brief gust of wind has slowed you down and then let up, or any other situation that briefly threatens to lower your otherwise sustainable speed. If you're running out of energy and only halfway up a hill, standing up won't help you.

Of course, in the real world you never have just a hill or just wind from the front or back. There are cross winds, cross-head winds, cross-tail winds, hills with wind from any direction, and everything in between. Add in traffic concerns, road conditions, etc., and you'll almost certainly have to find a balance between pedaling efficiency and dealing with the world around you.

If you'd like to read more, there is a great article on cycling up and down hills: http://www.sportsci.org/jour/9804/dps.html.

And the ever helpful sheldonbrown.com has an qually excellent article on the effects of wind resistantce here: http://sheldonbrown.com/brandt/wind.html.

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In many ways a crosswind is the worst. –  Daniel R Hicks Feb 17 '13 at 19:09
    
@DanielRHicks If it's so strong that it makes it hard to handle the bike, I agree. But I'll take a gentle crosswind over a gentle headwind any day of the week. –  jimirings Feb 17 '13 at 21:58
    
Nice answer. And good work expanding beyond what I meant to be the (very artificial) bounds of the question. –  Sparhawk Feb 18 '13 at 11:15
    
+1 for linking to the sportsci article. I think the summary is the answer. –  James Bradbury Feb 18 '13 at 12:22
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