Grade percent or angle ?

jautukas87

How are incline % calculated in cycling?

DirkVoodoo

Just the number of meters gained vertically for the number of meters travelled horizontally.

Below is the Koppenberg from the tour of flanders, you can calculate the "average" gradient over the whole climb pretty easily:



65m of ascent over 600m distance = 65/600*(100) = 11% Average.

Of course, this hides the fact that the max is 22%, but now you have the basic principle you can work it out!

xz

DirkVoodoo wrote: »

Just the number of meters gained vertically for the number of meters travelled horizontally.

Below is the Koppenberg from the tour of flanders, you can calculate the "average" gradient over the whole climb pretty easily:



65m of ascent over 600m distance = 65/600*(100) = 11% Average.

Of course, this hides the fact that the max is 22%, but now you have the basic principle you can work it out!

looks like 78m of ascent over 600m to me, making it 13%, whichever way, it's still tough

stopped_clock

DirkVoodoo wrote: »

Just the number of meters gained vertically for the number of meters travelled horizontally.

So it's the percentage of the horizontal distance rather than of the distance of road cycled (ie the hypotenuse)?

Does that make a 45 degree slope 100%?

DirkVoodoo

100m ascent over 100m of road would be a 100% climb I guess, but if you know any roads like this let me know!

I don't know many vehicles that would be able to make it up one, there must be a limit to the grade of a road when it's being designed, at least nowadays.

Lumen

DirkVoodoo wrote: »

100m ascent over 100m of road would be a 100% climb I guess, but if you know any roads like this let me know!

A quick google...

Wikipedia wrote:

Baldwin Street, in a suburban part of New Zealand's southern city of Dunedin, is reputed to be the world's steepest street. It is located in the suburb of North East Valley, 3.5 kilometres northeast of Dunedin's city centre.

A short straight street of some 350 metres length, Baldwin Street runs east from the valley of the Lindsay Creek up the side of Signal Hill. Its lower reaches are of only moderate steepness, and the surface is asphalt, but the upper reaches of this cul-de-sac are far steeper, and surfaced in concrete, for ease of maintenance (tar seal would flow down the slope on a warm day) and for safety in Dunedin's frosty winters. At its maximum, the slope of Baldwin Street is approximately 1:2.86 (19° or 35%) - that is, for every 2.86 metres travelled horizontally, the elevation rises by 1 metre.

Morgan

xz wrote: »

looks like 78m of ascent over 600m to me, making it 13%, whichever way, it's still tough

Altitude of graph starts at 13, not 0.

xz

Morgan wrote: »

Altitude of graph starts at 13, not 0.

oooooh yeah:D

stopped_clock

DirkVoodoo wrote: »

100m ascent over 100m of road would be a 100% climb I guess, but if you know any roads like this let me know!

I don't know many vehicles that would be able to make it up one, there must be a limit to the grade of a road when it's being designed, at least nowadays.

Sorry, I've slightly confused myself over this...

Wouldn't 100m ascent in 100m of road mean the road was vertical?

In your graph, is the horizontal distance measured along the axis or along the curve? I know I'm being pedantic and that the difference would be negligible in practice,

There's a road not far from me with a sign saying it's a 33%.

TinyExplosions

stopped_clock wrote: »

Sorry, I've slightly confused myself over this...

Wouldn't 100m ascent in 100m of road mean the road was vertical?

In your graph, is the horizontal distance measured along the axis or along the curve? I know I'm being pedantic and that the difference would be negligible in practice,

There's a road not far from me with a sign saying it's a 33%.

no, a vertical road would be one that climbed 100m in 0m, ie, straight up

a 33% grade is a 1 in 3, that means it rises 1 metre every 3

stopped_clock

TinyExplosions wrote: »

no, a vertical road would be one that climbed 100m in 0m, ie, straight up

a 33% grade is a 1 in 3, that means it rises 1 metre every 3

But if I cycled up (somehow), and there was 300m on the odo, I'd have climbed less than 100m?

scottreynolds

stopped_clock wrote: »

Does that make a 45 degree slope 100%?

I'm not clear on this either. If I cycle 100 metres distance and gain 100 metres, the gradient should be 45%.

Morgan

scottreynolds wrote: »

I'm not clear on this either. If I cycle 100 metres distance and gain 100 metres, the gradient should be 45%.

45 degrees, not 45%

niceonetom

distance is measured horizontally - not along the hypotenuse - so 100m of accent over 100m of horizontal distance would indeed make a 45* angle road, or 100% gradient.

Given the whole Pythagorean thing wouldn't a speedo on the bike actually register 141.42135623730950488016887242097m for that climb?

How is this accounted for in mapping? Are distance on things like google maps etc using elevation data in the background?

Never thought of this before....

stopped_clock

niceonetom wrote: »

distance is measured horizontally - not along the hypotenuse - so 100m of accent over 100m of horizontal distance would indeed make a 45* angle road, or 100% gradient.

Given the whole Pythagorean thing wouldn't a speedo on the bike actually register 141.42135623730950488016887242097m for that climb?

How is this accounted for in mapping? Are distance on things like google maps etc using elevation data in the background?

Never thought of this before....

That's what I'm getting at.

Although, the distances as read from a map would be horizontal distances (the world is flat - it makes the maths easier).

cantalach

In mathematical terms the gradient of a slope is the same as the tan, which is opposite/adjacent. For practical purposes however it can often be useful to approximate gradient to sine, which is opposite/hypotenuse. This is because the hypotenuse can in turn be approximated as the distance travelled along the road (strictly speaking hypotenuse is only equal to distance travelled if the slope is constant).

The good news is that if you use the sine approximation for slope with the formula (H2 - H1) / D you'll always be underselling your achievement! And the more variation there is in the slope the more you'll be underselling yourself.

paddy's hill

Its very simple as Dirkvoodoo said. For instance:
Laragh - Wicklow Gap
Start altitude 140
Summit Altitude 477
Altitude difference 337
Horizontal distance traveled 8400 meters
Gain divided by distance = 4.01%
Or
Drum Goff
Start altitude 130
Summit altitude 379
Altitude difference 249
Horizontal distance traveled 2900 Meters
Gain divided by distance = 8.59%
The data used here is from a garmin.

blorg

niceonetom wrote: »

distance is measured horizontally - not along the hypotenuse - so 100m of accent over 100m of horizontal distance would indeed make a 45* angle road, or 100% gradient.

Given the whole Pythagorean thing wouldn't a speedo on the bike actually register 141.42135623730950488016887242097m for that climb?

Speedo would register substantially more as you zig-zagged back and forth from one side of the road to another

Other than that, yes, it would register that on a magnet based computer.* Actual grades though are much less so that the distortion is minimal. For example 100m ascent in 1km (average 10% grade, a bloody steep hill) gives you a distance travelled of 1,005m, only .5% difference. You could well have more error on your speedo calibration.

*I think a GPS based computer will calculate distance on the virtual horizontal plane only ignoring elevation although I may be wrong, in any case it is a small variance.

cantalach

Morgan wrote: »

45 degrees, not 45%

No...if you cycle 100m then the hypotenuse is 100m (ignoring variations in slope along the way). Intuitively (and confirmed by Pythagoras) this makes the adjacent 0m which makes the gradient infinite.

blorg

cantalach wrote: »

No...if you cycle 100m then the hypotenuse is 100m (ignoring variations in slope along the way). Intuitively (and confirmed by Pythagoras) this makes the adjacent 0m which makes the gradient infinite.

Tough to cycle though

Morgan

cantalach wrote: »

No...if you cycle 100m then the hypotenuse is 100m (ignoring variations in slope along the way). Intuitively (and confirmed by Pythagoras) this makes the adjacent 0m which makes the gradient infinite.

That's pretty steep then.

However, you're cycling along the adjacent, not the hypotenuse.

TinyExplosions

Man, this maths is a complicated business

cantalach

blorg wrote: »

Tough to cycle though

Rebellin and Schumacher would probably have no problems with it.

Gavin

Morgan wrote: »

That's pretty steep then.

However, you're cycling along the adjacent, not the hypotenuse.

just make sure you get your weight on the back tire. No problem

Morgan

My head hurts.

cantalach

Morgan wrote: »

However, you're cycling along the adjacent, not the hypotenuse.

No, you're going along the hypotenuse (the diagonal bit) but the gradient is calculated based on the adjacent.

This might help: http://en.wikipedia.org/wiki/Grade_(slope)

Morgan

Now that I think about it ... yeah, that makes sense. Leaving cert maths is a long time ago...

scottreynolds

Morgan wrote: »

Now that I think about it ... yeah, that makes sense. Leaving cert maths is a long time ago...

All..... 45 degrees is 100%. Here's the image from the above link

TinyExplosions

It does make sense in a way because it's the distance travelled along vs the distance travelled up. Up to 100% or 45%, you are travelling further forward than up, over 45% you are travelling up more than forward, so a slope is now 4/1 (4m up, 1m forward) or 400%, rather than 1/4 (1m up, 4 forward) or 25%!

jautukas87

Reading through thread made me even more confused. But now I get it. It's grade not angle. Used to calculate angle using Pythagoras theorem, like in school.

victorcarrera

Very interesting thread.
Im going with the wikipedia article.
Especially where it states that there are "3 different ways to express the severity of a slope".
So when describing a climb accurately the units used are important.(Angle in degrees, gradient in %, or ratio as a fraction. I suspect not a lot of people know this.
The angle/gradient graph on wiki should answer most queries. ie 45` = 100% etc.
Horizontal distance should not be confused with distance travelled.

The problem remains unsolved for me though because now if I see a description of a climb I wonder did the originator use the correct algorithm, and variables within that algorithm.
If I state the stats of a climb in a particular format how is it percieved ?
My own bike computer is primitive by todays standards but I assume the supercomputers use distance travelled and GPS triangulation to produce instantaneous gradient values. But does it discard for example a short decent between two ascents when calculating overall trip gradient?