In a previous post, I discussed the role-playing game Orbital 2100 – A Solar System Setting Using the Cepheus Engine Game and how it could possibly be used for playing in The Expanse setting. In The Expanse, the Epstein Drive is the engine that powers spacecraft across the Solar System. But just how does the Epstein Drive perform, and how could it be portrayed in the Orbital: 2100 setting using Cepheus Engine?
When playing Traveller or today’s Cepheus Engine games like Orbital 2100, I tend to be (using Marc Miller’s definitions from T4) a “Detailed Role Player.” I stray into the “System Engineer” role at times, like for this post. Part of my intention here is to show RPG players and referees/GMs that “this isn’t rocket science” – between the setting, game rules, and the internet (and with the help of a spreadsheet/calculator) it is actually fairly easy to do this analysis.
Fortunately, we have a “canon” story that we can draw inspiration from. The novella The Drive (published in 2012 and available for free online) takes place 150 years before the events of the first novel in the series, Leviathan Wakes. The Drive tells the story of Solomon Epstein, the inventor of the Epstein Drive. It is a very short novella coming in at a mere seven pages. Those seven pages, however, give us plenty of information that can be used to derive the performance of the Epstein Drive.
“By the way, we’re accelerating at four gravities. Five. Six. Seven.”
“He wonders how much above seven he’s going. Since the sensors are pegged, he’ll have to figure it out when the run is over.” – p. 1
In the first pages of the novella, we find a common language between the novels and the Orbital 2100 setting. Like Cepheus Engine and the Traveller RPG it derives from, spacecraft performance is expressed in g’s of acceleration. One g (1g) of acceleration is 9.8 meters/second/second. [Cepheus Engine and Traveller round this to 10 m/s/s…but we will use the actual value for the purposes of this discussion] Seven g’s of acceleration works out to 68.6 m/s. Since Sol’s “sensors are pegged,” this passage also establishes an instrumentation limit of the time.
“The yacht is built for long burns, and he started with the ejection tanks at ninety percent. The readout now shows the burn at ten minutes. The fuel supply ticks down to eighty-nine point six. That can’t be right.
Two minutes later, it drops to point five. Two and a half minutes later, point four. That puts the burn at over thirty-seven hours and the final velocity at something just under five percent of c.” – p. 1
These passages help determine a fuel consumption rate.
- Using the 90% full tank as a beginning, and given that after 10 minutes 89.6% remains, we see that .4% was consumed in that short time for an hourly consumption rate of 2.4%.
- “Two minutes later,” or after 12 minutes of total burn, the tanks are 89.5% full; meaning that .5% has been consumed at a rate of 2.5% per hour.
- Finally, after 2.5 minutes more – or 14.5 minutes total – the tanks are at 89.4% full, or .6% consumed for a rough consumption rate of 2.4% per hour.
Using the 2.4% rate, 90% divided by 2.4% gives us 37.5 hours of “burn” endurance – right in line with Solomon’s “over thirty-seven hours” statement.
The later passage helps compute the acceleration performance of the Epstein Drive.
- The speed of light – c – is 299,792,458 m/s. Five percent (5%) of c is 14,989,623 m/s.
- The formula for acceleration is a=v/t where a equals acceleration in m/s, v is velocity in m/s, and t is time in seconds.
- Plugging in our numbers for velocity (5% of c) and time (37.5 hours or 135,000 seconds) we get an acceleration of 111.03424 m/s.
- Dividing this by 9.8 m/s, we get 11.33g acceleration.
Eleven g’s of acceleration is quite a lot, even for Cepheus Engine/Traveller where a top-grade maneuver drive is no more than 6g performance!
“Only the acceleration isn’t the problem either. Ships have had the power to burn at fifteen or even twenty g since the early chemical rockets. The power is always there. It’s the efficiency necessary to maintain a burn that was missing. Thrust to weight when most of your weight is propellant to give you thrust. And bodies can accelerate at over twenty g for a fraction of a second. It’s the sustain that’s killing him. It’s going for hours.” – p.3
NASA and the military conducted many experiments in the 1950’s and 1960’s that established a 20g human limit to acceleration. Sol is obviously in pain, but in terms of Cepheus Engine and Orbital: 2100, just how much damage is he taking?
There are no specific rules in Orbital 2100 for acceleration effects on characters. Looking at “Falling and Gravity “in Cepheus Engine (p. 164), we see that on a 1g world, the character will get 1d6 damage per 2m of fall. The rules further specify that for higher g worlds, multiple the 1d6 by the planet’s gravity number. The Epstein Drive accelerates at 11g, which we can compute as 11d6 damage. The question is the time period in which this damage takes place. Falling is assumed to be instantaneous, but declaring 11d6 damage per combat round (6 seconds) does not seem to fit the events of The Drive. This seems excessive because an average character in Orbital 2100 (7 Strength/7 Dexterity/ 7 Endurance) only has 21 damage points until death. The “average” damage from 11d6 is 44, meaning the character is dead twice over!
Perhaps we should assume the 11d6 damage takes place every space combat round (1,000 seconds/16.6 minutes) instead. This better reflects the painful, but non-instantaneous death like Solomon Epstein experiences. It still seems like an excessive amount of damage, guaranteeing character death.
Looking around for a solution, and not finding one in the rules, I suggest a “house rule” that acceleration couches absorb some of the damaging g forces. In This New Ocean: A History of Project Mercury, acceleration couches in the Mercury spacecraft were designed to absorb 9g (assumed to be the maximum g at reentry). If we use couches to absorb 9 of 11g, the character will have only 2g of damage (2d6) per space combat round. This means an average human may last as long as three space combat rounds, or about 48 minutes, before sub-coming to the strangling g forces.
“Even as he struggles to make the terminal respond, he’s also thinking what the drive means practically. With efficiency like this, ships can be under thrust all through a voyage. Acceleration thrust to the halfway point, then cut the engines, flip, and decelerate the rest of the trip. Even a relatively gentle one third g will mean not only getting wherever they are headed much faster, but there won’t be any of the problems of long-term weightlessness. He tries to figure how long the transit to Earth will take, but he can’t.” – p.5
Ah, here we can use the classic formula for interplanetary travel time where a ship constantly accelerates to a midpoint, flips over, and then decelerates at a constant rate to the destination. The formula is t=2*SQRT(d/a) where like before t = time in seconds, d = distance in meters, and a = acceleration in m/s/s. (see Cepheus Engine, p. 104)
Unlike Solomon, we do not have 11g’s of force crushing down upon us, so we can solve for the time it would take an Epstein Drive spacecraft to travel from Mars to Earth.
To figure distance, one must first realize that both Mars and Earth orbit the sun differently and the distance between the two planets is not constant. At opposition, the two can be as close as 56 million kilometers (Mkm); however, at conjunction the two can be as far as 401 Mkm apart!. On average, Mars and Earth are 225 Mkm apart.
[Interestingly, in Cepheus Engine, Chapter 6: Off World Travel, Interplanetary Travel, Table: Common Travel Times by Acceleration, there is a listing for “Far Neighbor” with a distance of 255 million km. This is close enough to the Earth-Mars average distance that I think it was the source for the entry. Orbital 2100, Chapter 6: Operating Spacecraft, Travel Times, Travel Between Inner Planets, uses a different process to determine distance (p. 71). In Orbital 2100 you start with the Basic Distance of 80 Mkm (Inner Planets: Basic Distance Table) PLUS seven squares of travel on the Travel Between Inner Planets chart (using the recommended starting setup). This works out to a total travel distance of 290 Mkm – within reason but a bit above the average.]
For the purposes of this example, lets use the 225 Mkm average. Using that average distance (225 Mkm), and Sol’s stated 1/3g (3.27 m/s acceleration), the formula gives us a travel time of Mars to Earth of just over 3 weeks. This may be a normal pre-Epstein Drive trip, given the 3.27g falls within the previously noted 7g instrument limit.
“The United Nations ordered that all shipyards on Mars shut down until an inspection team could be sent out there. Seven months to get the team together, and almost six months in transit because of the relative distances of the two planets in their orbits around the sun.” – p. 6
From this passage we can assume that Sol is telling us that the average transit time between Earth and Mars is about six months. The is an important figure to remember for later.
“And the war! If distance is measured in time, Mars just got very, very close to Earth while Earth is still very distant from Mars. That kind of asymmetry changes everything.” – p. 7
Once again, lets assume the Earth to Mars distance d to be 225 Mkm. Using the Epstein Drive with an acceleration of 11g ( a=111.03424 m/s) and solving for time t gets 12.5 hours. This is a major difference from the six months Sol was thinking about earlier. It is orders of magnitude better performance!
Think for a moment about Jupiter like Sol does. Assuming the Earth-to-Jupiter average distance is 588 Mkm, using the Epstein Drive the trip would take 1 day and 16 hours!
In Orbital 2100, the best TL 9 Nuclear Thermal Rocket (NTR, p. 41) can only travel a maximum of 330 Mkm per month, meaning it takes 1 month and 23 days to make the Earth to Jupiter transit. Even the best alternative TL 10 Fusion Drive, or Nuclear Pulse Fusion (NPF, p. 61), has an acceleration performance of 12 m/s for a travel time of 5 days and 21 hours. Even the best performing Maneuver Drive in Cepheus Engine (6g or 60 m/s acceleration – p. 122), takes 2 days and 7 hours to make the same trip.
Unfortunately, as much as we can learn from The Drive about Epstein Drive performance, the novella lacks other details like the size of the drive or the volume of fuel required. This means we will have to look elsewhere for that information, like maybe Leviathan Wakes.
In summary, the Epstein Drive is very efficient compared to the NPR and NTR in the Orbital 2100 setting. Even compared to maneuver drives available in Cepheus Engine the Epstein Drive is superior. The major drawback, as Sol discovered, is the crushing gravity of acceleration. In the default Traveller setting, the Original Traveller Universe, this is overcome by using handwavium acceleration compensators. In The Expanse, 150 years after Sol’s invention, you have “the juice.”
The juice was a cocktail of drugs the pilot’s chair would inject into him to keep him conscious, alert, and hopefully stroke-free when his body weighed five hundred kilos. Holden had used the juice on multiple occasions in the navy, and coming down afterward was unpleasant. –Leviathan Wakes
Leviathan Wakes, Copyright (c) 2011 by Daniel Abraham and Ty Franck.
The Drive (A Novella for The Expanse), Copyright (c) 2012 by Daniel Abraham and Ty Franck.
Cepheus Engine: A Classic Era Science Fiction 2D6-Based Open Game System. Copyright (c) 2016 Samardan Press.
Orbital 2100 Second Edition, Copyright (c) 2016 Zozer Games.
“The Traveller game in all forms is owned by Far Future Enterprises. Copyright 1977-2016 Far Future Enterprises.”