The Engines for the Movie Interstellar

The Engines for the Movie Interstellar

I’ve now devote 3 – 5 blog posts to the movie Interstellar when I could be posting about (and have started) 5 other worthy topics.

Why is that?

Frankly, I’m not sure.  I suspect it’s because the movie produced in me a sense of wonder at our place in the Universe, excited me with a sense of exploration, and portrayed space travel in a manner we might be able to achieve in the next couple of decades.

I’ve broken the movie into acts.  I have no idea whether this corresponds to the actual acts as laid out in the script but these divisions work for my purposes.

Act	Part of Movie
Act I	Prelaunch
Act II	Prewormhole voyage
Act III	Postwormhole exploration
Act IV	Black hole
Act V	Cooper Station & beyond

The movie shows 5 different spacecraft, order of appearance:

	Implied Mission Requirements		Apparent Vehicle	Performance Requirements
	delta Vel	Thrust to	Mass Ratio	Exhaust Vel	Impulse
Spacecraft	km/s	Weight		km/s	sec
Act I Ranger	1.0	N/A	1.7	5	459
Endurance	50	0.5	2.5	98	10,000
Act III Ranger	8.5	1.5	1.7	30	3,061
Cooper Station	66.0	1.2	Unknown	Unknown	Unknown
Act V Ranger	14,000	1.2	1.7	50,000	5,102,041

I’ll discuss each craft’s apparent propulsion system, its required performance, and whether any currently postulated propulsion system aligns with the capabilities shown in the movie.  For this analysis, I’ll heavily reference the Atomic Rocket’s Engine List as well as perform many calculations for myself.


Also let me preface this by two important points of spacecraft design missing from the movie; thermal radiators and radiation protection.  To make these craft work, we simply need to forget that these two elements would be essential for any such craft even though they are lacking in these designs.

Definitions

Payload Fraction

For these calculations, I’m using a term I call payload fraction, defined as the payload mass (not volume) divided by the apparent mass of the vehicle.  For the craft, the payload area appears almost entirely empty – usually just containing atmosphere and people.  I’m assuming most of the payload mass resides in the supplies and infrastructure used to maintain this livable area.  The remaining mass of the vehicle consists of vehicle structure + engine and its fuel.

Mass Ratio

A far more common and useful (for my purposes) number is the vehicle mass ratio.  This is the maximum weight of the vehicle divided by the vehicle weight without fuel and provides information about the amount of fuel the vehicle has available for completing the mission.  For my purposes, I’ll have to guestimate this number based upon other observations.

Fuel

In conventional chemical rockets, the rocket fuel (the substance used to generate energy) and propellant (the mass ejected for thrust) are the same substance.  For propulsion concepts in which the fuel and propellant are the same, I’ll use the term “fuel”.

Propellant

For some engine concepts (e.g. ion thrusters), the fuel and propellant are not the same substance.  In the case of a nuclear powered ion thruster, uranium would be the fuel while xenon might be the propellant.  In propulsion concepts like this, I’ll differentiate between the two and use both terms.

Spacecraft

Act I Ranger(s)

Multiple spacecraft are called Rangers throughout the movie, starting with the crash/dream sequence at the very beginning.

Performance

Metric			Value
Mission	delta V	km/s	1
	T/W	T/W	N/A
Vehicle	Apparent Mass Ratio	Mt/Md	1.7
Engine	Exhaust Vel	km/s	5
	Impulse	sec	460

As initially portrayed in this sequence as well as the launch sequence, the craft only performs orbital maneuvers (the launch stack provides the launch capabilities).  This would be comparable to the Space Shuttle Orbiter using its OMS engines for maneuvers.  My perspective on the craft from watching the movie is a very large fraction of the craft’s volume is devoted to payload (crew cabin).  My feeling is that this could be upwards of 40% but I’ll be generous and call it 25%.  That leaves 75% of the volume of the craft for structure, engines, and fuel.

The apparent payload volume is mostly empty space (e.g. crew cabins) and possesses very low density; however, at least some of this space contains the storage spaces and machinery of life which possesses a much higher density.  I also assume that other portions of the ship (fuel, propellant, engines, structure, etc.) contain little empty space and are packed as densely as possible.  All of these items would be stored in the aerodynamic structures, walls, floor, etc.  The nooks and crannies of the vessel.

The Ranger’s configuration; engines parallel to the passenger cabin, no apparent radiation shielding, and no bulk area in which to place a reactor; the craft can’t include a nuclear reactor for power or propulsion.  The craft’s configuration and lack of support infrastructure on the visited planets also eliminate concepts such as laser light craft, light gas gun, ram accelerators, space elevators, and mass drivers.  After eliminating infrastructure launch mechanisms, fission, fusion, and anti-matter power; then the drive table leaves only a few viable alternatives chemical and Metastable Helium.

The observed maneuvers only require engine performance characteristics consistent with chemical rockets or other engines displayed at the beginnings of the Atomic Rocket’s Engine List.  The minimum performance (it would be OK or even desirable for these numbers to be larger but this would be sufficient for observed capabilities) would therefore be something like:

Drive type	Exhaust Vel	Thrust / Weight	Min Engine Mass	Notes
	km/s		tonnes
Liquid Hydrogen - Liquid Oxygen Chemical	4.6	81,632	<1 span="">	Based upon Space Shuttle Main Engine performance

Space Shuttle Main Engine

 
Verdict: this craft is plausible and completely “doable” with today’s technology.  Think of it as a modestly improved space shuttle orbiter with a primary purpose of moving people and minimal cargo capacity.

Endurance

The Endurance flies to Saturn on a 2-year high energy trajectory (much higher energy than the 6-year minimum energy direct Hohmann transfer trajectory).  I assume that it reserved at least that much delta V for maneuvers in the Gargantua system, requiring a total delta V of 46 km/sec – a very high performance craft.

Metric			Value
Mission	delta V	km/s	50
	T/W	T/W	0.5
Vehicle	Apparent Mass Ratio	Mt/Md	2.5
Engine	Exhaust Vel	km/s	98
	Impulse	sec	10,000

If we assume all modules possess the same mass and use the online resources, the maximum mass fraction would be 1.18 – which requires performance far beyond anything in the Atomic Rockets Drive Table except for the Fission Fragment Rocket (FFR), Nuclear Pulse Propulsion (NPP), and VASIMR concepts.  Despite the fact that both the NPP and FFR possess far more performance than required, the Endurance configuration does not conform to either the FFR (humongous nuclear power plant with little measurable thrust) or NPP (nuclear bombs) engine concepts.  It does look a little like a VASIMR (Variable Specific Impulse Rocket) and VASIMR provides the necessary specific impulse/mission delta V, however, VASIMR also requires a very large nuclear reactor and provides thrust much smaller than shown (thousandths of a g instead of about ½ a g).

If we assume that another 4 non-engine modules contain propellant, then we get a slightly more reasonable mass ratio of 2.5.  This allows us to use a concept much more likely for the Endurance – a Nuclear Thermal Rocket with an open-cycle gas core.  This propulsion system requires nuclear reactors and spews radioactive materials in its exhaust.  However, it has the necessary thrust, specific impulse, and configuration to conform to that shown in the movie.

But that only leaves 4 modules for habitation, life support, and colonization.  One small consolation would be that the both Landers and Ranger 2 would likely be packed with supplies before departure – so consider that equivalent to 1-2 modules for a total of 5 or more modules devoted to habitation, life support, and colonization.

Drive type	Exhaust Vel	Thrust / Weight	Min Engine Mass	Notes
	km/s		tonnes
Nuclear Thermal Rocket (Open Cycle)	50	51	10	requires large separation between engine and people
VASIMR	60	0.0007	30	minuscule thrust, needs large sail or huge reactor
Nuclear Pulse Propulsion	9,800	100	8	requires large separation between engine and people
Fission Fragment Rocket	14,990	0.003	9	minuscule thrust, needs large sail or huge reactor

Open Cycle-Gas Core Nuclear Thermal Rocket

VASIMR

Fission Fragment Rocket

Act III Ranger(s)

Later in the movie we are treated to the same Rangers used as re-entry craft (minimal or no propulsion requirements due to aero-braking) with the ability to also perform Single Stage to Orbit (SSTO) back to Endurance after a trip to the planet.  It performed this feat multiple times.  The other space to ground ships (only called “Landers”) possess performance characteristics nearly identical to that of the Ranger.

Assumptions:

• The Ranger is refueled by Endurance between flights (no discussion or evidence of this, but let’s assume it’s true)
• Despite having higher surface gravity, Miller’s planet possessed much lower total mass than Earth (possible but unlikely)
• Mann’s planets possessed much lower total mass than Earth (likely)

As with the initial assessment of the Ranger craft, the configuration of the craft eliminates engine designs which release a large amount of radiation (fission, fusion, and anti-matter).  The performance requirements for this observed behavior also eliminates chemical rockets.

Metric			Value
Mission	delta V	km/s	10
	T/W	T/W	1.4
Vehicle	Apparent Mass Ratio	Mt/Md	1.7
Engine	Exhaust Vel	km/s	30
	Impulse	sec	3061

All measures of engine performance require vast improvement over the Ranger performance observed in Act I.  Most of them require an order of magnitude improvement and completely rule out any sort of chemical propulsion.  Since the Ranger’s configuration also eliminates the use of a nuclear reactor (no room for radiation shielding), nearly all other potentially viable candidates are also eliminated.

The only viable candidate is the Metastable Helium IV-A (provides performance of about 2/3 of desired).  This is real but almost entirely theoretical engine concept.  No serious investigation of its potential as a rocket engine fuel has been performed.

The fuel for the Metastable Helium engine is Metastable Helium IV-A, a diatomic metastable Helium atom bonded to stable helium and stored as a solid.  It should remain stable for about 8 years – which would be good enough for the Ranger trips to each planet.  However, Endurance would require a fuel production facility to generate the stuff because it could not store it for the period of time shown in the movie.

Since too much jostling, heat, sudden impacts, etc. would detonate your fuel (and destroy your ship).  This might explain why conventional chemical fuels were used for the initial launch from Earth.  You’d only use this fuel when no alternatives were available.  A side note to this would be that metastable Helium would not require a flame and therefore the flooded engines shown on Miller’s planet would not have been a problem.

Verdict: Short of using the Metastable Helium propulsion, this craft is not plausible.  This is not just an engineering problem.  Given our current understanding of physics, this configuration of the Rangers rules out the use of the high energy nuclear powered engines.  However, the plot required the crew to be able to return from forays to the planets and this was the plot “vehicle” used for that purpose (similar to Star Trek’s use of their transporters).

Drive type	Exhaust Vel	Thrust / Weight	Min Engine Mass	Notes
	km/s		tonnes
Metastable He IV-A	21	0.65**	10	Highly unstable fuel

**A thrust to weight of 0.65 excludes its use as a launch engine; however, improvements in engine design might reduce this engine mass so that it provided the necessary thrust.

Cooper Station

Don’t let the name fool you.  Cooper Station and its twin seen in orbit around Saturn (and potentially others not shown) are actually very large spacecraft and not stations.

Metric			Value
Mission	delta V	km/s	66
	T/W	T/W	1.2
Vehicle	Apparent Mass Ratio	Mt/Md	Unknown
Engine	Exhaust Vel	km/s	Unknown
	Impulse	sec	Unknown

Cooper station was either the station shown under construction back on Earth (or its twin).  Not shown but assumed in its presence around Saturn, the station needed to lift-off Earth and travel out to Saturn.  Since the timing of these events was not shown, we do not know the trip time.  I assume that Cooper Station requires a similar amount of delta V to reach its destination.

Based upon the dialog throughout the movie, we must assume that Cooper Station uses some sort of gravitic drive.  Since I have no idea what a gravitic drive is or how it works, I can’t compare it to other concepts discussed in this post and can’t realistically provide any estimate of its performance.
One conjecture is that a gravitic drive might allow you to magnify or dilute the amount of gravitational attraction exerted upon the ship from one direction or another.  Using such a technology allows the ship to nullify the pull of the Earth while amplifying that of the Moon or Sun and simply “fall” off the surface of the Earth.  If this could be made true, then the ship is literally capable of any acceleration since as long as the ship and its contents are all “falling” at the same rate they’ll all experience “free-fall” (zero-g) conditions.

This would be a form of reactionless drive and is expressly forbidden by the laws of physics (laws of thermodynamics) as we know it.  Depending upon the specifics of how it operated, it may also violate the conservation laws of energy and momentum but possibly not.

However, humans could have launched these sized vessels from Earth using vintage 1959 era technology, namely nuclear pulse propulsion.  This technology would not require the solving of Dr. Brand's equations in the first place.  I hope we would be intelligent to use this technique if the survival of the species depended upon it.

According to the Physics Today site a NPP type system could launch an O'Neill Cylinder of up to 3.2 km by 320 m in size (Model 2) with launch mass to spare (4.5 Mtonnes vs 8 Mtonnes capability).

O'Neill Cylinder

Drive type	Exhaust Vel	Thrust / Weight	Min Engine Mass	Notes
	km/s		tonnes
Nuclear Pulse Propulsion	9,800,000	100	8	requires large separation between engine and people
Gravitic	Unknown	Unknown	Unknown	Total fiction, unknown performance

Nuclear Pulse Propulsion

Engines which might provide the sort of performance portrayed in the movie.  None of these propulsion systems (except the gravitic) match the observed configuration of the Cooper Station Rangers.

Cooper Station Ranger

Metric			Value
Mission	delta V	km/s	1,400
	T/W	T/W	1.2
Vehicle	Apparent Mass Ratio	Mt/Md	1.7
Engine	Exhaust Vel	km/s	50,000
	Impulse	sec	5,000,000

This vessel doesn’t look much like the vessels called Rangers from the first part of the movie.  It is a much smaller two seat spacecraft (instead of the Rangers with a cabin from earlier in the movie).  At the end of the movie, Cooper steals the vessel to find Dr. Brand on Edmunds’ planet.

Assume that it must travel a distance in the Gargantua system (wormhole to Edmunds’ planet) equal to traveling from the Earth to Saturn – this provides us with the distance (about 1,000,000,000 miles).
This ship needs to provide life support for Cooper during the trip to Edmunds’ planet.  The vessel’s very small size doesn’t permit much life support (air, water, food, & thermal control).  Therefore, I assume it must make that trip in a matter of days or Cooper will die before he gets to Edmund’s planet.

The Atomic Rockets Mission Tables show that a round trip voyage to Saturn using constant 1-g acceleration can be done in 18 days (a one way trip would take 9 days).  Could Cooper survive on the food, oxygen, water, & power provided by the Future Ranger for 9 days?  I assume the answer is “yes”.

1-g of constant acceleration all the way to Saturn requires about 14,000 km/s of mission delta V.  Although Atomic Rocket’s drive table includes engines that could manage this sort of performance, none of them would fit on the Ranger craft shown in Cooper Station.

The engine types that might deliver this level of performance are only anti-matter, certain exotic high-energy fusion reactions, and photon (light sail).  Both of the reactor concepts require an extremely large separation (a kilometer or more) between the engine and crew to attenuate the radiation enough to ensure crew survival.  The photon propulsion system would not provide the necessary thrust.  Essentially, no engine concept that obeys the laws of physics as we currently understand it, could deliver the level of performance this vessel must possess.

Therefore, I’m left with the impression that the Ranger’s utilized “gravity” drives developed from Dr. Brand Sr.’s gravity equations and implied in the performance of Cooper Station.  We have no ability to estimate the type of performance available from such a divergent technology.  However, I did post the mission performance requirements.

Engines which might provide the sort of performance portrayed in the movie.  None of these propulsion systems (except the gravitic) match the observed configuration of the Cooper Station Rangers.

 

Drive type	Exhaust Vel	Thrust / Weight	Min Engine Mass	Notes
	km/s		tonnes
Nuclear Saltwater Rocket	4,700,000	24	33	requires large separation between engine and people
Nuclear Pulse Propulsion	9,800,000	100	8	requires large separation between engine and people
IC Fusion	10,000,000	10	1000	requires large separation between engine and people
Antimatter Beam	100,000,000	100	10	requires large separation between engine and people
Photon	299,792,458	low		minuscule thrust, needs large sail or huge reactor
Gravitic	Unknown	Unknown	Unknown	Total fiction, unknown performance

IC Fusion

Antimatter Beam Rocket