What is straight up and down?

Off-topic
1

All hills have a grade, obviously. That being said, what grade is a hill that is perfectly up and down?

This isn’t a trick question, and I’m sure it has a simple answer that all of you smartypantses will know. I just asked cuz I don’t know the answer!

2

You should go to Wikipedia more often. They have all kinds of answers to questions like that. For example: http://en.wikipedia.org/wiki/Grade_(geography)

3

so a 90* grade is undefined, unknown, and therefore impossible by tangential grade

4

is it’s vertical, is it actually a hill?

5

I think you might find the answer at wikipedia…

6

more like a cliff?

7

actually untrue. a flat land, or 0/0 slope would not be undefined,

lim x/x = 1
(x-0)

but for all intensive purposes, it can be undefined.

8

NO
90from horizontal is impossible in tangent, plug it in to a calculator, a 180slope is 0 , and a 270 is impossible again :slight_smile:

9

ok, i see, you were talking 90*, i was thinkin for 0* or flat ground for some reason

in the case of 90*, or (infinite)/0 slope it is truly undefined, but it is possible to be a tangent angle, as

d/dy (sqrt(9-x^2)) = - x/(sqrt(9-x^2)) or -x/y, equivalent to tangent of an angle placed in a unit circle.

if this equation is graphed y set to dx/dy, we end up with a tangent curve, in which y tends toward infinity.

therefore, a vertical slope is a legitimate tangent, however its numerical value tends toward infinity as x approaches 90*, leaving it undefined.

10

sigh

11

i rekon its a vertical cliff!

12

Now, how do you convert a grade in degrees to a grade in percents, and the other way around?

13

if you use grades like 1 in 10 then the answer is quite simple and easy to understand.

Hence 1 in 10 hill says that for every 1 foot you climb vertically, you move 10 feet horizontally.

1 in 1 is a slope of angle 45 degrees to the horizontal.

So a cliff, vertical, would be 1 in 0, for every foot you climb, you make no horizontal progress.

Applying percentages tends to confuse some of the public at large, many older people never studied percentages at school. Once gradient as a percentage approaches and exceeds 100% , it holds less meaning for many anyway. Mathematically people prefer to say the gradient is 4 rather than 400%. ( y=mx+c remember?) Mathematically a gradient of infinity applies to vertical cliffs. But when out driving most still understand 1 in 5 notation, because they can visualise it without the maths.

A gradient of infinity is not undefined, it refers to a perfectly vertical line.
. If its gradient is not infinity, it is not vertical.
Nao

14

Trig.

Klaas has a guide to making an inclinometer. It includes a TIFF image that gives measurements in both % grade and degrees.

To do the conversion for % grade to degrees (or vice versa) you need to do some trig calculations.

Tan is opposite over adjacent which would be the rise of the slope over the run of the slope. Percent grade also happens to be the rise of the slope over the run of the slope.

So the tangent of an angle gives you the slope. The arctan of the slope gives you the angle.

So for a 10 degree slope you have
tan(10) = 0.176 which gives you a 17.6% grade

For a 17.6% grade you have
arctan(0.176) = 9.98 degrees which is close enough to 10 for rounding errors

15

[jack]
What is an intensive purpose? The expression is “for all intents and purposes”
[/jack]