How Does the ENERGY CELL Work in Tears of the Kingdom? | All your Zonai device questions answered! 

As an engineering professor, I have to say you're really talented. The content, presentation/editing, and your delivery are really exceptional. Incredibly well done.

I'm surprised you didn't post it on the hyrule engineering subreddit, I think they'd probably appreciate this kind of research

Great video! We definitely need more people sciencing things properly in TotK. When you're done with Part 2, here's an interesting idea for a future video: Comparing the max speed and energy efficiency of different machines on land, water and air to find the fastest and most efficient designs for each! =)

Also, rockets don't really give you more lift with more than one rocket, they provide stability, but not lift

Dang this is a professional-as-hell video and you only have 300 views. Hope you get WAY more than that. The research alone is amazing, but then a calculator on top of that is a huge contiribution to the community. Here’s hoping you get found by more people, because wow this video is awesome.

Hey! Here's some interesting bonus things I've been thinking about. Maybe you could look into these for a follow up: - What is the base depletion rate of the Zonaite bow? - When you are in a shrine, any device you activate does not deplete your energy wells, and instead appears to pool energy from the shrine, giving you an infinite amount of energy. With that said, I'd like to pose a challenge. Out of all the shrines in the game, what is the highest depletion rate you can achieve in a shrine by using the devices available? Because the community has collectively reached a consensus that Link is a maniac, we should put that to the limits to see how quickly Link can completely deplete the available energy from a shrine 😂 I look forward to your future videos!

At 15:25, I'm intrigued by the nonlinear relationship. It would be informative to make a line/scatter plot of the values. What I observe is a generally linear trend, but where every fourth wheel requires less additional battery. My current hypothesis, if you ever feel inclined to test it, is that you would see 0.088 wl/s for 11 wheels, then almost the same for 12, and maybe around 0.096 wl/s for 13. The slope does appear to change after each fourth wheel, but it's not obvious what the underlying math might be.

this is super well done. I can tell every word choice, the pacing and flow, was very well scripted and probably with many trials of voice-over to get it perfect this is professional level work :D

From one engineer to another.... Mad respect, my good sir. This is very clear and concise. Well researched and beautifully presented. Well done!

Two things with the construct heads: you can make them pulse by attaching them to each other in a special orientation (it's hard to describe it, so you'll just have to see it in a video), which can make beam emitters more powerful while taking less energy (and it might make cannons even worse). It'd be interesting to see exactly how much of a difference the double head makes (although it'd probably be somewhat annoying to actually figure out) And assuming you're actually going to code up the calculator fully, you could make the construct heads a bit more accurate by essentially making it create a separate section, and then doing the calculations twice, once with all of the parts that are attached to the head and once without the parts on the head, and labeling it as "drain while attacking" and "drain while not attacking" respectively as for the way the calculator currently works, just create a "base machine" and "on construct heads" section, with the base machine being the total for while not attacking and the on construct heads being added to that to get the while attacking total

16:24 "what's worse, the first shot comes much faster than subsequent shot . . ." and that single idea gave birth to pulse cannons we salute you

As someone who loves math and has studied physics previously, I loved the presentation of the Zonai battery system and the formulation given in 12:37. Thank you for this scientific dissertation of the Totk battery mechanics, may this information bless our future zonai builds and help optimization procedures. I wonder if there is a way to calculate fan and rocket momentum and weight of several objects, I guess we could use coordinates as our distance measure for this purpose.

Your content is dangerously underrated and you deserve so many more subscribers and views. Your videos are of the highest quality and definitely deserve more attention.

Amazing, I love those research efforts, stuff like this is much more engaging to the community than having all values from a datamine!

I doubt I'm the first, but I found the pattern for the wheels. Instead of each wheel adding a new amount to the last total, it discounts all wheels when you hit certain markers. 1 - 0.015 - 0.015 each. 2 - 0.022 - 0.011 each (adding a second wheel give both the discount) 3 - 0.03 - 0.01 each (another little discount for trikes) 4 - 0.036 - 0.009 each (the standard 4 wheeler discount) 5 - 0.045 - 0.009 each 6 - 0.054 - 0.009 each 7 - 0.063 - 0.009 each 8 - 0.064 - 0.008 each (8th wheel is almost free because of the 8 wheel discount) 9 - 0.072 - 0.008 each 10 - 0.08 - 0.008 each Not sure if there will be a discount at 12 or 16 or if it will stay at 0.008 each for all greater than 8 because I'm too lazy to test. Hope that helps.

It might also be interesting to research how exactly fused zonai devices and the zonai bow work if you want even more work for part 2

Subbed for part 2! If you haven't already, I'd love to see an explanation of the battery usage of Mineru's construct included in it - both the base construct and devices attached to it. Another interesting area might be the lifetimes of various Zonai devices (both at base, like with the Wing, but mostly when attached to the construct).

Paradox you the goat man

If you consider that the hydrant is really a Water Emitter and the fan is a Wind Emitter, then you could almost rename the Standard Combination Rule to the Emitter Combination Rule. Maybe the Rocket is a Speed Emitter?

The real question is how this man managed to get a gf while doing all of this

This guy has brought math and engineering fundamentals to ToTK! Excellent stuff!

This video made me so happy. I love all the math. Allows us to make accurate predictions for the performance of complex builds

Hi this was a great vid and I would like to say something: I might seem like an idiot and someone prob came up with this first but I found a formula to calculate the “saving coefficient” when it comes to multiple devices of the same types, the formula is; S.C=1+(0.5xC.D) S.C is save coefficient and C.D is the total amount of devices in the vehicle-1 so the first device doesn’t have the 50 percent discount , anyway hope it helped for anyone so u don’t have to scroll down on that table !

Wow. All this time, I was so sure that the big wheel depleted faster than the small one.

awesome! This is incredibly informative and indepth. I love it

This is such a great video, and I’ve enjoyed your others as much as this one! You’ve earned a new sub!

Holy cow. Your methods are solid. Your math is clean. This is a rare gem of quality and precision. Bravo.

Love your work. Thank you for your dedication!

subbed out of respect for the insane amount of reasearch

You tricked me into learning and enjoying math! Well played... well played...

Really excellent research. Thank you. I didn't know about fans on water and rails. And I didn't know if combining different types of things improved their efficiency, or if they needed to be the same type. Thanks again!

Great video! Easy to understand and very useful.

This is fascinating and super useful. Thanks!

After finishing the video I was floored to see it only had 2000 views. This should be like the most viewed totk building video. Hope this blows up. Super great video!

This video is amazing! Really cool

I love the math behind, thank you so much for this!

Extraordinarilly underrated, that's all I have to say.

Super informative. Great stuff, man!

you're awesome, this vid was good. math teachers struggle to relay information like this all the time; you nailed it. your frustration over the wheels made me lol

Anyone like how the 3 elemental emitters are based off of their corrisponding dragons, but the beam emitter doesn't have any similarities so they just made it into a cool unicorn laser shooting thingy?

Did you ever try any of the emitters or hydrant on a shield to see how it changes the depletion rate.

After your most recent vid and the attention you're getting for it, I'm hyped for part 2

The fan thing also works when you attach it to spinners, like the ones on the sky archipelagos, pretty neat.

I only have 4 wells at the moment, so this information comes extremely helpful.

Very well put together!

I propose we use metric measurements for the fractions of wells. For example: A fan's base depletion is 0.156 Wl/s (Wells per second), or 15.6 CWl/s (Centiwells per second), or 156 MWl/s (Milliwells per second).

Great video, thanks for the deep dive into this! I hear you on the editing, always seems to take longer than you think it should, especially if you're a perfectionist. You're a fellow DaVinci Resolve user I see. 😀

This video is a masterpiece! Theres one thing, however, that kinda rubs me the wrong way: for the cannon, wouldnt it make more sense to plot the graph not from the point of activation but the point of the first shot? This would result in a better linear fit for its consumtion per second and a a fixed value of 0.75 seconds "bonus time" to add to the vehicle runtime.

Great video !! I love you, and didn’t knew you were the creator until the end 😂

Great work, you have done a fine job of translation changing science to layman understanding.

Super appreciate this!! Formula is get, thanks for deriving!

Great info and excellent work 👏

I know I'm a month late but take my like anyways. This was very well done and saves me a lot of work (trying to find time to do tests like this is hard to justify right now).

Nah. I think a 2 part series makes more sense. Just found your channel and this video just clicked with me. Dope to know more about the battery and how it works. Liked and Subbed Boss. +2 GG

I like how he just casually uses footage from one of the best paracopter launches in history 1:27

I am engineer, and this was delightful. Good show fellow nerd

Awesome video! I love seeing the whole number breakdown of the battery system. I would’ve loved to see the measurements in Seconds per Well in addition to the units you had as I feel it would be easier to mentally estimate how long a device would last, and personally I find it easier to understand and compare bigger numbers as opposed to fractional amounts. Looking forward to part 2!

"if any part is touching water" the game seems to treat ice as water in many circumstances, would attaching an ice block improve air bike performance?

As a physicist, I find the fact that the error in your measurements was only a singular frame (0.33 s) to be quite amazing-it is INSANELY accurate! If I may ask, where did that extra frame come from? (Maybe you explained it, but I didn’t catch it)

That launch up the chasm was 🔥

W o w . . . I wish I had this level of patience to do so much research.

Here before this blows up, fantastic video

Truly, you are by far one of the most professional TotK youtubers I've ever seen, bravo!

As a brief bit of maths modelling, you should be able to perfectly model a single cannon's well drain with the following equation: w = floor(max((t + 2.35),0)/3.1) * 0.9 Where w is wells drained and t is elapsed time in seconds. The inverse (how many seconds t it takes to drain w wells), would be: t = max(3.1 * floor(w/0.9),0) + 0.75 The general equations would be: w = floor(max(t + (p - i),0)/p) * d t = max(p * floor(w/d),0)+i where: w = wells used t = time in seconds d = wells drained per shot p = general firing rate in seconds i = initial delay before first shot in seconds Floor and max are both functions that you should have access to in any spreadsheet or programming language. Hope this helps you improve even further your calculator!

My personal headcanon is that the Energy Cell is kinda like a Tesla coil. It can power devices that it isn't in direct physical contact with, similar to how Nikolai Tesla has that iconic image of him holding a lightbulb that's lit despite not being screwed into anything.

If only the young Shigeru Miyamoto could have foreseen future Zelda fans discussing “Base Depletion Rate” and their impact on his game.

Im gonna use this for my next construction

Something I noticed is that when piloting a hovercraft driven by fans, my energy consumption decreased significantly when I was partly immersed in water. I think there might be something going on with that too.

Oof I'm so jealous. I was going to do this research as well. Glad someone who knows what they're doing beat me to it 😊

I think with the wheels they were going for an optimal power consumption in making a balanced vehicle. Note how all the even numbers are a lower than half cell usage, while uneven numbers have a larger increase. Especiallt the seeming favouritism around 8 wheels is interesting to me.

It definitely was done to reduce UI clutter. As weve seen in botw the UI around link can only stretch so far before it gets cut of and cant be seen. And the battery UI at max is literally just at the boundary so if there were any more they wouldn't be able to be seen. Thus we have the color change to denote an upgrade

As a math professor and Zelda fan, I love this! Have you looked at the time it takes for other types of devices to burn out (like the wing).

Wow, amazing video! You did so much research it's impressive! One thing that I wonder is: Do the wheels use the same amount of energy when going fast? When driving we can tilt the stick up to go faster, does it drains energy faster?

The Standard Combination Rule: formula Base Depletion = B Net Depletion = d # of attached, identical devices = n B((n/2) + (1/2)) = d A.K.A. B(0.5n + 0.5) = d

Warning, the following wall of text ends in a shrug and an "I don't know." The wheel combination rule looks like the standard combination rule with rounding errors, which makes some sense if you read the data-mined Zonai device values. The hydrant actually has an energy consumption of 1 (which as you've measured is .03 wl/s, or precisely 1 milliwell per frame), while the wheels have an energy consumption of 0.5 (which you've measured as 0.015 wl/s, or precisely half a milliwell per frame). Two wheels using the standard combination rule would be 0.75 milliwells per frame, but you measure 0.022 wl/s, or approximately 0.73 milliwells per frame. If we assume there is a very sleight error in your measurement, and it's actually 0.7 milliwells per frame, then it starts to *appear* to make sense: The game seems to track your energy supply in units of 0.1 milliwell, so the game can't reduce your supply by 0.75 milliwells and either rounds the reduction down or rounds the remaining supply up after performing the calculation. For three wheels everything matches the standard combination rule, but for four wheels we have your measured 0.036 wl/s, or 1.2 milliwells per frame. Our calculated value using the standard combination rule would be 2.5×0.5 or 1.25 milliwells per frame, which would round down to 1.2 just as we see above. Skipping over 5 because it again matches the standard combination rule, we come to 6 wheels, where our calculated usage would be 3.5×0.5, or 1.75 milliwells per frame, which should then be rounded to 1.7 milliwells per frame. You measure 0.054 wl/s, or 1.8 milliwells per frame. Perhaps a measurement error? Or does the game simply round 1.75 up rather than down for some thus-far unexplained reason? Seven wheels suddenly breaks the pattern. We expect there to be no different from the standard combination rule here, because that should have a multiplier of 4 and therefore no rounding. Our calculated usage should be 2 milliwells per frame, but you measure 0.063 or 2.1 milliwells per frame. At this point, I must admit that either your measurements degrade in precision from this point out, or my hypothesis is simply wrong. Would anyone care to perform the experiment themselves to see if they can repeat these numbers?

Each emitter, except for beam, is one of the 3 dragons (excluding Light and Demon). There are also zonai outfits for the dragons too, as well as the fact that the dragons were all once consumers of the secret stones that are heavily tied to zonai culture/religion. From this, we can extrapolate that the zonai base their dragon-related objects and items from existing dragons. But which dragons are the small wheel and the cannon? Are there actually 5 dragons, two from other lands or simply not around? Does one dragon use a combustion-based magic and another revolve around kinetic energy and friction?

Btw I Believe that a steering stick while being moved out of neutral slightly increases the energy consumption, this may not be true though, it just feels like more is being depleted

The fans using less power also works with sand if you have a sled, to my knowledge!

Shout out to the graphics girlfriend. You have a winner there!

Any idea if Mineru’s construct body has a more efficient Wells/sec than even the wheels? Or if she consumes zonai devices at the same rate as its base depletion rate?

This is really interesting. So for a flying vehicle as long as we are using more than two fans... using several electric motors and the accompanying fans, assuming that we power all fans with one electricity emitter, is actually more efficient? Not taking into account parts count and accessibility of course.

7:20(ish) - my only suggestion is to flip the units around a bit, to make them 'more relatable'...for example, instead of saying that a Fan has a Depletion Rate of .156wl/s, id say that the Fan takes 6 Seconds to deplete One Well... ...i mean, when you get into the Huge constructs (with like 15 Emitters, Wheels, HoverStones, etc), THEN it might be 'easier' to say "[x] Wells per Second", but while were still talking Small, i find "[x] Seconds per Well" a bit easier to follow along...

Not that it *truly* matters, but in the Miscellaneous Table at 19:17, all of the values in the right column are rational numbers with a shared denominator of 15.

Hey quick question and small gripe, the measurements for energy regeneration were using two different battery amounts. Is the time it takes to recharge your batteries to full independent of how many batteries you have? If so, that's kinda insane, making having more batteries also increase your Wl/s recharge rate.

I'm curious how the combination rule works for cannons, since they can fire separately with a construct head. If two are on one assembly, does one cannon take 0.9wl to fire and the other 0.45wl? Or do both take 0.675wl per shot? For that matter, can I make emitters more energy efficient by attaching additional emitters to a blind construct head?

"If you have something that needs like 14 stabilizers, first of all, give up, it's not going to work..." The Danger Noodle builders apparently took that as a challenge.

If you want, you could characterize zonai charge depletion as numbers of individual fans, rather than wells per second, which would give a conversion of ~6.41, as in 6.41 individual fans running simultaneously would reach a depletion rate of 1 well per second, and 19 fans all connected to one device would, due to the chaining efficiency bonus, have a combined total drain of 10 fans equivalent. If you have an intuition for the rate of depletion of a single fan, then this measure could be a more human way to relate the power-hungriness of various zonai devices to each other, and to the humble fan.

Curious about combining rockets - do multiple rockets attached to the same device activated at the same time make any difference? From what I can tell, if you attach 1 rocket to a base vs. 2,3,10 you will gain the same height only difference being you drain more energy.

8:50 I would have called it the ‘Synergy Rule: Standard’ but that’s okay

The Ancient Zonai equivalent of those Indian Math Videos; this got Rauru through High School

Does the fuse mechanic alter depletion rates for each item? How to emitters on weapons work?

Someone showed that 1 rocket makes things go up to almost the exact same height as multiple. So while the 2nd rocket is more efficient than the 1st, there isn't a good reason to use a second rocket *unless* the weight of some objects is enough to make there be a difference in distance traveled. I haven't tested this.

could the hydrant be used to trigger the wet devices effiency?

Bro was that the colgera blizzard in the background? You really haven’t gotten tulin yet?

This guy could do actual irl science and probably make crazy money. Source: I liked my own comment so it must be true

god i feel like im sitting through them most interesting engineering lecture ever.

15:38 With wheels there seems to be some advantage for multiples of four. Also consider rounding errors due to the precision of the measurements. I'd guess what you really measured is time a device runs using up X wl, by converting that to wl/s with a fixed 3 decimal places you likely lost precision. That precision issue will likely also affect the "miscellaneous" category. The reason is, that those categories have very low depletion rates, so first converting them to 3 decimal places, then dividing those numbers will result in larger rounding errors. Also one needs to take longer measurement times to get appropriate accuracy in those categories. If you still have the numbers from the measurements before conversion to wl/s those might yield more precise ratios.

...My non-american upbringing is showing - I immediately converted all the wl/s measurements into milli-wells/second, thus almost completely avoiding fractional units (darn you wheel and misc combination rules) and making them all easier to say (no more opening zero point...)

This game is so cool.

Oh and full energy meter!