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... like the mhyper(2.5,1,x) is scaled in UnitOf_Graphing as well as the all lot of math functions also the NURBS are in their base definitions, i.e: "UnitOf_Graphing". Open the collapsed area to see what we would pass as an export.
The task resumes in several scaling/dimensioning steps
1. assume you give a data set for the dome roof,
the next task is to scale Cheby style ...
2. Find the control points that will best fit the data set (not included in the work sheet under construction ...)
3. tabulate and export in "UnitOf_Graphing"
4. at this point the end user will convert back in his the original unit system (that we can do for him so that the QA department can check the entire contract made via Mathcad).
The QED is that the Engineer must first get rid of the unit system because unit systems have no mathematical meaning ... that's what I'm trying to explain and explain in this collab: unit systems don't belong to maths and if you use Mathcad for doing math task you must work without unit system .
In what unit were the Cathedrals built ?
... in the system "That Long"
... then the "that long" was graphed down with all the necessary "that long" correspondences to the taste of the Master of the Cathedral .
UnitOf_Graphing NURBS.mcd 35.1 K
On 10/14/2006 11:23:51 AM, jmG wrote:
>... suite of :
>� you advocate you can't do
>your job without units, then,
>could you or the could your
>profession do the job in DOS
>or else compiled languages
>that don't take units . Could
>you do the job in TI =59,
>HP-48SX ... ?
What is that supposed to mean? Even in the days of DOS and compiled languages I couldn't do my job without units! But that doesn't have anything to do with using units in Mathcad. I could ask you if you could have done your job in the days of slide rules. Certainly it was possible, but you had to do the accounting for the powers of ten by some independent means. That does not mean that you should say that Mathcad should only work in the range 1-10, and you should carry the exponent on a piece of paper. In the same way, why should I carry units in some separate accounting rather than have Mathcad do that for me. To repeat my mantra, get the computer to do the repetitive, dumb stuff and let us concentrate on the important creatice issues.
>Hankel or else functions only
>relate the dependent domain to
>the independent one. Do you
>have to put units in
>I see no units in the attached
>Galerkin finite differences.
>However some collab suggested
>Odesolve should carry unit.
>The PID Optimize (attached)
>starts with units and
>properties but by the "Harry
>magic" the final answer are
>unitless but they are not as
>they are in "repeat per
No, it does not start with units. If you look at it the numbers do not have units attached -- there are text boxes that say what the units should be which is a totally different thing. This sheet is a great example of why you DO want units. Example 1: If I have an amount of oil in the tank in lb rather than kg then it is trivial to do that with units. Not so with numbers and text boxes. (Here in the US it is common to have to go between imperial and SI units). Example 2: there is a line t.final = 10. What are the units? Not even given in a text box. And what If I want to go from min to hr, how do I do that? Example 3: As you say the coefficients are apparently unitless, but in reality they have units. It should be possible to include them with the right units transparently.
With a good units system you are (a) forced to maintain consistency, (b) allowed to used different units (lb/kg/tonne...) as is most convenient, and (c) have the power of unit checking to help validate equations.
>I'm short of time to look at
>your antenna sheet, other
>collabs might find useful.
What antenna sheet? Nothing was attached. I don't think that my sheets are sufficiently generally to be useful, and I don't have time to prepare them just as a didactical aid in this discussion. Suffice it to say that I can write the Hankel transform as an integral from 0 meter to 5.2 meter, of J0(kqr)rdr, where k, q, and r have suitable units also. I would define k = 2*pi/lambda where lambda is in mm.
... reply would be too long .
Maths are relational to domains (the dependent related to the independent ) and all accessory parameters are implicitly "related" .
You mentioned the antenna task
Mutiplying 2*3 = 6 in the slide rule is in watts if 2 = Volt and 3 = Amp . More Volts and more Amps = more watts. You measure 1000 Volts , Volts are not bigger in their scientific definition, only more of them ... only the dimension of the input then you don't need to carry "Volt", only the number of them which is the task of dimensioning the inputs (variables) in a formula.
Assume the Big Blue does not carry units like a luggage, then you couldn't do the antenna job ?
Variables have measured dimensions or measurable dimensions, which values are assigned and treated by the nature of the formula. The executable are only the 4 ops *, /, +, - which are arithmetic operations and arithmetic has no units . Only the operands have values.
On 10/15/2006 12:24:49 AM, jwlamb wrote:
== Example 1: If I have an amount of oil in the tank in lb rather than kg then it is trivial to do that with units. Not so with numbers and text boxes. (Here in the US it is common to have to go between imperial and SI units).
I would have thought that any Canadian would have a vested interest in keeping track of conversions ...
I think a search would reveal several other amusing unit conversion errors
The ground station was sending thruster data in English units -- in this case, pounds -- while NASA's navigation team was expecting metric units, Newtons. One pound is equal to 4.48 Newtons.
This is exactly the kind of mistake that Mathcad can obviate.
== To repeat my mantra,
Interestingly, the Sanskrit word 'mantra' can be translated as 'instrument of thought'.
== get the computer to do the repetitive, dumb stuff and let us concentrate on the important creative issues.
I have been a proselyte of this approach for some years.
OTOH, there are those that advocate the repetition of dumb activities as a way of clearing the mind to allow deeper concentration of thought. Menu-clicking and typing in units are obviously examples of such an approach.
Did you have a point here ?
Why don't you open the last little sheet "UnitOf_Graphing_NURBS"
To resume :
assign the values to vars, use native formulas done by knowledgeable persons and append the corresponding "Unit result" . That way get rid of units in Mathcad . Any QA team will check on a independent unitless calculator . Convert beforehand not after .
On 10/16/2006 10:29:47 AM, philipoakley wrote:
>On 10/16/2006 9:47:51 AM, jmG wrote:
>>...The answer is : work with unified
>The consistency of terminology is as
>important within pure maths, as is
>application of consistent units of
>measure and their conversion in
>Each group gets to draw its own line.
Yes, Philip !
We all agree now that engineering formulea must be be made coherent unit wise . Further, the task my require pre-processing (like scaling Cheby style or else like reduction ... ) before applying the best maths (curve fitting for instance... NURBS). And a final post-processing to render .
All that done correct, put the right values for the intrants ... bingo = job done !
Most engineering tasks need a solver of some kind, therefore not unit in the formula but true values instead, will output good result in "UnitOf_pertaining formula".
Nothing wrong carrying units for calculating the surface area of the toy box , though !
On 10/16/2006 12:12:46 PM, baxterp wrote:
>Thanks all for the
>entertaining banter. It's
>always fun to watch a
>conversation like this where I
>agree with exactly half (and
>usually every-other) posting.
Like you say, Preston:
Captivating to watch peoples that have agreed to disagree if you can also agree to disagree.
A bit circular, is it ?
Sometimes, watching forum is like watching a dog chasing his tail.
On 10/16/2006 8:41:51 AM, stuartafbruff wrote:
>On 10/16/2006 7:06:25 AM, fkohlhepp
>>If we're using Mathcad to do engineering tasks, is it okay to use units?
>Sometimes. For example, if you wish to
>set the gap on a spark plug, and look up
>the value in your workshop manual, then
>it is important to measure the thickness
>of the Mathcad CD in the appropriate
>units (in or mm) before using the CD to
>set the gap.
>But if you're going to use 'equations'
>or 'formulae' or other such mathematical
>constructs, I'm not so sure ...
Back to the very original question:
>>I am a structural engineer and work often with Kips, U.S. Tons, Yards, ft., inch.,etc. How do you mix these units in calculation and get the correct answer without keeping track of their different units? Help is appreciated. Thanks.<<
...The answer is : work with unified system like the Instrumentation Engineers do. You may have and you should convert formulas in unified unit system . For instance we measure flow in T/hr , it implies to relate "masse volumique" kg/m�, pipe size in m (meter) ... the geometrical constant is related to DP (pressure produced)... + some extra material properties (�C, cp, coefficient of expansion ...).
Once the formula is done, have colleagues review so to avoid receiving a 4 ft butterfly valve to be installed in a 4 " pipe (not a joke !).
On 10/16/2006 7:06:25 AM, fkohlhepp wrote:
>If we're using Mathcad to do engineering tasks, is it okay to use units?
Sometimes. For example, if you wish to set the gap on a spark plug, and look up the value in your workshop manual, then it is important to measure the thickness of the Mathcad CD in the appropriate units (in or mm) before using the CD to set the gap.
But if you're going to use 'equations' or 'formulae' or other such mathematical constructs, I'm not so sure ...
The 3 work sheets showed up , nut now = evaporated .
On 10/11/2006 5:39:01 PM, woodwise wrote:
>Yes, I agree. I use Mathcad
>largely for physics and
>problems. I /prefer/ to use
>units because I think that
>they contribute to
>traceability, though I can
>also see assigning the units
>in text near the equations. I
>am also a programmer of many
>decades, and agree that we can
>strip the units going into a
>process that can't handle
>them. As for restoring them
>upon return from some process
>-- well, I think that that
>might be possible during the
>assignment of the return
>variable. But there may be
>functions - such as solvers -
>that would be in the position
>of accepting divers sorts of
>units on the input, stripping
>the units, and then not
>knowing how to apply units
>upon return. In that case,
>assigning them after the
>return is the only recourse.
>Please understand that I have
>very little exposure to most
>of Mathcad compared to many of
>I also would like to use Maple
Rich, I think that the algorithms for assigning and tracking units are relatively trivial so they could be implemented in any type of solver or other functions. I know that there are considerably more complex things done in code. If you have a problem that causes unit errors in any algorithm then it means that you have entered something wrongly. For example, if you want power in dB then you might write P_dB = 20*log(P). Without units this would work, but it is wrong, since power cannot be expressed in dB. You would need to do it in dBm, say with P_dBm = 20*log(P/1mW), which is dimensionally correct.