value of GRAD angle mode, thought experiment

[brouhaha]

This is a thought experiment. Pretend that this is market research that a big calculator company was doing in the heydey of scientific calculators.

Imagine that you are buying a new RPN scientific calculator for daily use. It's not a specific brand, though it's a respectable brand. You're not buying it because it is rare or valuable, nor because you have any expectations that it will become rare or valuable. In other words, you're not buying it due to any collectable value, or as an investment, or as a toy.

Also imagine that you're on a modest budget. Maybe you're a college student, or a young professional.

The calculator is available in two models. One has settings for degrees, radians, and gradians. The other has only degrees and radians. They are otherwise identical. The one with gradians costs more.

Do you buy the calculator with gradians? How much of a price difference would there have to be for you to decide you do not need gradians? (Remember, the scenario is that you have to stay within a modest budget.)

Perhaps the non-gradians model costs $100. Would you be willing to pay $5 more for gradians? $10? $25? $50? More?

[Valentin Albillo]

(03-04-2023 04:06 AM)brouhaha Wrote:  Perhaps the non-gradians model costs $100. Would you be willing to pay $5 more for gradians? $10? $25? $50? More?

Not a single cent more. I've never used GRAD in my whole life, not even for challenges, so I wouldn't miss it and wouldn't pay for it.

Hyperbolics, I have used occasionally. GRADS, never ever.

By the way, if you want to have a look at a real-life calculator survey by HP (for the successor of the HP-67/97 no less,) have a look at this one I completed and sent back to HP in July, 1977, more than 45 years ago.

Regards.
V.

[Didier Lachieze]

(03-04-2023 05:03 AM)Valentin Albillo Wrote:  Not a single cent more. I've never used GRAD in my whole life, not even for challenges, so I wouldn't miss it and wouldn't pay for it.

Same for me.

Initially the HP Prime didn’t support GRAD, but it was added latter on. Here is a related discussion about GRAD usage: Surveying and 400 degree circles

@Valentin, thanks for sharing the HP survey from 45 years ago, that’s very interesting!

[Ángel Martin]

(03-04-2023 04:06 AM)brouhaha Wrote:  Do you buy the calculator with gradians? How much of a price difference would there have to be for you to decide you do not need gradians? (Remember, the scenario is that you have to stay within a modest budget.)

Perhaps the non-gradians model costs $100. Would you be willing to pay $5 more for gradians? $10? $25? $50? More?

My understanding is that GRAD was very meaningful for surveyors, to the point of being a must - but not being one myself I wouldn't know how much of a necessity vs. just convenience thing. Also surveyors probably don't qualify for your survey since they typically have a large budget.

[Massimo Gnerucci]

(03-04-2023 07:56 AM)Ángel Martin Wrote:  Also surveyors probably don't qualify for your survey

Nome omen.

BTW: never used GRAD myself, but it was cool to show it off.
So my answer would be in the range ¢0-¢2

[Massimo Gnerucci]

(03-04-2023 05:03 AM)Valentin Albillo Wrote:  have a look at this one I completed and sent back to HP in July, 1977, more than 45 years ago. :)

Quote:The result of all this ? Most likely the HP-41C and its many peripherals.

Probably so, but you also killed the 95C. :)

[Maximilian Hohmann]

Hello,

(03-04-2023 07:51 AM)Didier Lachieze Wrote:  

(03-04-2023 05:03 AM)Valentin Albillo Wrote:  Not a single cent more. I've never used GRAD in my whole life, not even for challenges, so I wouldn't miss it and wouldn't pay for it.

Same for me.

And another "Same for me" reply. By the way: "financial" functions wouldn't have been worth a single Cent either (back in those days it would have been either Lire or Pfennig for me).

Regards
Max

[Andres]

If the RAD-DEG-GRAD supporting model cost $ 100, then the RAD-DEG supporting model should cost $ 90... :-)

From time to time I found GRAD useable, but not as much as to pay a large difference for it. Is easy to do a scale operation ( 10 / 9 *) or (9 / 10 *) to convert GRAD "to" and "from" DEG.

I recall using GRAD mode in a simple game which ran on the HP25. It goes more or less as:

An object moves in a square board with X and Y coordinates ranging from 0 to 100. If, when updating the position of the object after an iteration, it hit the boundaries, it bounces back. If the calculator is set in GRAD mode, the following sequence can be used to implement the bouncing:

RCL X coordinate (or Y coordinate)
RCL deltaX (or deltaY)
+

SIN
ASIN
COS
ACOS

STO X coordinate (or Y coordinate)

(For clarity, in the example I'm not using 2-D vector addition by means of the summation function, which the original game did)

[rprosperi]

In college in the late 70s, I had an ME Professor that described grads as "only used by surveyors that can't think" and that such folks should be avoided.

I've never met anyone that used them for anything other than to explore them for curiosity sake and/or to see if they are buggy.

I'd never pay a cent more for such a model (other than for collecting purposes, excluded here).

What I wonder is what HP (and TI, etc) were thinking when deciding to include it. No doubt so form of "well, there are some people using it, maybe we can attract them to buy" but it seems to not have been well justified. I'd guess the extra work/costs to research, develop, test and document use of Grads was never offset by sales of units for that feature.

I suppose there are obscure bugs hidden within the use of grads, but we'll never know since no one cares....

[Gerson W. Barbosa]

(03-05-2023 01:00 PM)Andres Wrote:  From time to time I found GRAD useable, but not as much as to pay a large difference for it. Is easy to do a scale operation ( 10 / 9 *) or (9 / 10 *) to convert GRAD "to" and "from" DEG.

As far as I can remember, I have never used GRAD in all my life. Anyway, I decided to offer it for free, together with all the rest, as its implementation would not cost one single programming step:

(12c Platinum) Fast & Accurate Trigonometric Functions

  SIN:  R/S
  COS:  g GTO 090 R/S     
  TAN:  g GTO 100 RS            
 ASIN:  g GTO 137 R/S      
 ACOS:  g GTO 157 R/S        
 ATAN:  g GTO 177 R/S 

 DEG:   g GTO 270 R/S
 RAD:   g GTO 272 R/S
GRAD:   .9 1/x STO .0

Gerson.

[Valentin Albillo]

.
Hi, Didier Lachieze, Massimo Gnerucci, Maximilian Hohmann and Ángel Martin, {all highlighting and links are mine}

Didier Lachieze Wrote:@Valentin, thanks for sharing the HP survey from 45 years ago, that’s very interesting!

Thanks for your appreciation and kind words, Didier, I was very very young when HP sent me that Survey, not even in my 20's, and I felt quite honored and intrigued, so many questions ! A new top-of-the-line calculator in the works, surely surpassing my beloved HP-67's capabilities by far !!

Massimo Gnerucci Wrote:

Valentin Albillo Wrote:[...] have a look at this [HP survey] I completed and sent back to HP in July, 1977, more than 45 years ago. [...] The result of all this ? Most likely the HP-41C and its many peripherals.

Probably so, but you also killed the 95C.

Good riddance ! If I contributed ever so slightly to the HP-41 system being brought into existence instead of the stillborn HP-95C, so much the better.

Maximilian Hohmann Wrote:By the way: "financial" functions wouldn't have been worth a single Cent either

Yet financial functions can be used to very good effect, see for example HP-12C Serendipitous Solver, which is an 8-page article for the HP-12C financial calculator, featuring a 37-step program which makes use of the built-in microcode IRR solver and a number of assorted financial functions to find real roots of polynomials up to 14^th-degree (and up to 1480^th-degree or more if there are groups of repeated coefficients).

Both root finding and polynomial evaluation are implemented using built-in financial functions without user-code loops or branching, so it's the fastest and more convenient polynomial root solver for the whole Voyager Series calculators, greatly surpassing even the HP-15C's SOLVE function in this regard.

Ángel Martín Wrote:My understanding is that GRAD was very meaningful for surveyors, to the point of being a must. [...] Also surveyors probably don't qualify for your survey since they typically have a large budget.

If HP included GRAD to try and appeal to surveyors, they should also have included MIL, to try and appeal to the Military, as it's an angular measure (mil) used in many countries for land mapping and artillery, quoting from Wikipedia:

"For instance there are artillery sights and compasses with 6,400 NATO mils, 6,000 Warsaw Pact mils or 6,300 Swedish "streck" per turn instead of 360° or 2π radians, achieving higher resolution than a 360° compass while also being easier to divide into parts [...]"

I came across this angular unit when doing my Military Service back in the 80's. An Adjutant asked me to help him with his incoming exams for promotion to Sub Lieutenat, and upon inspecting the problems he needed to solve I noticed the angular unit "o/oo", called "milésimas". Never heard of it before, so I consulted his textbooks to get acquainted with this unit, as it was heavily used for artillery, to the exclusion of other angular units. See the following links:

Strich (Winkeleinheit) (in German)
Mil angulaire (in French)
Mil angular (in Spanish)

also see Milliradian (in English).

Sure enough, you can find o/oo used in many European armies, such as the Swiss Army, as you can see in this manual:

SHARP PC-1360 Schweizerische Armee TopoRechner

This is the Instruction Manual for a bundled system composed of a SHARP PC-1360 pocket computer, a 16 Kb RAM Card containing proprietary software. The software seems to deal with topographic calculations needed for the operation of Swiss Army's mobile artillery units back in 1986.

For example, in pp. 15-16 of the PDF, you can see the following inputs

Bereitstellungsazimut A o/oo
Seite A o/oo
Geländewinkel A o/oo
Azimut A o/oo

Should HP have released a model with the MIL angular mode, it would have been a real hit with the Military (pun intended), surely there's more of them than surveyors !

Best regards.
V.

[cortopar]

(03-08-2023 12:30 AM)Valentin Albillo Wrote:  If HP included GRAD to try and appeal to surveyors, they should also have included MIL, to try and appeal to the Military, as it's an angular measure (mil) used in many countries for land mapping and artillery,

Thanks for another great post, V. Mils are one of two main units used in marksmanship, artillery, etc. The other is MOA (minute of angle). Weapon optics and sights are generally calibrated to one or the other. Some even mix systems by having a sight calibrated in MOA with adjusting turrets calibrated in mils. Battlefield math and unit conversions. Yuck!

[agarza]

Never used GRAD's in 40+years. So I wouldn't pay for that feature.

[Maximilian Hohmann]

Hello!

(03-08-2023 12:30 AM)Valentin Albillo Wrote:  Yet financial functions can be used to very good effect, see for example HP-12C Serendipitous Solver, which is an 8-page article for the HP-12C financial calculator, ...

Thank you for reminding me/us of this excellent article of yours. All those years I had it somewhere on my hard drive and will now finally try out your algorithm. As a matter of coincidence I just received (yet another...) HP-12C, that was sold on eBay as "defective" for five Euros. Of cousre it is not defective, I have not come across a defective Voyager series calculator yet, it just required new batteries. And why should it be defective, it is only 41 years old :-)

(03-08-2023 12:30 AM)Valentin Albillo Wrote:  For instance there are artillery sights and compasses with 6,400 NATO mils

I do not want to know how many innocent people and how many friendly troops were killed over the years because of unit confusions. And how many ships and U-boats were rammed into cliffs because of that. In movies like "Das Boot" (which probably most have seen) they keep issuing commands like "steer two dez to port", "dez" must mean ten degrees, or "aim the torpedoes 4 strich starboard".

With the unit "mil" it gets even more confusing because it is also stands for a length: a millionth of an inch. And to maximise the confusion, native speakers in imperial units tend to also use "mil" when the refer to metric units. Please! use Mu (lowercase greek letter M) for that. A millionth of a metre (or a thousandth of a millimeter) is not a "mil" but a μm (micrometer). Again, I do not want to know how many rockets exploded, space probes missed their targets and aeroplanes crashed because of parts being out of specifications due to "mil-confusion".

Regards
Max

[brouhaha]

(03-10-2023 11:36 AM)Maximilian Hohmann Wrote:  With the unit "mil" it gets even more confusing because it is also stands for a length: a millionth of an inch.

In the US, a mil is a thousandth of an inch (a milliinch, but no one uses that). In the US, micoinches are also used, e.g. for thickness of gold plating on electrical contacts.

In elementary school in the US in the early 1970s, they taught us metric units and prefixes, and told us the US was going to switch to metric. I'm annoyed that we haven't.

NASA is required to use SI, but there's a waiver process. Every time they start designing a new booster (e.g. Ares I and V, and SLS), they apply for a waiver on the basis that a metric design will cost more. The waiver is always granted. (Same thing that happened when the DoD mandated the use of the Ada programming language.)

[cortopar]

(03-10-2023 06:18 PM)brouhaha Wrote:  

(03-10-2023 11:36 AM)Maximilian Hohmann Wrote:  With the unit "mil" it gets even more confusing because it is also stands for a length: a millionth of an inch.

In the US, a mil is a thousandth of an inch (a milliinch, but no one uses that). In the US, micoinches are also used, e.g. for thickness of gold plating on electrical contacts.

In elementary school in the US in the early 1970s, they taught us metric units and prefixes, and told us the US was going to switch to metric. I'm annoyed that we haven't.

NASA is required to use SI, but there's a waiver process. Every time they start designing a new booster (e.g. Ares I and V, and SLS), they apply for a waiver on the basis that a metric design will cost more. The waiver is always granted. (Same thing that happened when the DoD mandated the use of the Ada programming language.)

In the US military, a “mil” generally refers to a milliradian as Valentin described. Sometimes they’re called a “milrad.” I’d guess if you’re a military machinist or scientist, they might use it the way you described.

[brouhaha]

(03-10-2023 06:24 PM)cortopar Wrote:  

(03-10-2023 06:18 PM)brouhaha Wrote:  In the US, a mil is a thousandth of an inch (a milliinch, but no one uses that). In the US, micoinches are also used, e.g. for thickness of gold plating on electrical contacts.

In elementary school in the US in the early 1970s, they taught us metric units and prefixes, and told us the US was going to switch to metric. I'm annoyed that we haven't.

NASA is required to use SI, but there's a waiver process. Every time they start designing a new booster (e.g. Ares I and V, and SLS), they apply for a waiver on the basis that a metric design will cost more. The waiver is always granted. (Same thing that happened when the DoD mandated the use of the Ada programming language.)

In the US military, a “mil” generally refers to a milliradian as Valentin described. Sometimes they’re called a “milrad.” I’d guess if you’re a military machinist or scientist, they might use it the way you described.

I was, like Maximillian's post I quoted, referring to a mil length, not a mil angle. A mil length is used in just about every aspect of engineering and manufacturing in the US, not just military machinists. On the other hand, I've almost never seen US scientists use mil lengths; thankfully they prefer sensible SI units like mm.

[Terje Vallestad]

Whilst GRAD or “gon” seems to be universally derided in this thread it is/was a useful simplification in surveying compared to the backflips that have to be done to work with the degrees/minutes/seconds system. The theodolites were set to 400 degrees and everything worked as per normal decimal numbering. It was as far as I know universally used in Scandinavia and also France in the 80ties when I used it myself. At that time it would have been a dealbreaker for me, now I have no need for it anymore.

[john gustaf stebbins]

(03-10-2023 06:18 PM)brouhaha Wrote:  In elementary school in the US in the early 1970s, they taught us metric units and prefixes, and told us the US was going to switch to metric. I'm annoyed that we haven't.

Actually, and this may be more annoying, we (US) did switch to metric. All those "customary units" are now officially defined in SI units, so everyone is using metric whether they know it or not.

I've been working on a project to update lead safety rules. When surface contamination is measured for environmental purposes, the most common unit is the grotesque, mixed systems, unit ug/ft^2 (microgram per square foot). For occupational safety the common unit is at least all metric, but not really a unit, ug/100 cm^2 (micrograms per 100 square centimeters). I've used a proper unit, ug/dm^2 (micrograms per square decimeter), following NIST guidelines. This gets a fair amount comment because people want what they are familiar with. When they complain too much I often point out that slugs/ha actually gives relevant numbers in a convenient range. Though that could add additional confusion with lead based projectiles or unhoused snails of the Pacific Northwest.

[KeithB]

In my experience in industry, and here at Sandia National Labs, we always use English units for lengths and Celsius for temperature. I recently reviewed a document for an environmental test involving 3 parties and they used Fahrenheit for temperature which totally threw off my intuition as to how hot things were.