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GRADs in use?
Message #1 Posted by Tim Wessman on 17 May 2010, 9:07 p.m.

I remember in a discussion a while back someone asked why it seemed why many newer HP calcs didn't include grads as an option in the calculators. I kept meaning to ask (mainly because it is something I've been wondering now since I twas but a wee lad) in what fields/applications are grads still commonly used? I personally never encountered them anywhere other than as a setting on a 48g series calc.

I've always been wondering. . .

TW

Edited: 17 May 2010, 9:07 p.m.

      
Re: GRADs in use?
Message #2 Posted by Martin Pinckney on 17 May 2010, 9:51 p.m.,
in response to message #1 by Tim Wessman

Tim,

Not just the 48 series. The 20s, 32sii, and 42s all have this setting, and I am sure there are a lot more.

I don't for sure know the answer to your question, but I believe grads were used by the U.S. military at one time; don't know if still. My father was Army artillery in WWII, and he told me they used grads for aiming instead of degrees.

Perhaps today it's all automated...

            
Re: GRADs in use?
Message #3 Posted by Martin Pinckney on 17 May 2010, 10:27 p.m.,
in response to message #2 by Martin Pinckney

Also 10c,11c,15c,22s,25,25c,29c,31e,32e,32s,33c,34c,41c,45,55,65,67.

                  
Re: GRADs in use?
Message #4 Posted by Katie Wasserman on 18 May 2010, 12:02 a.m.,
in response to message #3 by Martin Pinckney

I can think of many more HP calculators that you left out.

Goodbye to GRAD, you'll be missed......

            
Re: GRADs in use?
Message #5 Posted by Dimitri Simitas on 17 May 2010, 10:35 p.m.,
in response to message #2 by Martin Pinckney

Quote:
I don't for sure know the answer to your question, but I believe grads were used by the U.S. military at one time; don't know if still. My father was Army artillery in WWII, and he told me they used grads for aiming instead of degrees.

I know US military maps like most maps in this world today use Mils. Which are in turn used for artillery strikes today.

However if you want confusion about the matter. One circle has 6,283 mils. The US use 6,400 divisions instead. The Russians use 6,000 mil divisions. The French use 6,280 mils, the Swiss use 6,300 mils.

Dimitri

                  
Re: GRADs in use?
Message #6 Posted by Tim Wessman on 18 May 2010, 12:02 a.m.,
in response to message #5 by Dimitri Simitas

Surprising the variation. I'd expect the US to be the only one that picked a stupid, non-standard value. Fits the way we do the rest of things regarding units.

TW

                        
Re: GRADs in use?
Message #7 Posted by Bart (UK) on 18 May 2010, 4:33 a.m.,
in response to message #6 by Tim Wessman

They wouldn't want potential enemies using their own maps against them, now would they?

Note: this is mere conjecture on my part :)

                        
Re: GRADs in use?
Message #8 Posted by Martin Pinckney on 18 May 2010, 7:48 a.m.,
in response to message #6 by Tim Wessman

Quote:
I'd expect the US to be the only one that picked a stupid, non-standard value. Fits the way we do the rest of things regarding units.
Actually, the U.S. did not "pick" the units system we have, we inherited it from the British. Although our units are not all identical to their Imperial counterparts, they have their origins there. In fact, these were the worldwide standard for a long time, since the British Empire was worldwide.

The metric system was developed by the French under Louis XVI, but not formally adopted until after the French Revolution. Just as the English and French have competed in many things for centuries, the two systems were in competition for years. It was another 100 years before the Metre Convention tried to standardize the metric system. The Système International was not established until 1960. The U.S. adopted SI in 1988 as the "preferred" system for commerce, but conversion is strictly voluntary from a Federal standpoint. Some states have attempted mandatory conversion for highway construction, with mixed success. Of course, metric units have been used in science and the military in the U.S. for over a century.

Sorry, I could not resist.

                        
Re: GRADs in use?
Message #9 Posted by bill platt on 18 May 2010, 1:35 p.m.,
in response to message #6 by Tim Wessman

Hey! I like my 3 teaspoons per tablespoon! ;-)

                        
Re: GRADs in use?
Message #10 Posted by Dimitri Simitas on 25 May 2010, 5:15 p.m.,
in response to message #6 by Tim Wessman

Quote:
Surprising the variation. I'd expect the US to be the only one that picked a stupid, non-standard value. Fits the way we do the rest of things regarding units.

It is not a bad method, consider that most of Europe today uses 6,400 Mils per revolution due to NATO.

A target ranged using 6,400 mils is only off by 2%. At 500 yards a 2 yard target is measured as 509 yards with American mils verses the proper 500 yards with the "natural". But if that target was a mere 2inches taller then it was assumed to be, then your target is really at 514 yards, measured with the American mils as being 523 yards away.

A slight variation of the target changes the measurement more then the relative error in range finding. Assuming good well known measurement values at the range, its under 2% the error caused by American mils.

Dimitri

                  
Re: GRADs in use?
Message #11 Posted by Thomas Klemm on 18 May 2010, 2:34 p.m.,
in response to message #5 by Dimitri Simitas

Quote:
the Swiss use 6,300 mils

Did you mean Sweden?

                        
Re: GRADs in use?
Message #12 Posted by Dimitri Simitas on 25 May 2010, 5:06 p.m.,
in response to message #11 by Thomas Klemm

Quote:
Did you mean Sweden?

Perhaps you are right, my mistake. The memory ain't what it used to be.

Dimitri

            
Re: GRADs in use?
Message #13 Posted by Tim Wessman on 18 May 2010, 12:00 a.m.,
in response to message #2 by Martin Pinckney

Well I know it was on other machines, I was just stating my personal exposure. :-)

I know it was/is? used for artillery, but I've not yet encountered any surveyor in europe who has reported using it. I've talked or corresponded with more than a few.

Other than "historical" things, are they any current uses?

TW

Edited: 18 May 2010, 12:00 a.m.

      
Re: GRADs in use?
Message #14 Posted by Jeff Kearns on 17 May 2010, 10:09 p.m.,
in response to message #1 by Tim Wessman

Wikipedia Article on History of GRADS

I first encountered this angular measurement unit in the 70's on my TI-30. What a crappy machine but I loved it... Looks like GRADS are an invention of the French Revolution and are used in some European countries for Surveying. Some militaries use it for Artillery calculations.

Ironically, I have a book called "Surveying: Theory and Practice" that makes no mention of it. Probably because it's a Yankee book. The HP-45, and 55 have it. So does the HP-32E but not my HP-21. It seems to be on every scientific calculator produced by HP post-Spice (unless I am gravely mistaken).

Jeff

Edited: 17 May 2010, 10:17 p.m.

            
Re: GRADs in use?
Message #15 Posted by bill platt on 17 May 2010, 11:36 p.m.,
in response to message #14 by Jeff Kearns

Not on the HP 27S

            
Re: GRADs in use?
Message #16 Posted by Frido Bohn on 18 May 2010, 4:01 a.m.,
in response to message #14 by Jeff Kearns

Quote:
I first encountered this angular measurement unit in the 70's on my TI-30. What a crappy machine but I loved it...

I just bought an TI SR-56 from a second-hand dealer (forgive me ;-). This machine even has a separate switch beside the ON/OFF switch to change from GRAD to DEG! Whereas radians is accessible over the keyboard with a shifted key. For whatever reason, TI must have conceded a high priority to this unit in the mid 70s.

Cheers Frido

      
Re: GRADs in use?
Message #17 Posted by Pierre Brial on 18 May 2010, 12:28 a.m.,
in response to message #1 by Tim Wessman

Grads are commonly used in France for surveying and mapping. As Grad is related to metric and decimal systems, it is a very practical unit :

Right angle = 100 grads

1 grad of latitude = 100 km

You don't have to bother with minutes and seconds, it's all decimal :

decigrad = 0.1 grad, centigrad = 0.01 grad, etc...

Grad is also named Gon in some countries.

Edited: 18 May 2010, 12:29 a.m.

      
Re: GRADs in use?
Message #18 Posted by db (martinez, ca.) on 18 May 2010, 1:07 a.m.,
in response to message #1 by Tim Wessman

when i was traveling i talked with surveyors from all over latin america, from europe and north africa, who had worked in saudi and antarctica. i had the same question and no one used grads.

i read once that the 360 deg circle / 90 deg quadrants are standard because of both nautical tradition, and that they can be divided up into so many kinds of even fractions before one needs to resort to minutes and seconds.

along with that; i can see why the compass rose is first divided into quadrants: toward and away from magnetic north, and toward sunrise or sunset. then you have half, third, ninth quadrants and half, quarter, eighth, third, sixth, twelfth, twenty-fourth, thirty-sixth, and even smaller fractions of the circle.

all those would have been useful until Precision Survey Solutions and hp50G came along.

            
Re: GRADs in use?
Message #19 Posted by geoff quickfall on 18 May 2010, 2:08 a.m.,
in response to message #18 by db (martinez, ca.)

We used grads for navigation up north in areas of magnetic anomalies.

Had to convert the headings back and forth based on the map and the use of a system called Omega nav.

Also shot the stars out the window of the 737 when flying in true.

Cheers, Geoff

                  
So Geoff:
Message #20 Posted by db (martinez, ca.) on 25 May 2010, 8:32 p.m.,
in response to message #19 by geoff quickfall

Speaking of goofy measurements; what are those 1:506880 scale maps of Canada all about, When you tell me that i'll have a clue how the 1:253440 scale from other places got chosen.

BTW: How's the book coming along?

                        
Re: So Geoff:
Message #21 Posted by Norris on 26 May 2010, 6:16 p.m.,
in response to message #20 by db (martinez, ca.)

1:506880 represents a map scale where 1 inch = 8 miles
8 mi x 5280 ft/mile x 12 in/ft = 506,880 inches

1:253440 represents a map scale where 1 inch = 4 miles
4 mi x 5280 ft/mile x 12 in/ft = 253,440 inches

In either case, the scale makes it easy to read distances off the map in miles, by using a conventional ruler marked with 1/2, 1/4, 1/8, and 1/16 inch gradations

Edited: 26 May 2010, 6:18 p.m.

                              
Re: So Geoff:
Message #22 Posted by db (martinez, ca.) on 27 May 2010, 2:10 a.m.,
in response to message #21 by Norris

Thanks Norris. I'd rhetorically ask why i didn't notice that but someone might answer me.

That's a great idea for a country that has a lot of inch rulers floating around. We can easily do the same sort of thing here if an architect draws in 1/4, 1/2, 1/8 etc scale. So of course they use 3/8, 3/16 & 3/4 scale just to mess with us.

                                    
Re: So Geoff:
Message #23 Posted by Norris on 28 May 2010, 1:15 p.m.,
in response to message #22 by db (martinez, ca.)

The traditional use of 1:24000 scale in 7.5-minute US topographic quadrangles also assumes the use of traditional inch rulers. With this scale, 1 inch = 2000 feet, and you can readily measure distances in feet using the traditional 1/2 inch, 1/4 inch, etc. gradations.

The 15-minute quads were traditionally mapped at 1:62500, which is very close to 1:63360, or 1 inch = 1 mile. For practical purposes, you could measure distances in miles on a 1:62500 map with a traditional inch ruler. The exact 1:63360 scale has been widely used for topographic mapping in Alaska.

Edited: 28 May 2010, 1:16 p.m.

                                          
Re: So Geoff:
Message #24 Posted by db (martinez, ca.) on 28 May 2010, 7:56 p.m.,
in response to message #23 by Norris

You know; i've used 15 minute maps a lot and must have known that, but i've always thought of it as one mile = the last joint of my index finger.

                        
Re: So Geoff:
Message #25 Posted by geoff quickfall on 1 June 2010, 10:57 p.m.,
in response to message #20 by db (martinez, ca.)

Hello DB

just saw your posting today! I am on course for a new aircraft and it is taking my time plus I had to write a 13 page article for the next HP Solve magazine at Richards Nelsons request.

That plus my car restoration and book have meant an absence from the forum.

I used many maps, we called them sectional 8 to 1 and 4 to 1 (eight and four mile to one inch). Lots of detail on the 4 to 1 and Norris has hit the nail on the proverbial imperial head!

The book is comming along, infact almost done, although everyone here keeps posting new stuff which may or may not get included. Oh well gives me something to add to a next printing.

Got to get back to the books!

Cheers, Geoff

Edited: 1 June 2010, 10:58 p.m.

      
Re: GRADs in use?
Message #26 Posted by Reth on 18 May 2010, 4:23 a.m.,
in response to message #1 by Tim Wessman

Grads or Gon are used across whole Europe except from the former USSR and England. I for one would never buy a HP calculator not having grads back then when HP calcs were main calc tool. Grads, being decimal are a lot easier to use thus logical and modern units. Same applies to metric - imperial units comparison. Strangely enough in Australia we use DMS for angles and metres for lengths. As they do in Russia. Long story short: today HP mighth abandon grads, no one will notice as no one uses calculators for real work in surveying. If you wanna find out if grads are dead or not, go check ALL modern surveying instruments made all over the world and if you find even one, let me know. I've noticed that "the world" for many is the USA. Well it's not.

Quote:
I personally never encountered them anywhere other than as a setting on a 48g series calc
??? what about HP41, 42, 28, 49/50?

Edited: 18 May 2010, 5:40 a.m.

      
Re: GRADs in use?
Message #27 Posted by Bart (UK) on 18 May 2010, 4:43 a.m.,
in response to message #1 by Tim Wessman

Quote:
I personally never encountered them anywhere other than as a setting on a 48g series calc.
Pretty much my experience too. The "G" setting was always something I had to skip past when changing angle mode or converting angles on my scientifics.

Then again I have never done artillery work or surveying. I've played a bit with navigation, but that was in degrees, and in electronic engineering work it is almost always in radians.

-B
            
Re: GRADs in use?
Message #28 Posted by John Mosand on 18 May 2010, 6:04 a.m.,
in response to message #27 by Bart (UK)

Grads are very much in use. They have been standard in surveying in most of Europe for about 100 years, in France for more than 200 years! Degrees mostly in astronomy and navigation.

                  
Re: GRADs in use?
Message #29 Posted by Stuart Sprott on 18 May 2010, 7:19 a.m.,
in response to message #28 by John Mosand

I am a bit surprised with some of the responses to GRADS.

From a practical point of view the GRAD system is far superior to any other syetem. 100 degrees to a right angle, then decimal degrees. A complete decimal system, very simple to use.

When you write a surveying program using the degree syetem, the most common bug is to forget either to decimalize the degrees or do the reverse process.

Years ago I taught surveying to builders. They had access to simple scientific calculators. One of the hardest parts of the course was to teach them conversion of degrees minutes and seconds into decimal degrees and the reverse. This is when I realised how backward our system was.

I come from a generation who were taught the imperial system at school and were used to strange units. The modern generation brought up on the decimal system find it difficult when using say miles, chains, feet and inches.

In Australia we had the option of changing to GRADS when we changed to the metric system, unfortunately the old surveyors who made the decision at the time could see no good reson for doing so. There are a heep of builders out there who could tell them that they made the wrong decision.

                        
Re: GRADs in use?
Message #30 Posted by Gerson W. Barbosa on 18 May 2010, 8:38 a.m.,
in response to message #29 by Stuart Sprott

Quote:
When you write a surveying program using the degree syetem, the most common bug is to forget either to decimalize the degrees or do the reverse process.

The problem is not forgeting to do this, but having to do it, which would take up precious memory space in low-memory calculators (not a concern anymore). The first version of this program was written for a land surveyor friend on his 4KB RAM CASIO PB-700 (which was later upgraded to amazing 16KB!). A GRAD mode was available (ANGLE 2), but I think no one uses GRADS here.

                  
Re: GRADs in use?
Message #31 Posted by Bart (UK) on 18 May 2010, 9:41 a.m.,
in response to message #28 by John Mosand

Sorry, I was just stating my personal experience. In no way did I mean to imply that GRADS was not in use.

Perhaps I should add a disclaimer to my messages.

-Bart
Disclaimer: the statements in this message are solely those of this opinionated author only and are based on his own experience.

      
Re: GRADs in use? - A non trig-related example
Message #32 Posted by Andrés C. Rodríguez (Argentina) on 18 May 2010, 10:33 a.m.,
in response to message #1 by Tim Wessman

If you need to model a bouncing ball (or body), moving in a (0,0 - 100,100) box, and bouncing at the edges, the sequence

GRAD COS ACOS SIN ASIN

is very handy to manage boundaries and so obtain the proper coordinates for the next position.

Best regards,

      
Re: GRADs in use?
Message #33 Posted by Martin Pinckney on 18 May 2010, 2:24 p.m.,
in response to message #1 by Tim Wessman

Well, there's your answer, Tim. If HP wants to serve the French market, keep Grads in, but call them Gons.


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