Hello, I would like to ask for some (unrelated to MoI) math help.

I don't know how to word it best, I can try to lay out what I have and see if i make sense to get help. I am helping my brother with a "Lead Mold"

The goal is a "X".oz result
Using a volume to weight calculator We create our volume which in "Lead material" should weight "X.oz"

Due to variable in lead type and pouring conditions, the resulting weight is off. But this is a repeatable difference as using the same material and conditions will produce predictable results (Not all lead weighs the same)

I have some real numbers for the difference, but need to be able to generate the numbers for a formula to express the difference at different weights.

Let me explain.

Looking to get a 2.0 oz result. Calculated volume should be 0.3051 Cubic inches
Generate actual part and result returns 2.2 oz

For this one part, we can just do a weight to volume calc and enter in "1.8" as the conversion and get a new volume of 0.2746 cubic inches and get a result of 2.0 oz

(This close is OK. We aren't going to mars!)

Here is the calculation i need help with.

the .2 difference as will be applied to future weights.

Since .2 diff was created by a .3 cubic volume, I will need to figure out the "ratio-percentage???" difference and method to apply to future numbers.

So the mathematically challenged just thought "remove .2 from ALL NUMBERS to achieve results. At some point they realized .2 was generated by a fraction of 1 whole of a cubic inch.

So the result needed is when a particular weight is desired, what is the deduction to perform that reproduces the lower difference. Or, calculating the overage at different weights, to remove from those weight to volume calculations. Like what would the number be on "7 oz?"

Does that make any sense written down?

Really appreciate any input.

Will be not more easy in decimal system ? :)

hi burrman,

it sounds like the variability is with the density. density is mass / volume. so you are on the right track. to get mass take the weight (that you measured) and divide by gravity. to get density, take the mass and divide by the volume of the part. once you have calculated what the density is for that particular batch, you can then make any future calculations with the new density value. hope that makes sense.

density = mass / volume

weight = mass * gravity

like Frenchy may have been alluding to, using metric units will prevent errors. you can use unit conversions, on the inputs and outputs, to work with english units. i don't think you need to worry about the difference. just focus on what the actual density is, for the particular batch of lead you are working with. you can use the same procedure to find the density for any given batch.

anthony

Hi Burrman,

Pilou shows a balance scale, which permits weight to be measured, using known mass counterweights.
So the result is that the earthly weight is given by the balancing mass. (Different on mars?)
The gravity at the earth worksite may be considered to be constant, so a spring scale or an electronic scale would also measure the mass.
So talking about gravity just makes for confusion.
The common practice of equating "weight" with "mass" will work just fine in the current scenario. Using label of "mass" would be more scientifically correct.

Anthony is right-on about density involvement.
I think that the weight(mass) to volume calculator uses a stock density for lead. A custom density ability would be nice, but absent custom density,
a conversion equation is needed to compensate for the different density of the batch of lead being used, or to compensate for pouring conditions discrepancy.

Compensation Equation:
**********
(corrected Volume in cu_in) = (Volume, in cu_in, from the conversion program) * [(desired weight, in oz) / (actual weight, in oz, of test pour)]
**********

0.2774 cu_in = (0.3051 cu_in) * (2.0 oz) / (2.2 oz)

So 0.2774 cu_in should be the volume of the corrected mold.

Note that (0.3051 cu_in) / (2.2 oz) is the reciprocal of the apparent density of the lead batch, based upon the initial test pour.

aqua_calc has weight to volume and volume to weight calculators.
(2.0 - (2.2 - 2.0)) = 1.8 oz, to yield from the calculator your volume of 0.2746 cu_in, which is close to the above 0.2774 cu_in.
(I think that the 1.8 method may not be quite the right way to make the compensation(?))

I say "apparent density" because "pouring conditions" is also talked about, which is in effect captured in the reciprocal density in the above Compensation Equation.
(note that ounce, oz, is a mass measure, NOT fluid ounce)

- Brian

max had a volume calculator with custom densities???...

Temperature and Bouyancy make a miniscule difference?

 

 

 

 

Thanks Anthony and Brian for the replies!

The density was definitely what i was looking for.

All the other “conditions” was just a lack of understanding of what made leads weigh different. (Going to mars requires exacting precision, which is not needed for us)

I think Brians walkthrough helped me simplify it for us to move forward.

I think with “base values” the aqua calc site uses 6.55609194538 ounces per cubic inch to do its calc.

So i can just figure out how much the 2.2 cal is per cubic inch and do my own conversions?

I like the idea if understanding the density. I’ll have to reread Anthony’s post a bit and see if i can figure out what original density was ussd and what it turned out to be.

But i have to try and keep it simplified for future changes.

Maybe just deducing the per cubic inch weight and adjusting that number for future batches gets me close enough.

Just to be sure i am not confused, What would be the weight per cubic inch on the 2.2 ounce pour?

And Anthony, can you tell me what the aqua calc density was (that gives 2 ounces) vs the one that gives 2.2?

Very helpful for me. Thank you!

hi,

i am not familiar with the aqua calc that is mentioned. if brian's post helps more, that's great! what i thought your first post was saying is that you built a solid part and measured it's weight. so you knew the weight and volume. however, you didn't know the density and based on what you are saying lead does not have a consistent density. i am not familiar with lead. so i was just reading your first post and it reminded me of some things from a previous life. it seems like you already know everything you need to, to calculate the density of the part you made. with that value you can do any calculation you wish. you shouldn't have to worry about how different it is from some other density and constantly adjust calculations. that would drive you nuts and possibly cause mistakes. just using the density per batch should be sufficient. obviously, the volume and weight will have accuracy limitations. so the density you calculate is not going to be perfect. but it will be as good as it can be. scales are not very accurate. i think your volume calcs will probably be of a higher accuracy. but it really doesn't matter much. it's only going to be so good. i'm assuming, also, that you have the standard density of lead to compare to. it seemed like you were saying it's not matching. lastly, i always do all my calcs in metric units. they are full proof. i use unit conversions on the inputs and outputs. this particular problem is simple enough that you could probably do it all in english units, if you have to. it's more of an issue when you write code with tens of thousands of calculations. it's full proof in all metric. also, all standards labs use metric. so any given constant is actually figured out in metric units.

i hope you figure it out. it seems like you are close and brian's help is pushing you over the finish line.

Ok, so i think i am good to go. Just a check in with you.

I can use 6.55609194538 as the density already fully converted from the 11.34 g.cm-3

From this i can deduce the 2.2 difference (and all future differences)

I will also do a water “volume” test to verify the actual parts volume to verify if diffs are coming from machine and cut.

Thank you Anthony (always nice seeing you in here again)

Thanks Brian. Appreciate your insight.

Burr

Hi Anthony, we replied at the same time.

Your last post is spot on!

Understanding “density” was my hill i had to climb.

But i think i got it figured.

Thanks again!

First of all, the density of Lead is 6.55609 ounces per cubic-in.
https://www.aqua-calc.com/page/density-table/substance/lead

Unless your lead alloy batch has gold or some other higher density metal, this tends to imply that true volume of the test Lead pour is quite a bit larger than the stated 0.3051 cubic-inches.
Does the Lead ingot/weight bulge up out of the mold?
A calculated density value of 7.21075 ounces/cu-in is much bigger than 6.55609.
*****

It occurs to me that the procedure, to determine the adjusted volume of the mold, should be clarified.
(At the bottom is an easier way...)

To obtain the corrected Volume for a new mold, in cubic-inches:

1. Use the empiric data from the experimental pour, for the desired 2 ounce lead weight.
With input of desired 2 ounce lead weight, the conversion program yielded a Volume of 0.3051 cubic-inches for the test mold. (0.30506+/-)
(The conversion program uses a particular value for the density of pure Lead)
The actual weight of the pour was 2.2 ounces.
So the apparent density of the batch of lead being used is 2.2 ounces per 0.3051 cubic-inches, which equals 2.2 / 0.3051 = 7.21075 ounces/cu-in.
which seems crazy.
(some pour condition factors may be included in this, and "per" means to divide)

1. Run the desired weight, in ounces, through the conversion program, to obtain the preliminary Volume which will need correcting.
Assuming that a 1 ounce weight is desired.
1.0 ounces converts to 0.15253 preliminary cubic-inch mold size. (Naturally this is half of 0.30506 +/- :)

2. Multiply the preliminary Volume by 2.0 and divide by 2.2, to get the adjusted volume for a new mold.
0.15253 * 2.0 / 2.2 = 0.15253 * 0.909091 = 0.13866363 cubic_inches. (per 1 ounce weight) <<<<<<<<<

So multiply the preliminary Volume by 0.909091 to get the adjusted mold volume.
*******

Or, using the above 0.13866363 cubic-inches per 1 ounce weight,
multiply the desired weight by 0.13866363 to get the desired adjusted mold volume.
*******

Depending upon the mold geometry and "top surface bulge", the correction factor may be different for different mold sizes???

I've been getting confused now, so that is it:-)

- Brian

Looks like you have it all sorted out. I hope that I have not made any math blunders :-)

Thanks for digging in Brian!

I think the “the difference is way off” part in your last post means i have to look at a few other things.

Just becaue i was “told” that this model was used to cnc THAT part, doesnt mean that is what happened too.

But your input sends me in the right direction!

Also, the “calculations” you just explained is exactly what i was asking for

Thanks you!

i haven't followed the numbers, math, and goals very closely. so i'm taking a lot on faith. brian's statement about the density difference works out to about 10%. again, i'm assuming everything being said by everyone is accurate. brian thought that density difference was crazy. to me, it's not that surprising. density accuracy is going to depend on the weight and volume accuracy. so a combined diff of 10% doesn't seem that bad to me. if you look at the resolution of scales, the fact that they may not be calibrated, and so on. they really aren't very accurate. especially as the load capacity increases. as for volume, i was originally assuming that you were using a number calculated by the cad software. then it seemed maybe you were measuring volume. either way, depending upon how complex the part is the theoretical volume vs real volume could be causing issues.

not sure if you have ever been to a standards lab, where they measure all sorts of things. density, volume, and so on. it's incredible how much goes into just this topic. you can spend a lifetime just in calibration and measurement. it's super expensive and time consuming. so the 'we aren't going to mars' aspect is important to keeping cost down. so going from 10% error down to 1% starts getting very expensive and time consuming. i do think it's worthwhile to check into the simple and cheap things that could give you problems though.

Cool!

I was expecting lead "alloys" to be less dense.

- Brian

Hi Anthony,
“””””””” brian thought that density difference was crazy. to me, it's not that surprising. density accuracy is going to depend on the weight and volume accuracy. so a combined diff of 10% doesn't seem that bad to me.””””””

Thats good perspective also. It was kindof how we had been doing it in the past. Understanding there are variables, but we could get it close.

When .2 ounces became sortof large to explain, i had to dig in deeper to gain more understanding.

So just for your information, here is how “the numbers” come about.

My brother has to make a lead mold. They are “canoe leads” that go on throw nets here in Hawaii. (The guys like to be very particular about the weight being “exact”!


Using the volume of the cad model given to us from our CAM software (and now MoI also) we scale the model to meet desired shape and dims to produce a volume that when plugged into a conversion calculator (the aqua one being mentioned is just one of thousands online) we can generate a model that “should” be x ounces when we cut a closed mold on the cnc.

Previously got him setup by doing some trial and error cuts and going back and forth on volume till he got “x ounces” from a pour. Then i told him, your lead is different by this much, so compensate. But that “compensation grew and grew because it was incorrect for future calcs.

The lead is sourced by diving in fishing spots and picking lost leads, then melting it down, scraping out coral and rubbish, and pouring the mold.

If “7 ounces” was the goal, we could get leads out at 7.02 ounces and just explain “results may vary”

.2 ounces was too much. I have to help him track down what is not right (yesterday)

You have directed me towards the density part, which had me understand better what i am looking at (and also understand how the number could have gotten so far off from what was expected (different density partially, but in combination with bad procedure of “scaling models” too, doubles the error then 2 and a half years later “nothing is right” lol….

I am reworking what will be done from scratch, with less variable from the proper “density”.

Anyway, long winded. But suffice it to say, you helped me a great deal on this. Thanks again.

oh thanks a lot. that was super helpful in understanding what is going on. i was getting lost at various points in the thread. so you have about 10x the variance than you want. .2 oz vs .02 oz. so yeah, that's a big problem. if it's possible to make a very simple cube as a test. that would help with measuring the density more. as a start to the whole process though, it would be a good idea to use whatever the stated density of lead is. that should be pretty reliable. using your measured density, at this point, seems too unreliable right now. i thought the model volume was well known and the weight measurement at least normal. i imagine your weight measurements are fine. it sounds like they have a way of measuring weight that they like. so no reason to change it. it is possible the lead density is varying, based on the unknown nature of your material and the debris that may be in there. hmm, tricky problem. not sure i can be of much help. it sounds fun though. i guess, right now, the only thing density is doing is telling you that there is probably a problem with your volume. of course assuming the weight measurement is decent. it's good that you are talking about low weights. the scales work better in that situation. you can find the scale resolution in the spec sheets. they also sell calibration weights. so that you can make sure the scale is working right. it would be very worthwhile to get those, at this point. they sell them on amazon. i think they are made of brass. sometimes they come in a set. having the set is nice because the scale error isn't always a constant.

hi again,

i had a little time to play with the numbers. i attached a LibreOffice Calc spreadsheet. Not sure if you will be able to open it or not. It should open in Excel though. I'm showing that if you just use the stated density of lead, it wouldn't take much of a volume difference to explain the difference you have (7.2oz vs 7.02oz). It would only take a volume difference of 2.56%. if the object were a cube, the length of each side would only have to be off by 0.85%. given 'you are not going to mars', this seems reasonable to me. the spreadsheet might have errors. i didn't spend a lot of time checking it. the unit conversions were from a quick search of the internet and the density was from an even quicker search.

maybe the calculator will help some in the future though.

anthony

updated the spreadsheet 1; added some more info about typical scales. added some more notes. fixed formatting issues
updated the spreadsheet 2; added more info, comparisons, and calculators
updated the spreadsheet 3; added more comparisons

https://drive.proton.me/urls/TEB0GX5Z4M#vqxN6Xru2rf5

i'll leave the link active for a few months. i don't keep things stored there for too long, due to space constraints.

Thanks Anthony!
I’ll take a look at the spreadsheet later. I’ll also post back to you if i discover the culprit in my workflow.

Hopefully it is legit and not something like a lack of attention

hi burrman,

i've updated the spreadsheet several times. this most recent update, i should mention something. brian's earlier post was comparing 2.2oz vs 2.0oz. that leads to a 10% diff in density or volume. Later, you compared 7.2oz to 7.02oz. that leads to a 2.56% diff in density or volume. the math is the same, it's just what two numbers are being compared. I added this into the spreadsheet. in reality; mass, density, and volume are all unknown to some degree. so you end up going in circles. you have to at least lie to yourself a little and say you know two things, in order to 'measure' the third thing. you can't not know all three things. there is only one equation so you can only have one unknown.

i think someone mentioned this, but you said your measurements are in ounces. so technically you are measuring mass, if the units are right. however, a lot of scales are measuring weight and reporting mass. so it gets confusing. also people say weight when they should say mass and vice versa. i used the word weight in the spreadsheet to match what you were saying. but the units are in mass, which is what you were also saying. i think i know what you mean. it's just weird. i also switched to inputting grams because the scales seem to work better in metric. all labs use metric as well. you can change the spreadsheet as you see fit though.

I've pretty much dropped out of this discussion, but did look up some lead alloy information, links attached:

Fishing lure, and tire lead talk: (alloys less dense than pure lead, usually)
https://www.tidalfish.com/threads/lead-for-pouring-jigs.279917/

Monotype lead, also links to Linotype lead, (whatever those terms mean):
https://www.matweb.com/search/datasheet.aspx?matguid=63031aa385cc4b72b103fa2dc9320ca8&ckck=1

- Brian

Thanks for everything. Working on it now

While researching anodizing, came across the fact that bismuth is also used for fishing sinkers.
http://www.observationsblog.com/sciencetechnologyexperiments/anodizing-and-dying-aluminum-without-battery-acid

There are also Bismuth 58%, Tin 42% alloys, (and other alloys). Melts at 520 degrees Fahrenheit +/_. Density 75% of lead.
Bismuth, 80% of leads density.
Bismuth is brittle.
Bismuth expands 3.3% when solidifying.

Lead melts at 621.5 degrees F.
Tungsten density is 19.25 grams per cubic centimeter, versus Lead at 11.33 g/cc. Melting point, 6,191.6°F, so not relevant.

- Brian