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14-Alexandrite

## Working with and evaluating volumes

Morning to all,

So a few of you have seen I have had varying questions about MC's abilities in the last 24 hours which have lead me to my ultimate question on working with and evaluating volumes.

I am looking to see if MC (and if not taking recomendations for other software) can help me in my next quest.

I am looking at defining a 3D shape (the underwater profile of a ship) and then being able to evaluate the shape i.e. what is its volume, where is its centroid, calculate moments about its centreline etc.

The shape I have in mind can be defined in one of two ways but in both a number of 'slices' of the ship's profile are defined usually in terms of x,y,z ordinates to give a number of 2D profiles either working from front to back or from top to bottom. I know that I could plot each 2D 'slice' in MC and could then evaluate using integration but is it possible to 'put these together' and evaluate the 3D shape in a similar method?

Or is there a better software out there for this? I thought of 3D CAD type softwares but don't know if these have the mathmatical caability of MC (It has been years since I have used CAD software but don't mind getting back into it).

Any thoughts or advice warmly welcomed.

A

PS to give a visual idea of what I am working with below is a google image of the sort of thing where by a number of vertical 'stations' are defined for a ship and I would need to essentially integrate them all to give a volumetric property.

1 ACCEPTED SOLUTION

Accepted Solutions
21-Topaz I
(To:awibroe)

How to intergrate along the vessel to get total volume.

Input is the station distances as x ordinates.

Input is the station bouyancy areas as y ordinates.

Integration is total volume.

Trick is to put a smooth spline through the points.

You can then integrate the interpolation of the spline.

Have enclosed MC14, PDF, and data file

Calculation with vessel on the roll requires a different approach but should be possible.  DelfShip free gives the metacentric height.  The difficulty is the ship on the roll should still have the same bouyancy volume.

30 REPLIES 30
21-Topaz I
(To:awibroe)

MathCad is good software.  You could create a worksheet that does as you wish.  Refer the following which is a mathcad sheet that does just that.

https://ocw.mit.edu/courses/mechanical-engineering/2-082-ship-structural-analysis-design-13-122-spring-2003/calendar/notes_10_shear_bending_fixed.pdf.   Poke around this websight and you will get a few more examples.

But it is not necessarily the best for everything.  In terms of ship and vessel hulls I recommend the following.  It is free!

http://www.delftship.net/DELFTship/index.php/delftship/delftship-free

DELFTship™Free is a fully functional 3D hullform modeling program perfectly suited for students, home users or anyone else with an interest in ship design. And as the name already implies it's completly free of charge!

Model any type of hull. DELFTship™Free is limited to hulls that are symmetrical with respect to the centerplane.
Perform basic hydrostatic and resistance calculations.
View, print and export the traditional 2D linesplan view which is calculated from the 3D model (shaded or black & white).
Use the Lackenby hullform transformation to automatically adjust hull parameters such as displacement and longitudinal center of buoyancy to specified values while maintaining fairness of your model.
Export to various 2D/3D file formats (.STL, .DXF, .OBJ, .GHS etc.)
View plate expansions.

21-Topaz I
(To:awibroe)

This is a Mathcad 14 file.  It calculates the bouyancy volume and longitudinal centre of gravity of a real ship at given draft of 3.8m.

I did it to check the results of Delf ship free software.  The Mathcad results are the same.

The file reads a DXF file that has been exported from Delf ship.  The DXF file are the vertical stations of a vessel hull 31 of them at 2 m apart for the 62 m long vessel.  DXF files are single lines of text and can be read and interpreted by MathCad.   The calculations are made a bit more complex as some of the station lines start at keel and go to deck, while some start at the deck and go to keel.  Splines are used through DXF points to perform intergrations.

The Mathcad reads the DXF file to obtain cordinates of the hull for the calculations.  A jpg of the DXF shows the stations and the hull.

Delf is far simpler to use and produces the same results.

14-Alexandrite
(To:terryhendicott)

Hi Terry,

I have looked at the MC14 file. Would it theortically be possible to do the same in Prime? I am slightly reluctnat to do all of this in MC 15 as I have not used it to date. I presume you have it in a 14 file as that is what you had when you did the work?

Also, how sophisticated can you get with this? i.e. You have shown that you can calculate underwater volume i.e. buoyancy mass and longitudinal position of centre of buoyancy.

Is it possible to do experiments i.e. see how buoyancy shifts with roll? I am thinking that you could build GZ curves is you are able to observe how the centre of buoyancy moves as the vessel heels?

Thanks,

Andy.

21-Topaz I
(To:awibroe)

Simple station example in Mathcad Prime 4

14-Alexandrite
(To:terryhendicott)
Hi,

All this looks super impressive and will look at later today in more detail. I don't have Prime 4 but feel like I'm going to need to get the express version to open files people share.

Excellent to know there is some free software for ships specifically out there.

I'll be back soon.

Andy.
21-Topaz I
(To:awibroe)

Hi Andy,

Here is a pdf of the Mathcad 4 sheet that is a calculation at one station of a ships hull.  it is an integration vertically

14-Alexandrite
(To:terryhendicott)
Terry,

So I have looked through the PDF and I'm daily comfortable with the calculations on the 2d front. I'm now trying to follow how you've integrated along the ship's centreplane I.e. To get the actual values in the 3D sense ie vertical and longitudinally centre of buoyancy?

Cheers

Andy
21-Topaz I
(To:awibroe)

How to intergrate along the vessel to get total volume.

Input is the station distances as x ordinates.

Input is the station bouyancy areas as y ordinates.

Integration is total volume.

Trick is to put a smooth spline through the points.

You can then integrate the interpolation of the spline.

Have enclosed MC14, PDF, and data file

Calculation with vessel on the roll requires a different approach but should be possible.  DelfShip free gives the metacentric height.  The difficulty is the ship on the roll should still have the same bouyancy volume.

14-Alexandrite
(To:terryhendicott)
Terry,

So this could in theory be done with my own tabulated data for xyz ordinates?

Definitely going to be looking into DelfShip.

Thanks,

Andy
14-Alexandrite
(To:awibroe)

Terry,

That last PDF is really really usefu!

2 follow up questions, is there an intellegent way to integrate each of the stations at once (or is it best to calculate each station area first)? So by this I mean if I have all the data in a matrix for the various point of the hull form (as you have done so by outputting this from a 3rd party softward DelftShip) is there some clever programming I can use to integrate the lot or do I have to work out each station area manually and then input these into a second data set and integrate them all to get the volume as you have done?

What is the CAD issue that would need to be sorted to show vertical centre of buoyancy?

Cheers, really really good stuff!

Andy

21-Topaz I
(To:awibroe)

What is the CAD issue that would need to be sorted to show vertical centre of buoyancy?

This is a problem with the datset only not with MathCad.

The flat bottom hull is not really flat!
It starts at 0.0009 m (0.9 mm) at keel. Drops down to 0.0008 (0.8mm) at halfway point before coming up.
This is only a difference of 0.1 mm but it plays havic with interpolation.

linterp(vx,vy,x) vx must be increasing ordinates. the 0.1 mm drop fails this condition.

So a different method is used in the calculations for the large ship.
I have used your x, y coordinates from one of your posts.
I have switched x and y for no reason other than using 3.8 for waterline.

This is the method you would need for G_Z curves and roll of vessel.

Enclosed is MC14 and PDF

21-Topaz I
(To:awibroe)

So this could in theory be done with my own tabulated data for xyz ordinates?

Yes.

2 follow up questions, if I have all the data in a matrix for the various point of the hull form (as you have done so by outputting this from a 3rd party softward DelftShip) is there some clever programming I can use to integrate the lot or do I have to work out each station area manually and then input these into a second data set and integrate them all to get the volume as you have done?

No. there are two reasons you need the volumes at each station.

1. You need this station data to calculate the shear and bending moments along the vessel while floating. Wave depth along the vessel may also need to be incorporated.
2. The calculation of centroids needs the values at each station.

You can get the programmimg to keep track of the variables it does not need to be manually done.

14-Alexandrite
(To:terryhendicott)

Hi Terry,

Sorry I have been away this week allot.

Plugging back into this and looks good. So in the example you have shown how to calculate a station area and the (traditional) y bar and z bar of the centre of buoyancy for that station i.e. the distance from centreplane and the distance from the keel of the centre of buoyancy.

How would you then integrate all the station properties together. i.e. I am comfortable with the approach to calculating a single station but not how to bring these together and find where the centre of buoyancy is within the entire ship.

Once this is done, I guess the next 'interesting' thing would be to consider a waterline at an angle i.e. the ship in a roll. I have some ideas on this by defining the underwarter shape of each station by defining the an intersection at either side of the ship and the new waterline.

Thanks,

Andy.

21-Topaz I
(To:awibroe)

The above web page directs you to free (both download, registration, and use) program for vessel hydrodynamics.
It goes further than DefltShip in that it does calculate the G-Z curves for you.
I recommend you look at this software. It finds the hydrodynamics without sections.
It must be possible to calculate volumes and centroids from the bezier and spline curves that make up the hull.

The vertical centroid of the whole ship is found as follows. My earlier sheets have not got to this stage yet.

At each station find the vertical centroid (with reference to the same datum. Traditionally the keel.)
Multiply each centroid by the "volume" at that station.
You can integrate the previously area calculations from halway between stations on each side of station under consideration to get the volume at that station.
Each station: say station 5, is vertical centroid at 5 x intergral of spline through areas from 4.5 to 5.5.
Once you have all these station products along the vessel add them up to a total and then divide by the total volume.
What you are left with is the centroid of the total volume.

I have enclosed MC14/15, PDF, that rolls one section to outline the steps needed to program this all along the vesssel.

14-Alexandrite
(To:terryhendicott)
Hi Terry,

I thought of something similar over my lunch.

If you have the z distance for each station I.e. The distance from keel to centre of buoyancy at each station you could, in MC, multiply each of these by the area of the buoyancy of this station to get a value of m^3 for each station.

You could then apply a spline to these as in your previous examples and integrate along the ship to get a value in m^4.

If you then divide the result by the volume you get a value on m^1 which I presume is the vertical height above keel of the total buoyancy.

At least I think this holds true.

Andy.
23-Emerald III
(To:awibroe)

Don't forget the 't' in DelftShip. I guess the tool was named after the Dutch city Delft...

Luc

14-Alexandrite
(To:LucMeekes)

Well noticed Luc!

I have started experimenting with this method of interpolating data.

What would I have to do to visually see (i.e. in a plot) the interpolated line created by the spline?

Andy

24-Ruby V
(To:awibroe)

@awibroe wrote:

What would I have to do to visually see (i.e. in a plot) the interpolated line created by the spline?

Maybe this:

21-Topaz I
(To:awibroe)

I will work through the responses. I am in a different time zone so your patience is appreciated.

So this could in theory be done with my own tabulated data for xyz ordinates? Yes. You can do the whole vessel like this.

Definitely going to be looking into DelftShip. I forget the t in delft myself.

Is there an intellegent way to integrate each of the stations at once (or is it best to calculate each station area first)?

I do not know a way to do it all at once. Only know how to do it per station then intergrate this.

What would I have to do to visually see (i.e. in a plot) the interpolated line created by the spline?

Have enclosed an MC14, PDF, and data. Have plotted it every 0.33 metres compared to input data every metre.

14-Alexandrite
(To:awibroe)
All,

Special thanks to Terry for all the input.

Cheers

A
24-Ruby III
(To:awibroe)

I think we can use same data and the ccpline function

14-Alexandrite
(To:ValeryOchkov)
Valery,

How do you mean?

Andy
24-Ruby III
(To:awibroe)

@awibroe wrote:
Valery,

How do you mean?

Andy

I think there is a lot of spesial programs for the ship calculation.

But we can do someone in Mathcad. For education, for example.

See please one my article on this subject for the journal "IT in schools"

http://twt.mpei.ac.ru/ochkov/Ship.pdf

14-Alexandrite
(To:ValeryOchkov)

Valery,

Looks like a good paper. Do you have a copy in English text?

My problem is I understand the underlying principles of Ship Science but want to learn more of how to perform these in MathCAD.

Cheers,

Andy.

24-Ruby III
(To:awibroe)

@awibroe wrote:

Valery,

Looks like a good paper. Do you have a copy in English text?

My problem is I understand the underlying principles of Ship Science but want to learn more of how to perform these in MathCAD.

Cheers,

Andy.

Thanks, Andy!

Only seven first studies of my book "Pysical and mathematical studies with Mathcad and Internet" are translated into English.

This study about ships has a number 23. The last is 30!

Can you translate it and help my?

Val

21-Topaz I
(To:awibroe)

Translation of paper in google translate up to Fig 5.

You just use the google translate from Russian to English one sentence at a time.  Lots of selecting text, cutting, and pasting.  It gives enough to get the gist of the paper.

It is about calculation of a small ballasted ship model.  I will let you translate the rest.

PDF enclosed.

24-Ruby III
(To:terryhendicott)

Thanks!

But I need edited english google tranllation by help of english language holder.

I can pay for it - not only money but by present - see for example

14-Alexandrite
(To:ValeryOchkov)
Valery,

I'll have a go at translating as an English Naval Architect Student for sure.

Terry, do you think my proposed approach to finding z bar would work?

Andy
21-Topaz I
(To:awibroe)