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Mathcad confusing two very different types of quantities

ptc-3007326
1-Newbie

Mathcad confusing two very different types of quantities

Hi,

I am trying hard to get used to Mathcad. I am running into a very simple issue when using SI units.

At first I calculated the amount of work done using the equation: Work = Force x Distance and the answer was dispalyed in "J" or Joules.

But then I defined a new unit called "Nm" to identify torque quantities.

After creating the "Nm" unit, the work equation is giving an answer in "Nm" instead of "J". It is very frustrating. Can anybody help?

CSR

====

17 REPLIES 17
MikeArmstrong
5-Regular Member
(To:ptc-3007326)

I don't understand. 1 Joule = 1 N*m. So what's the problem?

Mike

Joule (J) is used as a unit of ENERGY or WORK DONE. When the force (N) acts along the same direction as the displacement (m), we end up with energy.

Newton.Meter (Nm) is a unit to measure TORQUE. In this case, the force (N) acts perpendicular to the diatance (m).

Mathcad may not know which instance of the multiplication is being called for, i.e. whether we calculating an ENERGY or TORQUE. I would like to go and change the incorrect assignment of Nm to J for all my energy calculations.

MikeArmstrong
5-Regular Member
(To:ptc-3007326)

In the International System of Units (SI), a newton meter is known as a unit of torque. It can also be used as a unit of energy. N*m is also used when calculating bending moments.

Mathcad may not know which instance of the multiplication is being called for, i.e. whether we calculating an ENERGY or TORQUE. I would like to go and change the incorrect assignment of Nm to J for all my energy calculations.

You can tell Mathcad which unit to choose in the options.

Mike

When I am changing the units (Tools > Worksheet Options... > Unit System (Default Units = SI & Derived units = Energy Joule) then ALL the N.m products are displayed in units of J.

When I am changing the units (Tools > Worksheet Options... > Unit System (Default Units = Custom & Derived units = Torque ) then ALL the N.m products are displayed in units of N.m.

Now I am calculating both quantities in the same worksheet. If I get the ENERGY quantities displayed correctly, the TORQUE quantities become confusing. And vice versa if I do the tweaking in "options" mentioned above.

Mathcad claims it provides clarity which a spreadsheet does not. Displaying a torque in J or an energy in Nm does not help me at all. In the same worksheet, I want to be able to choose which unit applies to the given result. Is this beyond Mathcad 14? What about your latest releases?

MikeArmstrong
5-Regular Member
(To:ptc-3007326)

Mathcad claims it provides clarity which a spreadsheet does not. Displaying a torque in J or an energy in Nm does not help me at all. In the same worksheet, I want to be able to choose which unit applies to the given result. Is this beyond Mathcad 14? What about your latest releases?

They hold the same numerical value so Mathcad will only display what you tell it to. I honestly don't see the issue. You have the ability to choose either N*m or J.

Mathcad 15 is exactly the same. I have used both units in many calculations and never caused confusion.

Mike

There is no problem if you do not display the units. Yes, I know that both results are the same numerically.

My preference is to display the units in all my calculations to make sure I have not made mistakes.

MikeArmstrong
5-Regular Member
(To:ptc-3007326)

I do display results in every calculation I produce. I understand that the units mean something slightly different, but I don't see an issue because Mathcad allows you to choose your own units.

Mike

Chundra Ramful wrote:

In the same worksheet, I want to be able to choose which unit applies to the given result. Is this beyond Mathcad 14? What about your latest releases?

You can!

When you click in an expression a unit marker appears at the end. Put your cursor there and type the unit of your choice. If the unit balance isn't right, mathcad will put in units to make it balance.

You really can't expect mathcad to know whether you're talking about energy or torque, do you?

See attached.

Thanks Fred! Yes what you says does work ! I was able to display both units on the same worksheet. I can now justify upgrading to the latest version.

MikeArmstrong
5-Regular Member
(To:ptc-3007326)

That's why a worksheet is required with a thread on 99% of occasions.

Save the confusion.

Mike

I can't believe this was the issue. I thought you didn't Chundra didn't want to display both units in the worksheets.

Mike

PhilipOakley
5-Regular Member
(To:ptc-3007326)

The units of Torque aren't simply Newton.metres, rather it is Newton.metres per radian. That is, you need to multiply Torque by Angle turned to compute the work (Energy - joules) expended.

The fact that SI doesn't get it right from the point of view of dimenion checking for 'out of plane' lengths is a matter of regret. You sould not be able to divide a length in direction X by a length in direction Y (X-Y-Z 3d corrdinates) without introducing a some notation that indicates the cancellation of a Length dimension - that 'Unit' is Angle, with some discussion about the choice of default unit - is it the revolution (cycle) or the Radian.

There has been extensive previous discussions on the point. I also wrote http://communities.ptc.com/docs/DOC-1522 and http://communities.ptc.com/docs/DOC-1501 (variants on a theme 😉

Thank you for bringing up the subject again!

Philip

Philip Oakley wrote:

The units of Torque aren't simply Newton.metres, rather it is Newton.metres per radian. That is, you need to multiply Torque by Angle turned to compute the work (Energy - joules) expended.

The fact that SI doesn't get it right from the point of view of dimenion checking for 'out of plane' lengths is a matter of regret. You sould not be able to divide a length in direction X by a length in direction Y (X-Y-Z 3d corrdinates) without introducing a some notation that indicates the cancellation of a Length dimension - that 'Unit' is Angle, with some discussion about the choice of default unit - is it the revolution (cycle) or the Radian.

There has been extensive previous discussions on the point. I also wrote http://communities.ptc.com/docs/DOC-1522 and http://communities.ptc.com/docs/DOC-1501 (variants on a theme 😉

Thank you for bringing up the subject again!

Philip

If you are looking for work done then I agree. But when I put a wrench on a bolt and tighten it I'm doing work until the bolt stops turning. At that point I have a torque (Newton metres) without work. At that point torque and bending moment both are correctly force times shortest distance. No?

(Welcome back! Seems like I haven't seen you name in quite a while)

PhilipOakley
5-Regular Member
(To:Fred_Kohlhepp)

Fred Kohlhepp wrote:

Philip Oakley wrote:

The units of Torque aren't simply Newton.metres, rather it is Newton.metres per radian. That is, you need to multiply Torque by Angle turned to compute the work (Energy - joules) expended.

<snip>

At that point torque and bending moment both are correctly force times shortest distance. No?

Correct; It's 'No'.

The reason/problem that the two are different is that the Newton is force, which is mass * acceleration, and acceleration is length per time^2, so overall we have the confusion between Length * Lenght, and Length * Length, without any way to discriminate between the Length axes in use.

If we had Lx, Ly and Lz as independent (unit) dimensions, which clearly they are as geometry dimensions, then it would all be obvious (Proposed by Williams in ~1896 or thereby!). So we could see N_x.m_y as being Torque, while N_x.m_x as Energy. But William's ideas never got anywhere....

[Aside: the (1/2)m.v^2 kinetic energy is the same as E=mc^2 with relativity applied to the root(1-(v/c)^2) relativity term (with first order approximation), i.e. energy is the square of Length, not an area L_x.L_y ...]

The alternative to William's Lx;Ly;Lz is to monitor how often we cancel out independant terms, i.e Lx/Ly, which is "Angle", though it is used as an (in)correctness monitor. That's why we do dimensional analysis - to detect mistakes.

Historically all calculations were by hand, so could be done separately, but now with computers we no longer do those checks, especially if we code algorithms. But at least MathCAD will detect most unit/dimensions errors (not like MatLab....8-).

BUT PTC FAILS TO DISTINGUISH Nm from mN (apparently somewhere in Pro/e you had to use that convention for the difference).

PS You can define a variable called "Torque(Nm)" (using chemical notation) which can be put in the units place holder where required. You can even 'cheat and define Torque(Nm) := Joule instead of Torque(Nm) := metre.Newton <wink> . This will at least give the reader a proper understanding of the calculation result.

I'm going to have to pull up my socks.

I've never bothered to differentiate between "in lbf" and "lbf in", and I usually rely on context to decide whether we're talking about work or torque. I would point out that mathcad does handle vector notation (the standard carteasian type anyway) so we could rely on F*X for work and F x X for torque.

I do see your point.

PhilipOakley
5-Regular Member
(To:Fred_Kohlhepp)

Glad you liked my rant 😉

MikeArmstrong
5-Regular Member
(To:PhilipOakley)

I knew would get involved in this Philip

Mike

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