100% Hill

Rise over run, same as everyone else?

so 100% = 45°, 50% = 22.5° etc

Uk is rise over road length. Traditionally

I think 100% in 'hill parlance' is 45 degrees. It's what (used to be) also called "1 in 1", i.e. 1 unit along and one unit up.

Is it? I always thought it was perpendicular over base, not perpendicular over hypotenuse. Have I been wrong all these years?

Would 100 feet along the rise take you as far along the road as 100 feet along the flat?

I guess that's the ambiguity. Is 'along' along the surface or horizontal distance along.

The steepest road in the USA is Waipio Valley Road on the island of Hawaii. It features sections with grades approaching 45%, making it the steepest rural road in the United States.

The steepest gradient road in the UK is Ffordd Pen Llech in Harlech, Wales, with a maximum gradient of 37.45%, according to Guinness World Records

Hardknott Pass in the Lake District,has a maximum gradient of 33%

If it was hypotenuse, a 1 in 1 would be an equilateral triangle so a 60 degree slope. I don't think that's what is usually meant.

For most non-vertiginous slopes the difference between base and hypotenuse isn't that significant, but it is when they get steep.

Theo

I've never been sure. But the steepest road I've ever been up was 1 in 3.

If that's 1 up and 3 horizontal the hypotenuse is 3.16. The other way round is 2.83.

Not enough difference to notice.

Andy

Interesting, I've always understood it to be height risen per unit distance travelled. Many hills are curved, making actual horizontal distance tricky to measure, whereas distance travelled is easy.

It certainly was in the days of 'one in three' etc. The % thing may be different

It is my undertstanding that that was indeed the case back in the day

What the % thing means is debatable,. It doesn't seem as steep as the tangent would specify,.

Exactly,. these 33% and 45% hills would surely be unclimbable with a normal vehicle if it were a tangent

In an attempt to clarify this I found this in wiki. Not always authoritative:

I am not sure that road builders would bother to convert from tape along the road to height difference...

But yes, a 'one in one' slope is 45° not 90°. :-)

Apologies

I was just about to post a reply quoting that wiki! If you look at

So, in effect, it means sine rather than tangent - but it's one of the points that has no reference stated! It also doesn't make clear what happened after the 1970s.

FWIW, I think that Joe's reply makes sense a lot more than a direct tangent or sine. It's why zigzag roads (and pedestrian paths up cliffs) exist. A line-of-sight tangent or sine is meaningless, but a 1 in 8 slope over the full distance is clear.

Well the wiki implies that the 'run' is the horizontal run. The problem is that at low angles sin(alpha)->tan(alpha) so it isn't worth making the distinction for e.g. run of drainage or railway purposes.

But it does get to be important on roads. Where one in three is not unheard of

Agreed. In the end it isn't that critical.

There is a bit of road that used to give the family car some issues. Woe betide you if you missed a gear change...

https://earth.google.com/web/@51.23103601,-0.46670278,178.94200534a,0d,60y,299.11148182h,80.7058441t,0r/data=CgRCAggBIhoKFkxtMHg4el9pVFhySldkZHI0OThQU1EQAjIpCicKJQohMXdPU1NHNklyNXQxLTJTNGpBT3pmSS01UFktSkZXdXZGIAE6AwoBMEICCABKCAi7mvu-BBAB It's not even marked with a gradient sign these days

It's many years since I've been on that bit of road! It's surprising just how many steep roads there are in Surrey. Not my favourite method of transport, but:

Surrey spans the scarp slope of the North Downs - which that is as well as bits of the weald.

I used to cycle down that and end up in Guildford...Wish I were that fit today...

On one slope I overtook a van glanced in at his speedo and it said 35mph...

Op 01/07/2025 om 16:51 schreef Jeff Gaines:

Americans are built differently.

I wonder what the *real* safe top speed on a "regular" bike is.

Whatever it is, 35mph seems over it.

Quite apart from the fact that at that speed the brakes are merely a suggestion, just hitting the slightest bump in the road could throw the thing.

Rather you than me, as they say. (Despite having done pretty similar in my youth :) )