Hmm?
*looks at previous calculations*
Ah. You're using an inch diameter for marbles; I didn't notice that. My bad. My mental image is about 1.5cm, which, eyeballing (on bus, calculator is in bag, blah) it would pack to about 3000-ish cm3.
And yes, I am well aware what that does to your previous estimates.
Recalculation time!
D = 1.5
R = 1.5/2 = 0.75cm
V = 4/3*0.75^3*Pi = 1.77cm^3
Plugging this into:
Well it kind of is. At the 8.58cm^3 I calculated earlier and factoring in that the limit for sphere packing is ~74% efficiency means a thousand marbles takes up 11,595cm^3.
To make that easier to visualize that's 11.6 liters or 3 gallons.
For comparison the capacities of a a couple (only ones I could find with volumes listed) of sling bags from Amazon:
Everest Sling Bag - 730 cubic inches = 11,963cm^3 = 96.9% full
Port & Company Honeycomb Sling Pack - 1,326 cubic inches = 21,729cm^3 = 53.4% full
Everest Luggage Sporty Hydration Rugged Sling Bag - 850 cubic inches = 13,929cm^3 = 83.2% full
And from what I can tell most of them are around that same size. So even in the best case the sling bag is going to be over half full and from what I can tell this are adult bags and Mami probably has a smaller child version.
Gives:
V (n=1,000) = 1.77*1,000/.74 = 2,391.89cm^3 = 2.39L = 0.63gal
Everest Sling Bag - 730 cubic inches = 11,963cm^3 = 20% full
Port & Company Honeycomb Sling Pack - 1,326 cubic inches = 21,729cm^3 = 11%% full
Everest Luggage Sporty Hydration Rugged Sling Bag - 850 cubic inches = 13,929cm^3 = 17.2% full
So with a maximum fullness of one fifth I think Firnagzen's comment of there been plenty of room is fine.
However as he mentioned that's not the only calculation changed:
Time for...
Grief Math!!!
Lets assume that the average magical girl produces a marble of grief per day of general living. Lets also assume they fight a Witch every two days and that each fight produces 20 marbles.
Thus we can say this theoretical magical girl produces 4,017.75 marbles of grief per year.
Toy marbles are generally between 1/2 an inch to an inch. Lets assume grief marbles are 1inch in diameter, 2.54cm, and are perfect spheres. This gives them a volume of:
V = 4/3*Pi*1.27^3 = 8.58cm^3.
So the total volume of grief a theoretical magical girl produces per year is 34,473.29cm^3.
NBA regulation baskballs are between 74.93cm to 75.88cm in circumference. Assuming these are the lower end of the size spectrum:
74.93 = Pi*D
D = 74.93/Pi = 23.85cm
V = 4/3*Pi*11.93^3 = 7,103.36cm^3
We are told there are hundreds of basketballs. The smallest number that fits this description is 200 so using that the total volume of grief extracted is:
V = 200 * 7,103.36 = 1,420,671.83cm^3
This volume of grief is 41.21 times larger then the estimated grief produced by a single theoretical magical girl.
So theoretically a single cleansed grief seed could sustain one magical girl approximately 41 years or a group of say four magical girls for a decade.
This of course does not factor in grief production by the seed since that is as of yet unknown.
However before I start revising this there is one more piece of GM information to factor in:
You also forgot to account for the wings, and [REDACTED], though to be fair neither is entirely your fault.
We still don't know what [REDACTED] is however we can now estimate the capacity of Sabrina's wings.
You have three hundred and twenty seven Grief marbles in your sling bag, and one Grief Seed in your hand.
This is how many marbles we had before we collapsed them.
You have one thousand and thirty one Grief marbles in your sling bag, and two Grief Seeds in your pockets. Still plenty of room in the bag, by the way, a thousand plus marbles sounds like a lot, but isn't actually, volumetrically.
This is how many after. Now simple math tells us that's an increase of 704 marbles which gives us an upper boundary. However we know the wings actually contain less grief since between these two numbers we also degriefed Mami and Homura.
YHomura nods, and produces her Soul Gem, filmy with corruption. A casual wave of your hand has the Grief floating free into the air, and you compact it into your Grief marbles.
There is somewhat more Grief than what you'd expect of day to day living, and you give Homura a questioning look, which she meets with her usual poker face. "Thank you," she allows as she reforms her Soul Gem ring.
"No problem," you reply. "Mami?"
"Um, sure," she says holding out her own Soul Gem.
You cleanse that, too
Now Homura has more marbles of grief then normal but since there is no mention of Mami having more we can assume she's got about normal. Now the normal grief production per day is one marble. So that is at least 2 marbles of grief. Bringing down the maximum to 702.
Now it's a pure guess but I'm going to say Homura's extra grief was 2 marbles worth since 700 is a nice round number and humans tend towards round numbers so it's the most reasonable figure for Sabrina's grief wing capacity.
Now to the recalculations:
At a yearly grief production of 4,017.75 marbles and the corrected grief volume per marble of 1.77cm^3 the new yearly production in volume is 7,111.42cm^3.
Now the grief volume of the basketball shouldn't have changed at 7,103.36cm^3 and continuing the assumption of at least 200 basketballs gives a volume of basket balls at 1,420,672cm^3.
Now adding in the 1,239cm^3 provided by the 700 marbles from Sabrina's wings gives us a total grief seed capacity of 1,421,911cm^3.
That if sufficient to hold:
Years = 1,421,911/7,111.42 = ~200 years worth of grief
Which makes sense given that a basket ball is almost exactly the same amount of grief as a Puella produces in a single year.
Now we still don't know the effects of [REDACTED] however ignoring that a fully cleaned grief seed could theoretically power a pair of magical girls for
one hundred years.
The question is whether or not Puella in PMAS are immune to old age. There is some suggestion they age in the form of Mami. However we can't be sure if that's because:
- Mami expects to age so subconciously uses her magic to age her body
- Puella don't stop aging until they reach their physical prime
- Puella age normally and will die of old age
So either a single grief seed is enough of a pair of Puella's
entire lives or we only need to recharge a grief seed every 200 years for individual Puella or say every 40 years for a team of five.
If Sabrina spent an hour a day every day cleaning grief seeds and each clean from full to 0 took 1 minute then she could support 4.3 million magical girls. And that's assume she can only do it one seed at a time. There is no reason, AFAIK, she couldn't be cleaning
thousands at a time.
So theoretically Sabrina is really only limited by:
- The number of Grief Seeds avalible
- How fast/many she can drain
- The grief production of a Grief Seed
- [REDACTED]
- Morals?