EXTRAPLANETARY, Prep for the Stars
 
 

 
Two Types of Superconductor Magnets.
While CICC magnets are much more efficient then resistive magnets, they still use a small amount of power. For the short duration of interplanetary flights, this amount is almost inconsequential. Gforce accelerated trips to near planets will take days and at most weeks. Thus, CICC type magnets prove more than adequate. Their slight energy consumption will be relatively inconsequential compared to high momentum exchange from near light speed exhaust particles.
Wirewound magnets will not need an outside power source during most of long voyage's powered flight. Ramp up may take weeks; however, when complete, wirewound magnets disconnect from their power supply, because the superconducting current continues on its own.
For longer flights, the wire wound type will be even more important because the greatly reduced energy consumption will prove significant for an acceleration period of many months and possibly years.
 
Determine fuel requirement
for one day of gforce.
EXAMPLE: Let V_{Exh} be 86.6% light speed and arbitrarily assume perfect efficiency. At that speed, mass growth factor is 2.0 (i.e., mass doubles).
m_{r}= 1/√(1d_{c}^{2}) = 1/√(1.866^{2})= 2.00
Daily decrement of ship's mass is a small percentage of vessel's GW.
Δ = .2826%GW/√(m_{r}^{2}1) = 0.163%GW/Day  
DIFFERENT RANGES (R)
Theoretical Range:Assume fuel to be 100% of ship's GW (all fuel).
Approximate: R_{Theo} ≈ 1/Δ = 100%/0.163%/day = 613.5 days Feasible Range: assume ship's fuel between 10%90% of GW. For this example, let initial fuel be 40% of ship's initial GW. Approximate: R_{Feas }≈ 40%/Δ = 40%/0.163%/day = 245.4 days Practical Range: Assume much less than perfect efficiency (E=100%). For inner planetary, let E=25% and efficiency factor be 4 (ε = 1/E = 4). Approximate: R_{Prac }≈ 40%/(ε Δ) = 40%/(4 × 0.163%/day) = 61.35 days. Recall 4 phases of a typical gforce voyage. In brief, 1) Phase 1 is acceleration from departure to midpoint, 2) deceleration from midpoint to destination; returning from destination to departure, 3) is acceleration from destination back to midpt, 4) final phase is deceleration from midpt back to departure. Since all 4 phases are equal time/distance, Thought Experiment assumes one fourth of practical range is available for Phase 1, acceleration time, t_{Acc}.  
TOTAL TIME/DISTANCES
TO DIFFERENT DESTINATIONS
Phase I Acceleration Time (t_{Acc}): Previous tables show value derived from Particle Exhaust velocity. In turn, this value is basis for following terms.
Phase I Acceleration Distance (d_{Acc}): ... can be closely approximated via Newtonian method: d_{Acc }= g × (t_{Acc})²/2. Let g be acceleration due to gravity, g = 9.8065 m/sec² = 0.489 AU/day². Phase II Deceleration Time (t_{Dec}): Axiomatic that gforce deceleration time is same as acceleration time for same distance; thus, t_{Dec }= t_{Acc}
Total Time Destination (t_{Ttl}): Add acceleration time and deceleration time. Since those times are equal, it doubles accel time: t_{Ttl }= t_{Acc} + t_{Dec }= 2 × t_{Acc}
Total Distance Destination (d_{Ttl}): Since Phase I Accel takes vessel to midway point, half the distance to destination; then, Phase II Decel distance must be remaining half. Thus, total distance to destination is double the distance to midway. 
Inner Planetary Destinations
Gforce performance can be measured by particle exhaust velocity (V_{Exh}).For inner planets, exhaust velocities from .1c to .866c generate propulsion range in excess of 30 days.  SIDEBAR: Daily Decremental  

Decimal component of light speed (d_{c})
describes velocity of exhaust particles.

Fuel Burn Reduces GW
As with trains, planes and automobiles, gforce vessel's GW decreases with fuel consumption. How do we compute ever decreasing Gross Weight (GW)?
Daily Decremental Model is an intuitive model which approximates fuel comsumptions.
Following intuitive consumption model could approximate first few days. If a day of gforce propulsion requires 0.652% of vessel's initial Gross Weight (GW_{0}); then, first few days (0, 1, 2, 3, ..., t) of gforce travel would respectively consume following approximate amounts: 0%GW_{0}, 0.652% GW_{0}, 1.304% GW_{0}, 1.956%GW_{0}, ...., 0.652%GW_{0} × t. Finally, ever decreasing GWs could be approximated by following values: 100%GW_{0}, (1000.652)% GW_{0}, (1001.304)% GW_{0}, (1001.956)%GW_{0}, ...., (1000.652×t)%GW_{0}. Common sense leads to an arithmetic method of approximate fuel consumptions.< br /> EXAMPLE PROBLEM: If original fuel is 40% of ship's original GW, what is ship's range? Let daily differential of ship's GW (Δ) continue to be 0.17% GW_{0}. Intuition leads us to approximate range by dividing original fuel by Δ. Thus, Approximate Range (R_{App}) is 40%/Δ = 40%/0.652% per day =61.35 days.  
In previous tables (for inner planet ranges), intuition misleads us; it is wrong to divide original fuel load by daily decrement, Δ (% GW_{0}), to determine range capabilities of longer duration flights. Exponential methods are more accurate and more generous. (NOTE: Following section about Extraplanetary Ranges proposes a Daily Exponential Method to more accurately predict ranges.) 
 
EXAMPLE1 (Assume a very impractical 100% Efficiency): Previous work indicates exhaust particle speed of .866c could theoretically gforce propel a vessel with daily fuel consumption of Δ = 0.163%GW Thus, fuel consumption for 10 days of gforce could theoretically reduce vessel's GW as shown: GW_{10 }= (1  Δ)^{10} GW_{0} = (1  .163%)^{10} GW_{0} GW_{10} = (0.99837)^{10} GW_{0} = 0.98382 GW_{0}  EXAMPLE2 (Assume a very practical efficiency of E=25%) For every unit contributing to propulsion, vessel must consume 4 units; thus: ε =1/E=1/.25= 4 Practical fuel consumption for 10 days of gforce could reduce vessel's GW as shown: GW_{10 }= (1  εΔ)^{10} GW_{0} = (1  4×.163%)^{10} GW_{0} GW_{10} = (0.99348)^{10} GW_{0} = 0.93668 GW_{0} NOTE: Determine Fuel (F) consumed: F_{10 }=GW_{0 }GW_{10 }= .06332 GW_{0} 

ExtraPlanetary Ranges (greater than 100 AU)
When a propulsion system accelerates exhaust particles to near light speeds, resultant momentum can propel an even larger spaceship at gforce for a much longer duration. Outer Planetary Ranges has some key differences from the Inner Planetary Table. Use logarithms: R= log(1%TOGW)/log(1Δ) for more accurate, useful range durations. Use Efficiency Factor: ε = 4^{1/(mr1)}, an arbitrary, dynamic model which assumes continuous performance improvement. Use Einsteinian GForce Equation: d(t) = c×t_{Acc} + V(t) / ln(1Δ) for more accurate, useful distances.  
Mass consumed at rest (ff_{Sec}) expands to exhaust particle mass (ff_{Exh}). ff_{Exh} = m_{r}× ff_{sec}  

Determine fuel requirement
for one day of gforce.
EXAMPLE: Let relativity growth factor, m_{r}, be 5 and arbitrarily assume perfect efficiency.
Daily decrement of ship's mass is a small percentage of vessel's GW. Δ = .2826%GW/√(m_{r}^{2}1) Δ = .2826%GW/√(5^{2}1) Δ = .058%GW/Day  
DIFFERENT RANGES (R)
Computed Feasible Range: Like "Inner Planets", let initial fuel (%TOGW) be 40% of ship's initial GW. However, use a much different method (logarithms) to better model range durations. EXAMPLE: Let relativity mass growth (m_{r}) = 6.
Compute:: R_{Feas}=log(1%TOGW)/log(1Δ)=log(140%)/log(1048%)=1069 days Efficiency Factor, ε, of ship's propulsion system. TE uses an arbitrary function to generate dynamic values which map to m_{r }values. Actual efficiency factors will eventually come from observations of actual propulsion systems. Arbitrarily Compute: ε = 4^{1/(mr1)} Computed Practical Range: TE assumes Efficiency (E) will ever approach but never reach perfection (E = 100%)..Thus, TE assumes efficiency improves as propulsion performance improves (increasing value of m_{r}). Compute: R_{Prac }= log(1%TOGW)/log(1εΔ)=log(140%)/log(11.32×.048%)=810 days Phase 1 Acceleration Time (t_{Acc} ): Same as "Inner Planets Table", determine this value by taking one fourth of Practical Range: t_{Acc} = R_{Prac} /4 
TOTAL TIME/DISTANCES
TO DIFFERENT DESTINATIONS
Phase I Acceleration Time (t_{Acc}): Previously computed (see above.)
Einsteinian Velocity: Δ is daily progress of gforce vessel toward light speed, c. Δ = day×g/c = 86,400sec×9.8065m/sec² /299,792,500m/sec = .2826%c (1Δ) is daily remainder of ship's velocity till reaching light speed. (1Δ)=.997173c Earth observer measures subsequent daily reminders per exponential: (1Δ)^{t }c Earth observed vessel velocities: c  (1Δ)^{t }c Phase I Acceleration Distance (d_{Acc}): ... Calculus gives us distance solution. Phase II Deceleration Time (t_{Dec}): To maintain gforce, deceleration duration must be same as for acceleration (Phase I).
Total Time Destination (t_{Ttl}): Double acceleration duration from Phase I. This includes acceleration time from departure to midpoint and deceleration from midway to destination.
Total Distance Destination (d_{Ttl}): Double acceleration distance from Phase I which sums acceleration distance plus deceleration distance.. Note this distance is much less than distance achieved by gforce acceleration for same time. 
SIDEBAR: Daily Exponential 
Oort Cloud Destinations
Gforce performance can be measured by relativistic mass growth (m_{r}).
For Oort Cloud, m_{r} values 2 to 10 generate propulsion ranges exceeding 52,000 AUs.  

Fuel consumption reduces ship's Gross Weight (GW). Let daily decrement (Δ) be fuel consumed for one day of gforce propulsion.
EXAMPLE: if Δ = .163% GW; then, vessel's will decrease by .163% in one day. For subsequent days of powered flight, vessel's GW will continue to shrink.
Exponential Model
For longer duration voyages, use exponentials to readily determine vessel's gross weight for t days of gforce flight
GW_{t }= (1Δ)^{t} × GW_{0}
For corresponding fuel requirements.
F_{t }= GW_{0}  GW_{t}
For the lengthier voyages, the precise exponential model yields much more encouraging results than the daily decremental model.


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