Introduction
Because that's flipping cool.
Calc done for the Star Wars upgrade thead.
The Calculation
Step #1: Scaling Fingers
Yoda stands at 0.66 Meters, or 66 Centimeters. So 13 Pixels = 66 Centimeters.
The diameter of the finger is 58 Pixels.
58 / 13 = 4.461538461538462
66 * 4.461538461538462 = 294.4615384615385 cm, or 2.94 Meters (1.47 in Radius) (I have a feeling this wont yield nearly as high results as I think it will).
And the length of the finger is 160 Pixels.
160 / 13 = 12.30769230769231
66 * 12.30769230769231 = 812.3076923076925 cm, or 8.12 Meters
pi × r2 × h
pi × 1.47^2 × 8.12 = 55.123980629 m^3
They have 4 fingers on each hand (from my count), so exuding thumbs, that's a total of 6 fingers.
55.123980629 * 6 = 330.743883774 m^3
Step #2: Scaling the Body
Arms
Hoo boy.
So 46 Pixels = 2.94 Meters
The arm has a diameter of 128 Pixels.
128 / 46 = 2.782608695652174
2.94 * 2.782608695652174 = 8.180869565217392 Meters
8.180869565217392 / 2 = 4.09
The length of the arm is 410 Pixels
410 / 46 = 8.91304347826087
2.94 * 8.91304347826087 = 26.2 Meters
pi × 4.09^2 × 26.2 = 1376.885353 m^3
Double that for both arms.
1376.885353 * 2 = 2753.770706 m^3
Legs
The leg has a diameter of 123 Pixels.
123 / 46 = 2.673913043478261
2.94 * 2.673913043478261 = 7.861304347826087 Meters
7.861304347826087 / 2 = 3.930652173913044 Meters
The length has a length of 451 Pixels
451 / 46 = 9.8
2.49 * 9.8 = 24.402 Meters
pi × 3.930652173913044^2 × 24.402 = 1184.41670623 m^3
Double that for both legs.
1184.41670623 * 2 = 2368.83341246 m^3
Body
Width of the body is 44 Pixels.
46 / 44 = 1.045454545454545
2.49 / 1.045454545454545 = 2.381739130434784 Meters
The Length of the Body is 278 Pixels.
278 / 46 = 6.043478260869565
2.49 * 6.043478260869565 = 15 Meters
And the height of the body is 504 Pixels
504 / 46 = 10.95652173913043
2.49 * 10.95652173913043 = 27.28173913043477 Meters
LHW
15 * 27.28173913043477 * 2.381739130434784 = 974.6 m^3 (I expected it to be bigger)
East Spike
The diameter of the spike is 62 Pixels.
62 / 46 = 1.347826086956522
2.49 * 1.347826086956522 = 3.35 Meters
3.35608695652174 / 2 = 1.67804347826087
The height of the spike is 170 Pixels.
170 / 46 = 3.695652173913043
2.49 * 3.695652173913043 = 9.2 Meters
(pi × 1.67804347826087^2 × 9.2)/3 = 27.1283177618 m^3
(pi × r2 × 9.2)/3
Middle Spike
The diameter is 102 Pixels.
102 / 46 = 2.217391304347826
2.49 * 2.217391304347826 = 5.521304347826087 Meters
5.521304347826087 / 2 = 2.760652173913044 Meters
The height of the horn is at least 197 Pixels.
197 / 46 = 4.282608695652174
2.49 * 4.282608695652174 = 10.66369565217391 Meters
(pi × 2.760652173913044^2 × 10.66369565217391)/3 = 85.10 m^3
West Spike
The west spike has a diameter of 45 Pixels.
46 / 45 = 1.022222222222222
2.49 / 1.022222222222222 = 2.435869565217392 Meters
2.435869565217392 / 2 = 1.217934782608696 Meters
And the height is 154 Pixels.
154 / 46 = 3.347826086956522
2.49 * 3.347826086956522 = 8.33608695652174 Meters
(pi × 1.217934782608696^2 × 8.33608695652174)/3 = 12.9 m^3
Step #3: Total Volume and Mass
12.9 + 85.10 + 27.1283177618 + 974.6 + 2368.83341246 + 2753.770706 + 1376.885353 + 330.743883774 = 7929.961673 m^3
Density of Granite is 2750 kg/m^3
2750 * 7929.961673 = 21,807,394.6007 kg. Class M lifting strength.
Step #4: Potential Energy
PE = MGH
M = Mass
Mass = 21,807,394.6007 kg
G = Gravity
Gravity = 9.8
H = Height
Now just to fight the height.
Yoda is 14 Pixels (again?). So 14 Pixels = 66 cm
He threw it 127 Pixels.
127 / 14 = 9.071428571428571
66 * 9.071428571428571 = 598.7142857142857 cm, or 5.98 Meters
21,807,394.6007 * 9.8 * 5.98 = 1278000553.18 Joules
0.3 Tons.
Building level.
Well...that's incredibly underwhelming.
Using the entire height of the mountain would yield
21,807,394.6007 * 9.8 * 39.84 = 8,514,304,688.74 Joules, or 2 Tons.
Well then..I probably messed up somewhere. I might try redoing it scaling off the foot instead, but I doubt it'll increase the results, it might decrease them actually.
Edit: So, I recall Soldier Blue saying these Rocks were said to be abnormally strong and hard, so I guess using the density of Basalt could apply here. It has a density of 3.0 g/cm^3 or 3,000 kg/m^3
7929.961673 * 3000 = 23,789,885.019 kg
23789885.019 * 9.8 * 5.98 = 1394182421.65 Joules
0.33 Tons
Bleh
