# Viewing blog entries in category: Legend of Zelda calcs

• ### There she blows! A hump like Levias's Thunderhead! (Legend of Zelda)

Millenniums previous to the events of Skyward Sword, Hylia charged the sky leviathan Levias with the title of "Warden of the Skies". He was to protect the Isle of Songs as well as Skyloft, and he was presented one of the keys to the Sky Keep dungeon. However, he was infected by a parasite soon before the beginning of the game, which drove him mad. In this madness, his ambient magical energy was strong enough to create and maintain a giant Thunderhead northwest of Skyloft. I'm looking to calc it.

http://www.narutoforums.com/blog.php?b=21698

The width of the map is 3732km.

(3732000/1263)385=1137624.7m

(3732000/1263)365=1078527.316m

Now I will use these diameters to calculate the volume of the hemispherical shell.

(4/3)pi*(1137624.7/2)^3=770895766816599132.8m^3

(4/3)pi*(1078527.316/2)^3=656889120902618348.86m^3

770895766816599132.8-656889120902618348.86=114006645913980783.94m^3

114006645913980783.94/2=57003322956990391.97m^3

Cloud density is 1.003kg/m^3 or something, right?

57003322956990391.97*1.003=57174332925861363.14591kg

Now to get the moment of inertia. For a hemispherical shell, the formula would be...

I2/3)mr^2
I2/3)57174332925861363.14591*(1137624.7/2)^2
I=12332407921810399503314067742kg*m^2

I had a harder time with angular velocity simply because it was hard to find a reference point from which to scale, but it does noticeably rotate per frame. Therefore, I will use 1px per frame (25fps frame rate) as a low-end.

theta=s/r
theta=1/(703/2)
theta=0.0028449502133713

Now that I have the angular displacement, I can get the angular velocity.

w=theta/t
w=0.0028449502133713/(1/25)

And, finally, the rotational kinetic energy...

KE=.5Iw^2
KE=.5(12332407921810399503314067742)0.0711237553342825^2
KE=31192288894502867834922570.745J

• ### Express delivery done right (Legend of Zelda)

Part of getting to the Eldin Volcano dungeon requires the use of Faron's water basin. Fi decides she'll charm poor Scrapper into doing the heavy lifting and sends for him via her telepathy. He travels from Gondo's shop on Skyloft to Faron's sacred bathing hole or whatever in about 6 seconds.

(404734/86)222.74=1048261.06m

Of course, Skyloft is above the clouds, so the distance would be greater, but unless it's as high as it is far, it wouldn't change too much. Plus, I'm kinda lazy to get an exact altitude

1048261.06/6=174710.2m/s

• ### Faron does a shit job (Legend of Zelda)

Faron is a water dragon anointed by the goddess Hylia to protect the Faron Wood province...and she fucking floods it. A+ job.

She decides to test Link fucking twice after he was hand picked by Hylia herself because Faron doesn't believe he's hero material yet (this being after she was fucked up by Ghirahim...who Link combats several times throughout the game, even without the Master Sword). When he passes her second test, she decides to dump all the water elsewhere.

Faron floods the entirety of the woods except for the temple, but I figure what I have here, as well as the fact that I will calc it as a dome, will more than account for the topography. Hell, almost all of the ground south of the tree is less elevated than the tree is. Plus, it's just easier for me to make sense of it all this way.

That 86 pixel stretch of the Sand Sea is about 404.734km.

(404734/86)187=880061.14m

(404734/86)59.17=278466.4m

The red line is the smallest distance from the tree, our reference point, to the edge of the water. I will be using this for KE of CoM.

That opening is about the height of the water line. It's also a little less than twice Link's size, so about 3 meters.

(3/7)208=89.143m

Calcing as a dome (the volume of an ellipsoid divided by two)...

v(4/3)pi*a^2*b)/2
v(4/3)pi*(880061.14/2)^2*89.143)/2
v=36150271002828.21m^3

36150271002828.21*1000=36150271002828210kg

Now using the red line for movement in our time-frame of about 13 seconds...

278466.4/13=21420.5m/s

KE=.5mv^2
KE=.5(36150271002828210)21420.5^2
KE=8293555774192238730804626.25J

• ### Hyrule and shit (Legend of Zelda)

So upon attempting to quantify some shit in SS, Chaos suggested I use Lanayru Desert as a way of garnering the continent of Hyrule's size, and thus a scale to use.

Thousands of years before the events of Skyward Sword, before the severe climate change resultant of the war between Hylia and Demise, the Sand Sea of Lanayru Desert was once known as "the Great Sea" (separate from Wind Waker's Great Sea, quite obviously). We get to sail this sea while aboard Skipper's Sandship due to the power of the Timeshift Stones. Chaos explained that vessels as large as Skipper's ship would not have been made were it not for the necessity of traversing enormous bodies of water. Therefore, given Zeldaverse's Earth-like nature, it seems reasonable enough to take the area of our smallest sea, the Gulf of California, and apply it to the surface area of the Sand Sea, which was formerly the Great Sea.

Well, on to the scaling, I suppose.

(168*86)/2=7224 px^2

The area of the Sand Sea on this map is then 7224 px^2.

According to Wikipedia, the surface area of the Gulf of California is roughly 160,000 km^2.

Working backwards from the square law...

sqrt(160000/7224)*86=404.734km

The entire map is about 793px across.

(404.734/86)793=3732km

Makes sense, given what we know about our continents, namely Australia. Granted, this isn't the entire continent of Hyrule, but it's a sizable chunk.
• ### Racing, bro (Legend of Zelda)

The Racing Bros challenge ALBW Link to cross Hyrule in under 75 seconds. The time limit for the intermediate course is 65 seconds.

The map for ALBW is slightly different from the one for ALttP, so I went searching and came across one with the route already laid out--all I had to do was measure the path. Neat

Anyway, Chaos has Lake Hylia at 2748.207m.

(2748.207/60)645=29543.22525m

29543.22525/65=454.5m/s