The Wrong Side of my Car
The blog that wants to go obsolete
Are hills more difficult than flat terrain for cyclists?
Every couple of months I come across some article or video saying that ‘no, hills aren’t harder than the flat’.
Said no cyclist ever.
Let’s imagine some guy called Daniel *1, Danny for friends. He is riding his bicycle to his local café, 3 km up the road. He can go two ways. One way is a bit shorter but it goes over a hill with a big 5% climb. Can you guess which way he is going to go?
These articles, with their tables, and power to weight ratios, heartbeat sensors and power meters are not written for Danny. They are written for Sébastien *1 who is getting fit for la Marmotte, and who knows darn well that riding uphill is hard, that is why he has a training schedule to get fit.
Danny however is not in it for any bragging rights, he just wants to get to his café. So yeah, the flat route it is. Danny knows hills are harder than the flat.
Still, what about those articles?
Are we there yet?
The reasoning behind this claim is this: after some math you figure out that going 17 km/h on the flat requires the same amount of power as going 5 km/h on that 5% climb. Which is true, and getting that speed right is how you avoid running out of steam halfway. So here you go, uphill.
The thing is, after 15 minutes of work, Danny will be sitting down at his regular watering hole and you will be still be climbing that hill.
It turns out that going the hilly way slows you down, but they didn’t move that café closer to compensate for it. Distance is measured in kilometres, not in joules.
Power
There is a simple fact about casual bicycle trips you need to know:
Casual cycling requires almost no power. That is why we use bicycles in the first place.
This makes sense on several levels. Danny doesn’t have a training schedule so he can ride around on his bicycle. He also doesn’t like to arrive as a big ball of sweat.
Speaking of which, there are always people who say cyclists need showers at work. One word… no. Did you know Dutch supermarkets and restaurants have showers for those who arrive by bicycle? Me neither, because they don’t. *2
I mean, can you imagine what a pain in the backside it would be to get around like that?
So how much harder is that hill for Danny? *3
Without wind on the flat, he would only need about 60 W to go around 17 km/h. Without wind you fly on those bicycles.
Today we have a 10 km/h headwind, so he has to push a bit harder, 70 W, to go only 13 km/h. A bit slower overall, but still OK. And on the way back he can push a leisurely 40 W, to go 20 km/h. *4
So that is how much power to weight? Only 1 W/kg. One.
But what if he takes that hilly route? On that 5% slope it is going to be a 100 W slog to go just 7 km/h. Ouch.
And you know what you don’t have while doing all that work? The air flow to keep you cool. are those armpits turning into ponds already?
Going 1 km uphill like that costs you about the same amount of energy than going 4 km on the flat. And that 1 km downhill is fun, but you will burn most of that energy off with air resistance and some braking. So you just got 2 km for the price of 4.
So you could say a 5% hill both ways is twice as hard as the flat.
Getting Started
What if you’re really tired today? Or just getting started? Just go just a bit slower. How fast can Danny still go pushing only 0.5 W/kg? On flat terrain 30 watt still gets you up to 12 km/h, and with the wind, up to 10 km/h with just 40 watt. Still a pretty decent speed. You will overall use less energy because air resistance is so non-linear.
In contrast, on hills almost all the energy goes to climbing. This energy stays the same no matter what speed you go, even if you walk your bike. Halving your power almost exactly halves your speed. And halving that speed is basically a slow walking pace. How demotivational.
Bike lanes
Yes, we always have to talk about bike lanes. You naturally get a bit more wobbly when going slowly. So the last thing you need are cars squeezing past. Tip over the wrong way and you’ll find yourself under one. Not a good setting to relax and find your own rhythm to climb that hill.
In conclusion, hills are harder than the flat. Let’s not kid ourselves.
Google told me that is the most common name in New Zealand in 1980. If that sounds arbitrary, it is but I’m writing this post so deal with it.
(It might have been the list of male names)
And yeah, also the names in France. Actually Sébastien was № 2 but it sounded more French.
A similar assumption is that cycling takes a lot of ‘gear’. This is a myth, the only extra piece of gear you need compared to taking the bus or walking is your bicycle.
The reason you see these assumptions is that in areas where cycling is kind of niche, almost all cyclists are enthusiasts and MAMILs. The more casual cyclists just don’t ride in our circumstances.
It is somewhat tricky to find exact figures for how much power you need. Partially because it depends on so many things. Your clothes, your riding posture, the state of your bicycle, the state of the surface you’re riding on, and whether or not you know how much to pump your tyres.
We calculated 3 things for those graphs:
- rolling resistance: m · g · Crr · v: we assume 0.005 for the friction coefficient.
- air resistance: (12 · ρ · Cd · A) · v2rel · v: The product on the left is assumed to be 0.35. vrel, the relative wind is the speed relative to the air, it increases with stronger headwind.
- potential energy on slopes: m · g · slope · v.
For the mass m we assume the rider weighs 70 kg and the bicycle another 15. The orange line at 70 watt thus marks 1 watt per kg of body mass in this example.
Drivetrain losses are not considered but are often assumed to be some fixed percentage of total power.
For very windy areas, this spread between upwind and downwind becomes very unfavourable. Riding against a 30 km/h wind is about equivalent to climbing that 5% slope. In comparison you only save a small amount of power while going downwind. But Auckland almost never has wind that strong.
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