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...or is the extra energy used to overcome the exponentially increased air resistance on the flat best saved for overcoming gravity on the hill, when the air resistance penalty is much lower? Does that outweigh the benefit of a bit more momentum going up the hill?

I guess the answer could differ depending whether you want to be fastest up the hill or use the least energy.

Edit - this could be for large or small hills, but the boundary case might be a hill where any momentum you built up has reduced to zero right as you go over the crest.

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    It's going to depend on the hill vs your lung capacity. Are you thinking of big hills where you know you'll be working your way down the gears but it's a question of when, or little ones that you can carry some speed up?
    – Chris H
    Nov 10 '20 at 16:09
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    @AdamRice but I think coasting is the extreme example, carrying momentum into hills definitely makes it easier at first. I think we all have had experiences where we made it harder on ourselves by downshifted too early and losing momentum.
    – GageMartin
    Nov 10 '20 at 17:13
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    @GageMartin Absolutely, one can lose a lot of time by decelerating on a short hill too early where with a bit of more anaerobic effort one would crest at a reasonable speed and relax a bit on the short descend (albeit a short one).
    – Vladimir F
    Nov 10 '20 at 17:22
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    I would prefer to fix the flat before I climbed the hill. Nov 10 '20 at 19:11
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    air resistance is increasing quadratically not exponentially.
    – miroB
    Nov 11 '20 at 9:59
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Is it best to attack the flat before a hill?

NO

On flat ground, power is proportional to speed cubed because drag from air dominates. If you want to go twice as fast on flat ground, you need to expend eight times the power. So if you're going 20 mph/30 kph and double your power, you'll wind up going all of 25 mph/38 kph - and you'll blow yourself up really fast if you were riding close to your threshold power to begin with.

But on a steep enough hill where overcoming gravity dominates over drag, then when you double your power, you'll go twice as fast up the hill.

Lets say you're going 30 kph at 200W on the flats, and that's a power you can hold for good long while, but you can hold 400W for two minutes. Let's be generous and say 400W on flat ground gets you up to 40 kph. You'll cover 1 1/3 km in those two minutes - then lets say you can still hold 200W (you won't, though...) and it takes you four minutes to climb a short, steep hill at 200W. That's a total of 6 minutes to get to the top of the hill.

And I was really generous at how much faster doubling your power on the flats improves your speed and in assuming you'd be able to climb that hill at 200W after blowing yourself out on the flat...

OK, let's turn power outputs around. At 200W and 30 kph, covering that 1 1/3 km will take 2 minutes and 40 sec. But now you get to go up that hill at 400W and only take 2 minutes.

You're at the top of the climb in 4 minutes and 40 seconds - you just dropped the you that blew yourself up on the flat, getting yourself a minute and 20 second lead.

And you get to recover on the descent.

Heck, take it a bit easy up the hill at 350W, you only got a minute lead, but spent a lot less energy, saving it for later climbs or sprints.

You can spend less energy and go faster if you spend that energy where it gets you the most velocity.

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    It's also a matter of tactics. If you attack before the hill begins your opponents will smell the rat.
    – Carel
    Nov 10 '20 at 18:11
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    The tactics make it too complicated though. If you're a slower climber, you might want to get the featherweights off your wheel and give yourself a head start, hoping that they do more damage to themselves eating wind than you..
    – Paul H
    Nov 10 '20 at 20:14
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    @PaulH As a "slower climber" myself, anyone who falls for that wasn't going to beat you anyway. Save your energy for the climb - the worse you climb, the more important that is. You will long remember the day you drop a cat 3 on a 10-min 8-10% climb... Nov 10 '20 at 21:34
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    Forgive me if I've missed something, but won't momentum play a bigger role in this? There are a lot of factors going into this, but it's not immediately obvious that power output is the main player
    – Phill
    Nov 12 '20 at 5:18
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    @Phill Heck no. Momentum is waaaay overrated in cycling. Kinetic energy of a moving object is given by ( m * v^2 ) / 2. Potential energy by m * g * h. So h = v^2 / ( 2 * g ) 30 kph is 8.3333... m/s, g is 9.8 m/sec^2. 8.33333... ^ 2 is 69.44444... Divide that by 2 gives 34.7222.... Divide 34.72222.. by 9.8 and you get 3.54 meters. The momentum of going 30 kph gets you all of three and a half meters up your climb. Next time you hit a steep hill, sprint into it to "build your momentum", then stop pedaling completely when you start climbing and see how FAST you stop. Nov 12 '20 at 12:14
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As you’ve noted, drag increases non-linearly with speed. So to e.g. double your speed on a flat (drag dominated) section you’ll have to more than double your power output.

Slow uphill sections contribute much more to your overall time (and therefore also average speed) since you spend much more time there and gravity is constant.

So if you wanted to achieve the fastest time with the least amount of energy spent you’d go slow on the flat sections and as fast as possible on climbs.

“Unfortunately” the human body doesn’t work like that. We are great at sustaining moderate intensity for long times but bad at short, high intensity or recovery. It’s not like riding half an hour at 50% of your FTP¹ means you can ride another half hour at 150%.

I think most athletes in solo competitions try to ride at a more or less constant intensity with maybe a bit more when accelerating after turns or going uphill.

Of course in group rides everything is different and you try to stay as fresh as possible for attacking and sprinting.

1: Functional Threshold Power, basically the maximum power output you can sustain for an hour.

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I'm going to be contrary, with some caveats.

Yes, it may be worth attacking the flat just before a climb. If you can build momentum on the flat and carry that into the first part of a climb, it will put you further up the road than someone who just rides into it at a set power.

The downside is that you're pushing hard to get that momentum and to keep it up while the road pitches up. So if the climb is longer than your endurance, you'll fall back to steady state, or worse you'll go into deficit and have to slow down for recovery. This allows that other rider to gain and pass you.

Upshot - for short climbs of under a minute, feel free to sprint and recover on the downhill. For 1-5 minutes you can push hard but not a max effort. For anything over 5 minutes stick with your steady state, and for longer climbs you definitely need to pace the climb.

If you're not racing or training or going for a PR, just push up the climb at whatever comfortable speed you like.


The equations of air resistance vs power etc are certainly valid, but they don't account for race craft and tactics. If we were predictable machines, we'd just output our FTP wattage for the whole ride, and accept whatever speed that results in.

But we're squishy meatsacks with some power reserve. By using that additional power at a tactically advantageous moment, a rider can gain advantage. By hitting the top of a climb slightly in front of a competitor, one can start the descent early and gain distance.

Likewise, in a race one might HAVE to burn power reserves to cover a breakaway or to hold a wheel. The point of race craft is to gain advantage by forcing other racers to waste their reserves.

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    "If we were predictable machines, we'd just output our FTP wattage for the whole ride, and accept whatever speed that results in" - Not quite. We'd still need to focus our effort on the climbs because the math of average speed means that this is where we get the most bang for our expended energy. We would use whatever contingency we have of non-sustainable power on the climbs, and reduce speed in the flats by whatever necessary to rebuild enough contingency for the next climb. Nov 11 '20 at 10:30
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    The problem is: How much of your reserves can you really save on the flat sections? How much can you actually recover on downhill? Personally I’m constantly surprised how bad humans are once you go past the lactate threshold.
    – Michael
    Nov 11 '20 at 11:02
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    It might be worth it for riders to think about how long they can sustain an effort. I am actually thinking about power at VO2max (about 5 minutes) versus functional threshold power (20-60 min). Riders with FTP relatively better than VO2max power would be able to sustain an extended effort as described better than riders whose VO2max power is proportionately better.
    – Weiwen Ng
    Nov 11 '20 at 13:39
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    It's a 10km ride to the next town from me. This is 100 metres lower by elevation, with two 'hills' of around around 10-15m climb and the rest essentially a steady (invisible) 1% downhill. If I ride the flat(tish) section at FTP, then I have no more to put into the two 'hills'. OTOH if I ride at a very easy pace on the flat, then I can 'flatten' the hill and go up it considerably faster than I would if I had been riding at FTP for 15 minutes beforehand
    – thelawnet
    Nov 11 '20 at 18:27
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    Upshot - for short climbs of under a minute, feel free to sprint and recover on the downhill. Once or twice is completely different from over and over and over. If you can actually do that over 15 kms of roller after roller, you need to get a license and get yourself to a few races. Because while all-out sprints up short hills are the fastest way to get over them, you have to be able to both go into power ranges well over VO2Max and be able to recover quickly after each and every effort. That's basically racing shape - and that's hard to maintain if you aren't paid to do it. Nov 12 '20 at 12:30

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