Working out a gradient

[NEvans]

Is there an easy way to work out the gradient slope of a piece of road or hill? I'm sure all my local hills are at least 10-15 percent steep (1 in 10 plus), the likelihood is they are probably around 2-3%, just feel like that to me.

Short of going out with a tape measure and level is there an easy way to get a rough estimate?

[Mick F]

If you have a GPS unit, you can measure the altitude at the bottom and the top, then use arithmetic.

For instance, the bridge over the river between Cornwall and England is at 60ft and the top of the hill is at 750ft - 2miles as the crow flies.
That's an increase of 690ft over 10,560ft = 6.5%

That's an average over the whole height difference of course. In reality, one part of the roadway is 20%, and some parts only at 10%, and some hardly 2%.

[pwa]

The only truly accurate way is with measurements taken on the site, not with a bike GPS. A proper survey, using tape measure and level if you like, or proper surveying equipment. Then you have to decide over what distance you are measuring, because the gradient may well vary from one segment to the next.

More rough calculations can be done using OS Explorer maps or your bike GPS, but you will only get a rough idea using those.

[tatanab]

Probably good enough for your purpose, you can use this mapping to measure distance and gradient from which you can calculate a percentage if required. https://gb.mapometer.com/

[pwa]

Probably good enough for your purpose, you can use this mapping to measure distance and gradient from which you can calculate a percentage if required. https://gb.mapometer.com/

That's a nice tool.

[old_windbag]

Similar to tatanab's suggestion but with slightly different user interface( plus os map inset ) is bikehike:-

http://www.bikehike.co.uk

They probably use the same underlying map data interface.

[Brucey]

a simple DIY survey technique (for measuring instantaneous gradient, i.e. over a short length) is to take a spirit level of known length ('L')' and a tape measure out with you.

Set the spirit level with the uphill end resting on the ground and raise the other end until the bubble says it is horizontal. Measure the vertical distance from the end of the spirit level to the ground ('H').

Then using a scientific calculator, set in degrees

Inv Tan (H/L) = A

where A is the gradient in degrees.

Or (H/L) x 100 = gradient in %.

Note that measuring the 'run' along the road surface itself (eg using a mileometer reading or a long tape measure) introduces an error which requires that the first equation should be Inv Sin instead (because you have measured the hypotenuse of a triangle), and the second equation contains an error too; [really you should replace the term L with Cos(A) x (measured L) instead]. For small gradients the error is not great, (which means it is OK and is how they calculate gradient on railway lines) but for steep gradients the two answers will be quite different unless the correction is made.

cheers

[pwa]

a simple DIY survey technique (for measuring instantaneous gradient, i.e. over a short length) is to take a spirit level of known length ('L')' and a tape measure out with you.

Set the spirit level with the uphill end resting on the ground and raise the other end until the bubble says it is horizontal. Measure the vertical distance from the end of the spirit level to the ground ('H').

Then using a scientific calculator, set in degrees

Inv Tan (H/L) = A

where A is the gradient in degrees.

Or (H/L) x 100 = gradient in %.

Note that measuring the 'run' along the road surface itself (eg using a mileometer reading or a long tape measure) introduces an error which requires that the first equation should be Inv Sin instead (because you have measured the hypotenuse of a triangle), and the second equation contains an error too; [really you should replace the term L with Cos(A) x (measured L) instead]. For small gradients the error is not great, (which means it is OK and is how they calculate gradient on railway lines) but for steep gradients the two answers will be quite different unless the correction is made.

cheers

I used to make footpaths in woodland and other recreational areas, and wherever possible I kept gradients to something wheelchair friendly. 5% max or thereabouts. And for that I made a simple device consisting of a long, straight length of wood with a spirit level fixed to it, and a short length of wood at 90 degrees fixed to one end to give the correct drop. The idea was to have something handy for the people doing the work to use with their dirty hands. Worked a treat.

But getting a tape measure and spirit level out on your favourite hill climb could look a bit geeky to an observer. Best done very early in the morning when nobody is around to see?

[deliquium]

Probably good enough for your purpose, you can use this mapping to measure distance and gradient from which you can calculate a percentage if required. https://gb.mapometer.com/

Just tried that on a local climb 'up the Gwynant" up to the top of Llanberis Pass from the end of Llyn Gwynant where the ascending begins - it bears no resemblance to reality! Several sections indicate downhill, when in fact the whole climb is always uphill. The gradients too are so bizarre as to make no sense. I ride that climb at least once a week, so know it intimately.

Very odd

[Vorpal]

https://www.climbbybike.com/index.asp has statistics for many climbs.

[cotswolds]

You can get apps that do it for you - google clinometer. Mount phone to bike, calibrate on a known flat surface at home then you can have an instantaneous reading whenever you want. Will measure averaged over the distance between the contact points of your tyres, which is probably further than any spirit level you're likely to carry around.

For average gradient on a long climb, use OS maps, measure an accurate distance between contours then count the contours. The online sites I think rely on a digital elevation model that averages over a square i.e. one height is assigned to the whole of a square. Data for 5 metre squares exists but I suspect is expensive. I think I read that typically they use 10 metre squares. Fine in the lowlands, but for roads cut into slopes in steep gradients, can give some very funny results.

[Brucey]

if working out average gradients from a map, note that it works quite well if the road is pretty straight, but rather less well if it is a wiggly road, and/or with hairpins. Part of the reason for this is that the roads are (on OS maps) depicted at a fixed width, which is not realistic (at most scales).

For example a road might scale at ~20m wide on an OS map (vs a real width of 4-10m for a typical country road), which can result in an over or underestimate of the distance up a series of hairpins, depending on how they have approximated the bends in the mapping.

I would expect there to be a similar error in digital mapping, too, as well as that which occurs because of the altitude being averaged over squares of finite size as per the previous post.

cheers

[thirdcrank]

I'm embarrassed to realise it's now nearly sixty years since I stayed at the old YHA at Burley Woodhead, on the road across Rombalds Moor AKA Ilkla Moor. During the evening, I went for a walk with several other hostellers (all strangers to me) and we discussed this topic on a sharpish hill. I have a vivid memory of the suggestion being made of fastening a protractor under the top tube and hanging a plumbline from its focus (if that's what you call the intersection of all the lines. ) Over the years, when I've been struggling up some hill or other, I've thought about developing the idea.

All I can say is that every year, somebody jacks up the hills so they are that bit steeper than they were last time you struggled up.

[Brucey]

it all makes sense, what with sloping top tubes, every gradient might measure more that way, too....

cheers

[thirdcrank]

That's from the days when only girls' bikes didn't have a level toptube. There would be all manner of other things like one more source of baffling noises, so for one reason or another, it never caught on.