Introduction[]
This is major spoiler for anyone who did not see the movie, but regardless, here's the calc
In the final battle of Sonic the Hedgehog 2, Sonic transforms into Super Sonic and fights Eggman
While fighting, the following feat happens where the Giant Eggman Robot slams his fist against Super Sonic, who stops it effortlessly
Part 1: Calculating Sonic's size in the movie[]
Sonic seems to have gotten taller since the last movie, and in this picture he is compared to Tom
Tom = 5'10 = 1.778 meters = 520px
Sonic = 307px = (1.778/520) * 307 = 1.0497 m
That would mean that Sonic is 1.0497 meters tall in this movie
Part 2: Calculating Giant Eggman Robot's size[]
Sonic = 75px = 1.0497 meters
Eggman Robot Boot (Picture 1) = 384px = (384/75) * 1.0497 = 5.374464 meters
Eggman Robot Boot (Picture 2) = sqrt[(35px)^2 + (67px)^2] = 75.6px = 5.374464 meters
Lower Eggman Robot Body Height = 414px = (414/75.6) * 5.374464 = 29.4315886 meters
Upper Body Height = sqrt[(107px)^2 + (555px)^2] = 565.2px = (565.2/75.6) * 5.374464 = 40.1805166 meters
Full Height = 69.6121052 meters
The arms and legs of the robots appear to have a cylindrical shape. Volume of a cylinder is: V = π * R^2 * H
Since the widths of the limbs of the robot seem to vary, I'll simplify it by using the average width of the limbs
Egg Robot Arm Length: sqrt[(108px)^2 + (172px)^2] = 203.1px = (203.1/178) * 40.1805166 = 45.8464209 meters
Egg Robot Arm Min-Width: sqrt[(26px)^2 + (17px)^2] = 31.1px
Egg Robot Arm Max-Width: sqrt[(62px)^2 + (36px)^2] = 71.7px
Egg Robot Arm Average Width: (31.1 + 71.7)/2 = 51.4px = (51.4/177) * 40.1805166 = 11.6682404 meters
Egg Robot Arm's volume = V = π * R^2 * H = π * (11.6682404/2)^2 * 45.8464209 = 4,902.3696519 m^3
As there are 2 arms, the total volume would be twice of that or: 9,804.7393038 m^3
Egg Robot Leg Length: sqrt[(50px)^2 + (150px)^2] = 158.1px = (158.1/178) * 40.1805166 = 35.6884251 meters
Egg Robot Leg Min-Width: sqrt[(24px)^2 + (31px)^2] = 39.2px
Egg Robot Leg Max-Width: sqrt[(75px)^2 + (29px)^2] = 80.4px
Egg Robot Leg Average Width: (39.2 + 80.4)/2 = 59.8px = (59.8/177) * 40.1805166 = 13.5751124 meters
Egg Robot Leg's volume = V = π * R^2 * H = π * (13.5751123/2)^2 * 35.6884251 = 5,165.4020034 m^3
As there are 2 legs, the total volume would be twice of that or: 10,330.8040068 m^3
For the body, I'll assume for simplicity sake that the width of the robot body is equal to its length/thickness
Egg Robot Body Height: 178px = 40.1805166 meters
Egg Robot Leg Width: 140px = (140/178) * 40.1805166 = 31.6026535 meters
Using the elipsoid formula from this calculator: V = 4/3 * π * A * B * C = V = 4/3 * π * A * (B^2) (As the width and length are assumed to be equal)
A = Robot Body Height / 2 = 20.0902583 meters
B = Robot Body Width = Robot Body Length/Thickness = 15.80132675 meters
V = 4/3 * π * 20.0902583 * (15.80132675^2) = 21,011.7022236 m^3
Total Robot volume = (10,330.8040068 + 9,804.7393038 + 21,011.7022236) = 41,147.2455342 m^3
Using 50% hollowness since some of it is hollow: (20,135.5433106 * 0.5) = 20,573.6227671 m^3
Average density of steel: 7950 kg/m3
Death Egg Robot mass: (20,573.6227671 * 7950) = 163,560,300.998445 kg or Class M
As Super Sonic was able to easily lift the entire robot and resist its crushing, Sonic would scale to the robots full weight
Eggman used the robots whole arm to punch Sonic, who stopped all of his arm in its tracks.
As we calculated previously, the volume of each one of the robot's arm is 5,165.4020034 m^3. Using the density from before and the accounted 50% hollowness from before will give us:
Arm's mass = (5,165.4020034 * 7950) * 0.5 = 20,532,472.963515 kg
Part 3: Timeframe and Distance[]
Using Watch-frame-by-frame, Sonic stopped the Robots arm starting from Frame 2372 and completely stops at Frame 2377
The frames run on 25FPS
T = Timeframe = (2377-2372)/25 = 0.2s
For the distance the arm traveled, the arm did a 90 degrees arc, as Sonic was right next to the middle of the robot's body
As we calculated the robot's arm length before, it gave us a result of 45.8464209 meters for its length
The arc length formula in radians can be expressed as, arc length = θ × r, when θ is in radian. Arc Length = r × (π/180) × θ, where θ is in degree, where,
- L = Length of an Arc
- θ = Central angle of Arc
- r = Radius of the circle
Length of a 90 degrees arc would be: L = R * (π/180) * 90 = 45.8464209 * (π/180) * 90 = 72.0153895 m
Eggman begun to move his hand at Frame 2296 and his hand reaches Sonic at Frame 2372
t = (2372-2296)/25 = 3.04 seconds
V = 72.0153895 / 3.04 = 23.6892729 m/s
Part 4: Finding the Force of Eggman's punch[]
As we know, F = M*A, where A is the acceleration, M is the mass of the object and F is the force, according to Newton's Second Law of Motion
A = V/T = 23.6892729 / 0.2s = 118.4463645 m/s^2
F = 20,532,472.963515 * 118.4463645 = 2,431,996,776.7228929 N = 247,909,967.0461664 kg or Class M
Part 5: Additional End[]
Well, technically, Eggman tried to punch Super Sonic with both of his robot arms with the same result happening to the second arm as the first one.
Assuming that timeframe is the same from before, as Sonic basically stops the hand instantly before it explodes, this would give us a timeframe of 0.2 seconds for Sonic to stop Eggman's arm in its place
Timeframe is seen in Pictures 4 and 5 in this link
Eggman's robot hand started to move at Frame 2744 and reached Sonic at Frame 2768
t' = (2768-2744)/25 = 0.96 seconds
Given that the arm needs to traverse a 90 degrees arc, the distance would be the same as with the first arm, which would be D = 72.0153895 m
V = D/t = 72.0153895 / 0.96 = 75.0160307 m/s
A = V/T = 75.0160307 / 0.2 = 375.0801535 m/s^2
F = M * A = 20,532,472.963515 * 375.0801535 = 7,701,323,110.8898061 Newtons = 785,048,227.4097662 kg or Class M