UKC

I'm trying to compare the average gradients of two separate paths; path A and path B. Sods law they're on two separate maps of different scales.

Anyway path A rises 1362 feet in 1.59 miles and path B rises 1834 feet in 2 miles.

I'm not sure if I've used the correct arithmetic so I'd be grateful if any numerate UKCers could tell me what gradients they come out with( expressed as "one in X, Y or Z rather than percentage please)

Thanks.

In reply to FesteringSore:

Your maps are presumably in m and km, in which case "unconvert" your measurements and do (height/(1000*distance) for your answer.

In reply to FesteringSore

I reckon they're both about 1 in 6, but I expect I'm wrong.

In reply to Yanis Nayu:

Not far out by my reckoning.

I made A 1 in 6.2 and B 1 in 5.7

Thanks.

In reply to FesteringSore:
Hi
Assuming that the miles figure is the horizontal distance which is what a map would show then the gradient is the miles figure (converted to feet by multiplying by 5280) divided by the height gain.
On this basis I make the first one 1 in 6.16 and the second 1 in 5.76.
I was told this wee reminder - Gradient = Tangent, Incline = Sine to distinguish the two different ways of referring to slopes.

In reply to keith-ratcliffe:




Thanks. Tallies with mine and Yanis'

In reply to FesteringSore:
I get the same as you. I converted everything to feet, divided vertical by horizontal to get decimal, x 100 to get % then used this converter.

http://www.cactus2000.de/uk/unit/massgrd.shtml

I'm sure that's not the easiest way!

Just realised that 1 in type gradient is the divide the other way up. D'Oh.

In reply to FesteringSore:


Off topic (sorry) but does anybody actually think of gradients in percentage terms? Seems one of the most stupid ways of measuring things imaginable to me. If we had to changed all our road signs from "1 in X", (pointlessly because everybody understood them anyway) then surely changing them to degrees, the standard way to measure angles, would have made more sense.

In reply to pec:


Why? 23% means the road goes up 23m in 100m horizontally - height gained in a standard horizontal distance. Perfectly reasonable for comparisons and finer grained without using decimals than 1 in X.

In reply to pec:

Radians are surely the 'standard' way of measuring angles?

Regardless, using angles would cause confusion about whether you are measuring from the horizontal or vertical. I guess you could standardise for convention but that seems a bit more complicated than saying, the vertical height change is 16% of the horizontal distance.

In reply to pec:

I tend to think of decimals (or whole numbers for a steep one) because most of the time a gradient to me is of a graph not a hill. For example the gradient of y=2x has a gradient of 2. The joy of GCSE maths

In reply to XXXX:


Not in the real world?


If you said it was a "45 degree slope" I think most people would know what you meant?

In reply to galpinos:


I think that was the worst possible angle you could have chosen to make your point!

In reply to Robert Durran:
Having thought about it, I'd say a 1 in 5 slope is clearer than a 15 degree slope.

None of this is helping me update my progress figures though. Damn distractions......

In reply to FesteringSore:

When using a map you'll have to do two calculations because the horizontal distance you are measuring is flat horizontal and not 'along the slope'.

So first you have to find the angle:
angle = arctan(x/y) then convert it to gradient = sin(angle)

Then 1/gradient will give you the 1 in z figure.

In reply to FesteringSore:

I'm intrigued why you would want to differentiate a fairly minor amount of steepness, surely the biggest issue is what the path is like, i.e. what is the steepest section. No point walking for over a mile and then finding a vertical wall of 1000ft - your simple and easily understandable terminology of describing the route as a path indicates that it is a walk rather than a walk and a climb.

In reply to galpinos:

Was that a deliberate joke, choosing 45 degrees?

Giving an angle is meaningless unless you define a 0 degree direction from which to measure it. If you choose the horizontal then the angle will be different if you are at the top looking down or at the bottom looking up. (Unless it's 45)

Incidentally, hours, minutes and seconds are used more in everyday life than degrees.

In reply to L'Eeyore:

Curiosity

In reply to XXXX:


Why on earth, in the context of a path or road, would you quote the angle from the vertical? It would be a totally idiotic thing to do since flat (horizontal) is the default from which a slope deviates, and anyway who could possibly imagine they could walk or drive up a 30 degree slope if that was measured from the vertical because common sense tells you that's really a 60 degree slope.

In reply to pec:


Well this is a climbing forum, it's all about the vertical round here

On the other hand the x in y terminology is pretty useless when faced with a vertical wall!

In reply to MeMeMe:



I was talking about road signs!

In reply to pec:


Well if you are talking about road signs, why do we not use the following instead of some maths equation that most people need to convert in their mind;

Steep (covers anything from 1 in 8 to the following)
Very (covers anything from 1 in 4 to the following) - think Porlock Hill
Extremely (covers 1 in 3 to the following) - think Hardknott Pass
Dangerous (covers all the rest) - think Ffordd Penlech in Harlech

We could put % signs below the main signs to help people who don't have English as a first language.

In reply to FesteringSore:
This discussion has made me think about why gradient is a relevant concept. When I am walking I tend to think first about height gain and then look closely at the map to get an idea of steepness. It is the actual terrain that ultimately allows me to pace myself appropriately.
What do others think?

In reply to keith-ratcliffe:

I think we should just grade all climbs based on gradients.

In reply to L'Eeyore:
Hmmm - Tophet Wall & Devils Slide - same current grade but different gradients - this could make things very interesting. That appeals.