Low-Tech Containers and Storage Equation

[fritzbc]

Today, I was looking at the Containers and Storage article over and over. I needed to create an equation to quickly calculate costs and weights by inputting an amount of cups into a cell in Excel. I could not, for the life of me, get one that would work. Does anyone know the best way to do this, or is there an algorithm or equation already made for this?

[seasong]

A1: <price for 1 cup>
A2: <weight for 1 cup>
A3: <number of cups>


A4: A3^(2/3) * A1
A5: A3^(2/3) * A2


A4 is your price
A5 is your weight

[seasong]

Note that the final values were rounded off in Low-Tech, but this will give you close numbers.

[Polydamas]

Originally Posted by fritzbc

Today, I was looking at the Containers and Storage article over and over. I needed to create an equation to quickly calculate costs and weights by inputting an amount of cups into a cell in Excel. I could not, for the life of me, get one that would work. Does anyone know the best way to do this, or is there an algorithm or equation already made for this?

Do you mean the chapter in GURPS Low-Tech? Those are the only 4e rules for building containers which I know, and I think they have the algebraic formula.

[RyanW]

Originally Posted by Polydamas

Do you mean the chapter in GURPS Low-Tech? Those are the only 4e rules for building containers which I know, and I think they have the algebraic formula.

I seem to recall one from the html era of Pyramid. Can't recall any specifics from it, though, and my archives were lost long ago.

[fritzbc]

I ended up contacting Author Matt Riggsby about it. His advice and response is quoted below.

Originally Posted by Matt Riggsby

There was a spreadsheet, long since vanished, but IIRC (and I may not) it was kinda complex. In particular, I've entirely forgotten how the thickness of material changed with volume. It's entirely possible that it wasn't continuous, but rather jumped up in increments here and there. Anyway, what I'd recommend for off-size containers is straight extrapolation from the table. For a mid-size between A and B, just average the weight and cost for A and B. LT presents plausible stats for historical items, but there was enormous variability in real values without meaningful variability in quality or cost. Really, stats within a factor of two or more for a given size of container are more than reasonable. Trying to follow a more complex formula just takes a lot of work and provides false precision.

[Varyon]

If you want something that's just plug-and-play, a quick look gave pretty decent R^2 values with linear trendlines (somewhere north of 0.98; polynomial gave a bit over 0.99, but was more complicated and there's at least one - earthenware - where going much above the maximum size listed in LT actually caused weight to start going down, eventually becoming negative). For that, you can write out the volumes (I suggest just converting everything to cups - a quart is 4 cups and a gallon is 16) in one column and the weights from the books in another, then used =SLOPE() and =INTERCEPT() to get the relevant parts of the equation; the result will be Weight = Volume*SLOPE + INTERCEPT (provided you used Volume for x and Weight for y). Note most of the results won't match the book values; if going this route, you may want to only use those values for making the equation but then use the equation for anything the characters opt to make.

Note also this means the wall thickness of the container is increasing as the contained volume goes up, while the previous suggestion of using the 2/3 power I believe means the wall thickness is staying the same (it's having weight increase with surface area rather than with contained volume). The reality is probably somewhere between the two - wall thickness does need to increase as contained volume goes up, but not as rapidly as is seen with linear scaling. But linear is nice and simple to use.