Monday, January 29, 2007

7G TABLE: Accelerate 100 Days

To effectively accomplish an interstellar resupply mission, an Artificial Intelligent (AI) vessel could use 7G propulsion to quickly intercept the primary 1G vessel.  EXAMPLE:  the 7G vessel needs only 100 days to greatly exceed the 1G vessel cruise velocity. This table describes daily progress throughout a typical 7G acceleration duration planned to stop near the end of the 1G vessel's 1 year acceleration.
timeVelocityIncr. Dist.Total DistanceTotal Fuel
0 days0.00 AU/dy0.00% c0.0 AU0.0 AU0.0000 LY0.000% GW0
1 days3.43 AU/dy1.98% c1.7 AU1.7 AU0.0000 LY0.328% GW0
2 days6.80 AU/dy3.92% c5.1 AU6.8 AU0.0001 LY0.654% GW0
3 days10.09 AU/dy5.83% c8.4 AU15.3 AU0.0002 LY0.980% GW0
4 days13.32 AU/dy7.70% c11.7 AU27.0 AU0.0004 LY1.304% GW0
5 days16.49 AU/dy9.53% c14.9 AU41.9 AU0.0007 LY1.627% GW0
6 days19.60 AU/dy11.32% c18.0 AU60.0 AU0.0009 LY1.950% GW0
7 days22.64 AU/dy13.08% c21.1 AU81.1 AU0.0013 LY2.271% GW0
8 days25.62 AU/dy14.80% c24.1 AU105.2 AU0.0017 LY2.591% GW0
9 days28.55 AU/dy16.49% c27.1 AU132.3 AU0.0021 LY2.910% GW0
10 days31.42 AU/dy18.14% c30.0 AU162.3 AU0.0026 LY3.228% GW0
11 days34.23 AU/dy19.77% c32.8 AU195.1 AU0.0031 LY3.545% GW0
12 days36.98 AU/dy21.36% c35.6 AU230.7 AU0.0036 LY3.861% GW0
13 days39.68 AU/dy22.92% c38.3 AU269.1 AU0.0043 LY4.176% GW0
14 days42.33 AU/dy24.45% c41.0 AU310.1 AU0.0049 LY4.490% GW0
15 days44.92 AU/dy25.94% c43.6 AU353.7 AU0.0056 LY4.803% GW0
(1 - (1-Δ)t) ×c
dt - dt-1
c × t +Vt

ft = 1 - (1-ε∇)t
16 days47.46 AU/dy27.41% c46.2 AU399.9 AU0.0063 LY5.115% GW0
17 days49.96 AU/dy28.85% c48.7 AU448.6 AU0.0071 LY5.426% GW0
18 days52.40 AU/dy30.26% c51.2 AU499.8 AU0.0079 LY5.735% GW0
19 days54.79 AU/dy31.65% c53.6 AU553.4 AU0.0088 LY6.044% GW0
20 days57.14 AU/dy33.00% c56.0 AU609.4 AU0.0096 LY6.352% GW0
21 days59.44 AU/dy34.33% c58.3 AU667.7 AU0.0106 LY6.659% GW0
22 days61.70 AU/dy35.63% c60.6 AU728.2 AU0.0115 LY6.965% GW0
23 days63.91 AU/dy36.91% c62.8 AU791.1 AU0.0125 LY7.269% GW0
24 days66.08 AU/dy38.16% c65.0 AU856.1 AU0.0135 LY7.573% GW0
25 days68.20 AU/dy39.39% c67.1 AU923.2 AU0.0146 LY7.876% GW0
26 days70.28 AU/dy40.59% c69.2 AU992.4 AU0.0157 LY8.178% GW0
27 days72.32 AU/dy41.77% c71.3 AU1,063.7 AU0.0168 LY8.479% GW0
28 days74.32 AU/dy42.93% c73.3 AU1,137.1 AU0.0180 LY8.778% GW0
29 days76.29 AU/dy44.06% c75.3 AU1,212.4 AU0.0192 LY9.077% GW0
30 days78.21 AU/dy45.17% c77.3 AU1,289.6 AU0.0204 LY9.375% GW0

timeVelocityIncr. Dist.Total DistanceTotal Fuel
31 days80.09 AU/dy46.26% c79.2 AU1,368.8 AU0.0216 LY9.672% GW0
32 days81.94 AU/dy47.32% c81.0 AU1,449.8 AU0.0229 LY9.968% GW0
33 days83.75 AU/dy48.37% c82.8 AU1,532.7 AU0.0242 LY10.263% GW0
34 days85.52 AU/dy49.39% c84.6 AU1,617.3 AU0.0256 LY10.557% GW0
35 days87.26 AU/dy50.40% c86.4 AU1,703.7 AU0.0269 LY10.850% GW0
36 days88.97 AU/dy51.38% c88.1 AU1,791.8 AU0.0283 LY11.142% GW0
37 days90.64 AU/dy52.35% c89.8 AU1,881.6 AU0.0298 LY11.433% GW0
38 days92.28 AU/dy53.30% c91.5 AU1,973.1 AU0.0312 LY11.723% GW0
39 days93.88 AU/dy54.22% c93.1 AU2,066.2 AU0.0327 LY12.012% GW0
40 days95.46 AU/dy55.13% c94.7 AU2,160.8 AU0.0342 LY12.301% GW0
41 days97.00 AU/dy56.02% c96.2 AU2,257.1 AU0.0357 LY12.588% GW0
42 days98.51 AU/dy56.90% c97.8 AU2,354.8 AU0.0372 LY12.874% GW0
43 days100.00 AU/dy57.75% c99.3 AU2,454.1 AU0.0388 LY13.160% GW0
44 days101.45 AU/dy58.59% c100.7 AU2,554.8 AU0.0404 LY13.444% GW0
45 days102.87 AU/dy59.42% c102.2 AU2,657.0 AU0.0420 LY13.728% GW0
(1 - (1-Δ)t) ×c
dt - dt-1
c × t +Vt

ft = 1 - (1-ε∇)t
46 days104.27 AU/dy60.22% c103.6 AU2,760.6 AU0.0437 LY14.010% GW0
47 days105.64 AU/dy61.01% c105.0 AU2,865.5 AU0.0453 LY14.292% GW0
48 days106.98 AU/dy61.79% c106.3 AU2,971.8 AU0.0470 LY14.573% GW0
49 days108.30 AU/dy62.55% c107.6 AU3,079.5 AU0.0487 LY14.853% GW0
50 days109.58 AU/dy63.29% c108.9 AU3,188.4 AU0.0504 LY15.132% GW0
51 days110.85 AU/dy64.02% c110.2 AU3,298.6 AU0.0522 LY15.410% GW0
52 days112.09 AU/dy64.74% c111.5 AU3,410.1 AU0.0539 LY15.687% GW0
53 days113.30 AU/dy65.44% c112.7 AU3,522.8 AU0.0557 LY15.963% GW0
54 days114.49 AU/dy66.12% c113.9 AU3,636.7 AU0.0575 LY16.238% GW0
55 days115.66 AU/dy66.80% c115.1 AU3,751.8 AU0.0593 LY16.513% GW0
56 days116.80 AU/dy67.46% c116.2 AU3,868.0 AU0.0612 LY16.786% GW0
57 days117.92 AU/dy68.11% c117.4 AU3,985.4 AU0.0630 LY17.059% GW0
58 days119.02 AU/dy68.74% c118.5 AU4,103.8 AU0.0649 LY17.331% GW0
59 days120.10 AU/dy69.36% c119.6 AU4,223.4 AU0.0668 LY17.601% GW0
60 days121.15 AU/dy69.97% c120.6 AU4,344.0 AU0.0687 LY17.871% GW0

timeVelocityIncr. Dist.Total DistanceTotal Fuel
61 days122.19 AU/dy70.57% c121.7 AU4,465.7 AU0.0706 LY18.140% GW0
62 days123.20 AU/dy71.15% c122.7 AU4,588.4 AU0.0726 LY18.409% GW0
63 days124.20 AU/dy71.73% c123.7 AU4,712.1 AU0.0745 LY18.676% GW0
64 days125.17 AU/dy72.29% c124.7 AU4,836.8 AU0.0765 LY18.942% GW0
65 days126.13 AU/dy72.84% c125.6 AU4,962.4 AU0.0785 LY19.208% GW0
66 days127.06 AU/dy73.38% c126.6 AU5,089.0 AU0.0805 LY19.472% GW0
67 days127.98 AU/dy73.91% c127.5 AU5,216.5 AU0.0825 LY19.736% GW0
68 days128.88 AU/dy74.43% c128.4 AU5,345.0 AU0.0845 LY19.999% GW0
69 days129.76 AU/dy74.94% c129.3 AU5,474.3 AU0.0866 LY20.261% GW0
70 days130.62 AU/dy75.44% c130.2 AU5,604.5 AU0.0886 LY20.523% GW0
71 days131.47 AU/dy75.93% c131.0 AU5,735.5 AU0.0907 LY20.783% GW0
72 days132.30 AU/dy76.41% c131.9 AU5,867.4 AU0.0928 LY21.042% GW0
73 days133.12 AU/dy76.88% c132.7 AU6,000.1 AU0.0949 LY21.301% GW0
74 days133.91 AU/dy77.34% c133.5 AU6,133.6 AU0.0970 LY21.559% GW0
75 days134.70 AU/dy77.79% c134.3 AU6,268.0 AU0.0991 LY21.816% GW0
(1 - (1-Δ)t) ×c
dt - dt-1
c × t +Vt

ft = 1 - (1-ε∇)t
76 days135.46 AU/dy78.24% c135.1 AU6,403.0 AU0.1012 LY22.072% GW0
77 days136.21 AU/dy78.67% c135.8 AU6,538.9 AU0.1034 LY22.327% GW0
78 days136.95 AU/dy79.10% c136.6 AU6,675.5 AU0.1056 LY22.582% GW0
79 days137.67 AU/dy79.51% c137.3 AU6,812.8 AU0.1077 LY22.835% GW0
80 days138.38 AU/dy79.92% c138.0 AU6,950.8 AU0.1099 LY23.088% GW0
81 days139.08 AU/dy80.32% c138.7 AU7,089.5 AU0.1121 LY23.340% GW0
82 days139.76 AU/dy80.72% c139.4 AU7,229.0 AU0.1143 LY23.591% GW0
83 days140.42 AU/dy81.10% c140.1 AU7,369.0 AU0.1165 LY23.842% GW0
84 days141.08 AU/dy81.48% c140.7 AU7,509.8 AU0.1188 LY24.091% GW0
85 days141.72 AU/dy81.85% c141.4 AU7,651.2 AU0.1210 LY24.340% GW0
86 days142.34 AU/dy82.21% c142.0 AU7,793.2 AU0.1232 LY24.588% GW0
87 days142.96 AU/dy82.57% c142.7 AU7,935.9 AU0.1255 LY24.835% GW0
88 days143.56 AU/dy82.91% c143.3 AU8,079.1 AU0.1278 LY25.081% GW0
89 days144.15 AU/dy83.26% c143.9 AU8,223.0 AU0.1300 LY25.326% GW0
90 days144.73 AU/dy83.59% c144.4 AU8,367.4 AU0.1323 LY25.571% GW0

timeVelocityIncr. Dist.Total DistanceTotal Fuel
91 days145.30 AU/dy83.92% c145.1  AU8,512.5 AU0.1346 LY25.815% GW0
92 days145.86 AU/dy84.24% c145.6 AU8,658.0 AU0.1369 LY26.058% GW0
93 days146.40 AU/dy84.56% c146.1 AU8,804.2 AU0.1392 LY26.300% GW0
94 days146.94 AU/dy84.86% c146.7 AU8,950.8 AU0.1415 LY26.541% GW0
95 days147.46 AU/dy85.17% c147.2 AU9,098.0 AU0.1439 LY26.782% GW0
96 days147.98 AU/dy85.46% c147.7 AU9,245.8 AU0.1462 LY27.022% GW0
97 days148.48 AU/dy85.76% c148.2 AU9,394.0 AU0.1485 LY27.261% GW0
98 days148.98 AU/dy86.04% c148.7 AU9,542.7 AU0.1509 LY27.499% GW0
99 days149.46 AU/dy86.32% c149.2 AU9,691.9 AU0.1533 LY27.737% GW0
100 days149.93 AU/dy86.59% c149.7 AU9,841.6 AU0.1556 LY27.974% GW0
(1 - (1-Δ)t) ×c
dt - dt-1
c × t +Vt

ft = 1 - (1-ε∇)t
1) FUEL FACTOR: Exhaust flow, ∇
Assume exhaust particle speed is 99% light speed  (.99c).
Thus, ship needs exhaust flow, ∇= 0.2492% ship’s GW
for each day of powered flight (%GW/day),
for 7G acceleration.
2)     FUEL FACTOR: Efficiency Factor, ε
Compensate for inevitable inefficiencies by increasing ∇ by factor,  ε.
Compute daily fuel consumption rate:
ε∇ =0.003394 = .3394% GW/day.
1-ε∇ = 0.9966 = daily Remainder of ship's GW.


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