I wasn't sure about Lego Star Wars calcs for a while, as for a long time it was uncertain if they were human-sized or Lego-sized. However, Lego Star Wars: The Skywalker Saga reveals that all of the ships are equal in size to their canon counterparts, meaning they're human-sized, as we can see with a few examples below...
With this in mind, we can finally get to working on calcs! This is from multiple Lego games.
1. Starkiller Base vent explodes
Finn and Rey survive the vent of Starkiller Base exploding unscathed (you can even see they were flung out of the explosion from the centre of it too). X-Wings are 11.76m wide.
375 pixels= 11.76m
1 pixel = 11.76m/375 = 0.03136m
0.03136m X 975 = 30.57600m
119 pixels = 30.57600m
1 pixel = 30.57600m/199 = 0.153648241m
0.153648241m X 518 = 79.5897888m
79.5897888m/2 = 39.7948944m
Using Nukemap (for a radius of 39.7948944m), we get a result of 120 tons of TNT for our fireball. Alternately, using the MIT nuke calculator (using fireball radius at breakaway for contact surface burst), we get a result of 763 tons of TNT.
2. Dreadnaught destroys the Resistance Base
The Dreadnaught attacks the Resistance Base on D'Qar, which creates an explosion hilariously more powerful than the canon version.
D'Qar has a diameter of 10,400km.
R = 10,400km/2
= 5200km
R = (h/2) + c^2/(8h)
= (455/2) + 2105^2/(8 X 455)
= 1444.81456 pixels
1444.81456 pixels = 5200km
1 pixel = 5200km/1444.81456 = 3.59907779km
3.59907779km X 447 pixels = 1608.78777km
1608.78777km/2 = 804.393885km (804393.885m)
This explosion is too big for nukemap, and using the MIT nuke calculator doesn't yet us the exact yield for the radius (we can only get 44689999900 kilotons for a radius of 804390.8m and 44699999900 kilotons for a radius of 804462.8m, or 44.6899999 teratons to 44.6999999 teratons). So we'll also use the StarDestroyer.Net nuke calculator (using ground-contact airburst fireball radius) for a yield of 45330000 megatons, or 45.33 teratons. Finally, it took 4 shots, so we divide our result by 4.
E = 45.33 teratons/4
= 11.3325 teratons
That's actually pretty close to the MIT nuke calculator yield of 44 teratons, so let's also use that for a low end (using the first of the two values).
E = 44.6899999 teratons/4
= 11.1725 teratons
3. Average minifigure height
This will be important for some other calcs I am planing. An X-Wing has a length of 12.5m.
1063 pixels = 12.5m
1 pixel = 12.5m/1063 = 0.0117591722m
0.0117591722m X 21 = 0.246942616m
74 pixels = 0.246942616m
1 pixel = 0.246942616m/74 = 0.00333706238m
0.00333706238m X 478 = 1.59511582m
4. Stormtrooper survives the Death Star exploding
8:01
A Stormtrooper survives the first Death Star exploding.
1389 pixels = 1.59511582m
1 pixel = 1.59511582m/1389 = 0.00114839152m
0.00114839152m X 228 = 0.261833267m
0.00114839152m X 454 = 0.52136975m
0.00114839152m X 71 = 0.0815357979m
0.00114839152m X 397 = 0.455911433m
0.455911433m/2 = 0.227955716m
0.00114839152m X 509 = 0.584531284m
0.584531284m/2 = 0.292265642m
0.00114839152m X 54 = 0.0620131421m
0.00114839152m X 193 = 0.221639563m
We'll calculate the surface volume of the legs and hips as rectangles (multiplying the legs by two as there are two of them) and the head as an ellipse.
A = lh
= 0.261833267 X 0.52136975
= 0.136511945 X 2
= 0.27302389m^2
A = lh
= 0.0815357979 X 0.52136975
= 0.0425102986m^2
A = lh
= 0.0620131421 X 0.221639563
= 0.0137445657m^2
A = πab
= π X 0.227955716 X 0.292265642
= 0.209304287m^2
A = 0.27302389 + 0.0425102986 + 0.0137445657 + 0.209304287
= 0.538583041m^2
That's his head, hips and legs dealt with, but what about his torso? His helmet is partially blocking the view, so we'll use a generic minifigure to scale, as almost all minifigures are the same size in base).
420 pixels = 0.52136975m
1 pixel = 0.52136975m/420 = 0.00124135655m
0.00124135655m X 500 = 0.620678275m
0.00124135655m X 350 = 0.434474793m
0.00124135655m X 407 = 0.505232116m
0.00124135655m X 59 = 0.0732400365m
0.0732400365m/2 = 0.0366200182m
326 - 59 - 59 = 208 pixels
0.00124135655m X 208 = 0.258202162m
0.00124135655m X 182 = 0.225926892m
0.225926892m/2 = 0.112963446m
0.00124135655m X 301 = 0.373648322m
A = a + b/2h
= (0.434474793 + 0.620678275)/2 X 0.50523211
= 0.266548605m^2
While we're at it, let's find the surface area of the generic minifigures head as an ellipse and a rectangle (really two half ellipses, but that basically makes an ellipse).
A = πab
= π X 0.0366200182 X 0.112963446
= 0.0129959m^2
A = lh
= 0.258202162 X 0.373648322
= 0.0964768046m^2
A = 0.0129959 + 0.0964768046
= 0.109472705m^2
We'll pocket that for another Lego calc I hope to do in the near future. In the meantime, let's find the final surface area of the Stormtrooper.
A = 0.538583041 + 0.266548605
= 0.805131646m^2
Now all of that is finally out of the way, let's get to scaling the explosion itself. The first Death Star has a diameter of over 160km.
139 pixels = 160km (160,000m)
1 pixel = 160km/139 = 1.15107914km
1.15107914km X 1073 = 1235.10792km
The timeframe is 4.21 seconds.
T = 1235.10792km/4.21s
= 293374.803m/s
Now to find the energy for the Death Star exploding. There're two ways we'll go about this. For our low end, we'll go with the mass-scattering of the Death Star itself. We'll use the mass of the light ship container vessel 2700TEU, that being 102.56kg/m^3 (as always, I've a feeling this is a huge low end, but it's the best we've got).
V = 4/3πr^3
= 4/3 X π X 80000^3
= 2.14466058e15m^3
M = 2.14466058e15 X 102.56kg
= 2.19956389e17kg
KE = (0.5)mv^2
= (0.5) X 2.19956389e17 X 293374.803^2
= 9.46568848e27 joules
Now we're going to need the surface area that the Sotrmtrooper was hit with. We're going to need the surface area of the Death Star.
A = 4πr^2
= 4π X 80000^2
= 8.04247719e10m^2
With that, let's find the amount of energy withstood by the Stormtrooper using inverse square law.
E = 0.805131646/80000
= 1.00641456e-5 X 9.46568848e27
= 9.52640671e22 joules
= 22.768658484703632183 teratons
An order of magnitude more than what I thought it would be! That's our low end though; for our high end, we'll assume that the energy of the Death Star itself (AKA the energy enough to destroy entire planets) is released from the chain reaction in the core. For this, we'll use the Lego version of the game again.
0:42
Alderaan has a diameter of 12,500km (125000000m), while the Earth has a diameter of 12,756km (12756000m) and a mass of 6.0e24kg.
M2 = (H2/H1)^3*M1
= (12756000/12500000)^3*6.0e24
= 6.37624129e24kg
180 pixels = 12500km
1 pixel = 12500km/180 = 69.4444444km
69.4444444km X 1150 = 79861.1111km
Timeframe is 1.69 seconds.
69.4444444km X 591 = 41041.6666km
For our low end and how high end, we'll use the fireball and the ring of devastation.
(Low end)
T = 41041.6666km/1.69s
= 24285009.8m/s
KE = (0.5)mv^2
= (0.5) X 6.37624129e24 X 24285009.8^2
= 1.88023145e39 joules
= 449.38610181644361001 ninatons
(High end)
T = 79861.1111km/1.69s
= 47255095.3m/s
KE = (0.5)mv^2
= (0.5) X 6.37624129e24 X 47255095.3^2
= 7.11921378e39 joules
= 1.7015329302103251684 tenatons
Now we have all of that, we can finally go for a mid end and a high end for the Stormtroopers durability!
(Mid end)
E = 0.805131646/80000
= 1.00641456e-5 X 1.88023145e39
= 1.89229231e34 joules
= 4.5226871653919697991 yottatons
(High end)
E = 0.805131646/80000
= 1.00641456e-5 X 7.11921378e39
= 7.1648804e34 joules
= 17.124475143403440569 yottatons
Final Results
Finn & Rey survive Starkiller Base's vent exploding (low end) = 120 tons of TNT
Finn & Rey survive Starkiller Base's vent exploding (high end) = 763 tons of TNT
Dreadnaught destroys the Resistance Base (individual shots, low end) = 11.173 teratons
Dreadnaught destroys the Resistance Base (individual shots, high end) = 11.333 teratons
Dreadnaught destroys the Resistance Base (total energy, low end) = 44.69 teratons
Dreadnaught destroys the Resistance Base (total energy, high end) = 45.33 teratons
Average minifigure height = 1.595m
Weight of the Death Star = 219956389000000 tons
The Death Star destroys Alderaan (low end) = 449.386 ninatons
The Death Star destroys Alderaan (high end) = 1.702 tenatons
Stormtrooper survives the Death Star exploding (low end) = 22.769 teratons
Stormtrooper survives the Death Star exploding (mid end) = 4.523 yottatons
Stormtrooper survives the Death Star exploding (high end) = 17.124 yottatons
1. Starkiller Base vent explodes
Finn and Rey survive the vent of Starkiller Base exploding unscathed (you can even see they were flung out of the explosion from the centre of it too). X-Wings are 11.76m wide.
1 pixel = 11.76m/375 = 0.03136m
0.03136m X 975 = 30.57600m
1 pixel = 30.57600m/199 = 0.153648241m
0.153648241m X 518 = 79.5897888m
79.5897888m/2 = 39.7948944m
Using Nukemap (for a radius of 39.7948944m), we get a result of 120 tons of TNT for our fireball. Alternately, using the MIT nuke calculator (using fireball radius at breakaway for contact surface burst), we get a result of 763 tons of TNT.
2. Dreadnaught destroys the Resistance Base
The Dreadnaught attacks the Resistance Base on D'Qar, which creates an explosion hilariously more powerful than the canon version.
D'Qar has a diameter of 10,400km.
R = 10,400km/2
= 5200km
R = (h/2) + c^2/(8h)
= (455/2) + 2105^2/(8 X 455)
= 1444.81456 pixels
1444.81456 pixels = 5200km
1 pixel = 5200km/1444.81456 = 3.59907779km
3.59907779km X 447 pixels = 1608.78777km
1608.78777km/2 = 804.393885km (804393.885m)
This explosion is too big for nukemap, and using the MIT nuke calculator doesn't yet us the exact yield for the radius (we can only get 44689999900 kilotons for a radius of 804390.8m and 44699999900 kilotons for a radius of 804462.8m, or 44.6899999 teratons to 44.6999999 teratons). So we'll also use the StarDestroyer.Net nuke calculator (using ground-contact airburst fireball radius) for a yield of 45330000 megatons, or 45.33 teratons. Finally, it took 4 shots, so we divide our result by 4.
E = 45.33 teratons/4
= 11.3325 teratons
That's actually pretty close to the MIT nuke calculator yield of 44 teratons, so let's also use that for a low end (using the first of the two values).
E = 44.6899999 teratons/4
= 11.1725 teratons
3. Average minifigure height
This will be important for some other calcs I am planing. An X-Wing has a length of 12.5m.
1 pixel = 12.5m/1063 = 0.0117591722m
0.0117591722m X 21 = 0.246942616m
1 pixel = 0.246942616m/74 = 0.00333706238m
0.00333706238m X 478 = 1.59511582m
4. Stormtrooper survives the Death Star exploding
8:01
1 pixel = 1.59511582m/1389 = 0.00114839152m
0.00114839152m X 228 = 0.261833267m
0.00114839152m X 454 = 0.52136975m
0.00114839152m X 71 = 0.0815357979m
0.00114839152m X 397 = 0.455911433m
0.455911433m/2 = 0.227955716m
0.00114839152m X 509 = 0.584531284m
0.584531284m/2 = 0.292265642m
0.00114839152m X 54 = 0.0620131421m
0.00114839152m X 193 = 0.221639563m
We'll calculate the surface volume of the legs and hips as rectangles (multiplying the legs by two as there are two of them) and the head as an ellipse.
A = lh
= 0.261833267 X 0.52136975
= 0.136511945 X 2
= 0.27302389m^2
A = lh
= 0.0815357979 X 0.52136975
= 0.0425102986m^2
A = lh
= 0.0620131421 X 0.221639563
= 0.0137445657m^2
A = πab
= π X 0.227955716 X 0.292265642
= 0.209304287m^2
A = 0.27302389 + 0.0425102986 + 0.0137445657 + 0.209304287
= 0.538583041m^2
That's his head, hips and legs dealt with, but what about his torso? His helmet is partially blocking the view, so we'll use a generic minifigure to scale, as almost all minifigures are the same size in base).
1 pixel = 0.52136975m/420 = 0.00124135655m
0.00124135655m X 500 = 0.620678275m
0.00124135655m X 350 = 0.434474793m
0.00124135655m X 407 = 0.505232116m
0.00124135655m X 59 = 0.0732400365m
0.0732400365m/2 = 0.0366200182m
326 - 59 - 59 = 208 pixels
0.00124135655m X 208 = 0.258202162m
0.00124135655m X 182 = 0.225926892m
0.225926892m/2 = 0.112963446m
0.00124135655m X 301 = 0.373648322m
A = a + b/2h
= (0.434474793 + 0.620678275)/2 X 0.50523211
= 0.266548605m^2
While we're at it, let's find the surface area of the generic minifigures head as an ellipse and a rectangle (really two half ellipses, but that basically makes an ellipse).
A = πab
= π X 0.0366200182 X 0.112963446
= 0.0129959m^2
A = lh
= 0.258202162 X 0.373648322
= 0.0964768046m^2
A = 0.0129959 + 0.0964768046
= 0.109472705m^2
We'll pocket that for another Lego calc I hope to do in the near future. In the meantime, let's find the final surface area of the Stormtrooper.
A = 0.538583041 + 0.266548605
= 0.805131646m^2
Now all of that is finally out of the way, let's get to scaling the explosion itself. The first Death Star has a diameter of over 160km.
1 pixel = 160km/139 = 1.15107914km
1.15107914km X 1073 = 1235.10792km
T = 1235.10792km/4.21s
= 293374.803m/s
Now to find the energy for the Death Star exploding. There're two ways we'll go about this. For our low end, we'll go with the mass-scattering of the Death Star itself. We'll use the mass of the light ship container vessel 2700TEU, that being 102.56kg/m^3 (as always, I've a feeling this is a huge low end, but it's the best we've got).
V = 4/3πr^3
= 4/3 X π X 80000^3
= 2.14466058e15m^3
M = 2.14466058e15 X 102.56kg
= 2.19956389e17kg
KE = (0.5)mv^2
= (0.5) X 2.19956389e17 X 293374.803^2
= 9.46568848e27 joules
Now we're going to need the surface area that the Sotrmtrooper was hit with. We're going to need the surface area of the Death Star.
A = 4πr^2
= 4π X 80000^2
= 8.04247719e10m^2
With that, let's find the amount of energy withstood by the Stormtrooper using inverse square law.
E = 0.805131646/80000
= 1.00641456e-5 X 9.46568848e27
= 9.52640671e22 joules
= 22.768658484703632183 teratons
An order of magnitude more than what I thought it would be! That's our low end though; for our high end, we'll assume that the energy of the Death Star itself (AKA the energy enough to destroy entire planets) is released from the chain reaction in the core. For this, we'll use the Lego version of the game again.
0:42
Alderaan has a diameter of 12,500km (125000000m), while the Earth has a diameter of 12,756km (12756000m) and a mass of 6.0e24kg.
M2 = (H2/H1)^3*M1
= (12756000/12500000)^3*6.0e24
= 6.37624129e24kg
1 pixel = 12500km/180 = 69.4444444km
69.4444444km X 1150 = 79861.1111km
69.4444444km X 591 = 41041.6666km
For our low end and how high end, we'll use the fireball and the ring of devastation.
(Low end)
T = 41041.6666km/1.69s
= 24285009.8m/s
KE = (0.5)mv^2
= (0.5) X 6.37624129e24 X 24285009.8^2
= 1.88023145e39 joules
= 449.38610181644361001 ninatons
(High end)
T = 79861.1111km/1.69s
= 47255095.3m/s
KE = (0.5)mv^2
= (0.5) X 6.37624129e24 X 47255095.3^2
= 7.11921378e39 joules
= 1.7015329302103251684 tenatons
Now we have all of that, we can finally go for a mid end and a high end for the Stormtroopers durability!
(Mid end)
E = 0.805131646/80000
= 1.00641456e-5 X 1.88023145e39
= 1.89229231e34 joules
= 4.5226871653919697991 yottatons
(High end)
E = 0.805131646/80000
= 1.00641456e-5 X 7.11921378e39
= 7.1648804e34 joules
= 17.124475143403440569 yottatons
Final Results
Finn & Rey survive Starkiller Base's vent exploding (low end) = 120 tons of TNT
Finn & Rey survive Starkiller Base's vent exploding (high end) = 763 tons of TNT
Dreadnaught destroys the Resistance Base (individual shots, low end) = 11.173 teratons
Dreadnaught destroys the Resistance Base (individual shots, high end) = 11.333 teratons
Dreadnaught destroys the Resistance Base (total energy, low end) = 44.69 teratons
Dreadnaught destroys the Resistance Base (total energy, high end) = 45.33 teratons
Average minifigure height = 1.595m
Weight of the Death Star = 219956389000000 tons
The Death Star destroys Alderaan (low end) = 449.386 ninatons
The Death Star destroys Alderaan (high end) = 1.702 tenatons
Stormtrooper survives the Death Star exploding (low end) = 22.769 teratons
Stormtrooper survives the Death Star exploding (mid end) = 4.523 yottatons
Stormtrooper survives the Death Star exploding (high end) = 17.124 yottatons
