Specific Impulse and the Fuel Component of the Probe’s Mass
Importantly, part of what we need accelerate is the fuel required to decelerate the probe once it arrives at its destination. The greater the fuel we send along with a probe, the greater the initial launch energy required. We want fuel which is highly efficient by its mass, i.e, it has high specific impulse.
The amount of fuel mass required to decelerate a probe is extremely sensitive to the specific impulse (Isp) of the fuel used. Oliver Habryka noticed that Eternity in Six Hours may be making unreasonable assumptions about achievable specific impulses attainable. Further investigation revealed that which specific impulses are attainable may determine whether or not space colonization is affordable at all. To me, it is a major sensitivity in the paper.
Transformed to isolate initial mass, the relativistic rocket equation gives:
m0: initial mass
m1: final mass
c: speed of light
Isp: specific impulse
Δv: change in velocity
This formula for the initial mass is linear in final mass and exponential in specific impulse. For a fixed mass of 1kg, the initial fuel mass required to accelerate to different fractions of the speed of light are shown by:
Isp can be measured in m/s; the x-axis gives Isp as a fraction of the speed of light. The dotted lines correspond to 4% of c (the Isp for fission given by the paper) and half that value, 2% of c.
On page 11, Armstrong and Sandberg provide the following values of specific impulse (measured as a fraction of c).
Of these, we have only actually attained nuclear fission, however not in efficient rocket form. As Habryka pointed out, the paper makes the assumption that almost all of the energy released by nuclear fission is converted into kinetic energy, however that this may be unrealistic.
Habryka identified a nuclear rocket concept which may be capable of achieving an Isp of 3%-5% the speed of light. Fission fragment rockets, while not yet built, uses only existing materials. Habryka, who’s physics are stronger than mine, believes the the rockets simple design and mechanism should be feasible.
I’ll reiterate the importance of specific impulse by pointing out that to accelerate a mass of 1k to 50% requires 1.02 x 10^3 tonnes of fuel with Isp of 4%c (value given for fission) and 1.04 x 10^9 tonnes of fuel at 2% of c, i.e. half the value. A mere halving of the specific impulse of the fuel results in an increase of six orders of magnitude in the fuel mass required.
To give a sense of where we are at, the Falcon Heavy rocket has an Isp of only 0.001% of C (3110 m/s). Proven and prototyped propulsion systems are in this range too. Ion thrusters, an existing technology, may be able to achieve up to 3% (100,000 m/s), however these required a both source of electricity as well as propellant, likely requiring a nuclear reactor and nuclear fuel.
It seems to me that only by making innovations somewhere with rocket technology (fission, fusion, antimatter) or with something more exotic (light sails, Bussard ramjets, etc.) that space colonization to distances much beyond our immediate neighbors could be possible. What we have now would not be enough apart from perhaps some experimental ion thrusters, but those require both a source of electricity, e.g. nuclear reactor, as well as a propellant.
Specific Impulse and the Fuel Component of the Probe’s Mass
Importantly, part of what we need accelerate is the fuel required to decelerate the probe once it arrives at its destination. The greater the fuel we send along with a probe, the greater the initial launch energy required. We want fuel which is highly efficient by its mass, i.e, it has high specific impulse.
The amount of fuel mass required to decelerate a probe is extremely sensitive to the specific impulse (Isp) of the fuel used. Oliver Habryka noticed that Eternity in Six Hours may be making unreasonable assumptions about achievable specific impulses attainable. Further investigation revealed that which specific impulses are attainable may determine whether or not space colonization is affordable at all. To me, it is a major sensitivity in the paper.
Transformed to isolate initial mass, the relativistic rocket equation gives:
m0: initial mass
m1: final mass
c: speed of light
Isp: specific impulse
Δv: change in velocity
This formula for the initial mass is linear in final mass and exponential in specific impulse. For a fixed mass of 1kg, the initial fuel mass required to accelerate to different fractions of the speed of light are shown by:
Isp can be measured in m/s; the x-axis gives Isp as a fraction of the speed of light. The dotted lines correspond to 4% of c (the Isp for fission given by the paper) and half that value, 2% of c.
On page 11, Armstrong and Sandberg provide the following values of specific impulse (measured as a fraction of c).
Of these, we have only actually attained nuclear fission, however not in efficient rocket form. As Habryka pointed out, the paper makes the assumption that almost all of the energy released by nuclear fission is converted into kinetic energy, however that this may be unrealistic.
Habryka identified a nuclear rocket concept which may be capable of achieving an Isp of 3%-5% the speed of light. Fission fragment rockets, while not yet built, uses only existing materials. Habryka, who’s physics are stronger than mine, believes the the rockets simple design and mechanism should be feasible.
I’ll reiterate the importance of specific impulse by pointing out that to accelerate a mass of 1k to 50% requires 1.02 x 10^3 tonnes of fuel with Isp of 4%c (value given for fission) and 1.04 x 10^9 tonnes of fuel at 2% of c, i.e. half the value. A mere halving of the specific impulse of the fuel results in an increase of six orders of magnitude in the fuel mass required.
To give a sense of where we are at, the Falcon Heavy rocket has an Isp of only 0.001% of C (3110 m/s). Proven and prototyped propulsion systems are in this range too. Ion thrusters, an existing technology, may be able to achieve up to 3% (100,000 m/s), however these required a both source of electricity as well as propellant, likely requiring a nuclear reactor and nuclear fuel.
It seems to me that only by making innovations somewhere with rocket technology (fission, fusion, antimatter) or with something more exotic (light sails, Bussard ramjets, etc.) that space colonization to distances much beyond our immediate neighbors could be possible. What we have now would not be enough apart from perhaps some experimental ion thrusters, but those require both a source of electricity, e.g. nuclear reactor, as well as a propellant.