Working out how to measure 'steepness' of a hill...

garrynolan

Hi, I've asked this before and thought I understood it but I don't really so here goes... If a horizontal is 0 degrees and a vertical line is 90 degrees it follows that as a percentage they are 0% and 100% respectively. With me so far? If a hill is 45 degrees then logically it is a 50% hill. So, does this mean that a 20% hill is 72 degrees? This seems almost stupidly steep so am I doing this properly? Please help (in simple,easy to understand terms) as it's doing my head in.

rick_chasey

no 20% is 18 degrees...

Down the Road

Basic GCSE Maths

Gradient is TAN of the angle

Height of climb/Length of climb x 100 for Percentage

Therefore a 20% slope is 1 m up for every 5 m long or 18 degrees

Squillinossett

Mis read question, thought you wanted the %...

tarquin_foxglove

garrynolan wrote:

If a horizontal is 0 degrees and a vertical line is 90 degrees it follows that as a percentage they are 0% and 100% respectively. With me so far? If a hill is 45 degrees then logically it is a 50% hill...

That isn't my understanding. IIRC...
45 degrees is a 1 in 1 hill, which could also be expressed as 100%
26.5 deg is 1 in 2, which would be 50%
11.31 deg is 1 in 5, which would be 20%

I think hills over 45 degrees are 100+%

CiB

Hills used to be described as 1 in N, where the lower the value of N the steeper the hill, down to 1 in 1 which is a 45 degree hill - one foot / yard / meter / mile / chain / perch / whatever the climb is = the same in forward movement. So 1 in 2 = 1 yard up for 2 yards forward travel, 1 in 3 = 1 up for 3 forward, so on. It works for roads as anything even close to 1 in 1 isn't drivable, or wasn't when road-signs were being put up first time round.

All the change to % has done is to give an integer value to the ratio by simple rounded division, so 1 in 2 = 50%, 1 in 3 = 33%, 1 in 10 = 10% etc. AFAIK we've never described hills on roads in terms of angle.

I'm not clear if or why changing to a % value is any clearer than a good solid 1 in 8. But there yer go. I expect it was the EU. They're usually to blame <rambles on cont'd p 94...>

Edit - just to clarify, this just means that a hill expressed as a % value can be just as easily described with the % value expressed as a fraction: 20% = one fifth = 1 in 5, 12.5% = one eighth = 1 in 8 etc.

Mr Dog

If you fall off its too steep.. otherwise carry on. Thats all you need to know.

garrynolan

Thanks for the replies. 1st = CiB. Joint 2nd = the rest. My head is no longer wrecked trying to understand this - Thanks again .

stigofthedump

I always liked the 1 in N nomenclature. However I think the change was made because as a hill gets steeper the number falls, ie 1 in 3 is steeper than 1 in 4. But the % increases, so 10% is steeper than 5%. This might be more intuitive for the majority

Stewie Griffin

I use the percentage as a prediction of my chances of bonking on the hill.

Cleat Eastwood

Stewie Griffin wrote:

I use the percentage as a prediction of my chances of bonking on the hill.

isnt that the same formula Clarkson and MattC59 use

Aggieboy

Stewie Griffin wrote:

I use the percentage as a prediction of my chances of bonking on the hill.

You should use it as a prediction of the chances of TH winning the Champions League.......now that's*uckin' steep!









Thread hijack over.

Pep

Down the Road wrote:

Gradient is TAN of the angle

+1

That it. Nothing to add. If you don't get it you can still apply for a banking job and make millions. No math needed there, believe me.

deptfordmarmoset

stigofthedump wrote:

I always liked the 1 in N nomenclature. However I think the change was made because as a hill gets steeper the number falls, ie 1 in 3 is steeper than 1 in 4. But the % increases, so 10% is steeper than 5%. This might be more intuitive for the majority

Just ruminating, but perhaps using % or even degrees, is more consistent than 1 in N. The steeper the incline, the less precise the measurement. The difference between 1 in 3 and 1 in 2 is huge (in my cycling terms it's the difference between a vague outside chance of success and a guaranteed failure) and there's no simple way of expressing, say, the midway point between those 2. You'd end up having to abandon its intrinsic simplicity and complicating it with something like 1 in 2 1/2 or 2 in 5.

Stewie Griffin

Aggieboy wrote:

Stewie Griffin wrote:

I use the percentage as a prediction of my chances of bonking on the hill.

You should use it as a prediction of the chances of TH winning the Champions League.......now that's*uckin' steep!









Thread hijack over.

:roll:

Pep

garrynolan wrote:

If a horizontal is 0 degrees and a vertical line is 90 degrees it follows that as a percentage they are 0% and 100% respectively. With me so far? If a hill is 45 degrees then logically it is a 50% hill. So, does this mean that a 20% hill is 72 degrees? This seems almost stupidly steep so am I doing this properly? Please help (in simple,easy to understand terms) as it's doing my head in.

Wrong.
You must use SIN. The reason being you measure the distance travelled by the bike, not its horizontal projection (provided you use the odometer, with gps would be the reverse).
So,
SIN(45deg)=0.717, therefore 45deg=72%.
SIN(30deg)= 0.5, therefore 30deg=50%, or 1 in 2.
SIN(90deg)=1y, therefore 90deg=100%, 1 in 1

Sounds complicated but is not.

MaxwellBygraves

CiB wrote:

Hills used to be described as 1 in N, where the lower the value of N the steeper the hill, down to 1 in 1 which is a 45 degree hill - one foot / yard / meter / mile / chain / perch / whatever the climb is = the same in forward movement. So 1 in 2 = 1 yard up for 2 yards forward travel, 1 in 3 = 1 up for 3 forward, so on. It works for roads as anything even close to 1 in 1 isn't drivable, or wasn't when road-signs were being put up first time round.

All the change to % has done is to give an integer value to the ratio by simple rounded division, so 1 in 2 = 50%, 1 in 3 = 33%, 1 in 10 = 10% etc. AFAIK we've never described hills on roads in terms of angle.

I'm not clear if or why changing to a % value is any clearer than a good solid 1 in 8. But there yer go. I expect it was the EU. They're usually to blame <rambles on cont'd p 94...>

Edit - just to clarify, this just means that a hill expressed as a % value can be just as easily described with the % value expressed as a fraction: 20% = one fifth = 1 in 5, 12.5% = one eighth = 1 in 8 etc.

Wot he sed.

MattC59

I think this will conclusively end this discussion



So:
1:10 is 10% is 5.71 degrees
1:5 is 20% is 11.31 degrees
1:1 is 100% is 45 degrees

MattC59

Cleat Eastwood wrote:

Stewie Griffin wrote:

I use the percentage as a prediction of my chances of bonking on the hill.

isnt that the same formula Clarkson and MattC59 use

cheeky f*cker !!

rake

if you say 'christ' out loud when your on it, then the hill is steep.

morstar

MattC59 wrote:

I think this will conclusively end this discussion



So:
1:10 is 10% is 5.71 degrees
1:5 is 20% is 11.31 degrees
1:1 is 100% is 45 degrees

Thank you for posting that as I've often wondered. Having skied a lot in my younger days, I know damn well that 30 degree slope is pretty damn steep. I keep reading about bike ascents up 30% slopes and thinking there is no way you can ride up a 27 degree slope. Finally, it all makes sense.

deptfordmarmoset

rake wrote:

if you say 'christ' out loud when your on it, then the hill is steep.

If you say 'christ' out loud but only a frenzied wheeze comes out, the hill is even steeper...

Lightning

Why stick to 1 in N? 10% simply means if you were to ride 100m in a horizontal line, you'd end up 10m higher. In school (I don't know when exactly but around 7th grade I think), you're taught this with a famous example usually:

rake

if a pedestrian says smugly 'rather you than me' then the hill is fairly gentle and you can easily fake a chuckle.

verylonglegs

rake wrote:

if you say 'christ' out loud when your on it, then the hill is steep.

Ha, they should have traditional signs for motorists as well as alternative one's for cyclists ie. a face showing varying degrees of pain. For example if it's someone sobbing and crying for mum then you know to only attempt it if you are racing snake thin and at the top of your game!

One Man And His Bike

verylonglegs wrote:

rake wrote:

if you say 'christ' out loud when your on it, then the hill is steep.

Ha, they should have traditional signs for motorists as well as alternative one's for cyclists ie. a face showing varying degrees of pain. For example if it's someone sobbing and crying for mum then you know to only attempt it if you are racing snake thin and at the top of your game!

Only if they draft Bill Bailey in to do it as in Scales of Rock...

garrynolan

MattC59 wrote:

I think this will conclusively end this discussion



So:
1:10 is 10% is 5.71 degrees
1:5 is 20% is 11.31 degrees
1:1 is 100% is 45 degrees

See... that's why I was confustered. I always thought that a 20% hill was really steep but the diagram shows differently. As was said on here, why not just put the angle (steepness) measurement in degrees... 0 degrees being horizontal and 90 degrees being vertical with everything else in between. Simple. Isn't it??

Pep

Lightning wrote:

Why stick to 1 in N? 10% simply means if you were to ride 100m in a horizontal line, you'd end up 10m higher. In school (I don't know when exactly but around 7th grade I think), you're taught this with a famous example usually:

Sure this must be wrong.
How can a car odometer measure the horizontal projection of the distance travelled?
A car odometer knows only how many turns the wheel did. So, the only distance a car can measure is the slope distance. Percentage is the SIN of the angle. Not the TAN.
:!:

tarquin_foxglove

garrynolan wrote:

Thanks for the replies. 1st = CiB. Joint 2nd = the rest. My head is no longer wrecked trying to understand this - Thanks again .

How do you work that out? :?:

your question was...

garrynolan wrote:

does this mean that a 20% hill is 72 degrees?

Which only I answered correctly & then MattC59 posts a graph

MattC59 wrote:

I think this will conclusively end this discussion

So:
1:10 is 10% is 5.71 degrees
1:5 is 20% is 11.31 degrees
1:1 is 100% is 45 degrees

confirming my answer & still nothing.

I demand kudos for my correct response :!:

rolf_f

verylonglegs wrote:

rake wrote:

if you say 'christ' out loud when your on it, then the hill is steep.

Ha, they should have traditional signs for motorists as well as alternative one's for cyclists ie. a face showing varying degrees of pain. For example if it's someone sobbing and crying for mum then you know to only attempt it if you are racing snake thin and at the top of your game!

They did that on the tarmac of Park Rash last year for the Richmond 5 Dales. It was quite nice; the anticpation of hopefully getting as far as the next face!

Lightning

Pep wrote:

Sure this must be wrong.
How can a car odometer measure the horizontal projection of the distance travelled?
A car odometer knows only how many turns the wheel did. So, the only distance a car can measure is the slope distance. Percentage is the SIN of the angle. Not the TAN.
:!:

Not sure if serious. The car could be a bike, a person or nothing at all. The purpose of this is just to represent what a slope is exactly.