Talk:Grade (slope)

Order of bullet points

The second and third bullet points need to be reversed, for the comment (about "the last two") in the following paragraph to make sense. It would also match them up with the table on the right. In fact, I'm going to make that change right now - if anyone has objections, change it back.

Qseep 05:24, 7 December 2006 (UTC)

This doesn't explain much

After reading the article I still found myself wondering how grades are calculated. The table would suggest a 9% grade is merely 5°, but I was on a 9% road today and it must have been at least 30°. The linked page [1] offers a much clearer answer, that the grade is simply 100*(rise/run). Perhaps this is not a common standard but it is certainly used in Northern Alberta and BC. :-)

Though, I still don't understand why percentages are used at all. :-/ 142.59.173.240 05:29, 4 April 2007 (UTC)

I too came away from this article with little greater understanding of grades/slopes/inclines/ramps/hills etc. Please rework it for concise clarity.

Czech railway sign

Surely the "20" on the sign cannot represent a 20% grade. The "Railways" section of the article on railway list four of the steepest grades for a non-rack railroads as ranging between 1 in 40 (2.5%) and 1 in 18 (5.5%). The Czech railroad (which looks pretty flat in the photo) would be 3.5 to 8 times steeper than that if the sign really means 20%.

If you look closely, you will see that it says "20‰"; see Permille (which ironically features the same photo). So you should be interpreting this number as 20⁄1000 or 2%. I've included this on the article, because I'm sure that this confusion is common. +mt 17:35, 25 July 2007 (UTC)

bad article

I would fix it if I understood the subject. But I came to read it, justbecause I wanted to learn more. After reading this I still don't understand the various ways slopes are indicated and I am missing information. Why, for example, is a 45° equal to 100%? My gut feeling is that a vertical (90°) wall would be 100%. And why is there no explanation (perhaps drawing) of 1:10. 1:20, 1:50 etc. slope indication? Why is there no comparison table that is understandable? Why is "sine" mentioned in table but not explained in text? Etc. --VanBurenen (talk) 08:48, 25 July 2008 (UTC)

I agree with what you said and so I changed the definitions section of the article. The 3 definitions of slope were not correctly stated and so I changed that. I also added more explanation to explain the siginifcance of the tangent / sine table. The reason I changed this is that I was writing a slope calculator for my own website and consulted Wikipedia for some information and noticed that this article needed rewording. Wolf1728 (talk) 07:01, 28 July 2008 (UTC)wolf1728

Thank you. My understanding of the subject is increasing. :) --VanBurenen (talk) 12:03, 28 July 2008 (UTC)

I noticed a repetition of information: in the introductory paragraphs information was added that also is mentioned under "Expression". Therefore I edited some. Also added picture and straightened out some other stuff. --VanBurenen (talk) 12:36, 8 August 2008 (UTC)

VanBurenen - it seems your understanding of the subject has greatly increased. You did a fine job of clearing up the edits I had made. Wolf1728 (talk) 02:12, 10 August 2008 (UTC)wolf1728

I might rework the definitions someday, since def'n 2 and 3 are mathematically the same, except that #2 is arbitrarily multiplied by 100, and def'n #3 uses wording described in the ratio article but worth describing here for convenience. Some gradients use per mil (e.g., the photo in this article). Basically I'll merge #2 and #3, and reword it to mention that often the ratio is expressed as a percentage for roads, etc., or worded as 1 in x. The previous version of this article previously stated a "sine" definition, which existed in the table (now removed). Does anyone know who uses this definition for describing gradients of terrain? If it is not used, we could remove this definition, since this can only add to confusion (as expressed above). Otherwise this would be set as the third definition (again). +mt 03:46, 10 August 2008 (UTC)

Instead of making a table, would it not be more illustrative to make a drawing showing the slope at different angles, %'s, and ratio's? Does any of you have a drawing application to make such? --VanBurenen (talk) 13:43, 10 August 2008 (UTC)

Review the figure Image:Grade_slope.pdf‎ and add some feedback here (it's a PDF for now and needs to be downloaded, but I'll make it an SVG after it is reviewed). I used angles 0° to 70° since the graph becomes unusable after 70° since the y-axis scales to accommodate the trend to ∞ for 90°. +mt 18:12, 10 August 2008 (UTC)

All I get is a .pdf-icon. Nothing to review. What do I miss? --VanBurenen (talk) 19:53, 10 August 2008 (UTC)

Under the PDF icon is the download link (PDFs are quickest for me to make) ... regardless, the SVG version of the same figure is at Image:Grade slope.svg. However, now I see the referenced figure below and I'm starting to get a a few more ideas ... +mt 03:56, 11 August 2008 (UTC)

Wow this article is getting a serious redesign. (It needed it). Not to "plug" my own website but I got interested in this subject when I was writing a a "grade, angle, and ratio" calculator here Look at the chart there (done with MS Paint). Is that something you would like from 0 to about 85 degrees?

My understanding of the definitons of slope is that it has 3 definitions (not including the fourth "sine or slope length" definition). All 3 definitions are shown on my graph.

Since the "sine" column has been eliminated from the Wikipedia table maybe the definition in the article should be removed entirely, especially since it references values in the table that aren't there anymore. (I mentioned this "sine definition" on my website mainly because it was in the Wikipedia article.) Wolf1728 (talk) 00:04, 11 August 2008 (UTC)wolf1728

I removed the sine column from the table because it is distracting from the primary definition with the tangent function. Although the sine definition is fine within mathematics, I haven't seen it being used in engineering, geology, etc. to describe slopes and grades. It may, however, exist as an obscure surveying definition. Presently, it is mentioned in the article below the main definitions, which is fine, but it shouldn't be up with the other definitions unless it is referenced in the literature as a definition of "grade" (again, because it will only add to any confusion). Anyway, the figure in your website is nice, and I might redo a similar figure for inclusion here (someday). +mt 03:56, 11 August 2008 (UTC)

The graph I see on Wolf's website is something I had in mind. With not as many 'red' markers to make it a little less crowded and easier to read. Maybe Wolf could do a little redesign and upload it? --VanBurenen (talk) 07:14, 11 August 2008 (UTC)

Sure. I like the idea that the slope is visual, and shows both the % and 1:# notations side-by-side. Give me a few days to draft a similar figure. My version will probably have fewer divisions so that it isn't too large, but it should still be effective. +mt 14:43, 11 August 2008 (UTC)

Hello. I finished with the graph and it is located here on my website at: http://www.1728.org/gradient.htm (You'll have to scroll toward the bottom to see it). I mentioned I'd make a graph from zero to 85 degrees but 80% takes up too much space as it is. Anyway, please go to the graph and post your comments here. Wolf1728 (talk) 04:02, 17 August 2008 (UTC)wolf1728

Looks great .. I've added your image to Image:Grade_slope.png with your credit, and put in on this article. Change the license if you care (I just chose a compatible one). I've been too busy to draft a figure (you beat me to it), but I might (someday) redo this figure as a vector SVG, since these are generally preferred. +mt 05:34, 17 August 2008 (UTC)

Well done! --VanBurenen (talk) 07:52, 17 August 2008 (UTC)

Well that certainly made it to the article very quickly. That chart and my rewriting of some of the article are the biggest contributions I've made to Wikipedia (so far). Thanks. Wolf1728 (talk) 20:07, 17 August 2008 (UTC)

Change the graph?

I'd like to change the current graph with one I just uploaded here: http://commons.wikimedia.org/wiki/File:Grades_degrees.svg -- Reasons: a) the aspect ratio should display better, and b) it's in SVG format.BW95 (talk) 04:55, 21 March 2010 (UTC)

Illustration of grades in percent and angles in degrees (300px)

Illustration of grades in percent and angles in degrees (250px)

It does better show what the graph is supposed to show. But making it fit appropriately into the article seems more challenging. Once it's scaled to fit, the numbers will be rather hard to read. —EncMstr (talk) 06:10, 21 March 2010 (UTC)

I made the text larger. Seems to work OK at 300px wide. BW95 (talk) 07:54, 21 March 2010 (UTC)

That's a major improvement. Would it be hard to make the angle text larger too? Seems like it should be the same size as the other text. —EncMstr (talk) 18:15, 21 March 2010 (UTC)

I thought about that but decided against it for two reasons: a) The angle text may run into the grade lines and cause confusion, even with the color coding, and b) The main thrust of this graph is to show grades, and angles are secondary information. But anyway, it can be done if you think it's important enough. BW95 (talk) 19:01, 21 March 2010 (UTC)

What does this mean?

From the "Railways" section list:

• 1.66% (1 in 60) Rudgwick platform with non-continuous brakes - too steep.
• 0.77% (1 in 130) Rudgwick platform with non-continuous brakes - not too steep.

That makes no sense at all without some form of explanation. 109.149.143.15 (talk) 23:52, 31 March 2012 (UTC)

It is better explained on the linked page on Rudgwick station. Put simply, the gradient in a station had to be lessened to remove the chance of a stationary train running away down the gradient. — Preceding unsigned comment added by 86.175.152.206 (talk) 15:50, 17 June 2012 (UTC)

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Example slopes comparing the notations

For reference and to show the accuracy of the values, some examples of the values in the table of comparative values of gradient slopes are calculated as follows. The table entries are selected from round numbers in per-mille or ratio or angle along with some documented or reasonably well known examples. Appropriate rounding is applied for presentation. Copy, paste and tweak to explore other values. Philh-591 (talk) 11:25, 6 July 2022 (UTC)

$ perl -d -MMath::Trig -e '1;'

> for $ratio ( qw( 20 25 37.7 50 80 90 100 125 200 660 1320) ) { print( "1 in $ratio is ", 1000/$ratio, " per-mille, angle is ", rad2deg( atan( 1/$ratio)), " degrees \n"); }
1 in 20 is 50 per-mille, angle is 2.86240522611175 degrees
1 in 25 is 40 per-mille, angle is 2.29061004263853 degrees
1 in 37.7 is 26.525198938992 per-mille, angle is 1.51942566781725 degrees
1 in 50 is 20 per-mille, angle is 1.1457628381751 degrees
1 in 80 is 12.5 per-mille, angle is 0.716159945470409 degrees
1 in 90 is 11.1111111111111 per-mille, angle is 0.636593575963487 degrees
1 in 100 is 10 per-mille, angle is 0.572938697683486 degrees
1 in 125 is 8 per-mille, angle is 0.458356458000432 degrees
1 in 200 is 5 per-mille, angle is 0.286476510277074 degrees
1 in 660 is 1.51515151515152 per-mille, angle is 0.0868117207103118 degrees
1 in 1320 is 0.757575757575758 per-mille, angle is 0.0434058852666681 degrees


> for $permill ( qw( 70 50 40 35 33 25 20 14 10 8 5 3 2 ) ) { print( "$permill permill is 1 in ", 1000 / $permill, " : angle is ", rad2deg( atan( $permill/1000))," degrees \n"); }
70 permill is 1 in 14.2857142857143 : angle is 4.00417294070939 degrees
50 permill is 1 in 20 : angle is 2.86240522611175 degrees
40 permill is 1 in 25 : angle is 2.29061004263853 degrees
35 permill is 1 in 28.5714285714286 : angle is 2.0045340321059 degrees
33 permill is 1 in 30.3030303030303 : angle is 1.89007482589896 degrees
25 permill is 1 in 40 : angle is 1.43209618416465 degrees
20 permill is 1 in 50 : angle is 1.1457628381751 degrees
14 permill is 1 in 71.4285714285714 : angle is 0.802088512805638 degrees
10 permill is 1 in 100 : angle is 0.572938697683486 degrees
8 permill is 1 in 125 : angle is 0.458356458000432 degrees
5 permill is 1 in 200 : angle is 0.286476510277074 degrees
3 permill is 1 in 333.333333333333 : angle is 0.171886822880016 degrees
2 permill is 1 in 500 : angle is 0.114591406237786 degrees


> for $degree ( qw( 60 45 30 20 15 10 5 4 2 1 ) ) { print( "$degree degrees is 1 in ", 1 / tan( deg2rad( $degree)), " or ", 1000 / (1/tan(deg2rad( $degree ))), " permill \n"); }
60 degrees is 1 in 0.577350269189626 or 1732.05080756888 permill
45 degrees is 1 in 1 or 1000 permill
30 degrees is 1 in 1.73205080756888 or 577.350269189626 permill
20 degrees is 1 in 2.74747741945462 or 363.970234266202 permill
15 degrees is 1 in 3.73205080756888 or 267.949192431123 permill
10 degrees is 1 in 5.67128181961771 or 176.326980708465 permill
5 degrees is 1 in 11.4300523027613 or 87.488663525924 permill
4 degrees is 1 in 14.3006662567119 or 69.9268119435104 permill
2 degrees is 1 in 28.6362532829156 or 34.9207694917477 permill
1 degrees is 1 in 57.2899616307594 or 17.4550649282176 permill


Philh-591 (talk) 11:26, 6 July 2022 (UTC)