What actually makes a road curvy (and how an app scores it)

Ask ten riders to name a curvy road and they will agree instantly. Ask them to define curvy and the conversation falls apart. Software does not have that luxury — it needs a number.

Here is how that number gets made, and why it matters when you are choosing an app.

The raw ingredient: heading change

Underneath every map is a set of ways, each stored as a chain of coordinates. Straight road, few points, all in a line. Twisty road, many points, each one a slightly different direction.

The basic measure of curviness falls straight out of that. Walk the chain, and at each point calculate the change in bearing from the previous segment. Sum those changes, divide by the length of the road, and you have degrees of turning per kilometre.

A flat highway might turn 10 to 20 degrees per kilometre. A good mountain road runs into the several hundreds. A hairpin-laden pass can be four figures.

That single number gets you most of the way, and it is what “twistiness score” means in most apps.

Why bend count alone lies to you

The trouble is that the metric flattens two very different roads into the same figure.

A road with long, fast, 200-metre-radius sweepers might accumulate the same total heading change as a road of tight, second-gear switchbacks. On the score they look identical. In your wrists, at the end of the day, they are not remotely the same ride.

So a better model looks at each bend individually and estimates its radius — fit a circle through three consecutive points and see how tight it is — then weights the score by severity. Now:

• A 20-metre-radius hairpin counts heavily.
• A 300-metre sweeper counts, but gently.
• A very slight drift over 500 metres barely registers, which is right, because you would not call it a corner.

This is also how an app can offer meaningfully different flavours rather than one slider: flowing (rewards sweepers, penalises hairpins), technical (the opposite), balanced.

The things curviness does not know

If you optimise for bends alone, you get a route that is technically correct and practically miserable. Real routing has to combine curviness with:

Road class. A residential street can be extremely twisty and completely inappropriate. Riding through a housing estate at 40 km/h past parked cars is not the ride you asked for.

Surface. Bend geometry says nothing about whether the road is sealed. Gravel with a hundred corners scores brilliantly and is a genuinely dangerous suggestion for a sports tourer on cold tyres. Surface has to be a first-class input, which is why we treat unsealed roads as an explicit choice rather than a surprise.

Width and traffic. Single-track lanes with blind crests and farm traffic are curvy and unpleasant.

Elevation. Not required, but a road that climbs tends to be a better ride than the same geometry on a flat plain, and models that reward gradient generally produce nicer routes.

Direction. Rarely modelled, and genuinely matters — many roads are noticeably better in one direction than the other, because of where the crests and the tightening radii fall.

Why two apps disagree about your favourite road

The roads are the same roads. What differs is the scoring — the set of rules each app applies when it decides which road is worth sending you down.

That model encodes a set of opinions:

• How expensive should a motorway be? Twice a back road? Ten times?
• Is a 60-degrees-per-km road worth a 15-kilometre detour, or 5?
• Should the router avoid towns, or route through them because that is where the fuel is?
• How much penalty does an unsealed section get before it is excluded outright?

Different teams answer differently, tune against roads they personally know, and out come different routes. It is why trying two planners on a road you know well is the fastest way to work out which model matches your taste. If a router sends you down the road you would have picked yourself, its opinions match yours.

The counterintuitive part: maximum is not best

Riders new to curvy routing usually crank the setting to maximum and are then slightly disappointed. Here is what actually happens at the top end:

• Average speed collapses. A 120-kilometre route can take three hours.
• The route starts preferring tiny roads, which brings gravel, gates, and blind crests.
• Corner after corner becomes work. Concentration fades. The last hour is not fun.
• Fuel range gets awkward, because you are covering far less ground per tank than the odometer suggests.

Most riders settle a notch below maximum: enough bends to be the point of the day, enough flow to keep a rhythm, and a road wide enough to enjoy. The planning guide covers how to dial that in.

The input no curviness model has

Here is the limit of the whole approach. Curviness is a property of the road. It never changes. The best curvy road near you scores the same today as it did the first time you rode it, and the router will keep suggesting it, forever, because on its own terms it is still the right answer.

But it is not the right answer the twelfth time.

That is why our router takes one more input that has nothing to do with geometry: whether you have ridden the road. Roads on your GPS-confirmed ridden-roads map can be made expensive on request, so the search goes looking for something else — a slightly less twisty road you have never turned onto, which on the day is a far better ride than the perfect one you know by heart.

Curviness tells you which roads are good. Memory tells you which good road is next.