### PUSH PARTICLES TO INTERPLANETARY

Making the leap from ion drives to onboard particle accelerators will be an enormous technological challenge. While current ion propulsion greatly reduces travel time to nearby planetary destinations, it has serious limitations. The travel time is still lengthy, i.e., several months to Mars at near zero g conditions. However, Thought Experiment (TE) proposes a sufficient flow of high speed (10% to 50% c, light speed) exhaust particles to accelerate vessel at rate, g. Such performance would enable Einstein's "equivalence" (simulating gravity), and quick flights to other planets will inevitably become routine.

EXPAND ENVELOPE | |
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from current ion propulsion | ... which exhausts milligrams/sec of xenon ions at about 30 km/sec to accelerate a relatively small vessel much slower than g. Thus, flight time to Mars reduces by a few months. Vessel occupants will experience "micro-g" conditions. |

to onboard particle accelerator | ... which will transform several grams/sec of water to ions and expel them at speeds from 10% to 50%c (about 30 to 150 million meters per second). Thus, flights to nearby planets will be relatively quick (days to weeks). Furthermore, such propulsion can produce equivalence (occupants feel same gravity as if static on Earth's surface); thus, the term "g-force". |

**I. Assume onboard particle accelerator....**
...can consume reasonable quantities of fuel particles, original fuel flow per second (ff

_{sec}), and accelerate them into a constant flow of exhaust particles (ff_{Exh}) .
For this initial example, further assume particles' exhaust speed (V

_{Exh}) is 10% c. One can express exhaust velocity as a product of decimal component (d_{c}) and light speed, c.**EXAMPLE: V**

_{Exh}= d_{c }

**× c = .1 c**

**Thus, d**

_{c}= .1 = V_{Exh }/ c**Particle Size**

Lorentz Transform quantifies the relativistic growth due to particle speed. Thus, fuel flow per second (ff

_{sec}) is the original mass at rest, and exhaust fuel flow (ff_{Exh}) is the relativistic mass at an accelerated velocity.
Notional fuel quantity increases per following table.

**ff**

_{Exh}= n × ff_{sec}Original Fuel Flow | Exhaust Velocity | Growth Factor | Exhaust Fuel Flow |
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ff_{sec} | V_{Exh} =d_{c}×c | n | ff_{Exh} |

1 gm | 10% c | 1.005 | 1.005 gm |

Given | 1 √(1-d _{c}^{2}) | n×ff_{sec} |

**II. Assume g-force ...**

Original Fuel Flow | Exhaust Speed | Growth Factor | Ship Mass |
---|---|---|---|

ff_{sec} | V_{Exh} = d_{c}×c | n | M_{Ship} |

1 gm | .2 c | 1.0206 | 6.24 mT |

2 gm | .2 c | 1.0206 | 12.48 mT |

Given | Given | 1 √(1-d _{c}^{2}) | √(n^{2}-1)×30.57×10^{6}ff_{sec} |

Rewrite equation as shown:

M_{Ship} = (n × ff_{sec}) × (√(n^{2 }- 1) / n × (c/g) |
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Note decimal component, d

_{c}, defined in terms of n, growth factor.
or

**d**_{c}= √(n^{2 }- 1) / n**c = 299,792,458 m/sec g= 9.80665 m/sec**

^{2}**c/g = 30,570,323 sec = 30.57 mega-sec**

_{sec }cancels out the sec from c/g.M_{Ship} = √(n^{2 }- 1) × 30.57 mega-ff_{sec} |
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*(happens to equal acceleration due to near Earth gravity, g).*M_{Ship} × g = ff_{Exh} × V_{Exh} |
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d_{c} | = | V_{Exh}c | Define decimal componentof decimal light speed. | ||
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n | = | 1 √(1 - d _{c}^{2}) | AXIOMATIC: 'n' = Growth factor.As if LT's m_{o} = 1 | ||

n^{2} | = | 1 (1 - d _{c}^{2}) | Square both sides. | ||

1-d_{c}^{2} | = | 1 n ^{2} | Rearrange. | ||

d_{c}^{2} | = |
| Rearrange. | ||

d_{c}^{2} | = | (n^{2 }- 1)n ^{2} | Rearrange. | ||

d_{c} | = | √(n^{2 }- 1)n | Square root both sides. |

_{Exh}) can be rewritten as growth factor, n, times fuel flow per second (n×ff_{sec}). Particle exhaust velocity (V_{Exh}) can be rewritten as decimal component times light speed (d_{c}×c).M_{Ship} × g = (n×ff_{sec}) × (d_{c}×c) |
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III. Assume g-force ship's gross weight decreases... | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

... due to a fairly consistent fuel consumption. EXAMPLE: If ship's g-force propulsion system consumes 1 gm/sec anytime during a particular day; then, one could further assume that day's consumption as about 86,400 gm. We don't know exact amount of consumption per second for any given ship; however, we can designate that value as an variable, ff._{sec}
(One day = 24 hours × 3,600 sec /hour = 86,400 seconds.)
∇ = .2826% / √(n^{2}-1)CONCLUSION. By inspection we can see the daily decrease depends on particle size, n (multiple of original ff_{o}), which depends on particle speed, d (decimal portion of c, light speed). It does not depend on actual quantity of ff_{sec} nor actual ship's gross weight, GW. |
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IV. Assume ship's range...
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EXAMPLE: Independently vary particle's exhaust speed from 10%c to 60% c. Assume initial fuel load to be 50% of ship's Gross Weight (%TOGW=50%); thus, continuous flow of high speed exhaust particles will decrease ship's weight over a range of days until a minimum gross weight of half of ship's initial GW.Efficiency factor, ε, enables us to account for inevitable inefficiencies in the propulsion system. Artificially set efficiency factor at 2 (ε = 2.0); thus, TE assumes consumption rate is two times the exhaust flow. Daily exhaust flow,∇, is the amount of charged particles needed to achieve g-force momentum. Daily consumption rate. ε∇, is the amount of charged particles needed to ensure required exhaust flow. It accounts for inevitable inefficiencies. AXIOMATIC: ε∇ always exceeds ∇. Percent Take Off Gross Weight (%TOGW) is the portion of ship's initial mass allocated for fuel.
CONCLUSION. As particle exhaust speed increases, vessel's range increases. | .... can be modeled with daily decrease, ∇, in ship's mass to reflect fuel consumption. Model must also consider efficiency factor, ε, and Percent Take Off Gross Weight, %TOGW.EXAMPLE: Independently vary ship's %TOGW (portion of ship's mass dedicated to fuel) from 40% to 60%. Assume particle's exhaust speed as constant 56.5% c; then, previous work leads us to determine following values. Decimal component (d_{c}) is .565; growth factor (n) is 1.211; and daily exhaust flow, ∇, is 0.5% Ship's GW per day.Efficiency factor (ε) is inverse of efficiency (1/E). For interplanetary performance, Thought Experiment arbitrarily assumes an efficiency of 50%, E=.5; thus, ε = 1/E = 2. (NOTE: There's no way of knowing the actual efficiency of the future g-force propulsion system, but we're sure it's less than 100%.)Daily exhaust flow,∇. Previous work approximates this value by 86,400×ff_{sec} divided by ship's current Gross Weight (GW); this reduces to 0.2826% divided by √(n²-1).Daily consumption rate. ε∇, product of efficiency factor and daily exhaust flow. ε∇ ensures sufficient quantity for daily exhaust. Design flaws and peripheral needs compel a consumption rate greater than exhaust flow.Percent Take Off Gross Weight (%TOGW). For any given particle exhaust speed, range increases as %TOGW increases. (NOTE: Range is also known as propulsion time (t_{p}). See following table.)Logarithm helps transform %TOGW into available propulsion time.CONCLUSION. As fuel load (%TOGW) increases, range increases. |

VOLUME 0: ELEVATIONAL |
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VOLUME I: ASTEROIDAL |

VOLUME II: INTERPLANETARY |

VOLUME III: INTERSTELLAR |

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