How Does the ENERGY CELL Work in Tears of the Kingdom? | All your Zonai device questions answered!
ฝัง
- เผยแพร่เมื่อ 15 มิ.ย. 2024
- After dozens of hours of research and editing, here is the first part of my Zonai device deep dive. Basic info about the energy cell, device depletion rates, combination rules, and plenty of math... It's all here!
Link to the calculator: docs.google.com/spreadsheets/...
I will keep updating the calculator as I improve my calculations. If for some reason I need to change the link, I will update it here, too.
Chapters:
00:00 Introduction
01:24 CHAPTER 1: MEASURING ENERGY
01:43 Defining the well [wl]
02:55 Defining depletion [wl/s]
04:35 Zonaite armor effects
06:03 CHAPTER 2: POWERED DEVICES
06:14 Fan
11:08 Emitter (Flame, Frost, Shock, Beam)
14:06 Hydrant
14:36 Wheel (Small, Big)
16:03 Cannon
18:45 Misc. (Stabilizer, Construct Head, Hover Stone, Homing Cart, Light)
20:11 Rocket
21:37 Epilogue and how to use the calculator
Music used (in order)
Eldin Shrine (in botw. idk what it's called in this game.)
Sky Maze
Water Temple 3
Construct Factory 5
Depths Maze
Fire Temple 3
Tarry Town (Zora Invited)
See you in part 2! - เกม
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.
Thanks! I sometimes wonder about becoming a professor at some point. It’s good to know that I can communicate well.
@@paradox_guardiangenuinely, let me know if you'd like to chat about that potential as there are some steps you should try to take earlier than later. (I use my TH-cam channel for my lab, so you can see examples of work from my group there)
@paradox_guardian …or consider becoming an engineer!
@@drchuck9*tf2 intensifies*
@@awkwurdtalke-gamesandgamer8236ENGINEER GAMING
I'm surprised you didn't post it on the hyrule engineering subreddit, I think they'd probably appreciate this kind of research
got tired and went to bed. Gonna post today
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! =)
I fully agree! The thing is, it's often possible to do this sort of thing by reading code, which is often faster or made more available. Makes real science like this less likely, which is sad.
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.
Yeah, I do it because I care about this stuff. I could probably do more to try to get my channel some exposure (ex. distracting brightly-colored thumbnails or telling people to subscribe), but I HATE stuff like that and I adamantly refuse to do it.
thankfully it popped off and i saw it in my recommended! for once youtubes does something right
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!
I think the Zonaite bow is .75 wl/s if my memory is correct
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.
Make sense since most normal vehicles use 4 wheels
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
Thanks! This was actually kinda unscripted. Instead of writing each line in advance, I just had more of a general plan and said each line as I went. I did need to redo them many times to get the audio right, though!
@@paradox_guardian That's effectively scripted, it's just that you did the scripting in audio format, and you could take any one of your scripts and put it directly into the video.
From one engineer to another.... Mad respect, my good sir. This is very clear and concise. Well researched and beautifully presented. Well done!
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?
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
Amazing, I love those research efforts, stuff like this is much more engaging to the community than having all values from a datamine!
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.
Wow. All this time, I was so sure that the big wheel depleted faster than the small one.
Me too! It was cool and surprising seeing that there isn’t any difference
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.
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
Hmm. I’ve completed version 2 of the calculator and am working on the video for it. Maybe that can go into version 3 if I make it eventually, but that would need a HUGE rework
Paradox you the goat man
Thanks. Hope you like it. It was fun doing the research and slowly seeing a pattern emerge
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).
These are on the list. It just takes time to do all the research. Part 2 should be out in the next couple days!
This video made me so happy. I love all the math. Allows us to make accurate predictions for the performance of complex builds
awesome! This is incredibly informative and indepth. I love it
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
That will be for a proverbial part 3. There's a lot to talk about with fuse.
W o w . . . I wish I had this level of patience to do so much research.
This guy has brought math and engineering fundamentals to ToTK! Excellent stuff!
Holy cow. Your methods are solid. Your math is clean. This is a rare gem of quality and precision. Bravo.
subbed out of respect for the insane amount of reasearch
Extraordinarilly underrated, that's all I have to say.
You tricked me into learning and enjoying math!
Well played... well played...
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 !
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!
The real question is how this man managed to get a gf while doing all of this
As a woman: very easily.
Easy it is called time management. Balance your time with your loved one and your game, and you'll be fine 🙂
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. 😀
Thanks! Yes, I have had a mostly wonderful time with Resolve! I don’t have the money or need for the studio version, but I really wish there was a way to donate like $100 or so to them, just for making such a cool piece of free software.
This is such a great video, and I’ve enjoyed your others as much as this one! You’ve earned a new sub!
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!
Great video !!
I love you, and didn’t knew you were the creator until the end 😂
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?
Love your work. Thank you for your dedication!
Great video! Easy to understand and very useful.
Did you ever try any of the emitters or hydrant on a shield to see how it changes the depletion rate.
Fused devices work completely differently! I plan on investigating it at some point, perhaps in a part 3 if people want it.
@@paradox_guardian I would be interested. Also great video
This is fascinating and super useful. Thanks!
I love the math behind, thank you so much for this!
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
This video is amazing! Really cool
After your most recent vid and the attention you're getting for it, I'm hyped for part 2
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).
Super informative. Great stuff, man!
The fan thing also works when you attach it to spinners, like the ones on the sky archipelagos, pretty neat.
Shout out to the graphics girlfriend.
You have a winner there!
Great work, you have done a fine job of translation changing science to layman understanding.
I am engineer, and this was delightful. Good show fellow nerd
I only have 4 wells at the moment, so this information comes extremely helpful.
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.
I address this in the video
@@paradox_guardian oops, must have missed that part!
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
Very well put together!
Here before this blows up, fantastic video
I like how he just casually uses footage from one of the best paracopter launches in history 1:27
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!
That is a good idea! I did consider adding seconds per well, but decided against it because it is harder to use with combination rules. Maybe I’ll make a followup video at some point.
Or just use milliwells? Also, judging from your numbers, I suspect actual units used in the game code are different. Maybe we could figure out what they are without diving in the code, based on your findings and the assumption they're actually integers. Maybe there's a number of "units per well" that gives nicer numbers for depletion rates (when considered per frame and not per second).
I did look at per frame but they still weren’t integers. I have since found a datamined spreadsheet that gives the depletion in wl/s so I think that’s what the devs were going for also.
Super appreciate this!! Formula is get, thanks for deriving!
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 info and excellent work 👏
That launch up the chasm was 🔥
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.
"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?
I haven't tested that yet. I'll add it to the list! I also want to look into fuse-entanglement to see if there is something to work with there.
Just tested, ice blocks don't seem to count as water for the purpose of fan efficiency.
If only the young Shigeru Miyamoto could have foreseen future Zelda fans discussing “Base Depletion Rate” and their impact on his game.
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.
Truly, you are by far one of the most professional TotK youtubers I've ever seen, bravo!
Thanks :). I am hard at work on part 2 as we speak
@@paradox_guardian Looking forward to it😁
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!
Oh and as a (probably) obvious note, you'd amend this for multiple cannons by multiplying d with your group discount before multiplying the output!
Im gonna use this for my next construction
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 😊
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
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.
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?
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).
The fans using less power also works with sand if you have a sled, to my knowledge!
Any kind of sand, or just the flowing "quick sand" sort?
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)
8:50 I would have called it the ‘Synergy Rule: Standard’ but that’s okay
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
"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.
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
The Ancient Zonai equivalent of those Indian Math Videos; this got Rauru through High School
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.
I think stuff like that does matter, but it is hard to tell exactly why. The devs had something in mind, but I am not sure 100% what.
I can’t thank you enough for this. This game has taken over my life and you have done some truly amazing work here. Bravo!
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?
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...
I agree with your thoughts in the case of single devices. But we get issues with using s/wl when we try to combine devices together. Instead of simple addition (with the extra work of looking at combination rules), we would have to add a bunch of weighted fractions and then invert the result. If you have seen the equation for parallel electrical resistors, it would look much like that. I think this would take some getting used to for the average audience member, and I hate animating fractions because video editing is not designed for math lmao. So I decided to use a slightly more opaque unit to make the calculations a bit more clear, if that makes sense. If it helps, when you use the calculator, it does give the machine's duration (s/wl).
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?
Wheels are unaffected by steering stick position from what I’ve found
@@paradox_guardian I see, that's interesting! Thank you for your answer! 😄
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.
Yup, it’s always 21 seconds
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.
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?
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.
Following the video, emitters all have a base depletion rate of ~1.15 fans, which is what 0.18/0.156 is
god i feel like im sitting through them most interesting engineering lecture ever.
This guy could do actual irl science and probably make crazy money.
Source: I liked my own comment so it must be true
I am currently studying for my PhD in electrical engineering.
Did you notice how faster time flows when you are watching Paradox Gaming videos?
This game is so cool.
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?
Just did a quick test, and it seems to be based on how many devices on the machine are actually active (rather than just the total attached to the machine). So, for a device with two construct heads with a cannon each:
- if only one construct head is currently activated, that cannon will use 0.9wl
- if both construct heads are activated, the cannons will each use 0.675wl (even if they fire at different times)
So this means you can't really cheat on efficiency by using idle construct heads - the devices have to be active to benefit from combination rules. (You _might_ technically be able to get up to some shenanigans with the discrete nature of cannons, but even if it is possible it probably wouldn't be practical.)
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.
In terms of height, from what I've seen it only matters to balance the forces out. I don't think you get much more height from using a ton of rockets. However, I did not rigorously test this.
you can technically take any of the fanned flyers anywhere if you just do a couple donuts in the air before you battery runs out, stop your vehicle, instantly use recall on it, and then just wait while your battery recharges during recall. you won't lose any position because you are just doing circles, like a vulture. you get a net gain and can fly anywhere until the timer of the fans breaks.
Does the fuse mechanic alter depletion rates for each item? How to emitters on weapons work?
Yes it does! This is an idea in the future video list.
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.
It appears to be mainly to evenly distribute the thrust, ie not have a platform go lopsided because there's only rocket(s) on one side. Or perhaps to get more nuanced with the angle of thrust.
Oh and full energy meter!
What about when you have zoni divine connected to a weapon?
Bro was that the colgera blizzard in the background? You really haven’t gotten tulin yet?
Hey for anyone that knows where do i get the hylian shield (i'm tired of using guides for EVERYTHING)