How do u measure the slope of a hill?

Question

i am try to measure the slope of a hill i bike up

Answer 1

Well, you are trying to do a real measurement here; for example, you may be curious about the percent grade of a hill that you climb a fair amount. I've had the same question myself, and I know that the folks saying that it is change in elevation divided by change in distance aren't helping much -- I mean, getting the distance is easy enough, but how do you get the change in elevation?

The best way is to get topographic maps of the area. With these maps, you can find out the starting elevation and finishing elevation of that killer hill. If you can't find any maps, you'll have to get creative, like find some surveyor's equipment to measure the angle. I've even tried using the sun by finding out how soon before sunset the sun disappeared behind the hill and estimating every four minutes before sunset should equal about 1% grade -- but I'd imagine this technique may not be too precise, and it only works when the road is heading west. :)

Answer 2

Depends. If this is a math problem, then you are probably told to assume that the hill has a constant slope. If you can measure both the distance along the slope from the bottom to the top, AND can measure the difference in height between the bottom and the top, you can get the angle, which will be inverse sine of (height divided by length of slope).

In real terms, you could also measure the angle from a stick (or something more sophisticated) at the bottom to one at the top. This can be done using some surveying gear such as a theodolite, or even something simple such as a plumb line attached to a protractor - you sight along the bottom edge of the protractor, and get a pal to read off what angle the plumb line gives.

EDIT TO ADD:
Just thought I should mention Google's pedometer webpage. Like google maps, but you can plot your cycle route etc and it'll give distances covered as well as elevation. Could be useful if you do a lot of training!

Answer 3

height / base

slope = m = ∆y/∆x = change in y / change in x = "rise" / "run"
y is the vertical, or the "rise."
x is the horizontal, or the "run."

In this case the height of the hill is the y and the base is x.
So the slope is height / base, assuming the hill resembles a straight line and therefore has a constant slope.

If the hill looks like a parabola for instance (curved and not constant), the slope is always changing, and you can only find the slope at a specific point using derivatives. I'm assuming the hill looks like a right triangle, in which case the slope is simply height / base.


You can get a general idea of the slope if u find the angle x of the hill and take tan(x).

Answer 4

The slope of a hill shown on road signs is normally measured as the vertical height divided by the distance along the ground (provided the slope is uniform).

This represents the sine of the angle which the slope makes with the horizontal, rather than the mathematical gradient (which is the tangent) as used on maps.

Answer 5

Go to the top of the hill. Find out how high it is from the ground, h, say
Go to the bottom of the hill, find out the horizontal distance from the top, d, say
then slope = -h/d

Answer 6

From a known distance , x , from the foot of the hill, measure the angle of elavation to the top of the hill.
Let this angle be θ
Let height of hill be y
tan θ = y / x
y = x tan θ
x and tan θ are known so y can be calculated.

Answer 7

Where are the data such that we could measure the slope of a hill? Samples, please.

Answer 8

vertical distance from edge to top divided by horizontal distance from edge to top. rise over run, just like in algebra.