Ref Mat'l: Review Rate and Range
First discuss how we can most conveniently express these values.
Intuitively, take a nice round number (i.e., 10,000 kms/sec) and use as increment. This becomes the Independent Variable (IV). Above table compares absolute speed with decimal light speed. 
Alternatively, we could independently vary speed as decimal light speed values. An inherent benefit, decimal c implicitly increases precision, because c by definition is exact speed of light. On the other hand, c = 300 million m/sec is a gross approximation. 

Per Lorentz Transform, fuel particle size strictly depends on fuel particle speed. 
We could even make fuel particle size the IV. In above table, n is multiple of original particle size at rest. 

ff_{sec} =  g * M_{Ship} c * √(1  n^{2}) 

In a more practical way, realtime ff_{sec} will likely be closely controlled by sophisticated servos which monitor perceived "weight" of control objects and subsequently adjust fuel flow. Thus, fuel flow will constantly adjust in accordance with how closely propulsion force resembles near Earth gravity.
n * ff_{Sec}  dec. c  Exhaust  Daily Fuel  

n  d  km/sec  ∇  
1.1  0.42c  124,979  0.63%  
1.2  0.55c  165,831  0.43%  
1.3  0.64c  191,691  0.35%  
1.4  0.70c  209,956  0.29%  
1.5  0.75c  223,607  0.26%  
1.6  0.78c  234,187  0.23%  
1.7  0.81c  242,607  0.21%  
I.V.  √(1  n^{2})  d * 3x10^{5}km/sec  g * 86,400 
∇ =  ff_{1} GW_{1}  =  ff_{2} GW_{2}  =  ff_{i} GW_{i} 

Example: ratio of 1:100 = 1%
Thus, the daily mass of fuel consumed is ever decreasing, but the ratio of daily fuel consumed vs. current ship's GW stays the same if the ship's acceleration remains constant.
n * ff_{Sec}  

n  d  km/sec  Δ  t_{p}  
1.1  0.42c  124,979  0.63%  54.8  
1.2  0.55c  165,831  0.43%  79.5  
1.3  0.64c  191,691  0.35%  99.6  
1.4  0.70c  209,956  0.29%  117.6  
1.5  0.75c  223,607  0.26%  134.2  
1.6  0.78c  234,187  0.23%  150.0  
1.7  0.81c  242,607  0.21%  165.1  
I.V.  √(1  n^{2})  d * 3x10^{5}km/sec 


i = t_{p} =  log .5 log(12∇) 

If practicality considers these efficiency factors; then, above "i" can be the definition of "Practical Range"
Determine Range  Final  Cumm.  Examples  

n * ff_{Sec}  Velocity  Distance  Dest.  Dist.  
n  d  km/sec  ∇  t_{p}  AU/Day  AU  AU  
1.01  0.14  42,111  2.03%  16.7  8.4 AU/day  69.8 AU  NEA  1 AU 
1.02  0.20  59,117  1.43%  23.8  11.9 AU/day  142.1 AU  Mars  2 AU 
1.03  0.24  71,877  1.17%  29.3  14.7 AU/day  215.3 AU  Asteroids  3 AU 
1.04  0.27  82,401  1.01%  34.0  17.0 AU/day  289.5 AU  Jupiter  5 AU 
1.05  0.30  91,473  0.90%  38.2  19.1 AU/day  364.4 AU  Saturn  10 AU 
1.06  0.33  99,500  0.82%  42.0  21.0 AU/day  440.1 AU  Uranus  20 AU 
1.07  0.36  106,726  0.76%  45.5  22.7 AU/day  516.7 AU  Neptune  30 AU 
1.08  0.38  113,312  0.71%  48.7  24.4 AU/day  593.9 AU  Near Kuiper  40 AU 
1.09  0.40  119,368  0.66%  51.8  25.9 AU/day  671.9 AU  Mid Kuiper  70 AU 
1.10  0.42  124,979  0.63%  54.8  27.4 AU/day  750.7 AU  Far Kuiper  100 AU 
I.V.  √(1  n^{2})  d * 3x10^{5}km/sec  .00288  log(50% TOGW)  g * t t = t_{p}  g * t^{2}/2 t = t_{p} 
Determine Range  Acceleration Phase  Deceleration Phase  

n * ff_{Sec}  Time  Distance  Velocity  Velocity  Distance  Time  
n  Dec. c  ∇  t_{p}  t_{Acc}  d_{Acc}  v_{Acc}  v_{Dec}  d_{Dec}  t_{Dec}  
1.1  0.417  0.628%  54.8 Days  27.4 Days  182 AU  13.1 AU/Day  8% c  0.003 LY  0.08 Yr  
1.2  0.553  0.434%  79.5 Days  39.7 Days  379 AU  18.7 AU/Day  11% c  0.006 LY  0.11 Yr  
1.3  0.639  0.347%  99.6 Days  49.8 Days  590 AU  23.1 AU/Day  13% c  0.009 LY  0.14 Yr  
1.4  0.700  0.294%  117.6 Days  58.8 Days  814 AU  26.9 AU/Day  16% c  0.013 LY  0.16 Yr  
1.5  0.745  0.258%  134.2 Days  67.1 Days  1,053 AU  30.4 AU/Day  18% c  0.017 LY  0.18 Yr  
1.6  0.781  0.231%  150.0 Days  75.0 Days  1,305 AU  33.6 AU/Day  19% c  0.021 LY  0.21 Yr  
1.7  0.809  0.209%  165.1 Days  82.5 Days  1,571 AU  36.6 AU/Day  21% c  0.025 LY  0.23 Yr  
1.8  0.831  0.192%  179.8 Days  89.9 Days  1,850 AU  39.5 AU/Day  23% c  0.029 LY  0.25 Yr  
1.9  0.850  0.178%  194.1 Days  97.0 Days  2,142 AU  42.2 AU/Day  24% c  0.03 LY  0.27 Yr  
2.0  0.866  0.166%  208.1 Days  104.0 Days  2,447 AU  44.8 AU/Day  26% c  0.04 LY  0.28 Yr  
I.V.  √(1  n^{2})  .00288  log(%TOGW) %TOGW=.5 ε = 2.0  t_{p} 
 cc(1Δ)^{t} t = t_{Acc} c = 172.8 AU/day 



Determine Range  Acceleration Phase  Cruise Phase  Deceleration Phase  

n * ff_{Sec}  Time  Distance  Velocity  Distance  Time  Velocity  Distance  Time  
n  ∇  t_{p}  t_{Acc}  d_{Acc}  v_{Acc}  d_{Cru}  t_{Cru}  v_{Dec}  d_{Dec}  t_{Dec}  
2.0  0.166%  208.1 Days  104.0 Days  2,447 AU  44.8 AU/Day  3.92 LY  15.13 Yr  26% c  0.04 LY  0.3 Yr  
3.0  0.102%  340.0 Days  170.0 Days  6,157 AU  67.0 AU/Day  3.80 LY  9.82 Yr  39% c  0.10 LY  0.5 Yr  
4.0  0.074%  465.7 Days  232.9 Days  10,934 AU  84.5 AU/Day  3.65 LY  7.47 Yr  49% c  0.17 LY  0.6 Yr  
5.0  0.059%  589.2 Days  294.6 Days  16,609 AU  98.9 AU/Day  3.47 LY  6.07 Yr  57% c  0.26 LY  0.8 Yr  
6.0  0.049%  711.6 Days  355.8 Days  23,039 AU  110.9 AU/Day  3.27 LY  5.10 Yr  64% c  0.37 LY  1.0 Yr  
7.0  0.042%  833.4 Days  416.7 Days  30,104 AU  120.8 AU/Day  3.05 LY  4.36 Yr  70% c  0.48 LY  1.1 Yr  
8.0  0.036%  954.8 Days  477.4 Days  37,701 AU  129.2 AU/Day  2.81 LY  3.75 Yr  75% c  0.60 LY  1.3 Yr  
9.0  0.032%  1076.0 Days  538.0 Days  45,747 AU  136.2 AU/Day  2.55 LY  3.24 Yr  79% c  0.72 LY  1.5 Yr  
10.0  0.029%  1197.0 Days  598.5 Days  54,170 AU  142.0 AU/Day  2.28 LY  2.78 Yr  82% c  0.86 LY  1.6 Yr  
11.0  0.026%  1317.9 Days  658.9 Days  62,909 AU  147.0 AU/Day  2.01 LY  2.36 Yr  85% c  1.00 LY  1.8 Yr  
12.0  0.024%  1438.7 Days  719.3 Days  71,914 AU  151.1 AU/Day  1.72 LY  1.97 Yr  87% c  1.14 LY  2.0 Yr  
I.V.  .00288  log(%TOGW) %TOGW=.5 ε = 2.0  t_{p} 
 cc(1Δ)^{t} t = t_{Acc} c = 172.8 AU/day  4LY  d_{Acc}  d_{Dec}  d_{Cru} 



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