History of "percent grade" for slope esp. in civil engineering?

In summary: The channels for water are of three types: conduits built with solid masonry, lead pipes, or clay pipes. Each of these has its own reasons. If the conduit is made as solid as possible, with no openings except for the conduits, and the conduits are spaced at intervals not less than one quarter of an inch, and the bed of the channel has a slope not less than one quarter of an inch for every one hundred feet,In summary, the usage of the term "percent grade" for 100 times slope in, especially but not exclusively, civil engineering may have originated in the early days of U.S. railroads. The term may have come from the use of measures of grades, rather
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What is the origin and/or history of "percent grade" as a way to describe slope?
What is the origin and/or history of the usage of the term "percent grade" for 100 times slope in, especially but not exclusively, civil engineering?

The combinations of search terms I've tried so far only bring back the definition, examples of how to use quantities in this format, and other related practical topics.
 
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  • #2
Percent slope is the rise or fall in feet per 100 feet of run (length).
This makes it real easy in the field for the folks digging the ditch, no math needed!

Cheers,
Tom
 
  • #3
I thought I implied that I know what it is. I've been using the terminology of percent grade for decades. What I want to know is where it came from, how the terminology originated and evolved over time, etc.
 
  • #4
It may have been originated in the early days of U.S. railroads.

Copied from:
https://www.trains.com/trn/train-basics/abcs-of-railroading/grades-and-curves/

"On main lines, grades are generally 1 percent or less, and grades steeper than about 2.2 percent are rare.
...
The effect of grades on train operations is significant. For each percent of ascending grade, there is an additional resistance to constant-speed movement of 20 lbs. per ton of train. This compares with a resistance on level, straight track of about 5 lbs. per ton of train. A given locomotive, then, can haul only half the tonnage up a .25-percent grade that it can on the level."
 
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  • #5
I think @Tom.G 's point was that practices arising from common use by laborers in the field are unlikely to be documented in any historical record.

I'll wager that the Egyptians, the Greeks, and especially the Romans (who did so much plumbing), used measures of grades rather than angles.

If your question is about use of the word percent, rather than a ratio of lengths, that may be even more obscure and poorly documented. When did the word percent first come into use? https://www.etymonline.com/word/percent says 1500s. But even that is a ratio of lengths; but assuming one of the lengths is 100. If they assumed one length was 1000, they would have said permil rather than percent.
 
  • #6
I found a historical reference.

Ten Books on Architecture, by Vitruvius. (Marcus Vitruvius Pollio, 80–70 BC, Roman Republic)

CHAPTER VI
AQUEDUCTS, WELLS, AND CISTERNS 1. There are three methods of conducting water, in channels through masonry conduits, or in lead pipes, or in pipes of baked clay. If in conduits, let the masonry be as solid as possible, and let the bed of the channel have a gradient of not less than a quarter of an inch for every hundred feet,

Vitruvius. The Ten Books On Architecture (Illustrated) (p. 230). Kindle Edition.

Of course, he was not necessarily the first. It could have started 2000 years before that.

EDIT: Use of the words "inch" and "feet" in that book might have been injected by the translator.
 
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  • #7
anorlunda said:
If they assumed one length was 1000, they would have said permil rather than percent.
Right, and in reactor physics we use "units" of pcm ("per cent mille") for reactivity. That's one in one hundred thousand.
 
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  • #8
anorlunda said:
EDIT: Use of the words "inch" and "feet" in that book might have been injected by the translator.
The Romans did not use inches, however they did have the concept of a subdivision of 1/12 in general: a unica. One quarter of a unica was called a sicilicum and so this appears to be a correct translation of 'fastigata ne minus in centenos pedos sicilicus': 'a fall of not less than one forty-eighth (of a foot) in one hundred feet'.

This is a gradient of about 1 in 5000 which seems very shallow. I cannot find any reliable source for Vitruvius' original text online, however Vitruvius is extensively quoted by Pliny in Naturalis Historiae, here as 'ne minus in centenos pedos semipede' i.e. 'not less than half a foot in one hundred feet'.

Now that's only 1 in 200 which is too steep as a minimum: the Romans built aqueducts averaging 1 in 1000 to 1500 over tens of kilometres, so perhaps 1 in 5000 as a minimum (over a short distance) is correct after all.

Edit: from http://www.fh-augsburg.de/~harsch/Chronologia/Lsante01/Vitruvius/vit_ar08.html:
...fastigata ne minus in centenos pedes <sicilico ne plus> semipede.
I don't know the reason for the <...> braces, but this translates as 'a fall of not less than 1/48 of a foot and not more than 1/2 of a foot in one hundred feet', which seems to tie in well with the structures we know of, some of which we can still see today.
 
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  • #9
Here is where you can read the full text of De Architectura:
http://thelatinlibrary.com/vitruvius.html

The specific topic is described in the eighth book, sixth chapter, first paragraph:

Latin:
Ductus autem aquae fiunt generibus tribus: rivis per canales structiles, aut fistulis plumbeis, seu tubulis fictilibus. Quorum hae sunt rationes. Si canalibus, ut structura fiat quam solidissima, solumque rivi libramenta habeat fastigata ne minus in centenos pedes semipede eaeque structurae confomicentur, ut minime sol aquam tangat.

English:
There are three types of pipes: masonry channels, lead pipes, and terracotta pipes. The construction criteria are as follows: in the first case the construction must be carried out in solid masonry, with a slope of between a quarter and a half foot every hundred, equipped with a vaulted roof to protect the water from the sun.

For the calculation of the slope the Romans used two instruments, the chorobates, of their own invention, and the dioptra, of Greek origin.

It is certain that the Babylonians already built aqueducts, as did the Egyptians and the Greeks, but they did not leave any description of the construction technique and engineering design choices, as Vitruvius did in De Architectura.
 
  • #10
Roberto Teso said:
Here is where you can read the full text of De Architectura:
http://thelatinlibrary.com/vitruvius.html

The specific topic is described in the eighth book, sixth chapter, first paragraph:

Latin:English:For the calculation of the slope the Romans used two instruments, the chorobates, of their own invention, and the dioptra, of Greek origin.

It is certain that the Babylonians already built aqueducts, as did the Egyptians and the Greeks, but they did not leave any description of the construction technique and engineering design choices, as Vitruvius did in De Architectura.
Two problems with that:
  1. The words 'between a quarter and' do not appear in the Latin text on that page and appear to have been inserted by the translator.
  2. This implies a gradient of between 1 in 400 and 1 in 200 for masonry aqueducts (or in the context of this thread 0.25%-0.5%) whereas the examples we have in Rome and Southern France are of c.1 in 1000-1500.
 
  • #11
Sicilico mean a quarter of an ounce, for Romans, I now it's a mass unit, not a lenght, but this is one of the translation currently of per centenos pedes sicilico, using sicilico to mean a quarter of something.
Gradient varies for different climate and many other reasons, Pliny suggest to use a quarter of an (Romans) inch to a hundred (Romans) feet.
 
  • #12
Roberto Teso said:
Sicilico mean a quarter of an ounce, for Romans, I now it's a mass unit, not a lenght, but this is one of the translation currently of per centenos pedes sicilico, using sicilico to mean a quarter of something.
But the words per centenos pedes sicilico do not appear in the text you quoted.
Roberto Teso said:
Gradient varies for different climate and many other reasons, Pliny suggest to use a quarter of an (Romans) inch to a hundred (Romans) feet.
This was all covered (with more direct references) in post #8 above, do you have anything new to add?
 
  • #13
@anorlunda's https://www.physicsforums.com/threads/nominate-a-thread-to-be-featured.773069/page-14 got me to looking at some of my old books.

I have this text:
Surveying.jpg

image compliments of https://www.ebay.com/

and it says "In working with cuts and fills for highway construction, the side slopes are generally based on the material involved. The slope is given as a ratio of so many units horizontally to so many units vertically." So I guess surveying history would be relevant?
 
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