I have been trying to learn about gradients and how a gradient is expressed. A check online tells me there is no Gradients for Dummies.
Things got a bit frightening when I began to try to analyse this para.
There is a fourth method in which slope may be expressed: the rise is divided by the hypotenuse (the slope length). This is not a usual way to measure slope but it is useful when one only knows the slope length and not the horizontal run. This follows the sine function rather than the tangent function and this method diverges from the "rise over run" method as angles start getting larger (see small-angle formula )
I vaguely recall that I failed both Pure and Applied Algebra....or was it Trigonometry or Calculus? I think I passed Simple Arithmetic. Amazingly, I have managed through life without ever having to use anything I learnt in these subjects. I did not even keep my logarithm table book and slide rule and I have no recollection of what I actually did with them in class. Probably poked other boys in their groins with the slide rule and set fire to the log book with a Bunsen Burner.
I have learnt that a gradient can be expressed as degrees. This sounds so simple and obvious and I am not sure why there are other methods. Just visualise a protractor and where say ten degrees would be, and you get a mental picture of how steep a hill is. But when talking about railways and tramways, they use a different method.
I heard that the Blue Mountains railway was very steep, but since the time when it was first built, the slope has been decreased. (What? They chopped the top off the mountain?)
Rail gradients are expressed as a gradient of say, 1 in 20, to use Wikipedia's example. So, for every 20 metres, you would rise 1 metre. I don't get an instant mental picture but it is very vivid if drawn to scale on a piece of paper. I am led to believe that it is quite steep, but drawn on paper, it does not look steep.
Remember my post about the Balmain counterweight dummy, the system which assisted the Balmain tram up and down from the Darling Street Wharf? That was said to be about a 1 in 8 gradient.
I just drew that inclination on a piece of paper and it does not look at all steep to me.
And by writing this post, I think I have worked out why gradients never look steep to me when drawn on paper. In the above para where I mention Wikipedia, I altered something for we Australians' benefits. I converted the measurements to metric. What it actually said was 'For example, a slope that has a rise of 5 feet for every 100 feet of run would have a slope ratio of 1 in 20.'
Am I on the right track here? It the ratio method won't translate to metric? I have no idea how to represent feet on on a sheet of paper.
All too hard and I have my sock drawer to tidy. I will just accept that the Blue Mountains train line is steep.