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G2HGE Part 1 : Canon-Gleaning - Post 6a : How Much Faster Than Light ? (Speed, Acceleration and Inertia, and Speculation Thereof)

Hi ! This post (???? 202X ----ERROR : Insert Date Here) is the sixth post in the Galactic Geography and History of Galactic Exploration series (or G2HGE, announced and explained with excessively verbose details here). In this chain of posts, I air out my thoughts and hypotheses on the geography of the Milky Way in the Mass Effect setting - in particular, in order to determine when the various mass relay-centered clusters were opened and accessible, based on what canon data we have. I tell you what I think, and you tell me what you think of that.

A long time ago, I did a five-part post on the various regions of the Milky Way. It was fun !

Right here, right now : How fast are starships in the Mass Effect universe ? Isaac Newton ? Why are there interludes on acceleration and inertia ? What are the constraints of FTL travel ? Do we have any indication as to the evolution of FTL travel throughout history ? What is that about constant acceleration ? Those questions will eventually lead us to what really interests me : How would all of that impact the development of clusters ?

1 - How fast are starships in the Mass Effect universe ?

You know me ; the questions we'll be asking are : What's the data in canon ? How can we complicate the picture ?

The major indication we get on FTL speeds is from a comment in ME1, when Ashley reacts to Shepard admiring her for making the trip from the Czarnobóg Fleet Depot to Amaterasu : "It was only a dozen light-years. Like a day's cruise. It's not like I was going to Earth or something." The phrasing suggests people expect to travel more than a day if they're travelling.

Moreover, Ashley tells us that Czarnobóg and Amaterasu are in the same cluster, and what being "a dozen L.Y. away" represents to the average person : "Close enough to talk regularly, too far to make it back in an emergency. I couldn't afford a fast packet flight."

(To keep you from wondering : a packet flight would be a starship travelling at regular intervals between two ports ; historically, a packet boat or a steam packet refers to boats that did so to convey mail from one port to another.) (In a cut ambient conversation from ME1, extracted by @lyricsaboutcats,the salarian businessman Rulamin mentioned trying to get "a packet" from Noveria to Ryskos to a friend, then finding that it won't be possible to get "a packet flight" for at least six days.)

(The mention of a "fast packet flight" suggests that you have a range of options among packet flights : presumably, the faster ones are more expensive.)

To provide a sense of perspective, the Tempest, which benefits from using "several once-proprietary technologies" and "[not] being weighed down by heavy armor or a main gun", has an "average speed" (see below) of 13 light-years per day, making it "easily the fastest ship in her class", i.e. a frigate-sized survey ship. Given that lighter starships can accelerate to greater FTL speeds than more massive ships, with the fastest military ships being frigates, as well as the unique conditions that made the Tempest possible, I find it probable that the Tempest is one of the fastest ships ever made by the current Citadel species. It is certainly faster than the heavier Normandy SR-1 or SR-2.

The Reapers "can travel nearly 30 light-years in a 24-hour period". This is "more than twice the speed of Citadel ships", in keeping with what we've outlined above. In addition, this sets a very hard upper limit : at the moment, there is no Citadel ship which can reach a speed virtually or absolutely equal to 15 light-years per day (which would be exactly half the estimated Reaper speed).

2 - Which starships are the fastest in the Mass Effect universe ?

In canon, there are at least two factors which have an impact on a starship's speed : its thruster type (or how much motive power they can have, given that starships "use their sublight thrusters for motive power in FTL") and its mass (or how much eezo and power is required to move the damn thing).

The Codex is fairly clear that a starship's speed depends on its type and what thrusters it has ; there are "several varieties of thruster, varying in performance versus economy" :

"All ships are equipped with arrays of hydrogen-oxygen reaction control thrusters for maneuvering." Note that those are "liquid hydrogen/liquid oxygen reactions", not gas. From my own research, I found that the exhaust velocity of a rocket flame usually is several thousands of meters per second.

"Ion drives electrically accelerate charged particles as a reaction mass. They are extremely efficient, but produce negligible thrust. They are mainly used for automated cargo barges." The noble gas xenon appears to be the propellant of choice, in keeping with real life, as there is evidence that it is harvested specifically for ion drives on the planets Alingon, Uzin (in the Eagle Nebula), and Venture, and logically elsewhere. Per my research, the exhaust of an ion drive would be an order of magnitude faster than a chemical rocket's.

"The primary commercial engine is a "fusion torch", which vents the plasma of a ship's power plant. Fusion torches offer powerful acceleration at the cost of difficult heat management. Torch fuel is fairly cheap: helium-3 skimmed from gas giants and deuterium extracted from seawater or cometary bodies. Propellant is hydrogen, likewise skimmed from gas giants." If I can trust my own research, the exhaust velocity of a torch drive would supposedly be measured in thousands of kilometers per second.

"In combat, military vessels require accelerations beyond the capability of fusion torches. Warship thrusters inject antiprotons into a reaction chamber filled with hydrogen. The matter-antimatter annihilation provides unmatched motive power. The drawback is fuel production; antiprotons must be manufactured one particle at a time. Most antimatter production is done at massive solar arrays orbiting energetic stars, making them high-value targets in wartime."

Finally, in 2185, some cutting-edge technology like the Helios Thruster Module uses "metastable metallic hydrogen" both as a superior alternative to "liquid H2/O2" reactions powering "maneuvering thrusters", as well as a slower but cheaper viable alternative to antiprotons for "forward impulse".

Since the fusion torch is the primary engine type in the setting by the time ME1 rolls, we can conclude that the fusion torch allows the average Citadel spaceship, including military starships when out of combat, to travel at a cruising speed around 12 light-years per day (24 Earth hours) - "cruising speed" being defined as "the maximum speed at which a vehicle is able to travel continuously and comfortably, without using a large amount of fuel or effort". In other words, starships can in all likelihood reach FTL speeds faster than 12 ly/day, but that isn't meant to happen, as they are not designed for that, and doing so would a) make the trip uneconomical, and/or b) start damaging the ship.

The other significant limit is the mass of the starship, as "[the] amount of eezo and power required for a drive increases exponentially to the mass being moved and the degree it is being lightened. Very massive ships or very high speeds are prohibitively expensive." What is in bold suggests that mass relates to the mass effect field in two ways : it appears that the more massive an object, the harder it is to affect it ; and that the lighter one wants to make an object, the more eezo and electricity one will need.

This is apparent in the various weights of large military vessels : a dreadnought needs to be as long and massive as possible to bring the greatest firepower to bear, resulting in ships ranging "from 800 meters to one kilometer long" and weighing "millions of tons" - but this mass results in low maneuverability and the slowest speed. By contrast, frigates are the lightest and smallest large military starships, the only large vessels "able to land on planets" ; as a result, they "achieve high FTL cruise speeds because of their high-performance drives. They also have proportionally larger thrusters and lighter design mass, allowing them greater maneuverability. In combat, speed and maneuverability make frigates immune to long-range fire of larger vessels."

Given that cruisers appear be to the standard for military starships, balanced between frigates (faster, but with far lower offensive and defensive capabilities) and dreadnoughts (far more destructive and tough, but slower), it may be that most commercial vessels are in the same weight and have access to the same FTL speeds, perhaps slightly faster because of their lack of guns and armor. Thus, I posit that most Citadel starships probably fall close to cruisers when it comes to FTL speeds.

As a logical consequence of the above, some of the fastest ships you could find travelling in the Milky Way would be couriers, as the shortest travel time possible would be vital for their job ; this would be in keeping with the analysis presented here over on Atomic Rockets. We know the galaxy at large relies on "high-speed couriers" when comm buoys aren't available, as well as "diplomatic couriers". However, we know that courier ships aren't substantively faster out of FTL than other ships, since the ship of the Rachni Queen's emissary in ME2 - should you spare the rachni on Noveria - had been a courier's ship which was nonetheless ambushed by pirates and forced to land on an uncharted world.

But it's probable that the very fastest are fighters, whose extremely low mass makes them "capable of greater acceleration and sharper maneuvers than starships". Contrary to what I thought for years, fighters are FTL-capable, as what separates spaceplanes (any vessel that can fly both in an atmosphere and in space) from "true deep-space fighters" is that the former "have no FTL drive".

That being said, this probably doesn't amount to much, since fighters won't be travelling through star clusters. Fighters aren't independent ; indeed, they rely on cruisers and carriers to get them anywhere. This is logical : since you want the lightest possible vessel to reach the highest possible speed, there's probably little in the way of life support or other systems that don't anything to do with getting close to some enemy starship as fast as possible without getting shot down. In other words, fighters are irrelevant when considering how FTL speeds impact the development of clusters.

To sum up :

the cruise speed of Citadel starships is around 12 light-years/Earth day. The Tempest, at 13 ly/day, is exceptional.

this speed of 12 light-years/day is presumably the average speed one can reach with a fusion torch ; starships with ion drives are going to be much slower, because their design concern isn't how fast you can get anywhere but how cheaply.

the less massive a ship, the faster it will be in FTL. Out of military ships, dreadnoughts would be the slowest, while frigates would be the fastest. Because the Tempest is extraordinary for its size, that means the FTL speed of frigates (Normandies included) is probably superior or equal to 12 ly/day and certainly strictly inferior to 13 ly/day.

the fastest starships would be even lighter than the Tempest and only be concerned with speed - the Tempest is built for scientific survey and analysis, as well as long-term habitation. Nonetheless, the Tempest is canonically the fastest ship by far for a ship its size (for the reasons outlined above).

the fastest ships of them all are therefore likely to be fighters, but they are not going to have an impact on the economic development of star clusters because they are not independent. I posit that the fastest after them are couriers, but that's a very specific, somewhat uncommon kind of ship.

basically, you're probably going to find vessels going at different FTL speeds depending on their purpose, with very specialized (and therefore rarer) vessels at the extremes of performance ; 12 ly/day is either the average or the median Citadel FTL speed.

tl;dr : 12 light-years per day is the relevant speed for our purposes.

3 - How fast can starships accelerate ?

3.a : The basics of acceleration in canon

There is an additional consideration which is barely touched upon in canon : the rate of acceleration and deceleration.

In the Codex, we are told this : "Any long-duration interstellar flight consists of two phases: acceleration and deceleration. Starships accelerate to the half-way point of their journey, then flip 180 degrees and apply thrust on the opposite vector, decelerating as they finish the trip. The engines are always operating, and peak speed is attained at the middle of the flight."

(The reason the Codex stresses that engines are always operating is to emphasize that a starship is never moving at a constant speed - because if the goal is to remain in motion, then a starship doesn't need engines, it just needs to keep on drifting. Indeed, in the vacuum of space - i.e. a virtually frictionless environment - a starship in motion stays in motion at a constant speed in a straight line until and unless acted upon by an outside force, sir - AND THAT IS WHY SIR ISAAC NEWTON IS THE DEADLIEST SON-OF-A-BITCH IN SPACE!)

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So ! The Codex informs us that a starship is either accelerating or decelerating at any given time, that its engines are always operating, and that its speed therefore constantly varies, with its maximum FTL speed during the journey achieved at the exact middle of the flight.

In the games, this is referenced in an exchange Shepard may have with Marab, the manager of the Saronis Applications store in Zakera Ward, in ME2 (link).

SHEPARD : You know, I use quite a bit of software in my line of work.

MARAB : It's a shame so few understand their own equipment. Besides the most obvious point-and-go nav interfaces anyway.

SHEPARD : You wouldn't believe how often I hear, "Why is the ship turning around ? We're only halfway there !" [MORDIN nods in sympathy.]

MARAB : [He chuckles.] Oh, I would !

In space nerd parlance, this is known as a brachistochrone, while the midpoint flip-over is alternatively called a "skew flip" or a "flip-and-burn" in sci-fi. A brachistochrone is typical of starships with fusion torches, or torchships, which indeed fits with what we've seen, as we've established that fusion torches are the standard thruster type for Mass Effect starships as of 2183. For more information on brachistochrones, let me refer you to the supreme space nerd website, the wonderful and exhaustive Atomic Rockets ; I'll be quoting select excerpts throughout.

tl;dr : Starships are always either accelerating or decelerating, and reach their maximal speed at the exact halfway point of their journey, at which point they turn around and start decelerating. This is known as a brachistochrone.

Corollaries of that piece of information worth stressing include :

if a starship's peak speed is attained at the middle of the flight - e.g. 12 hours in during your 24-hour trip where you'll be travelling 13 light-years - because it takes exactly as much time for a starship to decelerate as to accelerate, then you're also halfway to the destination at the same moment - in our example, 6.5 light-years from your starting point (see also Shepard's exchange with Marab above) ;

however, because that starship is always accelerating (then decelerating), it starts covering very little distance at the beginning of its journey before progressively picking up speed ; this means that at 25% of its travel time, it will not have travelled 25% of the distance. The reverse is also true : at 75% of its travel time, our hypothetical starship will have flown more than 75% of the journey.

Moreover, we know that the initial mass of the starship and its type of drive core (i.e. how much eezo there is in it and how much power they can inject in it) are the hard constraints on how much a ship can accelerate. Again : "Faster-than-light drives use element zero cores to reduce the mass of the ship, allowing higher rates of acceleration. … The amount of eezo and power required for a drive increases exponentially to the mass being moved and the degree it is being lightened. Very massive ships or very high speeds are prohibitively expensive."

Until now, I've talked about starships in terms of which is the fastest ; but really when we are discussing the speed of starships, we are talking about how quickly a starship can change its speed. The size of an eezo drive core relative to the vessel has an impact on the vessel's acceleration : deep-space fighters, for example, "are economically fitted with powerful element zero cores, making them capable of greater acceleration and sharper maneuvers than starships" (Source : Codex : Starships: Fighters). For the other military vessel types, frigates, which can achieve "high FTL cruise speeds", would have the second-fastest acceleration, followed by cruisers, with carriers and dreadnoughts dead last.

tl;dr : Talking about a starship's "average speed" or "cruising speed" doesn't mean much because what really matters is how much it can accelerate. Lighter starships can achieve greater acceleration.

So, uh, I have to address some things about acceleration in physics.

OH BOY HERE COMES THE INTERLUDE

Interlude : A genteel Reminder on Fundamentals of Acceleration

The speed of an object is a measure of how much distance it travels (change in position) over time ; the velocity of an object is its speed alongside the direction in which it moves. Both speed and velocity are usually noted v, and both are measured in meters (for distance) per second (for time), or m/s. You will note that "12 light-years per day" is a measure of speed, since it is expressed by units of distance ("light-years") and time ("day"). In SI base units, that should be (if I can calculate) 1.314e+12 m/s, or 1.31 trillion meters every second ; as the speed of light in vacuum (c) is exactly 299,792,458 m/s, I'll note that the cruise speed of a starship is about 4380 times the speed of light in vacuum, or 4380 c.

Acceleration is any change in the speed or direction (or both) of an object in motion ; from the point of view of physics, deceleration is acceleration. Acceleration is noted a ; since it measures the change of speed and/or direction over time, it is measured with the unit of velocity (m/s) divided by the unit of time (s), or meters per second per second (or (m/s)/s), which mathematically entails that it's the same as meters per second squared, or m/s^2.

Another unit which is going to be very useful soon is g (not to be confused with "G" [the gravitational constant] or "g" [that's grams]). g is another unit of acceleration, measuring the standard acceleration due to Earth's gravity, i.e. how much the gravity of Earth causes an object near the surface of Earth to steadily gain speed (i.e. accelerate) in a vacuum - that is to say, in a context where the only force acting upon that object is Earth's gravity. g is a constant defined as 9.80665 m/s^2 ; in Mass Effect, you probably know it because, on the data description for every single planet, g is used as the unit of gravity, with Earth as the standard at 1 g.

In classical mechanics (i.e. the Newtonian equations that don't involve anything starting to try to get close to the speed of light, since the closer you get to it, the more Einstein starts to mess with your stuff ; by convention, the threshold is 0.14 c), the sacrosanct equation is F = m*a (or a = F/m), where F is the net balance of all forces acting on an object, m is the object's mass, and a is its acceleration (quoth Wikipedia). In plain English, the more acceleration you want, the more force you'll need (and that is Sir Izzy's Second Law of Motion) - something you're likely to have experienced if you have ever ridden a bike, for example : your top speed is limited by how much energy you can pour into your pedaling (and friction, thankfully virtually absent from the deadly vacuum of space, is always slowing you down).

Now, to prepare yourself for what's to come, I'll also note two things :

in the context of spaceflight, acceleration is equal to rocket thrust divided by starship mass (a = F/Mc, where F is the starship's thrust measured in Newtons (N), i.e. in kg*m/s^2 ; and Mc is the starship's mass at a given point in time measured in kg) ; because the mass of a starship decreases during its flight as it expends propellant and fuel, any equation trying to calculate the acceleration of a spacecraft will have to take that variation into account.

also relevant to our talking about mass and acceleration is inertia, i.e. the phenomenon in the deadliest son-of-a-bitch in space's First Law of Motion described above, i.e. how tough it is to change the speed of any object (such as setting an object at rest in motion), i.e. how tough it is to accelerate (or decelerate) anything. SPOILERS : inertia is dependent on mass, because the more massive an object, the harder it is to accelerate it, and the more energy will be required to do so (drop a rock and a sock, try rolling them forward on the floor ; one is significantly easier to move than the other). A consequence of this is that it requires increasingly ludicrous quantities of energy to accelerate any object with mass to a velocity close to the speed of light (c), and it would require an infinite amount of energy to accelerate any object with mass to c ; it's only because light is virtually massless that it can get to c in the first place.

But that's not a problem when you have magical eezo allowing you to travel faster than light without any physics-breaking consequence !

Thus endeth the Interlude.

The Interlude Has Ended - please return to your seats

All of that is important because all starships have an upper limit to how fast they can go, a maximum speed past which they can no longer accelerate (at which point the sensible thing is to turn off the engines), perhaps even the same speed in starships of different weight classes, for all we know ; but crucially, some starships can reach that top speed much faster than others.

So, uh, how much acceleration can the starships in Mass Effect (and the squishy people inside) take ? Well, we know that large ships like cruisers and dreadnoughts actually rely on constant acceleration to simulate gravity : "Mass effect fields create an artificial gravity (a-grav) plane below the decks, preventing muscle atrophy and bone loss in zero-gee. Large vessels arrange their decks perpendicular to their thrust axis. The "highest" decks are at the bow, and the "lowest" at the engines. This allows a-grav to work with the inertial effects of thrust. Ships that can land arrange their decks laterally [i.e. frigates and smaller vessels], so the crew can move about while the vessel is on the ground."

This is achieved because acceleration can effectively simulate gravity, what is known as the equivalence principle : inertia "pulls" you in the direction opposite that of the vehicle's motion (think about how your body is pulled back when the car or public transport you're in starts moving forward, whereas you're thrust forward if the same vehicle brakes suddenly). In effect, if you are in a vehicle accelerating at 9.80665 m/s^2, i.e. 1 g, every object within that vehicle behaves as if they were on Earth, "falling" toward the back of the vehicle.

That is what the larger starships rely upon : presumably to avoid spending power (thus fuel, thus money) on a-grav, Alliance cruisers or dreadnoughts, for example, need to be constantly accelerating at 1 g to simulate Earth's gravity, never changing that acceleration because it would change the pseudo-gravity.

tl;dr : The heavier starships use acceleration to simulate gravity. This means even the heaviest Alliance starships can reach at least 1 g of acceleration. Because lighter starships are capable of greater acceleration, they are also able to accelerate to at least 1 g.

(By the by, this suggests that whereas frigates like the Normandy may have thrusters which can fire in opposite directions to accelerate and decelerate, the larger starships do need to physically "turn around", otherwise "gravity" would shift and stick them to the ceiling ; if such a starship doesn't "park in reverse" when it leaves FTL, as it does in cutscenes (for example when Hackett's ship arrives guns first in ME3), this suggests in turn that its engines are killed, stopping any deceleration, and that the starship then turns around a second time before switching off FTL.)

The problem of course is that starships need to be accelerating much, much faster to achieve the range that has been observed in the OT : at a constant acceleration of 1 g, a starship would cover 9,144,576,000 meters in 12 hours, i.e. 9,144,576 km, i.e. 0.00000000000095 light-years - and twice that over 24 hours if we assume this is a brachistochrone, or 0.0000000000019 light-years - a very far cry from 12 light-years.

Now, there are some things we should keep in mind :

there's all the timey-wimey handwavium stuff related to FTL travel in Mass Effect ; it appears that there is a difference between the speed of the starship as perceived within the envelope by aboard observers (the subjective speed) and the speed of the starship as perceived outside the envelope (the "objective" speed). FTL is a can of worms best left unopened, but suffice to say 1 g will, in all likelihood, allow a starship within an FTL envelope to travel faster and farther than it would under normal circumstances.

there's also the hard limits of engineering : to maintain a continuous acceleration, i.e. to keep going faster and faster, the starship is going to need more and more thrust, thus more energy, which will be harder to provide and start taxing the ship at some point. Now, Atomic Rockets kindly informs me that a torchship is just about the only ship type which can manage constant acceleration, but nonetheless, there's going to be an upper limit at some point. This in fact appears to be a non-issue ; after all, the Codex takes it as a given that a starship never stops accelerating. I'd argue this is likely because of how the Mass Effect franchise enjoys the benefits of the, uh, mass effect : if the starship's mass is decreased as it accelerates, then no additional energy may be needed, and continuous acceleration may just be maintained.

and then of course we need to talk about inertial dampeners.

3.b : Inertial dampeners

Inertial dampeners, also known as inertial dampers, inertial compensators, inertia compensators, internal compensators, acceleration compensators and many, many other things, are a mainstay of science-fiction, as they're the piece of technology which explains why everyone inside a starship isn't crushed to a pulp by their acceleration to truly plaid ludicrous speeds.

Their effect can be inferred in Mass Effect every time we're aboard the Normandy (a ship whose active artificial gravity isn't aligned to its thrust but perpendicular to it) and we don't see the crew thrust toward the engines screaming for their lives whenever the ship is flying. In text or dialogue, the earliest reference I could find was in some of Joker's ambient dialogue in ME2 when you come to the bridge : "Sometimes I get the urge to turn off the internal compensators and pull a Crazy Ivan, you know ?" (i.e. he wants to yaw 180° with full inertia to send people and small objects flying).

But the technology got the spotlight during the Citadel DLC if you spend some time with Steve, where he demonstrates what happens when you turn off the inertial dampeners in the Kodiak shuttle :

CORTEZ : Before mass effect fields, there was no such thing as inertial dampeners.

SHEPARD : Yeah ?

CORTEZ : Here, feel this.

[The Kodiak roars to life and elevates off the landing pad. SHEPARD stumbles and falls into his chair.]

SHEPARD : Whoa.

CORTEZ : That, my friend, is unadulterated momentum. Want to really feel it ?

[If "Go for it" is selected.] SHEPARD : Show me.

[The Kodiak goes up and down and does a barrel roll. CORTEZ and SHEPARD's bodies move with the momentum, through they remain in their seats despite the lack of visible seatbelts. SHEPARD hoots and laughs.]

CORTEZ : See ? Doesn't take much to pull a few [g's].

[If "Keep it steady" is selected.] SHEPARD : You can turn those dampeners back on anytime.

CORTEZ : Okay, okay. Doesn't take much to pull a few [g's], and we don't want to paint the windows with your breakfast, right ?

[End of branching conversation] CORTEZ : Back in the day, pilots would wear G-suits. It squeezes your body so that the blood stays in your head in tight maneuvers. I'd wear a G-suit flying my Trident. In a fighter it's common to transfer power from the inertial dampeners to other systems.

Here is how inertial dampeners are relevant to the conversation about acceleration simulating gravity : presumably, a cruiser or a dreadnought can accelerate at a rate much higher than 1 g and still use its inertial dampeners to compensate that acceleration and simulate 1 g regardless of its actual acceleration, as long as it is in excess of 1 g. This is very nice, because human beings tend to die at some point after 4 g.

In-universe, this is logical and worthwhile as it allows a spaceship to turn off its artificial gravity and use its inertial dampeners less, instead of nullifying 100% of the effects of acceleration and wasting power on a-grav.

tl;dr : Inertial dampeners can be and probably are used to make starships accelerate at rates far superior to 1 g.

(How mass effect fields make inertial dampeners work is entirely speculative and quite beyond the purview of this very long post. Likewise, whether negating inertia has an impact on Newton's First Law of Motion and the object in motion staying in motion is beyond me, though I should note that neither the games nor the Codex show anything that would suggest this law is altered.)

3.c : What factors in a starship's acceleration ?

So let's say I am Joker and that I have a spaceship. When I want to go anywhere, I light up my thrusters to get going, i.e. accelerate ; I use eezo and the mass effect to lower my spaceship's mass to accelerate even more without changing my thrust ; and I use my inertial dampeners to survive enormous acceleration, the type of acceleration which would otherwise purée me and anyone made of pulpy meat.

Is there something else we can surmise about a starship's acceleration ? Yes. Yes, I think we can.

You see, we might expect how much a starship accelerates to depend on the variously varying variables of an individual journey : after all, sometimes you may want to get somewhere as fast as you can, whereas sometimes using as little propellant and fuel as you can and making the journey less expensive are your top priorities. The problem is that muddles what might be plausibly considered everyone's highest acceleration.

Luckily for us - and unfortunately for everyone else - in Mass Effect 3, we know how fast everyone is moving during the Reaper War, when everyone's priority is either a) get somewhere as fast as you can because you are a warship and time is of the essence, or b) get somewhere as fast as you can because eldritch starships from the depths of dark space want to kill you and everyone you love ; either way, everyone wants to get anywhere as fast as technologically possible, i.e. at a speed less than half the speed of the Reapers ; as we've seen, this fits with the idea that a Citadel ship with a torch drive is moving at 12 ly/day, accelerating then decelerating from the midway point.

This means that the range of 12 light-years in a single day is in all likelihood what a Citadel spaceship can achieve when it is moving at the maximum acceleration it can generate, because maximum acceleration is what will allow a starship (or anything) to get anywhere as fast as possible. A corollary of this is that we understand that Citadel spaceships are always moving at maximum acceleration in all circumstances, including in times of peace. Remember this : this will be relevant later.

Complicating matters is that we (ugh) have to get into the specifics of FTL travel. As I've said before, the crux of what we know is in this phrase : "Faster-than-light drives use element zero cores to reduce the mass of the ship, allowing higher rates of acceleration. This effectively raises the speed of light within the mass effect field, allowing high speed travel with negligible relativistic time dilation effects."

The problem is that there can be no causal link between the two sentences above, not with the way they are presented. Logically, we appear to have two discrete effects instead :

if, theoretically, a starship's mass is reduced to 0 kg, i.e. is made mass-less (and we don't know if the technology can do that), then this does allow "higher rates of acceleration" - but only up to the speed of light. You can't go faster than light if you have no mass because light, which has no mass, can't - that's why it's called the speed of light. (Before someone says anything : There's nothing in canon which suggests negative mass is involved, and we don't even know what negative mass would be beyond a number in an equation.) But in any case, the lighter a ship becomes, the less energy it will need to accelerate. That's your bog-standard mass effect, or Effect #1.

then something else happens that "effectively raises the speed of light" within the envelope, which allows for FTL travel relative to the universe outside the envelope, but presumably never going past lightspeed within the envelope. That's Effect #2.

So it appears that "how much a starship can accelerate" and "how far the speed of light is raised" are separate phenomena but which are difficult to distinguish (let alone to see how they relate together) from an outside perspective. There's going to be a difference between the spaceship's perspective on its acceleration from inside the envelope, and everyone else's perspective on the spaceship's acceleration from outside the envelope.

We can actually safely assume that a starship doesn't lower their mass all the way to 0 kg and get to lightspeed at any point of the journey, even subjectively, because if they did that they would just turn off the engines - and we know that a starship never coasts, they just keep on accelerating (this always was very likely because if you reach the speed of light, time effectively stops for you, but there's no way to know if Mass Effect writers know that and take that into account). This probably tells us something about the limits of mass effect fields and the associated technology : it might just take exponential power to get to pure masslessness - perhaps even infinite power.

So, to sum up : a spaceship's maximum speed is dependent on maximum acceleration - because if they're no longer able to accelerate then they just turn off the engines and drift. A spaceship's maximum acceleration, in turn, will be dependent on :

its thrust ;

how much its drive core can lower its mass ;

and how much its inertial dampeners can cancel out its acceleration's effects on the squishy crew.

(Note that if you increase one, you don't have to increase the others. If you lower your mass, you will start accelerating without increasing your thrust or demanding more of the inertial dampeners. The inertial dampeners come into play when you're undergoing accelerations that would be putting your starship on a high-gravity world.)

We've already established that, in any context, the current generation of Citadel starships in the 2180s is always traveling at the maximum acceleration they're capable of, i.e. what gets a starship at FTL to travel 6 light-years in 12 Earth hours from an initial state of rest.

We can also deduce that it takes more than 12 Earth hours for a starship to reach the point where they wouldn't be able to pile more energy to keep accelerating. Otherwise a spaceship would accelerate in as little time as possible to their top speed, then turn off its engines and its inertial dampeners to make huge savings as it drifts at constant speed (there ain't no friction in space after all).

Another corollary is that, at 12 light-years per day, a starship's mass is lowered and a starship's inertia is dampened as much as the starship can without risking its integrity and the lives of everyone aboard - we might speak of "cruising mass-lowering" and "cruising inertia-dampening" to reach "cruising acceleration". In other words, I think it's safe to assume that, since a spaceship would be undergoing cruising acceleration, i.e. the highest acceleration it can provide at all times without damaging itself or endangering its crew, then its inertial dampeners would be handling at all times the maximum acceleration they can safely take.

"Please, crapeaucrapeau," I hear a fictional stand-in for the reader hypothetically whine, "I can't take it anymore, just stop talking about acceleration." Ah, but dear long-suffering reader, the reason I'm doing all this is that, while we've established that starships in Mass Effect are always in continuous acceleration, the fact they appear to be actually always going at their maximum acceleration entails that they are also moving in constant acceleration.

And that's interesting because we can actually get actual numbers from that.

3.d : Constant acceleration

If a starship is always moving at the maximum acceleration it can reach, then it's undergoing constant acceleration, i.e. a rate of acceleration that remains the same throughout the duration of the flight. The longer a starship flies, the faster it gets.

I should point out that Mass Effect, in keeping with its original hard science-fiction ambitions, is once more entirely coherent with the science and science-fiction it pilfers is influenced by : every single article I've read suggests that constant acceleration is indeed what anyone with a starship able to do brachistrochrones would be doing.

Constant acceleration (which we need, even with inertial compensators) leads to a speed which is proportional to that acceleration ; hence why it's assumed by everyone who mentions it in the OT that it always takes exactly as much time to decelerate as to accelerate.

We actually can squeeze what is our average 12-light-years-per-day starship's constant acceleration out of the data, focusing only on a single burst of constant acceleration during the initial half of that journey :

its initial time - t0 - is when it starts moving, i.e. 0 seconds, i.e. 0 hours, i.e. 0 days ;

its initial velocity - v0 - is how fast it is at t0, i.e. 0 ly/day or 0 m/s^2, since it is at rest relative to the frame of reference ;

its final time - t - is at the midpoint of the entire journey, i.e. 12 hours, i.e. 0.5 day, i.e. 43,200 seconds ;

its average velocity is 12 light-years per day, since it has covered 6 light-years in 12 hours ;

therefore, at constant or uniform acceleration for the duration of the flight, its final velocity - v - will be twice its average velocity, or 24 ly/day.

Assuming that this starship's acceleration - a - is constant, then its average acceleration is the same as its acceleration at any point of its journey ; therefore, a starship's acceleration can be calculated first by subtracting the starship's initial velocity from its final velocity, or v - v0 ; then by dividing the result by the starship's final time, i.e. t.

In other words : a = (v - v0)/t ; and therefore v = v0 + a*t

In our example, v - v0 = 24 - 0 = 24 ly/day = v ;

and a = v/t = 24/0.5 = 48 ly/day^2.

(Of course, the constant acceleration for the other half of the journey - the decelerating part - would be -48 ly/day^2.)

Now, if we put those results in SI units : we need to change "days" to "seconds" as the unit of time, and "light-years" to "meters" as the unit of distance. As a reminder, there are exactly 9,461,730,472,580,800 meters in a light-year, or 9.46 quadrillions.

If v = 24 ly/day, then it's equal to 227,064,000,000,000,000 m/day (or 227.1 quadrillion m/day), which is equal to 2,628,055,555,555.56 m/s (or 2.6 trillion m/s).

If a = v/t = 48 ly/day^2, then it's equal to 2.6 trillion m/s divided by 0.5 day, or 2.6 trillion m/s divided by 43,200 seconds, or 60,834,619.3 (m/s)/s (that's 60.8 million (m/s)/s).

To check if we are correct, a*t should equal v ; or 60.8 millions multiplied by 43,200 should equal 2.6 trillions — which is indeed the case.

Note that this is the starship's constant acceleration as measured by a stationary observer outside the envelope : within the envelope, where an observer is not measuring any speed that is superior to the speed of light in a vacuum, the values would be much lower, and the corresponding energy required to generate that acceleration would also be lower.

(Yet another piece of circumstantial evidence in favor of constant acceleration is that the fact the average distance covered by Citadel starships in the OT becomes comparable to the Tempest's average speed in ME:A actually makes sense : with constant acceleration, average speed is equal to range/distance travelled.)

3.e : Putting it all together

So, if we keep in mind a maximum and constant acceleration of 48 ly/day^2, here is what the average velocity/range of a starship for a full brachistochrone would look like depending on time :

One minute : 30 seconds acceleration, 30 seconds deceleration - 30 seconds being 1/2880 of a day, 0.000347 day. If a = v/t, then v = a*t ; 48*0.000347 = 0.016667 ly/day for final velocity ; its average velocity, in a constant acceleration situation is, v/2, or 0.0083335 ly/day. To calculate the final position of the starship at the mid-point of the flight (x), one must multiply average velocity (here, 0.0083335) by t (here, 0.000347) ; the result is 0.00000289 ly. Double it, and you have the full length of the minute-long FTL brachistochrone, or 0.00000578 ly, which is about 0.365526 AU, or 54,681,895.93 km.

Five minutes : 2.5 minutes accel, 2.5 minutes decel ; 2.5 minutes is 0.001736111 days. Now, wonderfully, the way the math works, you can simplify the equations by multiplying v (final velocity) by t (time) to get the final result. v = 48*0.001736111 = 0.083333328 ; 0.083333328*0.001736111 = 0.0002 ly, which is about 9.1495 AU (far greater distance than the distance between the Earth and the Sun, at 1 AU, though still short of the average distance between Earth and Jupiter).

Ten minutes : 5 minutes accel, 5 minutes decel ; 5 minutes is 0.003472222 days. v = 48*0.003472222 = 0.166666656 ; 0.166666656*0.003472222 = 0.0006 ly, which is about 36.5971 AU (an enormous distance, but a bit short of the average distance between Earth and Pluto at 39.5 AU ; keep this in mind, this will be relevant later).

Fifteen minutes : 7.5 minutes accel, 7.5 minutes decel ; 7.5 minutes is 0.005208333 days. v = 48*0.005208333 = 0.249999984 ; 0.249999984*0.005208333 = 0.001 ly, or about 82.3434 AU (greater distance than the average distance between Earth and Jump Zero).

Thirty minutes : 15 minutes accel, 15 minutes decel ; 15 minutes is 0.01041667 days. v = 48*0.01041667 = 0.50000016 ; 0.50000016*0.01041667 = 0.005 ly, or about 329.37 AU.

One hour : 30 minutes accel, 30 minutes decel ; 30 minutes is 0.02083333 days. v = 48*0.02083333 = 0.99999984 ; 0.99999984*0.02083333 = 0.02 ly, or about 1317.49 AU.

Two hours : 1 hour accel, 1 hour decel ; 1 hour is 0.04166667 days. v = 48*0.04166667 = 2.00000016 ; 2.00000016*0.04166667 = 0.08 ly, or about 5269.98 AU.

Three hours : 1.5 hours accel, 1.5 hours decel ; 1.5 hours is 0.0625 days. v = 48*0.0625 = 3 ; 3*0.0625 = 0.19 ly, or about 11,857.45 AU

Six hours : 3 hours accel, 3 hours decel ; 3 hours is 0.125 days. v = 48*0.125 = 6 ; 6*0125 = 0.75 light-years.

Twelve hours : 6 hours accel, 6 hours decel ; 6 hours is 0.25 days. v = 48*0.25 = 12 ; 12*0.25 = 3 light-years.

1 day : 12 light-years (duh) ; v = a*t = 48*0.5 = 24 ; v/2 = 24/2 = 12 = Average velocity ; x = 12*t*2 = 12*0.5*2 = 12

As you can see, the distance travelled increases exponentially to the time spent travelling. Note that the above numbers do not take into account minutiae like any trajectory other than a straight line, or the time when, presumably, the engines are switched off, the starship does a skew flip, and the engines are reignited.

Now, theoretically, assuming that starships can accelerate indefinitely and don't need to stop to get fuel/radiate heat/discharge drive charge/etc…

2 days : 48 ly ; v = a*t = 48*1 = 48 ; v/2 = 48/2 = 24 = Average velocity ; x = 24*1*2 = 24*2 = 48

3 days : 108 ly ; v = 48*1.5 = 72 ; 72/2 = 36 ; x = 36*1.5*2 = 108

4 days : 192 ly ; 48*2 = 96 ; 96/2 = 48 ; x = 48*2*2 = 192

5 days : 300 ly ; 48*2.5 = 120 ; 120/2 = 60 ; x = 60*2.5*2 = 300

But we can pretty much guess that's not the case, or the mass relays would be obsolete.

Going forward, our concerns are :

what are the non-mathematical limits to constant acceleration in FTL ?

And do whatever pieces of information we have about travel time and distance travel in Mass Effect agree with the numbers I've figured out ?

And oh, gosh, I've run out of letters again, I'll have to split this post in twain.

UP NEXT (eventually) : Camala ! Drew Karpyshyn ! Hawking Eta ! Oh, and every data point on speed and travel time in canon. Plus, all those nice numbers I calculated are shown to be… pointless. Fun !

G2HGE Index :

Post 0 : Presentation and Purpose

Post 1 : Methodology and general lamentation over the incoherent state of the lore.

Post 2a : Oldest canon date for activity in every single cluster

Post 2b : Organization and Visualization of the above

Post 3 : The oversized impact of the asari, and a surprising amount of stuff to discover.

Post 4 : The Problem with the Galaxy Maps

Post 5a : The Regions of the Milky Way : Overview and Council Space

Post 5b : The Regions of the Milky Way : The Terminus Systems

Post 5c : The Regions of the Milky Way : The Attican Traverse and Earth Systems Alliance Space

Post 5d : The Regions of the Milky Way : The Nemean Abyss and the Perseus Veil

Post 5e : The Regions of the Milky Way : The Skyllian Verge

Post 6a : You're here !

#mass effect #reblog

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crapeaucrapeau · 7 days ago