Interactive Volume of a Dome

[cpcfreak]

Hi to all,

Is anyone able to explain how to make an interactive 3D plot of a dome that will report volume of a dome as height varies? I'm using MathCAD 6.0e.

Regards,
Justin

[AlvaroDíaz]

On 5/25/2009 8:11:20 PM, cpcfreak wrote:
>Hi to all,
>
>Is anyone able to explain how
>to make an interactive 3D plot
>of a dome that will report
>volume of a dome as height
>varies? I'm using MathCAD
>6.0e.
>
>Regards,
>Justin

The answer could be that all mathcad worksheets are interactive, in the sense that you can parameterize your specific problem and have "interactive" answers depending on the "setup" parameters.

The notation for this kind of tasks that I see usual is using global assignaments for the "setup" variables anywhere wiht the identical assignation (tripe 😃 and let the user to changing the problems parameters.

This method is typical in mathcad and is very unusual in other programing langs (like maple, mathematica, matlab). Even they can emulate this mathcad feature is needed some kind of programation with the interface to obtain this functionality, natural in mathcad.

Other times, is enough that you highlight the assignations for your problem to make enough clear that varying this values all the problem is rewriting. This with only normal := assignments.

This is, for me, the aception of the "interactive" meaning in your request, and the usual (and easy) implementation in mathcad.

If you want an animation (as synonymous of interactive) you can read the mathcad help, but this isn't the usual technology within mathcad. For mathcad animations isn't a synonymous of interactive.

Alvaro.

[ptc-1368288]

On 5/25/2009 8:11:20 PM, cpcfreak wrote:
>Hi to all,
>
>Is anyone able to explain how
>to make an interactive 3D plot
>of a dome that will report
>volume of a dome as height
>varies? I'm using MathCAD
>6.0e.
>
>Regards,
>Justin
____________________________

Pretty easy !

Make a matrix and display 3D solid from that matrix and as you will play with some of the governing coefficient(s) in the function definition, you will see the solid change shape. You can do otherwise as you mention "volume". volume is an answer, therefore you can discretize for a range of parameters and plot a 1d bar. Not seeing the solid formula for the volume, that's about all possible suggestion(s).If the volume depends upon + 1 parameters, you then have family of solutions.

jmG

[IRstuff]

On 5/25/2009 8:11:20 PM, cpcfreak wrote:
>Hi to all,
>
>Is anyone able to explain how
>to make an interactive 3D plot
>of a dome that will report
>volume of a dome as height
>varies? I'm using MathCAD
>6.0e.
>
>Regards,
>Justin

Unclear whether M6 has the capability of accepting the slider control, but that would be another way. You would set up the slider to accommodate the minimum to maximum parameter range, and the slider position would then result in a particular volume.

TTFN,
Eden

[ptc-1368288]

>Unclear whether M6 has the capability of accepting the slider control...<<br> ________________________________

The slider was introduced at version 2001i. Apparently, later on there was a trick or add-on to accommodate 2001.

jmG

[ValeryOchkov]

See http://twt.mpei.ac.ru/MCS/Worksheets/cono-it.xmcd
Val
http://twt.mpei.ac.ru/ochkov/v_ochkov.htm

[ptc-1368288]

On 5/25/2009 8:11:20 PM, cpcfreak wrote:
>Hi to all,
>
>Is anyone able to explain how
>to make an interactive 3D plot
>of a dome that will report
>volume of a dome as height
>varies? I'm using MathCAD
>6.0e.
>
>Regards,
>Justin
____________________________

Not clear what you want !

The dome could be: spheroid, oblate/prolate ellipsoid and many more. The point is that if you want to know the volume of the liquid in a horizontal tank, you are confronted to only measuring the level of the liquid. The way we do in Process Control & Instrumentation, we calculate 'C ', a correction factor for Pi and we get the volume. We have a work sheet showing the cross section of the tank and the volume filled depending upon the measured level. This one sheet is not attached because you don't give enough details.

"Interactive" might mean something to you but what does it mean ? The attached "Dome" is created 11 saved 6. In case it does not open, the "Segment" is an image of the sheet. That should guide you to be more specific about what you want or what you think you might want and what can be done quick from various pieces available.

All what that means is that if you don't come back with a project description that can be interpreted, your visit to this collab will not result in more material usable or suggestions. Very many "Dome problems" were done quick. Eventually, all what you need might be in this attachment.

Enjoy, but: please do not hesitate for more !

jmG

[cpcfreak]

Hi jmG,

Thanks for the files, they are a great help.

Regards,
Justin.

[ptc-1368288]

On 5/26/2009 7:53:30 PM, cpcfreak wrote:
>Hi jmG,
>
>Thanks for the files, they are
>a great help.
>
>Regards,
>Justin.
_______________________________

Good thing you have specified more in your previous reply. The "interacitivity" resumes to plugging the relevant function into a triple integral and some of the limits. That will give the volume of the dome .

jmG

[cpcfreak]

Hi People,

Thanks for the feedback, I need to look into this a bit more. For my initial requirements I had made the assumption that the dome would be created from the intersection of a plane with a sphere. But as usual it may be more complex than that.

A good analogy would be calculating the volume of a radio telescope dish, which is of course parabolic. Using a slider to vary the depth of the dish while the diameter remains is fixed means I may have to upgrade!

To model accurately I need to create a curve for a known profile that may be spherical, elliptical, parabolic or hyperbolic. Then use a rotation to create a surface model from which I would have to calculate the volume.

In general the domes or dishes I have to model have very low profiles, usually the height is less than half the diameter.

Thanks for all your help.

If anyone has anything else to offer it will be greatly appreciated. Your experience is invaluable.

Regards,
Justin.

[TomGutman]

The plot does not give you the volume, it is just a visual. The volume of a figure of rotation as you describe is a simple integral, that, given the profile as a function, Mathcad can evaluate numerically. For simple enough curves it can be evaluated symbolically. For example, for a paraboloid of height h and with radius r the volume is just ½πhr². Spherical caps are also easy to calculate.

Interactive can mean many different things. I don't know what facilities are in MC6 (it's rather old). If it supports scripted components, a slider is a possible way of varying a parameter. But a simple assignment that can be edited is another way, supported by all Mathcad versions.
__________________
� � � � Tom Gutman

[cpcfreak]

Thanks to everyone,



Your help is greatly appreciated and has put me on the right track. Once I'm happy with the result I'll post a copy of my final worksheet here for others to use.



Regards,

Justin.