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Old 09-20-2021, 03:37 AM   #1
Ratty
 
Join Date: Sep 2021
Default Infinite Worlds, pages 28-29 - error in calculations?

In the Infinite Worlds book, on pages 28-29 it gives calculations for jury-rigging a charger for conveyor batteries.
I'll probably never use this in my games, but I was looking at the maths and it seems wrong for people/oxes on TL1 treadmills.

The calculation on page 29 is as follows:

Treadmill output:
Strength of treader*20W

Efficiency of charging:
(above result)*90%(motor efficiency)*5%(TechLevel1 efficiency)
(The TechLevel efficiency is TL*5%)

So...
A ST10 treader outputs:

(10*20)=200W
At efficiency of:
200*.9*.05 = 9Ws (9Wattseconds)

An example conveyor needs 1000kWs (kiloWattseconds).
so:
9Ws = 0.009kWs

1000(conveyor need)/0.009 = 111,111 seconds (how long the conveyer needs to be charged for.

111,111 seconds = 30.86hours

The book's result is 61.7hours. Basically twice my result. Either I or the book have halved or doubled something.

-

For the ST27 ox on a treadmill, my result is:
11.43 hours. The books says 10.2 hours.
But...
If the setup runs at 100% motor efficiency:

Efficiency of charging:
(above result)*100%(motor efficiency)*5%(TechLevel1 efficiency)


We get the same result of 10.2 hours.

-

Using these calculations, the other results in the book all seem to fit.

(horses on a treatmill, 1760s steam engine, Roman vertical water wheel, Persian windmill.)

The TL2 penteconter takes just over half an hour, while the book says 'a little under an hour', but that's close enough I suppose.

--
So I have drawn two conclusions:
1) For the ox/person on a treadmill, the book has an error in the calculations.
2) I am wasting my life.

If I've made a mistake, please let me know, this has obviously tickled a puzzle-hungry part of my brain!

--

Edit:

Because I'm obsessive...

Human strength (10) * hours worked (61.7) = 617
should equal
Ox strength (27) * hours worked (10.2) = 275.4

But they don't match...

However, if you use the results I got from my post (half the human strength result, run the ox at 100% efficiency)...

Human strength (10) * hours worked (30.86) = 308.6
vs
Ox strength (27) * hours worked at 100% efficiency (11.43) = 308.6

Which fits.

--

Are we to believe this is some sort of MAGIC xylophone?

Last edited by Ratty; 09-20-2021 at 04:03 AM. Reason: clarity
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Old 09-20-2021, 07:18 AM   #2
Varyon
 
Join Date: Jun 2013
Default Re: Infinite Worlds, pages 28-29 - error in calculations?

I'm not seeing anything wrong with your calculations, given the equations you provide, so I'd say some sort of math error is in play in the book. Of course, power output shouldn't scale linearly with ST - it should scale linearly with BL.

More realistically, a creature moving at walking speed (as per hiking, losing around 1 FP every hour) should probably produce something like 5xBL W, moving at jogging speed (as per paced running, losing FP markedly more quickly) should produce around 10xBL W, and all-out running (as per sprinting) should produce around 20xBL. For ST 10 (and thus BL 20), 200 W output corresponds to jogging, so it should burn FP pretty readily; maintaining that over a long time period would likely call for multiple joggers, swapping out as each gets tired (note speed gets cut - in half IIRC - at less than 1/3rd FP, so you'll probably want to swap out as soon as that happens so you aren't producing 50% energy). If you want hiking-speed to produce energy at the same rate as is currently the place, double TL efficiency, to a maximum of 100% at TL10 and higher. Note this means your 90% efficient motor is, by the equation, TL9 (which feels roughly "right" for Infinity and the like) rather than TL18.

If you do the above, then using the current efficiency (5%*TL) a character with ST 10 (BL 20) would take around 61.7 hours with a sustained hiking-speed tread, while that ST 27 (BL 145.8) ox would take around 8.5 hours. Note in both cases you'll either need to swap the subject out a few times or have some time gaps where you aren't charging, to allow for rest. Doubling the efficiency gets you down to your 30.86 hour value for the first, and cuts the oxen-powered treadmill down to something like 4.23 hours.

EDIT: As a "fun" variant, if you instead design something to be cranked by the arms, you're looking at around 70% of BL - although if it's something where you can get the rest of your body involved, like a rowing machine, you're back up to 100% BL. Still the same FP expenditure - hiking for 5x, jogging for 10x, sprinting for 20x.
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Last edited by Varyon; 09-20-2021 at 07:24 AM.
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Old 09-22-2021, 11:19 AM   #3
Ratty
 
Join Date: Sep 2021
Default Re: Infinite Worlds, pages 28-29 - error in calculations?

I'm glad my maths was holding up, I was really doubting myself.
And wow you thought about it well, thanks for the response!
I think I enjoy just looking at the maths, and the idea of translating these hypotheticals into game mechanics almost as much as I enjoy playing!
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