Delicious in Dungeon - Undine's water attack
(From chapter 18 of the manga and episode 8 of the anime)
The Undine can shoot spouts of water with enough force to break stone, which several characters can react to. Firstly, we need the rough diameter of the undine, which we can find easily scaled from Senshi a couple of chapters later. Senshi is 140cm tall.
1194 pixels = 140cm
1 pixel = 140cm/1194 = 0.117252931cm
0.117252931cm X 224 = 26.2646565m
30 pixels = 26.2646565m
1 pixel = 26.2646565cm/30 = 0.87548855cm
0.87548855cm = 32.3930764cm
Now let's scale to our feet. Let's find the distance between the undine and Marcelle. Marcelle is 160cm tall.
367 pixels = 160cm
1 pixel = 160cm/367 = 0.435967302cm
0.435967302cm X 504 = 219.72752cm
0.435967302cm X 27 = 11.7711172cm
0.435967302cm X 104 = 45.3405994cm
311 pixels = 32.3930764cm
1 pixel = 32.3930764cm/311 = 0.104157802cm
0.104157802cm X 35 = 3.64552307cm
3.64552307cm/2 = 1.82276153cm
Let's find the distance to Marcelle.
= 0.535383099 rad
= 30.6751919954108203 degrees
Enter this through the angscaler and we have a distance of 291.68cm to Marcelle. Next we need the distance to the undine.
= 0.369411799 rad
= 21.1657369850875874 degrees
The distance to the undine in the first panel is 86.689cm. We can now find the distance between the undine and Marcelle.
L = 291.68cm - 86.689cm
= 204.99100cm
Next we need the distance between the pillars and the walls. We can also find the diameter of the hole in the wall.
11 pixels = 11.7711172cm
1 pixel = 11.7711172cm/11 = 1.07010156cm
1.07010156cm X 271 = 289.997523cm
Now we can find the total length of the water beam.
L = 204.99100cm + 289.997523cm
= 494.988523cm (4.94988523m)
Let's find it's surface area (as a cylinder).
A = 2πrh + 2πr^2
= 2 X π X 1.82276153 X + 2 X π X 1.82276153^2
= 5689.85468cm^2 (0.568985468m^2)
Now we have the dimensions of the water beam, let's find the area of the hole in the wall.
1.07010156cm X 10 = 10.7010156cm
10.7010156cm/2 = 5.3505078cm
35 pixels = 10.7010156cm
1 pixel = 10.7010156cm/35 = 0.305743303cm
0.305743303cm X 11 = 3.36317633cm
Volume of the area destroyed as a cylinder.
V = πr^2h
= π X 5.3505078^2 X 3.36317633
= 302.47502cm^3 (0.00030247502m^3)
We see fragments sent flying out, so I think violent fragmentation would be justified. Violent fragmentation of rock is 69000000 joules per m^3.
E = 0.00030247502 X 69000000
= 20870.7764 joules
Impressive, but what we're really here for is the speed. Drag coefficient of a cylinder is 1.17 (and using this calculator to find the square root).
DF = ½ρCAv2 X d
20870.7764 X 2 = 1.17 X 0.568985468 X 4.94988523
V^2 = 41741.5528/3.29520293
V^2 = 12667.3694
V = 112.54940870568801m/s
Final Results
Undine's water beam punctures wall (energy) = 20870.776 joules
Undine's water beam puncture's wall (speed) = 112.549 m/s
Another of it's beams takes out part of a pillar, but unfortunately I can't get a good frame of reference for scaling.
The Undine can shoot spouts of water with enough force to break stone, which several characters can react to. Firstly, we need the rough diameter of the undine, which we can find easily scaled from Senshi a couple of chapters later. Senshi is 140cm tall.
1 pixel = 140cm/1194 = 0.117252931cm
0.117252931cm X 224 = 26.2646565m
1 pixel = 26.2646565cm/30 = 0.87548855cm
0.87548855cm = 32.3930764cm
Now let's scale to our feet. Let's find the distance between the undine and Marcelle. Marcelle is 160cm tall.
1 pixel = 160cm/367 = 0.435967302cm
0.435967302cm X 504 = 219.72752cm
0.435967302cm X 27 = 11.7711172cm
0.435967302cm X 104 = 45.3405994cm
311 pixels = 32.3930764cm
1 pixel = 32.3930764cm/311 = 0.104157802cm
0.104157802cm X 35 = 3.64552307cm
3.64552307cm/2 = 1.82276153cm
Let's find the distance to Marcelle.
= 2*atan(367/(634/tan(70/2)))
= 0.535383099 rad
= 30.6751919954108203 degrees
Enter this through the angscaler and we have a distance of 291.68cm to Marcelle. Next we need the distance to the undine.
= 2*atan(250/(634/tan(70/2)))
= 0.369411799 rad
= 21.1657369850875874 degrees
The distance to the undine in the first panel is 86.689cm. We can now find the distance between the undine and Marcelle.
L = 291.68cm - 86.689cm
= 204.99100cm
Next we need the distance between the pillars and the walls. We can also find the diameter of the hole in the wall.
1 pixel = 11.7711172cm/11 = 1.07010156cm
1.07010156cm X 271 = 289.997523cm
Now we can find the total length of the water beam.
L = 204.99100cm + 289.997523cm
= 494.988523cm (4.94988523m)
Let's find it's surface area (as a cylinder).
A = 2πrh + 2πr^2
= 2 X π X 1.82276153 X + 2 X π X 1.82276153^2
= 5689.85468cm^2 (0.568985468m^2)
Now we have the dimensions of the water beam, let's find the area of the hole in the wall.
10.7010156cm/2 = 5.3505078cm
1 pixel = 10.7010156cm/35 = 0.305743303cm
0.305743303cm X 11 = 3.36317633cm
Volume of the area destroyed as a cylinder.
V = πr^2h
= π X 5.3505078^2 X 3.36317633
= 302.47502cm^3 (0.00030247502m^3)
We see fragments sent flying out, so I think violent fragmentation would be justified. Violent fragmentation of rock is 69000000 joules per m^3.
E = 0.00030247502 X 69000000
= 20870.7764 joules
Impressive, but what we're really here for is the speed. Drag coefficient of a cylinder is 1.17 (and using this calculator to find the square root).
DF = ½ρCAv2 X d
20870.7764 X 2 = 1.17 X 0.568985468 X 4.94988523
V^2 = 41741.5528/3.29520293
V^2 = 12667.3694
V = 112.54940870568801m/s
Final Results
Undine's water beam punctures wall (energy) = 20870.776 joules
Undine's water beam puncture's wall (speed) = 112.549 m/s
Another of it's beams takes out part of a pillar, but unfortunately I can't get a good frame of reference for scaling.
