# Thread: Seeking a specific formula to allow for materials shrinkage

1. ## Seeking a specific formula to allow for materials shrinkage

My maths education didn’t really prepare me to even begin to try to figure this one out!

I have a material that shrinks 15% as it dries. I have objects that need to be molded in this material, and they must end up at a specific size. I am making a set of molds for the objects, and I need to account for the shrinkage of the mold material to make the final product end up the right size. For example, If I make the mold at 2” wide to start, the wet material will go into the mold, and then will come out of the mold and dry, and then end up at 1.7” wide. I need to make the mold slightly bigger than 2” for it to come out dry at 2”. If I have a part that needs to end up at 6.75” wide, then I need to make it slightly bigger than 6.75” wide for it to come out at the correct width. I just don't know how to figure out how to do this.

I would like to find a maths formula that allows me to enter a value for the finished size of an object, allowing for 15% shrinkage from the original condition, that will give me the starting size for the mold, no matter what my finished size is. All I know is, the material shrinks at a standard amount of 15%.

This isn’t the kind of percentage or algebra maths I am familiar with.

For some of you, this will be the easiest thing in the world. For me, not so much. All my maths teachers wrote problems on the board, and then the answer to that problem, without ever putting anything that goes in between on the board. When asked what the steps were, I was always told "you should know how to do this already" I got suspended from school once for telling this one teacher that it was his job to teach us the stuff in the middle, not just how to write a problem and answer, and expect us to "already know" how to go from one to the other. No wonder so many people don't like maths!

2. ## Re: Seeking a specific formula to allow for materials shrinkage

If the assumption is that the material shrinks in the single dimension, width, then a formula to solve your question would be:

length needed * 0.85 = length desired
which can be rewritten by multiplying both sides by 100/85 (note 0.85 = 85/100 and 85/100 * 100/85 = 1)
length needed = length desired * 100/85

ex. Desired width = 6.75'', hence initial width needed = 6.75'' * 100/85 = 675 / 85 which is 7.9412''

However, I would caution that I would make no assumption that the rate a material shrinks is in a single dimension. I would assume instead the area (if 2D object) or volume (if 3D object) shrinks at a uniform rate, and additional calculations would be required to determine the rate a single dimension (such as width) decreases as the area/volume decreases

3. ## Re: Seeking a specific formula to allow for materials shrinkage

Originally Posted by LostX
>I have a material that shrinks 15% as it dries.
>For example, If I make the mold at 2” wide to start, the wet material will go into the mold,
>and then will come out of the mold and dry, and then end up at 1.7” wide.

r = 1 - 15/100 = .85 (shrinkage factor)
x = 2 (mold at start)
f = ? (mold after shrinkage)

f = x * r
f = 2 * .85 = 1.7

>If I have a part that needs to end up at 6.75” wide, then I need to make it slightly bigger
>than 6.75” wide for it to come out at the correct width.

r = 1 - 15/100 = .85 (shrinkage factor)
x = ? (mold at start)
f = 6.75 (mold after shrinkage)

x = f / r
x = 6.75 / .85 = ~7.9412

" For some of you, this will be the easiest thing in the world. For me, not so much. All my maths teachers wrote problems on the board, and then the answer to that problem, without ever putting anything that goes in between on the board. When asked what the steps were, I was always told "you should know how to do this already" I got suspended from school once for telling this one teacher that it was his job to teach us the stuff in the middle, not just how to write a problem and answer, and expect us to "already know" how to go from one to the other. No wonder so many people don't like maths!"

Li'l Johnny's 1st day in school:
Teacher: Johnny, what's 20 times 4?
Johnny : dunno teacher
Teacher: Johnny, if your father gives you 20 dollars allowance per week and owes you for 4...
Johnny: Stop! He owes me 80 bucks!!!
All clear?

4. ## Re: Seeking a specific formula to allow for materials shrinkage

If the assumption is that the material shrinks in the single dimension, width, then a formula to solve your question would be:

length needed * 0.85 = length desired
which can be rewritten by multiplying both sides by 100/85 (note 0.85 = 85/100 and 85/100 * 100/85 = 1)
length needed = length desired * 100/85

ex. Desired width = 6.75'', hence initial width needed = 6.75'' * 100/85 = 675 / 85 which is 7.9412''

However, I would caution that I would make no assumption that the rate a material shrinks is in a single dimension. I would assume instead the area (if 2D object) or volume (if 3D object) shrinks at a uniform rate, and additional calculations would be required to determine the rate a single dimension (such as width) decreases as the area/volume decreases

Without going into too much detail, the material will shrink over all dimensions. I don't know of anything that only shrinks in one dimension. I think this may be a situation where too much focus on one detail is derailing the end result.

Suffice it to say, I recently saw a video of an object made with this material, and it was in fact 15% smaller than the original from which the mold was made. The two were side by side, and measurements were given.

This is just like the example given in the "How It's Made" video of lost-foam aluminum investment casting. The narrator plainly stated that the foam blank had to be 11% larger, because the aluminum shrinks as it solidifies and cools.

My material shrinks 15%

I plugged in a few numbers, and either I don't understand how this works, or something else is wrong. Most likely the former.

If I multiply my mold-form dimensions by .85. then the actual piece will end up smaller than that. Not larger.

I'm starting with a piece that is 1.5" wide, 3.8" tall, and .25" deep. If I make the mold with that multiplier of .85, then the piece that comes out of it will be 1.275" W x 3.23" H x .212" deep. And then the material shrinks by 15%, and will be even smaller than that. This is not what I was going for.

I have an original piece that is 1.5" wide, 3.8" tall, and .25" deep. I need to make it 15% bigger. I don't understand how to do that.

Call me stupid, but it would seem that the mold would have to be something like 1.75" x 4.5" x .4" deep (I made those numbers up)

How do I figure out how to calculate how much bigger this piece is? I have about 14 more pieces coming that I will have to replicate by this method, so an easy formula is what is needed.

5. ## Re: Seeking a specific formula to allow for materials shrinkage

Originally Posted by DenisB
All clear?
If it were any clearer, I'd need a seeing-eye dog to find it.

I'm afraid that I simply don't understand any of that. It may as well be Attic Greek.

6. ## Re: Seeking a specific formula to allow for materials shrinkage

If the assumption is that the material shrinks in the single dimension, width, then a formula to solve your question would be:

length needed * 0.85 = length desired
which can be rewritten by multiplying both sides by 100/85 (note 0.85 = 85/100 and 85/100 * 100/85 = 1)
length needed = length desired * 100/85

ex. Desired width = 6.75'', hence initial width needed = 6.75'' * 100/85 = 675 / 85 which is 7.9412''

However, I would caution that I would make no assumption that the rate a material shrinks is in a single dimension. I would assume instead the area (if 2D object) or volume (if 3D object) shrinks at a uniform rate, and additional calculations would be required to determine the rate a single dimension (such as width) decreases as the area/volume decreases
I wrote a nice, long reply explaining that the numbers here don't work out that way for me. I don't know why it didn't post.

The piece I have is 1.5" wide. I need to make the mold BIGGER, not smaller, because the molding medium shrinks.

My example was, if I use that .85 multiplier, my part for the mold comes out smaller, and then when that gets molded, and dries, it comes out even smaller then.

1.5 * .85 = 1.275 That's smaller. I can't make the mold part smaller and then have it turn out even smaller. I have to know how much bigger to make it.

Call me stupid, but I just don't get it.

7. ## Re: Seeking a specific formula to allow for materials shrinkage

r = 1 - 15/100 = .85 (shrinkage factor)
x = ? (mold at start)
f = 6.75 (mold after shrinkage)

x = f / r
x = 6.75 / .85 = ~7.9412
.................................................. ..........

You want to end up with 6.75

The shrinkage is 15%

What is beginning size?

Step1: 100% - 15% = 85%
Step2: 6.75 / 85 = .0794
Step3: .0784 * 100 = 7.94

So if you start with approximately 7.94, you'll end up with 6.75 : got that?

8. ## Re: Seeking a specific formula to allow for materials shrinkage

Originally Posted by LostX
I wrote a nice, long reply explaining that the numbers here don't work out that way for me. I don't know why it didn't post.

-Dan

9. ## Re: Seeking a specific formula to allow for materials shrinkage

Originally Posted by LostX
I wrote a nice, long reply explaining that the numbers here don't work out that way for me. I don't know why it didn't post.

The piece I have is 1.5" wide. I need to make the mold BIGGER, not smaller, because the molding medium shrinks.

My example was, if I use that .85 multiplier, my part for the mold comes out smaller, and then when that gets molded, and dries, it comes out even smaller then.

1.5 * .85 = 1.275 That's smaller. I can't make the mold part smaller and then have it turn out even smaller. I have to know how much bigger to make it.

Call me stupid, but I just don't get it.
I've already told you (see post#7) that to make it bigger, you DIVIDE:
1.5 DIVIDED BY .85 = 1.7647...

AND STOP calling yourself stupid!!!

10. ## Re: Seeking a specific formula to allow for materials shrinkage

Originally Posted by LostX
Without going into too much detail, the material will shrink over all dimensions. I don't know of anything that only shrinks in one dimension. I think this may be a situation where too much focus on one detail is derailing the end result.
For my first answer, I made an assumption that the information given was that for the object you were molding, that after cooling, a single dimension shrink at 15%
It is now clear that the given value for shrinkage refers to the total volume of the mold. ie. new volume X = initial volume V * 0.85

You cannot multiply each dimension by 0.85, as you've stated.

Restated question:
Given a mold in the shape of a rectangular prism of length l, width w, height h.
Given an initial volume V
If the new volume X is V * 0.85 due to shrinkage as it dries,
And given that length, width, and height shrink uniformly at the same rate, as the mold shrinks.

1) What are the new dimensions of l, w, and h after drying? (call these L, W, H respectively)
2) What must l, w, h, be initially to get desired values L, W, H

For #1

V = l*w*h
X = L*W*H

X = 0.85 * V
L*W*H = 0.85 * l * w* h
If again it's true that l,w,h shrink uniformly, then we can take the cube root of 0.85 = 0.94726823718 = m and redestribute.

ie. L*W*H = m*l * m*w * m*h and L = m*l, W = m*w, H = m*h

For 2,
l = (1/m)*L
w = (1/m)*W
h = (1/m)*H
where 1/m = 1.055667191984587

Application
I want a piece 1.5" wide, 3.8" tall, and .25" deep

1.5 * 1.055667191984587 = 1.58350078797688
3.8 * 1.055667191984587 = 4.011535329541431
0.25 * 1.055667191984587 = 0.2639167979961468

My initial mold is 1.58350078797688 * 4.011535329541431 * 0.2639167979961468
Initial Volume V = 1.67647058827
Result Volume X = 1.42500000003 (due to intermediate rounding), and 1.425 = 1.5*3.8*.25

11. ## Re: Seeking a specific formula to allow for materials shrinkage

Here's the problem as stated in post#1:
I have a material that shrinks 15% as it dries.

I have objects that need to be molded in this material, and they must end up at a specific size.

I am making a set of molds for the objects, and I need to account for the shrinkage of the mold
material to make the final product end up the right size.

For example, If I make the mold at 2” wide to start, the wet material will go into the mold,
and then will come out of the mold and dry, and then end up at 1.7” wide.

I need to make the mold slightly bigger than 2” for it to come out dry at 2”.

If I have a part that needs to end up at 6.75” wide, then I need to make it slightly bigger
than 6.75” wide for it to come out at the correct width.

I would like to find a maths formula that allows me to enter a value for
the finished size of an object, allowing for 15% shrinkage from the
original condition, that will give me the starting size for the mold,
no matter what my finished size is.
All I know is, the material shrinks at a standard amount of 15%.
Clearly, the ONLY question is:
Knowing the ending size, how is the beginning size calculated if the shrinkage rate is 15% ?

E = ending size
E / .85

If E = 6.75", then 6.75 / .85 = ~7.94

NOTHING ELSE is required or has been asked.

12. ## Re: Seeking a specific formula to allow for materials shrinkage

There was ambiguity in the original question when the original poster stated "I have a material that shrinks 15% as it dries."
I originally interpreted this as you did that it was given the width becomes 15% smaller with no regards to other dimension.

However, if it's meant that the volume of the mold shrinks by 15%, and each dimension shrinks uniformly, my answer above stands.

It is clearly wrong to assume all sides shrink by 15% we have new dimensions (0.85)*l * (0.85)*w * (0.85)*h = (0.85)^3 * l * w * h = 0.614125 * original volume, an approximate 38% volume decrease.
To suppose only one dimension such as width decreases by 15% when volume decreases by 15% isn't realistic.