
An analysis of the Lego City deep space rocket - wh313
http://h313.info/blog/aerospace/2020/05/09/an-analysis-of-the-lego-city-deep-space-rocket.html
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gorgoiler
My intuition, as a rocket scientist[1].

Once the boosters have come off, it feels like the drag from the nose is going
to flip the rocket around. Those control surfaces _on the nose_ are at the
exact wrong end of the rocket.

They don’t even need to be dynamic — a set of static stabilizers at the rear
of the liquid stage is should be added to provide stabilizing drag after the
boosters have been detached.

This might not be a problem if the rocket has reached an altitude where it is
subsonic or the drag from air is small enough to be countered by the torque
provided by thrust vectoring.

Those engines have a gimbal, right?

[1] I’ve worked at KSC[2] since almost the very beginning[3] of the programme.

[2] Kerbal Space Center.

[3] 0.18.

 _...written with apologies to those who are actually qualified in this area._

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sandworm101
Looking at their nozzles, the boosters also appear to be SRBs. That's a real
rookie mistake. Nobody has dared launch humans in a capsule atop SRBs. The
general consensus is that, in an emergency, deploying a parachute under a hail
of burning solid rocket fuel will not end well.

~~~
NikolaeVarius
Is Nozzle design actually a method of determining Solid/Liquid?

I know that the design depends on expected stage of flight use and things like
exhaust velocity, but i didn't think just seeing a nozzle would be enough to
make a determination,

~~~
sandworm101
(1) Relative size. Solid fuel is much more energy dense. In this case, if the
nozzle was for liquid then its tank is so small that it would burn out very
quickly. So it is likely an SRB. Note the other nozzles for the relatively
wider center tank.

(2) Shape. You can look to the shape of the nozzle to see which altitude it is
optimized for. SRBs are generally optimized for lower altitude.

(3) Throat diameter. By following the shape of the nozzle towards the tank
above you can estimate the throat. SRBs have wider throats.

(4) Gimble (not seen here) SRBs can be steerable but they don't 'gimble' the
same as liquid engines. Their nozzles are moved rather than the whole engine
(see shuttle). So any moving nozzle bits suggests an SRB.

So ya, there is much to read from just the nozzle. In fact deep in the CIA
there are probably some experts with magnifying glasses studying pictures of a
North Korean rocket nozzle doing exactly that.

~~~
NikolaeVarius
1) I think relative size is a bit of a crapshoot. The size of the strap-ons is
effectively the same size as the center core, The second stage of the core
makes it look like a full sized LOX/LH2 tank because its painted orange, but
it isn't.

2-3) Sure, but that is a general principal, not a sure sign its an SRB.

4) I don't see a sign of a gimbal. It may actually not even be a nozzle, and
just the skirt.

~~~
sandworm101
Relative size of nozzles to attached tank. The sides are much much larger in
proportion to their tanks.

SLBMs (ie SRBs)
[https://upload.wikimedia.org/wikipedia/commons/6/6a/SLBM_Com...](https://upload.wikimedia.org/wikipedia/commons/6/6a/SLBM_Comparison.jpg)

Atlas missile (liquid fuel)
[https://en.wikipedia.org/wiki/File:Atlas_2E_Ballistic_Missil...](https://en.wikipedia.org/wiki/File:Atlas_2E_Ballistic_Missile.jpg)

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simonh
Clearly this line of reasoning is the wrong way round. Surely the correct
approach is to calculate the gravity and size of the LEGO planet and it's moon
from the characteristics of the rocket.

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mabbo
Okay, I did it. Lego Planet is 20 (edit: actually 5) times less massive than
earth.

Let's presume Lego Planet has the same density as Earth, so that the math is
easy and I can make fewer assumptions. If we assume a planet with the same
density, then our radius is just a function of the mass. Then all we need to
do is pick a mass that lets us reach escape velocity- I presume a Deep Space
Rocket wants to fully escape the planet, after all.

V_escape = ((2 * G * M) / R)^(1/2). G is constant, M for earth is 5.97E24 kg,
R is 6.38E6 m.

Doing some math, if Lego Planet has a mass of 3E23 kg (20 times smaller than
earth), then the radius is 2.35E6 m (a little bit bigger than 1/3 Earth's
radius), and the escape velocity is 4120 m/s. The author calculated this
rocket would have 4246 m/s of delta-V, so that leaves this rocket 125 m/s of
Delta-V to maneuver where it needs to go.

Edit later: Okay, people have suggested Lego Planet is made of Lego
(sensible). So let's fix these numbers.

According to this[0] Lego bricks with optimal packing have a density 0.64
g/cm^3, which is 640 kg/m^3 - FAR less dense than Earth, which will have
consequences. If we then guessed that Lego Planet's mass is 1.25E+24 kg, 1/5th
of Earth's mass, the the escape velocity is 4213.2 m/s which is close to this
Rocket's delta-V.

This also means that Lego Planet is 47% _larger_ than Earth, by radius, and
has more than double the surface area (which is based on radius squared). No
wonder there's so many different Lego sets!

[0][https://www.brickodyssey.com/what-is-the-density-of-
lego/](https://www.brickodyssey.com/what-is-the-density-of-lego/)

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codeulike
Lego Planet is made up of how many 2x4 bricks? (assuming they dont compress)

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mabbo
tldr: A little bit more than 400 million billion billion standard 2x4 bricks,
roughly.

Given my calculated radius of 9.39E6 m (47% larger than earth), the volume of
Lego Planet is 1.95313E21 m^3.

Brickepdia[0] (of course that's a thing) shows that a standard 1x1 block of
standard height is 8 mm x 8 mm x 9.6 mm, or 6.14E-7 m^3. A 2x4 brick would be
8 times that, or 4.92E-06. Simple division then gives us that Lego Planet is
made of 3.97E26 standard 2x4 bricks.

[0][https://brickipedia.fandom.com/wiki/Brick#Sizes](https://brickipedia.fandom.com/wiki/Brick#Sizes)

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zoomablemind
This assessment completely omits an important source of impulse -- the kid
driven by imagination. This has to be scaled up too!

I've been locating some of our Lego models at home in places that defy
traditional notions of gravity, can only guess what was the intended target of
our little Commander at launch.

So the base assumption should be that the tanks are filled with Magic, and the
main stage houses a warp-core. The destination is indeed Deep Space! (Picard
to the Bridge)

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anemic
It could be decoy program to hide development of an intercontinental ballistic
missile?

I haven't seen any LEGO centrifuges in stores. Those could have been hoarded
by someone to encrich LEGO uranium?

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codeulike
Lego City is a rogue state? This changes everything.

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TomK32
It is, or did you read anything about a proper governmental transition from
SYSTEM to City? All hush hush.

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codeulike
They always seemed to have more police stations than supermarkets, always a
bad sign

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twic
The only productive industry is Octan, the oil company, and in the movie, the
president of that company is also the de facto ruler of the city. Is Lego City
a classic petro-state?

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kevin_thibedeau
It's all a massive jobs program that doesn't need to accomplish anything to
achieve it's true goals. Very realistic.

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bootloop
I believe the flaw is in assuming a Lego figure is not in 1:1 scale. So
instead of upscaling the Lego figure we should just down-scale "earth" (in
reality now Lego-earth) and re-run these numbers with Lego-earth gravity.

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kolinko
Lego figures are more bulky than humans. This would suggest that Lego-earth
has actually a higher gravity than earth, right?

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SahAssar
Lego minifigs are mostly filled with air, while humans are mostly water. Water
is heavier than air, so wouldn't that mean lower gravity?

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kolinko
Good question, haven’t thought of that!

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Ygg2
Solution is simple. LEGOTimespace functions based on consensus of observers
and rule of imagination.

Thus, they need big rockets to merely get out of sight. Once they are
unobservable, they only need enough "fuel" to convince the two astronauts
aboard they are doing fine.

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lfnoise
Choosing the Orion capsule as a reference seems unnecessarily large. The
Gemini capsule had crew 2, and was 3,851 kg.

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JorgeGT
Not only that, it assumes the payload stage weights as much as the Orion
capsule...

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Gravityloss
Yeah. This is a single person capsule so Mercury would be a better comparison.
1090 kg.

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karatestomp
Without reading TFA: no. Probably could reach space. Maybe— _maybe_ —orbit,
but barely and I'd lean toward no on that, too.

Source: Kerbal Space Program intuition (hey, served me well when I took one
look at that SpaceX starship design and went "oh that's not going past Earth
orbit without an orbital re-fuel and nearly-dry top stage tanks at launch"
and, sure enough, that was the plan)

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dang
The title was "Will the Lego City Deep Space Rocket Go into Deep Space?" when
this was posted. We changed it to that of the article.

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londons_explore
Lego city isn't on earth... So requiring earth amounts of delta-v doesn't make
sense...

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wh313
That's a good point! I'm assuming that it's on Earth as [this
set]([https://www.amazon.com/dp/B003A2JCOA?tag=duckduckgo-
fpas-20&...](https://www.amazon.com/dp/B003A2JCOA?tag=duckduckgo-
fpas-20&linkCode=ogi&th=1&psc=1#immersive-view_1589080320217)) shows cities on
Earth as destinations for the train.

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slg
The routes include Moscow and Dublin. What city on Earth has train routes that
can reach both of those cities? Another point in favor of Lego City not being
on the Earth we know.

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JackFr
Instead of scaling the Legos up, assume that they're life size beings on a
Lego sized pseudo-Earth. It's been years since I've done any physics so, I
hope I'm not badly off, but I think the gravity will be around 1/900th that of
Earth (if we assume radius of Lego world at 1/30 earth, mass of Lego world
proportional to the cube). If we ignore the fact that there probably won't be
an atmosphere on Lego world, I'm sure there are are various other applications
of the square-cube law, etc. that will work in their favor as well.

I believe they'll make it.

~~~
wh313
It'll actually still be 1/30th of the Earth, since from Newton's law of
universal gravitation:

F = G * (m_1 * m_2) / r^2

m_2 * a = G * (m_1 * m_2) / r^2

a = G * m_1 / r^2

If we make m_1 1/30th of its original size and to the same to r:

a = G * (m_1 / 30^3) / (r / 30)^2

a = G * (m_1) / r / 30

As escape velocity v_e is where GPE + KE = 0:

v_e = sqrt(2 * g * r) from the surface of the planet

If g is now 1/30th of it's original amount as shown above, the escape velocity
would be sqrt(30) = 5.477 times less, or about 2042 m/s. So yup, they would
make it if it's at 1/30th the size of the Earth, with thrust to spare for air
resistance.

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layoutIfNeeded
> A minifigure, 3 blocks high, is repesentative of an average American adult

Ummm... why? Lego is from Denmark.

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wh313
An average Danish adult is 1.80 m, so I would be off by 0.05 m. That gives me
an additional 9,000 litres of volume in the main stage, which can hold 3,240
kg of extra fuel. It also gives each SRB an extra 1.47 cubic meter of volume,
or an extra 2,980 kg of fuel. This gives me an extra delta-v of 144.8 m/s,
which is still a far cry from the 11,186 m/s you need for escape velocity.

[0]
[http://www.dst.dk/pukora/epub/upload/17958/headword/dk/29.pd...](http://www.dst.dk/pukora/epub/upload/17958/headword/dk/29.pdf)

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mikl
Well, obviously, the brilliant scientists of LEGO City have invented better
rocket fuel.

Some sort of direct matter-to-energy converter to power the engines, and then
fill the tanks with something really dense, osmium or whatever.

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vmilner
This is indeed the case - as indicated in the award-winning documentary "LEGO
City Adventures: 3,2,1"

[https://www.youtube.com/watch?v=bKcR_RMxIBY&t=5m43s](https://www.youtube.com/watch?v=bKcR_RMxIBY&t=5m43s)

("This is a specially modified rocket engine for my new rocket fuel that can
get us to Mars in one month, as opposed to the normal ten months it would take
non-geniuses.")

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beckingz
This is great. Would love to see this for the original space shuttle lego
sets.

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xwdv
I hate when people criticize and don’t offer a solution. The obvious follow up
would be to calculate exactly how big of a rocket must be built to reach the
moon, or even deep space.

~~~
wh313
Being able to go to the moon also provides the ability to go to deep space
(just point the rocket away from the moon). Escape velocity is 11,186 m/s, so
(assuming a rocket with specific impulse similar to the one in the post):

11,186 m/s = 263.1 s * 9.81 m/s^2 * ln( x kg / 20,800 kg )

That's roughly 1.58591*10^6 kg of propellant, which is actually less that
what's in the first stage of a Saturn V. Of course, this doesn't include air
resistance or anything beyond just hitting escape velocity and leaving Earth's
orbit.

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mcv
Considering the fuel capacity of earlier Lego spaceships, I think the
assumptions about the energy density of lego fuel are off by a couple of
orders of magnitude.

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djsumdog
Similar video explanation:

[https://www.youtube.com/watch?v=5VfdwjEJO7A](https://www.youtube.com/watch?v=5VfdwjEJO7A)

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wh313
I saw that! I thought that his idea to compare heights was interesting, but he
failed to account for volume, since LEGO City rockets are wider than normal
rockets (an Ariane V, for example, has diameter 3.06m vs 3.51m for the LEGO
one) and so could potentially hold the same amount of propellant as our real-
life counterparts.

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dathinab
> Why does the set include a rover and a grappling arm, if it will never reach
> the moon? What’s the satallite used for if it doesn’t have the delta-v to
> reach even low-earth orbit? LEGO, we need answers!

It's because the small hook like think on the nose is a anti-gravity hook,
which "magically" fixes all problems ;)

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cosmodisk
I don't think he took into consideration LEGO gravity,which isn't the same as
the gravity we are used to.

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D13Fd
Idea for next article: How to build an appropriate third stage using existing
spare pieces to enable GEO, LLO, reaching Mars...

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trackofalljades
better link? [http://h313.info/blog/aerospace/lego/2020/05/09/an-
analysis-...](http://h313.info/blog/aerospace/lego/2020/05/09/an-analysis-of-
the-lego-city-deep-space-rocket.html)

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RedShift1
Link is dead? Getting a 404 here...

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chris_wot
This is a scandal.

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turowicz
Those are some serious accusations!

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yaur
I think this is the first time it’s ever felt appropriate to me to post an
xkcd on hacker news... [https://xkcd.com/356/](https://xkcd.com/356/)

