Is it best to attack the flat before a hill?

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.

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.

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.

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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.