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Calculating the volume of Burial Urns

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Forum topic by Jack Lewis posted 08-15-2018 05:18 PM 1165 views 1 time favorited 16 replies Add to Favorites Watch
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Jack Lewis

334 posts in 1249 days


08-15-2018 05:18 PM

I have racked my brain to simplify being able to change the volume in cubic inches of a known urn drawing to desired size. I have utilized the formula (cylinder) of R^s x Ht x pi as the basis of my calculations. I determine the average radius by dividing 1/2 the area by the height. I could use the whole area but that would result in the diameter vice radius. My cad program has a plotted area function. I change the scale of a drawing somewhat and recalculate over and over until I narrow toward the target size I want. I have devised a spreadsheet to calculate for me. My reason for this post is to solicit someone to QC the formulas and general idea.

My problem is the SS is “Works” and most people have Excel. Can Excel import Works?

Would some one be kind enough to tackle this task?
If so PM and I will (attempt) to send it to you along with my notes.

And YES, I am designing and making several models and styles.

-- "PLUMBER'S BUTT! Get over it, everybody has one"


16 replies so far

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Mr_Pink

136 posts in 542 days


#1 posted 08-15-2018 05:40 PM

I don’t know anything about CAD or Works; however, if Excel can’t read the native spreadsheet format directly, you could output as a delimited text file and read that into Excel.

I also don’t think you’re finding the radius the right way.

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mpounders

894 posts in 3066 days


#2 posted 08-15-2018 07:44 PM

You could just use an online calculator to get your answer!

-- Mike P., Arkansas, http://mikepounders.weebly.com

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TheFridge

10499 posts in 1657 days


#3 posted 08-15-2018 08:17 PM

^yup

PiR2 for area of the circle times height.

Or use an online calculator which much easier

-- Shooting down the walls of heartache. Bang bang. I am. The warrior.

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Jack Lewis

334 posts in 1249 days


#4 posted 08-15-2018 08:35 PM

Thanks for the replies. Yes I have the formula for a cylinder/urn/etc. I am trying to calculate what amount of increase/decrease to what I have to re dimension my existing plan without doing the math/calculator thing for a guesstimate. The problem is just scaling the plan, for example 110%. does not increase the volume just 10%. Thus my reason for a SS chart to get closer on the first re scale.

-- "PLUMBER'S BUTT! Get over it, everybody has one"

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sras

4914 posts in 3300 days


#5 posted 08-15-2018 08:42 PM

I think I understand:

1. When I look at your urns they are not cylinders.

2. The inside volume is a more complex shape.

3. Your method of using a cross section of the inside volume and focusing on half makes sense.
—> a. Calculating the area of a half cross section and dividing by the height gives you a representative radius.
—> b. While representative, this radius estimate will not be accurate, but close.
—> c. Using that representative radius and the formula for the volume of a cylinder will also be close, but not accurate.

Questions:

1. How accurate do you need to be?
—> a. Is an extra cubic inch (or 3) okay?

2. Are you trying to determine the volume before making the urn or after it is completed?

Suggestions:

1. I would suggest breaking the cross section into layers and using an average radius for each layer will be more accurate.
—> a. More layers will be more accurate.

2. You could try the layering technique a couple times with decreasing layer height (more layers) and see how the answer converges.
—> a. This may help you determine how many layers are required for your desired accuracy.

-- Steve - Impatience is Expensive

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HokieKen

6557 posts in 1309 days


#6 posted 08-15-2018 09:09 PM

What CAD program do you have? I use Solidworks and for similar things, I will enter dimensions as functions of whatever it is that I want to be able to adjust on the fly. So in this case, I would dimension the height and diameter as functions of a desired volume (needing a second relation of course to fully define the equation set) then enter the desired volume into the model data. The height and diameter are then populated automatically. Similar can be done with non-cylindrical shapes. It just takes a good deal more work on the front end.

-- Kenny, SW VA, Go Hokies!!!

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Lazyman

2556 posts in 1558 days


#7 posted 08-15-2018 09:43 PM

For a reasonable estimate I would divide it into rings and measure the volume of those rings as small truncated cones using a calculator such as this. All you need is the radius of the ends of each ring and the height of that ring.

-- Nathan, TX -- Hire the lazy man. He may not do as much work but that's because he will find a better way.

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Lazyman

2556 posts in 1558 days


#8 posted 08-15-2018 10:27 PM

One other thought. If you already know the volume of a given shape and you know the volume you want it to be, you should be able to compute the scale up/down factor. If for example you scale up the entire shape by a factor of 2, the volume will increase by the cube of the scale factor or 8. If you scale it down by 20% (factor of 0.8), you can compute the new volume with the factor of 0.8 cubed or 0.512. So if your known volume is 100 and you want it to be 120, you take the cube root of 1.2 or 1.06. Note that that this probably does not take into account the wall thickness of the vessel. It probably assumes that the thickness (and volume) of the wall increases proportionally but I think that the interior volume should scale correctly.

And if I am thinking about this right, you can also scale in only 2 dimensions (radius or diameter for example) and use the square and square root. If you scale in a single dimension (height for example), I think that you can simply multiply the volume by the factor directly.

-- Nathan, TX -- Hire the lazy man. He may not do as much work but that's because he will find a better way.

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pete724

68 posts in 980 days


#9 posted 08-16-2018 02:41 AM

If for example you scale up the entire shape by a factor of 2, the volume will increase by the cube of the scale factor or 8.

Lazyman has the right stuff as the line above.

This is sometimes called the “sqare-cube” Law.

If you “double” one of the linear sizes(length, width or height) you Square(double times double in this case or 4x)the surface area and “cube”(2×2x2 – factor of eight) the volume!

If you tripled one of the linear legnths, you would increase the surface area 9 times and the volume increase 27 times.

Is that clear enough?

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Lazyman

2556 posts in 1558 days


#10 posted 08-16-2018 02:18 PM

If you “double” one of the linear sizes(length, width or height) you Square(double times double in this case or 4x)the surface area and “cube”(2×2x2 – factor of eight) the volume!
If you tripled one of the linear lengths, you would increase the surface area 9 times and the volume increase 27 times.

- pete724

Not sure you said that right. I think that the cube of the factor only applies if you scale all 3 dimensions by the same factor. If you scale up a single dimension, you can simply multiply the volume by the scale factor to get the new volume. If you have a cylinder that is 3” tall and 3 inches in diameter, it has a volume of 21.2 cubic inches. If you double the height, it is the same as adding a second 3” tall 3” diameter cylinder on top so it simply doubles the volume to 42.4 because you changed only one dimension. If you triple the height only, the new volume is 3 times the original, not 27 times. If you double the diameter (but not the height), that is really the same as doubling 2 dimensions so the area of a cross section will increase by 4 times and volume of the scaled up cylinder is 84.8 which is the same as multiplying the original volume (21.2) by the square of the scale factor (4).

-- Nathan, TX -- Hire the lazy man. He may not do as much work but that's because he will find a better way.

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Lazyman

2556 posts in 1558 days


#11 posted 08-16-2018 02:42 PM

Jack, One more thing…Google Sheets is a free online spreadsheet that is mostly compatible with XL and should also able to import from other spreadsheets such as MS Works. You probably have to setup a Google ID to use it but if you already use Gmail, you are ready to go. It is pretty handy for sharing and collaborating on spreadsheets. If you need some help setting up any of these calculations in spreadsheet form, just PM me.

-- Nathan, TX -- Hire the lazy man. He may not do as much work but that's because he will find a better way.

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clin

947 posts in 1167 days


#12 posted 08-17-2018 03:13 AM


Not sure you said that right. I think that the cube of the factor only applies if you scale all 3 dimensions by the same factor. If you scale up a single dimension, you can simply multiply the volume by the scale factor to get the new volume. If you have a cylinder that is 3” tall and 3 inches in diameter, it has a volume of 21.2 cubic inches. If you double the height, it is the same as adding a second 3” tall 3” diameter cylinder on top so it simply doubles the volume to 42.4 because you changed only one dimension. If you triple the height only, the new volume is 3 times the original, not 27 times. If you double the diameter (but not the height), that is really the same as doubling 2 dimensions so the area of a cross section will increase by 4 times and volume of the scaled up cylinder is 84.8 which is the same as multiplying the original volume (21.2) by the square of the scale factor (4).

- Lazyman

Lazyman has it right. Though I had to re-read it a few times to understand it.

I’ll restate in my own way. Assuming you have a known volume for some size of urn you already have. Call it Vold.

The new volume is proportional to the change in height. Vnew is given by.

Vnew = Vold x Kh

Kh = Height new / Height old

If you are changing the diameter (width), the volume changes by the square of the change in diameter. As Lazyman pointed out, you are effectively changing width and depth (2 dimensions). If you only changed one of these dimensions, it would become elliptical and not be circular.

Vnew = Vold x Kd^2 = Vold x Kd x Kd (squaring Kd)

Kd = Diameter new / Diameter old

If you are changing both, it make no difference what order you apply these in. You can just say:

Vnew = Vold x Kh x Kd^2

If both the height and width change by the same proportion ( K = Kh = Kd) then you have:

Vnew = Vol x K^3 = Vold x K x K x K (K is cubed).

Note: These of course are based on the interior dimension, not the exterior.

-- Clin

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pete724

68 posts in 980 days


#13 posted 08-17-2018 05:07 AM


Not sure you said that right. I think that the cube of the factor only applies if you scale all 3 dimensions by the same factor. If you scale up a single dimension, you can simply multiply the volume by the scale factor to get the new volume.
- Lazyman

You are correct again. I didnt say it right!

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whiteshoecovers

63 posts in 1255 days


#14 posted 08-17-2018 02:28 PM

If you make your design in google sketchup, it will calculate volume for you.

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Lazyman

2556 posts in 1558 days


#15 posted 08-17-2018 04:22 PM



If you make your design in google sketchup, it will calculate volume for you.

- whiteshoecovers

I’ve never done that in Sketchup but that was sort of what prompted my post #8 above. If you know the volume, you can use the SU scale tool to grow the entire object by a certain factor. By using my calc method in #8, I think that you can compute the factor to use.

-- Nathan, TX -- Hire the lazy man. He may not do as much work but that's because he will find a better way.

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