Q: How do we calculate the volume of complicated shapes?


A: We use a few thousand 20mm plastic balls, and a lot of tubs!


How? We use the excitingly named ASTM F2153 Standard Test Method for Measurement of Backpack Capacity (for the nerds: link here 😉), or as close to that process as we can get in our workshop.
▪️ First we clear a table (and remove all dogs from the room in case we drop any balls… News Flash: We always drop a few🙃).
▪️Then, over a box, we fill the item that we are wanting to measure with balls until we cannot fit any more in. In the photos you can see Will is measuring the volume of a Roo.
hands filling a bum bag with plastic balls
 ▪️ For a Roo we fill until the zip is still functioning, if it’s a backpack then we fill until we can get 3 rolls on the roll top, then we pour out the contents into a tub that has a scale on the inside.
hands filling a bum bag with plastic balls
▪️ We then tamp the balls down and measure the height. We have a spreadsheet that converts this height to volume and Presto! We have our volume. (sometimes we do this a few times just to make sure)
A tub of balls with a scale
▪️ Each tub holds 20L, so if we are measuring a big backpack then we need to use a few tubs. We have about 70L of balls in total, or about 12,000 balls.
measuring the volume
▪️ Details time: Things get a little more complex when you measure a lower volume item like the Roo as, sub 4L the process isn’t as accurate owing to the diameter of the tub compared to the size of the balls (the balls tend to settle into single layers, and the fewer layers you get the lower your degree of accuracy). To get around this we measure the weight of balls that fit, then scale this up by a factor of 5, then measure the volume of that scaled up weight of balls, then divide by 5 to get the answer. Still with me? Good.
▪️ To double check our working we also have a weight vs volume calculation. We work out the weight of all the balls used, then cross reference that against our volume chart.
We aim to get as close as we can to our stated volumes across our range, that way you can be confident that a 40L Atom fits the same volume of stuff as 40L Mo.
P.s if you are wondering if anyone has ever knocked a tub containing 4000 balls off the cutting table and onto the floor then the answer is yes, ask Rachel! 😀
Tom Gale