I've had this idea for a more “realistic” boost drive for some time, but had to work out the equations and numbers first.
Mass Conversion Boost Drive (TL10^) [Any!]
This drive is a Reactionless Engine (SS1:p24) that directly converts fuel mass into directional kinetic energy instantaneously applying it to the ship and its contents boosting it to a c-fractional velocity. The kinetic energy of a ship travelling at relativistic velocities is the difference between the total energy of its rest mass (M) and that of its relativistic mass (M/τ) where τ=sqrt(1-(v/c)²) (also known as the tau factor). Thus, with K=Mc²(1/τ-1), the mass converted to kinetic energy would be m=M(1/τ-1), making τ=M/(M+m) and (v/c)=sqrt(1-τ²). The table below assumes that for safety, the fuel tanks contain mass for two boosts; one to accelerate, the other to decelerate. (For this I used M=sqrt(1-0.05*N) and m=r*(1-M) where N is the number of fuel tanks and r is the rate of mass conversion.) The conversion rates are 60% at TL10^, 80% at TL11^ and 100% at TL12^. Use Subwarp drive prices.
[Spaceships] FWIW: Semi-Hard Science Boost Drive
Mass Conversion Boost Drive (TL10^) [Any!]
This drive is a Reactionless Engine (SS1:p24) that directly converts fuel mass into directional kinetic energy instantaneously applying it to the ship and its contents boosting it to a c-fractional velocity. The kinetic energy of a ship travelling at relativistic velocities is the difference between the total energy of its rest mass (M) and that of its relativistic mass (M/τ) where τ=sqrt(1-(v/c)²) (also known as the tau factor). Thus, with K=Mc²(1/τ-1), the mass converted to kinetic energy would be m=M(1/τ-1), making τ=M/(M+m) and (v/c)=sqrt(1-τ²). The table below assumes that for safety, the fuel tanks contain mass for two boosts; one to accelerate, the other to decelerate. (For this I used M=sqrt(1-0.05*N) and m=r*(1-M) where N is the number of fuel tanks and r is the rate of mass conversion.) The conversion rates are 60% at TL10^, 80% at TL11^ and 100% at TL12^. Use Subwarp drive prices.
Code:
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Fuel | Velocities/Tau Factors for Mass-Conversion Boost Drive |
Used | 60% Conversion (TL10^) | 80% Conversion (TL11^) | 100% Conversion (TL12^) |
(Tanks)| v/c v(AU/hr) τ-Factor| v/c v(AU/hr) τ-Factor| v/c v(AU/hr) τ-Factor|
-------+-------------------------+-------------------------+-------------------------|
1/3 | 10.03% 0.7233 0.99496 | 11.56% 0.8341 0.99329 | 12.91% 0.9314 0.99163 |
2/3 | 14.21% 1.0254 0.98985 | 16.37% 1.1811 0.98651 | 18.26% 1.3172 0.98319 |
1 | 17.45% 1.2591 0.98465 | 20.08% 1.4484 0.97964 | 22.36% 1.6132 0.97468 |
2 | 24.88% 1.7947 0.96856 | 28.50% 2.0563 0.95852 | 31.62% 2.2814 0.94868 |
3 | 30.71% 2.2158 0.95166 | 35.05% 2.5284 0.93657 | 38.73% 2.7941 0.92195 |
4 | 35.76% 2.5801 0.93386 | 40.63% 2.9315 0.91372 | 44.72% 3.2264 0.89443 |
5 | 40.33% 2.9096 0.91506 | 45.62% 3.2913 0.88987 | 50.00% 3.6072 0.86603 |
6 | 44.58% 3.2160 0.89515 | 50.19% 3.6210 0.86492 | 54.77% 3.9515 0.83666 |
7 | 48.60% 3.5061 0.87397 | 54.45% 3.9286 0.83873 | 59.16% 4.2681 0.80623 |
8 | 52.46% 3.7846 0.85136 | 58.48% 4.2191 0.81116 | 63.25% 4.5628 0.77460 |
9 | 56.21% 4.0548 0.82710 | 62.32% 4.4963 0.78203 | 67.08% 4.8395 0.74162 |
10 | 59.87% 4.3195 0.80094 | 66.02% 4.7628 0.75111 | 70.71% 5.1013 0.70711 |
11 | 63.50% 4.5809 0.77254 | 69.59% 5.0208 0.71810 | 74.16% 5.3503 0.67082 |
12 | 67.10% 4.8408 0.74146 | 73.08% 5.2720 0.68264 | 77.46% 5.5882 0.63246 |
13 | 70.71% 5.1012 0.70712 | 76.48% 5.5178 0.64423 | 80.62% 5.8164 0.59161 |
14 | 74.35% 5.3641 0.66870 | 79.83% 5.7596 0.60219 | 83.67% 6.0360 0.54772 |
15 | 78.06% 5.6317 0.62500 | 83.15% 5.9986 0.55556 | 86.60% 6.2478 0.50000 |
16 | 81.87% 5.9067 0.57417 | 86.44% 6.2361 0.50280 | 89.44% 6.4527 0.44721 |
17 | 85.84% 6.1926 0.51303 | 89.73% 6.4736 0.44139 | 92.20% 6.6513 0.38730 |
18 | 90.03% 6.4950 0.43528 | 93.05% 6.7129 0.36632 | 94.87% 6.8441 0.31623 |
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Dalton “who thinks this makes boost drives relatively realistic” Spence
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