UKC

Am looking at doing some hill riding in Europe, they all quote the % incline in distance of km, is there a difference in % incline if I change the distance to miles?

Brain cant handle these conversions

In reply to Pids:

Eh? Why would there be? A percentage figure is just another way of describing the "1 in X" system we sometimes use in this country, to convert % to 1-in divide 100 by the percentage to give the "X", so 16% => 100/16 => 1 in 6. This works the other way too: 100/6 = 16%

In reply to Pids:

Get Strava app on your phone, change units to K's and off you go.

In reply to Pids:

Oh dear, a QS not good with numbers...

The gradient is the gradient whether you cycle 1.6km or 1 mile up the hill.

In reply to Pids:

Where are you off to? I'll be riding about in the Dolomites in July.

In reply to Pids:

Ignore the above, of course there's a difference between metric and imperial percentages. If you travel 1 kilometre that isn't as far as 1 mile, in the same way a 10% metric incline isn't as steep as the imperial equivalent.

In reply to Sir Chasm:

I see what you are trying to do

To the OP. Percentage is just a number without any units or dimensions. Distance traveled is a vector, i.e. a number attached to a direction, in this case the number has units of miles or kilometers or whatever. The gradient given as a percentage is simply the vertical component divided by the horizontal component of the distance vector. As long as you use the same units for the vertical and horizontal part then your percentage is the same no matter what unit you choose to measure the distance with.

In reply to Sir Chasm:

You're an idiot. the percentages work for the height gain as well as the distance.
So:
10% gradient will have you traveling 10% of a mile up in every mile along you go.
10% gradient will have you traveling 10% of a km up in every km along you go.

These are the same angle of slope.

I can't decide if you're trolling or stupid.

In reply to Sir Chasm:

That's not right. A 10% hill is always the same gradient. The formula for % incline is the height gained devided by the run (distance travelled horizontally). So the units cancel giving a percentage.

In reply to Jimbo C:

I didn't think it was vertical and horizontal components. I thought it was measured as vertical gain against distance travelled along the slope.

If it's components then percentages are a bit of a ridiculous way of expressing a slope, as 45 degrees is 100%. Which would imply that you can't have a a gradient more than 45 degrees.

In reply to DancingOnRock:

A road steeper than 45° would be quite a sight

In reply to DancingOnRock:
It's rise over run - see http://en.wikipedia.org/wiki/Grade_%28slope%29

So, yes, 45 degrees is 100% as it's 1 in 1 but why would that imply you couldn't have a gradient of 200%, i.e. 2 in 1?

The percentage/one-in confusion is often heard on ski slopes by bullsh***ers: "I skied down a 50degree piste today", what they actually skied down was a 50% slope or 1 in 2, about 30 degrees which is quite a difference.

In reply to Bob:



Because you start to approach an infinitely steep hill very quickly.

In reply to Pids:
Are these what you are after?

Metric:
http://www.csgnetwork.com/inclinedeclinegrademcalc.html

Imperial
http://www.csgnetwork.com/inclinedeclinegradecalc.html

In reply to DancingOnRock:

But then the 1 in X way of stating things also gets peculiar, i.e. a vertical wall is 1 in 0.

In practice we seem to use either percentage or "one in ..." for gradients over which we walk or drive or bike or ski but degrees for anything steeper than that so a "70 degree slab". Some overlap obviously in what some people regard as ridable/drivable.

In reply to Pids:

Sir Chasm has it right

I'll race you up a 1 km 10% hill while you take the 1 mile 10% hill. Loser buys the pies.

In reply to Sir Chasm:


Which of course is what caught out so many unsuspecting continentals during last year's Grand Depart.

In reply to Bob:



No. I was saying they're all measured as distance traveled against elevation.

So a vertical wall is 100% or 1 in 1. ie travel 1m along the slope and you go up 1m.

In reply to DancingOnRock:

Did you follow the links both to Wikipedia and to those ChrisJD provided? The convention is rise over run not rise over slope

In reply to Bob:

Indeed. I was just saying it's a strange convention.

Vertical is an infinite slope. Which doesn't seem right.

In reply to DancingOnRock:

Its a very logical convention as its what you would get by looking at contours on a map.

In reply to GrahamD:

But the odometer on my car measures the distance I have travelled not the horizontal distance.

In reply to DancingOnRock:

But you are measuring different things

In reply to DancingOnRock:


So it does, but you are unlikely to have any height gain information to make it meaningful in terms of a gradient.

In reply to GrahamD:


What's the sign do then?

In reply to DancingOnRock:
It makes perfect sense that vertical is an infinitely steep slope (which it is). What we define as steepness is the height gain per distance travelled. If you travel 'n' meters vertically you have always travelled exactly 0 meters horizontally. As any number 'n' can be expressed as n*1, and we know 1/0 is infinity, we can safely say that the steepness is n*(infinity)= infinity.
As for the original question, distance makes no difference as both quantities (vertical distance and horizontal distance) are measured in the same units, so the resulting unit for gradient is km/km= no unit, or miles/miles= no unit, so it is just a ratio and therefore never changes regardless of your chosen unit to do the calculation with. I'm not a mathematician but hope this makes sense. And yes, 1 in 1 is 100% is 45 degrees.

In reply to Pids:

Metric gradients are measured in % whereas imperial gradients are measured in shillings.

In reply to Sir Chasm:

Ha ha troll, of course it's the same think about it,if you use any units of measurement in the vertical and the horizontal you'll always end up with the same gradient ie 1 in 6 could be cm,mm,metres, inches ,bananas or even pigeons if you can keep them still for long enough.

To the OP: It is exactly the same

height gained = distance travelled horizontally * %gradient/100;

So for a 15% gradient:

You travel 1km horizontally you go up 150m (1000m*0.15).
You travel 1mi horizontally you go up 792ft (5280ft*0.15).

The distance along the slope is different to the distance horizontally but for small gradients it is approximately the same (in the above example the distance along the slope is ~1010m instead of 1000m)*.

For those more mathematically inclined, the % gradient is the tangent of the slope angle expressed as a percentage eg %g=100*tan(angle). The angle of the slope is given by the inverse tangent: angle = atan (%g/100).

As Strachan says: 1 in 1 is the same as 100% and is the same as a 45 degree angle. Horizontal is 0% and vertical is infinity%.

* if you are interested the slope distance = horizontal distance / cos(atan(%g/100)), taking the small angle approximations for sin(a)~a and cos(a)~1 we get slope distance ~ horizontal distance. This is good to 5% accuracy up to angles of about 18 degrees / gradient of ~30% or an accuracy of 1% to gradients of ~15%.

In reply to Strachan:
I just don't think it's very useful.

You have no idea how far you have travelled horizontally. You can easily measure how far along a slope you have travelled.

I think using arcsin is more practical.

ie for every h m you physically travel along the road your altitude increase by o m.

I can see how mathematically and graphically arctan works on paper, but in the real world it's practically useless as gives no real world figures.

Horizontal distance of 1cm with a gain of 1m give a 10,000% incline.

In reply to DancingOnRock:

But the % incline system isn't used to express distance, it is just to tell you how steep it is? And I think in practical terms, for a cyclist to calculate the extra distance over a whole ride would be impractical... especially as it is not going to be very far, given the small angles involved. And this ability to consider the extra distance negligible at small angles probably explains why the % incline is not really used anywhere beyond the road, but is entirely suitable when cycling.

In reply to DancingOnRock:


The sign gives you gradient for an unspecified distance (could be 10% for 20m or 10% for 20km) hence it doesn't really tell you much about height gain.

The whole point of gradient is to give you information about steepness so you can be prepared for that. If you wanted information on height, you need spot heights.

With the system as is (gradient is Tangent of the elevation angle, not Sin), even without the signs you can prepare yourself using a map and the distance between contours (which I suspect is how they decide whether to put signs up or whether to put steep hill markers on maps in the first place, rather than by individually surveying