1G TABLE:Decelerate for 1 Year

CONTENT
INTRODUCTION
1G DECEL DAYS 0-15	LEGEND
1G DECEL DAYS 16-30	INTRODUCTION
1G DECEL DAYS 31-45	IV: time (t)
1G DECEL DAYS 46-60	AU and c
1G DECEL DAYS 61-75	GRAVITY
1G DECEL DAYS 76-90	DAILY DIFF
1G DECEL DAYS 91-105	SPOT VEL (AU/dy)
1G DECEL DAYS 106-120	SPOT VEL (%c/dy)
1G DECEL DAYS 121-135	COUNTDOWN
1G DECEL DAYS 136-150	BRAINSTORM
1G DECEL DAYS 151-165	DIST TO GO (AU)
1G DECEL DAYS 166-180	DIST as LY
1G DECEL DAYS 181-195	FUEL FACTS O/V
1G DECEL DAYS 196-210	CLASSICAL MOM
1G DECEL DAYS 211-225	RELATIVITY
1G DECEL DAYS 226-240	EFFICIENCY
1G DECEL DAYS 241-255	DAILY FUEL
1G DECEL DAYS 256-270	HOW FAST?
1G DECEL DAYS 271-285	HOW FAR?
1G DECEL DAYS 286-300	HOW FUEl?
1G DECEL DAYS 301-315	INITIAL GW
1G DECEL DAYS 316-330	DAILY GW
1G DECEL DAYS 331-345	CLASSICAL FUEL
1G DECEL DAYS 346-360	PRACTICAL FUEL
1G DECEL DAYS 361-365¼	CONCLUDE
SUMMARY

1G Deceleration for 365¼ Days

time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT LEGEND time (t) is Independent Variable (IV) which counts deceleration days up from 0 to 365¼. Spot Velocity (Vt); same formula as acceleration. However, decelerated velocities require "reverse order"; thus, use "365¼-t" as exponent.  Spot Velocity (VAU) Convert Astro Units per day to %c.   EXAMPLE:  Value = 110.72 AU/dy × c/173.AU/dy = 63.95% c.  IDENTITY:  c = 173.145 AU/day.  Countdown Distance (dt)  Uses same "Einsteinian" formula as for acceleration. Deceleration leads to shrinking distances; countdown to 0 AUs. Countdown Distance (dLY) IDENTITY: 1 LY = 63,240 AUs Convert Astro Units (AUs) to Light Years (LYs) 22,945.2 AU × 1 LY/63,240 AU = 0.3628 LY Total Fuel (ft) is total fuel consumed due to  G-force propulsion: Assume: ε∇ = 0.0468% GW/day After 1 yr of 1G acceleration, total fuel is 15.72% GW0. Deceleration's G-force daily fuel increases from 15.72% GW0.
0 days	111.80 AU/dy	64.57% c	23,875.9 AU	0.3775 LY	15.72% GW0
1 days	111.38 AU/dy	64.33% c	23,710.3 AU	0.3749 LY	15.76% GW0
2 days	111.25 AU/dy	64.23% c	23,599.0 AU	0.3732 LY	15.79% GW0
3 days	111.08 AU/dy	64.13% c	23,487.9 AU	0.3714 LY	15.83% GW0
4 days	110.90 AU/dy	64.05% c	23,376.9 AU	0.3697 LY	15.87% GW0
5 days	110.72 AU/dy	63.95% c	23,266.1 AU	0.3679 LY	15.91% GW0
6 days	110.55 AU/dy	63.85% c	23,277.0 AU	0.3662 LY	15.95% GW0
7 days	110.37 AU/dy	63.74% c	23,166.2 AU	0.3644 LY	15.99% GW0
8 days	110.19 AU/dy	63.64% c	23,055.6 AU	0.3636 LY	16.03% GW0
9 days	110.01 AU/dy	63.54% c	22,945.2 AU	0.3628 LY	16.07% GW0
10 days	109.83 AU/dy	63.43% c	22,835.0 AU	0.3611 LY	16.11% GW0
11 days	109.65 AU/dy	63.33% c	22,725.0 AU	0.3593 LY	16.15% GW0
12 days	109.47 AU/dy	63.23% c	22,615.1 AU	0.3576 LY	16.19% GW0
13 days	109.29AU/dy	63.12% c	22,505.4 AU	0.3559 LY	16.23% GW0
14 days	109.11 AU/dy	63.02% c	22,395.9 AU	0.3541 LY	16.27% GW0
15 days	108.93 AU/dy	62.91% c	22,286.6 AU	0.3524 LY	16.31% GW0
Given	Vt=(1- (1-Δ)365¼-t)× c		dt=c×(365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT INTRODUCTION RECALL THREE PHASES:Ph. I: Accelerate for one year at G-force propulsion.  Achieve considerable velocity and simulate gravity. Ph. II: Cruise for several years to nearby star, at considerable speed, perhaps 64% light speed (c). Simulate Earth like gravity via centrifugal force due to longitudinal spin. Ph. III: Decelerate for one year at G-force in reverse of Phase I.  Achieve operational velocity upon arrival at destination stellar system. This table assumes success for PHASEs I & II, and now considers PHASE III.
16 days	108.75 AU/dy	62.81% c	22,177.4 AU	0.3507 LY	16.34% GW0
17 days	108.57 AU/dy	62.70% c	22,068.5 AU	0.3490 LY	16.38% GW0
18 days	108.38 AU/dy	62.60% c	21,959.7 AU	0.3472 LY	16.42% GW0
19 days	108.20 AU/dy	62.49% c	21,851.1 AU	0.3455 LY	16.46% GW0
20 days	108.02 AU/dy	62.38% c	21,742.7 AU	0.3438 LY	16.50% GW0
21 days	107.83 AU/dy	62.28% c	21,634.4 AU	0.3421 LY	16.54% GW0
22 days	107.65 AU/dy	62.17% c	21,526.4 AU	0.3404 LY	16.58% GW0
23 days	107.46 AU/dy	62.06% c	21,418.5 AU	0.3387 LY	16.62% GW0
24 days	107.27 AU/dy	61.96% c	21,310.9 AU	0.3370 LY	16.66% GW0
25 days	107.09 AU/dy	61.85% c	21,203.4 AU	0.3353 LY	16.70% GW0
26 days	106.90 AU/dy	61.74% c	21,096.1 AU	0.3336 LY	16.74% GW0
27 days	106.71 AU/dy	61.63% c	20,989.0 AU	0.3319 LY	16.77% GW0
28 days	106.52 AU/dy	61.52% c	20,882.1 AU	0.3302 LY	16.81% GW0
29 days	106.33 AU/dy	61.41% c	20,775.3 AU	0.3285 LY	16.85% GW0
30 days	106.14 AU/dy	61.30% c	20,668.8 AU	0.3268 LY	16.89% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT INDEPENDENT VARIABLE: time (t) Each row is numbered sequentially from 0 days  to 365¼ days to reflect days of deceleration.
31 days	105.95 AU/dy	61.19% c	20,562.4 AU	0.3251 LY	16.93% GW0
32 days	105.76 AU/dy	61.08% c	20,456.3 AU	0.3235 LY	16.97% GW0
33 days	105.57 AU/dy	60.97% c	20,350.3 AU	0.3218 LY	17.01% GW0
34 days	105.38 AU/dy	60.86% c	20,244.5 AU	0.3201 LY	17.05% GW0
35 days	105.19 AU/dy	60.75% c	20,138.9 AU	0.3185 LY	17.09% GW0
36 days	105.00 AU/dy	60.64% c	20,033.5 AU	0.3168 LY	17.12% GW0
37 days	104.80 AU/dy	60.53% c	19,928.3 AU	0.3151 LY	17.16% GW0
38 days	104.61 AU/dy	60.42% c	19,823.3 AU	0.3135 LY	17.20% GW0
39 days	104.41 AU/dy	60.30% c	19,718.5 AU	0.3118 LY	17.24% GW0
40 days	104.22 AU/dy	60.19% c	19,613.9 AU	0.3101 LY	17.28% GW0
41 days	104.02 AU/dy	60.08% c	19,509.4 AU	0.3085 LY	17.32% GW0
42 days	103.83 AU/dy	59.97% c	19,405.2 AU	0.3069 LY	17.36% GW0
43 days	103.63 AU/dy	59.85% c	19,301.2 AU	0.3052 LY	17.40% GW0
44 days	103.43 AU/dy	59.74% c	19,197.3 AU	0.3036 LY	17.43% GW0
45 days	103.24 AU/dy	59.62% c	19,093.7 AU	0.3019 LY	17.47% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT ESSENTIAL CONSTANTS:  ASTRO UNIT:  AU = 149,597,871 km  LIGHT SPEED:  c = 173.144 AU/day c = 299,792.5 km sec = 173.1439 AU day = c Different expressions for lightspeed, c.
46 days	103.04 AU/dy	59.51% c	18,990.2 AU	0.3003 LY	17.51% GW0
47 days	102.84 AU/dy	59.40% c	18,887.0 AU	0.2987 LY	17.55% GW0
48 days	102.64 AU/dy	59.28% c	18,784.0 AU	0.2970 LY	17.59% GW0
49 days	102.44 AU/dy	59.16% c	18,681.1 AU	0.2954 LY	17.63% GW0
50 days	102.24 AU/dy	59.05% c	18,578.5 AU	0.2938 LY	17.67% GW0
51 days	102.04 AU/dy	58.93% c	18,476.0 AU	0.2922 LY	17.70% GW0
52 days	101.84 AU/dy	58.82% c	18,373.8 AU	0.2905 LY	17.74% GW0
53 days	101.64 AU/dy	58.70% c	18,271.7 AU	0.2889 LY	17.78% GW0
54 days	101.43 AU/dy	58.58% c	18,169.9 AU	0.2873 LY	17.82% GW0
55 days	101.23 AU/dy	58.46% c	18,068.3 AU	0.2857 LY	17.86% GW0
56 days	101.02 AU/dy	58.35% c	17,966.8 AU	0.2841 LY	17.90% GW0
57 days	100.82 AU/dy	58.23% c	17,865.6 AU	0.2825 LY	17.94% GW0
58 days	100.62 AU/dy	58.11% c	17,764.6 AU	0.2809 LY	17.97% GW0
59 days	100.41 AU/dy	57.99% c	17,663.8 AU	0.2793 LY	18.01% GW0
60 days	100.20 AU/dy	57.87% c	17,563.1 AU	0.2777 LY	18.05% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT EARTH GRAVITY Different terms for g= 9.8065 m/sec² g = 0.2826%c day = 847  kps day = 0.489 AU day2 After one day of g-force propulsion,  vessel velocity = .002826c, light speed.
61 days	100.00 AU/dy	57.75% c	17,462.7 AU	0.2761 LY	18.09% GW0
62 days	99.79 AU/dy	57.63% c	17,362.5 AU	0.2745 LY	18.13% GW0
63 days	99.58 AU/dy	57.51% c	17,262.6 AU	0.2730 LY	18.17% GW0
64 days	99.37 AU/dy	57.39% c	17,162.8 AU	0.2714 LY	18.20% GW0
65 days	99.16 AU/dy	57.27% c	17,063.2 AU	0.2698 LY	18.24% GW0
66 days	98.95 AU/dy	57.15% c	16,963.8 AU	0.2682 LY	18.28% GW0
67 days	98.74 AU/dy	57.03% c	16,864.7 AU	0.2667 LY	18.32% GW0
68 days	98.53 AU/dy	56.91% c	16,765.7 AU	0.2651 LY	18.36% GW0
69 days	98.32 AU/dy	56.78% c	16,667.0 AU	0.2636 LY	18.39% GW0
70 days	98.11 AU/dy	56.66% c	16,568.5 AU	0.2620 LY	18.43% GW0
71 days	97.90 AU/dy	56.54% c	16,470.2 AU	0.2604 LY	18.47% GW0
72 days	97.68 AU/dy	56.42% c	16,372.1 AU	0.2589 LY	18.51% GW0
73 days	97.47 AU/dy	56.29% c	16,274.2 AU	0.2573 LY	18.55% GW0
74 days	97¼ AU/dy	56.17% c	16,176.5 AU	0.2558 LY	18.59% GW0
75 days	97.04 AU/dy	56.04% c	16,079.1 AU	0.2543 LY	18.62% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT DAILY DECREMENT (Δ):  1 day of reverse g-force propulsion decreases velocity equal to 0.2826%c  as observed by crew of interstellar vessel.** day × g c = 86,400 sec × 9.8065m/sec² 299,792,500 m/sec = 0.2826% Compliments of Thot Exp Brainstorm!
76 days	96.82 AU/dy	55.92% c	15,981.9 AU	0.2527 LY	18.66% GW0
77 days	96.61 AU/dy	55.79% c	15,884.8 AU	0.2512 LY	18.70% GW0
78 days	96.39 AU/dy	55.67% c	15,788.0 AU	0.2497 LY	18.74% GW0
79 days	96.17 AU/dy	55.54% c	15,691.4 AU	0.2481 LY	18.78% GW0
80 days	95.95 AU/dy	55.42% c	15,595.1 AU	0.2466 LY	18.81% GW0
81 days	95.73 AU/dy	55.29% c	15,498.9 AU	0.2451 LY	18.85% GW0
82 days	95.51 AU/dy	55.16% c	15,403.0 AU	0.2436 LY	18.89% GW0
83 days	95.29 AU/dy	55.04% c	15,307.3 AU	0.2421 LY	18.93% GW0
84 days	95.07 AU/dy	54.91% c	15,211.8 AU	0.2405 LY	18.97% GW0
85 days	94.85 AU/dy	54.78% c	15,116.5 AU	0.2390 LY	19.00% GW0
86 days	94.63 AU/dy	54.65% c	15,021.5 AU	0.2375 LY	19.04% GW0
87 days	94.41 AU/dy	54.52% c	14,926.7 AU	0.2360 LY	19.08% GW0
88 days	94.18 AU/dy	54.40% c	14,832.1 AU	0.2345 LY	19.12% GW0
89 days	93.96 AU/dy	54.27% c	14,737.7 AU	0.2330 LY	19.16% GW0
90 days	93.74 AU/dy	54.14% c	14,643.5 AU	0.2316 LY	19.19% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT SPOT VELOCITY (AU/DAY) COMPUTE Velocity (VAU) as AU/day. EXAMPLE: t = 91 days, compute as follows: Vt=(1 - [1-Δ]365¼-t) × c V91=(1 - (0.99717)274¼)×173.145 AU/day V91 = 93.51 AU/day
91 days	93.51 AU/dy	54.01% c	14,549.6 AU	0.2301 LY	19.23% GW0
92 days	93.28 AU/dy	53.88% c	14,455.9 AU	0.2286 LY	19.27% GW0
93 days	93.06 AU/dy	53.75% c	14,362.4 AU	0.2271 LY	19.31% GW0
94 days	92.83 AU/dy	53.61% c	14,269.2 AU	0.2256 LY	19.34% GW0
95 days	92.60 AU/dy	53.48% c	14,176.2 AU	0.2242 LY	19.38% GW0
96 days	92.37 AU/dy	53.35% c	14,083.4 AU	0.2227 LY	19.42% GW0
97 days	92.15 AU/dy	53.22% c	13,990.8 AU	0.2212 LY	19.46% GW0
98 days	91.92 AU/dy	53.09% c	13,898.5 AU	0.2198 LY	19.50% GW0
99 days	91.69 AU/dy	52.95% c	13,806.4 AU	0.2183 LY	19.53% GW0
100 dy	91.45 AU/dy	52.82% c	13,714.5 AU	0.2169 LY	19.57% GW0
101 dy	91.22 AU/dy	52.69% c	13,622.8 AU	0.2154 LY	19.61% GW0
102 dy	90.99 AU/dy	52.55% c	13,531.4 AU	0.2140 LY	19.65% GW0
103 dy	90.76 AU/dy	52.42% c	13,440.3 AU	0.2125 LY	19.68% GW0
104 dy	90.52 AU/dy	52.28% c	13,349.3 AU	0.2111 LY	19.72% GW0
105 dy	90.29 AU/dy	52.15% c	13,258.6 AU	0.2097 LY	19.76% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT SPOT VELOCITY (V%c) as per cent light speed, c. V%c = (1 - (1-Δ)365¼-t) × c V%c = 100 per centiles 1.0 × c EXAMPLE: V106=[1-(0.997174)259¼]× c = 52.01% c
106 dy	90.05 AU/dy	52.01% c	13,168.1 AU	0.2082 LY	19.80% GW0
107 dy	89.82 AU/dy	51.87% c	13,077.9 AU	0.2068 LY	19.83% GW0
108 dy	89.58 AU/dy	51.74% c	12,987.9 AU	0.2054 LY	19.87% GW0
109 dy	89.35 AU/dy	51.60% c	12,898.1 AU	0.2040 LY	19.91% GW0
110 dy	89.11 AU/dy	51.46% c	12,808.6 AU	0.2025 LY	19.95% GW0
111 dy	88.87 AU/dy	51.33% c	12,719.3 AU	0.2011 LY	19.98% GW0
112 dy	88.63 AU/dy	51.19% c	12,630.2 AU	0.1997 LY	20.02% GW0
113 dy	88.39 AU/dy	51.05% c	12,541.4 AU	0.1983 LY	20.06% GW0
114 dy	88.15 AU/dy	50.91% c	12,452.8 AU	0.1969 LY	20.10% GW0
115 dy	87.91 AU/dy	50.77% c	12,364.5 AU	0.1955 LY	20.13% GW0
116 dy	87.67 AU/dy	50.63% c	12,276.4 AU	0.1941 LY	20.17% GW0
117 dy	87.43 AU/dy	50.49% c	12,188.6 AU	0.1927 LY	20.21% GW0
118 dy	87.18 AU/dy	50.35% c	12,100.9 AU	0.1913 LY	20.25% GW0
119 dy	86.94 AU/dy	50.21% c	12,013.6 AU	0.1900 LY	20.28% GW0
120 dy	86.69 AU/dy	50.07% c	11,926.5 AU	0.1886 LY	20.32% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT SPOT VELOCITY COUNTDOWN G-force Deceleration Table decrements ship's velocity from cruise velocity of 111.8 AU/day, reverse order of G-force Acceleration Table, which counts velocity up from zero to 111.8 AU/day. Daily decrements of ship's velocity are Δ = 0.283% c.   Accordingly, vessel velocity shrinks same daily percentage of light speed, c; eventually reaching a relative zero velocity at the stellar destination to conduct normal ops.  Without the deceleration phase, the interstellar vessel speeds quickly past the stellar destination, barely able to grab a peek.
121 dy	86.45 AU/dy	49.93% c	11,839.6 AU	0.1872 LY	20.36% GW0
122 dy	86.20 AU/dy	49.79% c	11,752.9 AU	0.1858 LY	20.39% GW0
123 dy	85.96 AU/dy	49.64% c	11,666.6 AU	0.1845 LY	20.43% GW0
124 dy	85.71 AU/dy	49.50% c	11,580.4 AU	0.1831 LY	20.47% GW0
125 dy	85.46 AU/dy	49.36% c	11,494.5 AU	0.1818 LY	20.51% GW0
126 dy	85.21 AU/dy	49.21% c	11,408.9 AU	0.1804 LY	20.54% GW0
127 dy	84.96 AU/dy	49.07% c	11,323.5 AU	0.1791 LY	20.58% GW0
128 dy	84.71 AU/dy	48.93% c	11,238.4 AU	0.1777 LY	20.62% GW0
129 dy	84.46 AU/dy	48.78% c	11,153.5 AU	0.1764 LY	20.65% GW0
130 dy	84.21 AU/dy	48.64% c	11,068.8 AU	0.1750 LY	20.69% GW0
131 dy	83.96 AU/dy	48.49% c	10,984.4 AU	0.1737 LY	20.73% GW0
132 dy	83.71 AU/dy	48.34% c	10,900.3 AU	0.1724 LY	20.77% GW0
133 dy	83.45 AU/dy	48.20% c	10,816.4 AU	0.1710 LY	20.80% GW0
134 dy	83.20 AU/dy	48.05% c	10,732.8 AU	0.1697 LY	20.84% GW0
135 dy	82.94 AU/dy	47.90% c	10,649.4 AU	0.1684 LY	20.88% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT TE BRAINSTORMS DAILY DIFF (Δ)  DAILY DIFFERENCE: Δ =0.2816% c/day  Observers at departure (Earth) and  stellar destination constantly measure vessel's decreasing velocity. Vessel crew sees Earth retreating slower and dest star as approaching slower.  every day of  1G deceleration. HOWEVER, ALL OBSERVERS (DEPT, VESSEL, DEST)   continually measure light speed as persistent c. DAILY REMAINDER: R=1-Δ=99.7174% c/day
136 dy	82.69 AU/dy	47.76% c	10,566.3 AU	0.1671 LY	20.91% GW0
137 dy	82.43 AU/dy	47.61% c	10,483.4 AU	0.1658 LY	20.95% GW0
138 dy	82.17 AU/dy	47.46% c	10,400.8 AU	0.1645 LY	20.99% GW0
139 dy	81.91 AU/dy	47.31% c	10,318.5 AU	0.1632 LY	21.03% GW0
140 dy	81.66 AU/dy	47.16% c	10,236.4 AU	0.1619 LY	21.06% GW0
141 dy	81.40 AU/dy	47.01% c	10,154.6 AU	0.1606 LY	21.10% GW0
142 dy	81.14 AU/dy	46.86% c	10,073.0 AU	0.1593 LY	21.14% GW0
143 dy	80.88 AU/dy	46.71% c	9,991.7 AU	0.1580 LY	21.17% GW0
144 dy	80.61 AU/dy	46.56% c	9,910.6 AU	0.1567 LY	21.21% GW0
145 dy	80.35 AU/dy	46.41% c	9,829.8 AU	0.1554 LY	21.25% GW0
146 dy	80.09 AU/dy	46¼% c	9,749.3 AU	0.1542 LY	21.28% GW0
147 dy	79.82 AU/dy	46.10% c	9,669.0 AU	0.1529 LY	21.32% GW0
148 dy	79.56 AU/dy	45.95% c	9,589.1 AU	0.1516 LY	21.36% GW0
149 dy	79.29 AU/dy	45.80% c	9,509.3 AU	0.1504 LY	21.39% GW0
150 dy	79.03 AU/dy	45.64% c	9,429.9 AU	0.1491 LY	21.43% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT COUNTDOWN DISTANCE (dt) as (AUs) Distance shrinks on the way to destination. dt = c × (365¼-t) + Vt ln(1-Δ)  RECALL: Spot Velocity (Vt)  is in the dt formula. EX: d151= 173.145AU day ×211¼  days + 78.76AU/dy -.00283 = 9,350.7AU
151 dy	78.76 AU/dy	45.49% c	9,350.7 AU	0.1479 LY	21.47% GW0
152 dy	78.49 AU/dy	45.33% c	9,271.7 AU	0.1466 LY	21.50% GW0
153 dy	78.22 AU/dy	45.18% c	9,193.1 AU	0.1454 LY	21.54% GW0
154 dy	77.96 AU/dy	45.02% c	9,114.7 AU	0.1441 LY	21.58% GW0
155 dy	77.69 AU/dy	44.87% c	9,036.5 AU	0.1429 LY	21.61% GW0
156 dy	77.41 AU/dy	44.71% c	8,958.7 AU	0.1417 LY	21.65% GW0
157 dy	77.14 AU/dy	44.55% c	8,881.1 AU	0.1404 LY	21.69% GW0
158 dy	76.87 AU/dy	44.40% c	8,803.8 AU	0.1392 LY	21.72% GW0
159 dy	76.60 AU/dy	44.24% c	8,726.7 AU	0.1380 LY	21.76% GW0
160 dy	76.32 AU/dy	44.08% c	8,650.0 AU	0.1368 LY	21.80% GW0
161 dy	76.05 AU/dy	43.92% c	8,573.5 AU	0.1356 LY	21.83% GW0
162 dy	75.77 AU/dy	43.76% c	8,497.3 AU	0.1344 LY	21.87% GW0
163 dy	75.50 AU/dy	43.60% c	8,421.3 AU	0.1332 LY	21.91% GW0
164 dy	75.22 AU/dy	43.44% c	8,345.7 AU	0.1320 LY	21.94% GW0
165 dy	74.94 AU/dy	43.28% c	8,270.3 AU	0.1308 LY	21.98% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT Spot Distance (dt) as (LYs) Convert AUs to LYs: dLY = dAU × LY 63,241.1 AU = 0.000 015 8 × dAU Consider example: d166= 8,195.2AU × .0000158LY/AU =0.1296LY
166 dy	74.67 AU/dy	43.12% c	8,195.2 AU	0.1296 LY	22.02% GW0
167 dy	74.39 AU/dy	42.96% c	8,120.3 AU	0.1284 LY	22.05% GW0
168 dy	4.11 AU/dy	42.80% c	8,045.8 AU	0.1272 LY	22.09% GW0
169 dy	73.82 AU/dy	42.64% c	7,971.5 AU	0.1261 LY	22.13% GW0
170 dy	73.54 AU/dy	42.47% c	7,897.5 AU	0.1249 LY	22.16% GW0
171 dy	73.26 AU/dy	42.31% c	7,823.8 AU	0.1237 LY	22.20% GW0
172 dy	72.98 AU/dy	42.15% c	7,750.4 AU	0.1226 LY	22.24% GW0
173 dy	72.69 AU/dy	41.98% c	7,677.3 AU	0.1214 LY	22.27% GW0
174 dy	72.41 AU/dy	41.82% c	7,604.4 AU	0.1202 LY	22.31% GW0
175 dy	72.12 AU/dy	41.65% c	7,531.8 AU	0.1191 LY	22.35% GW0
176 dy	71.84 AU/dy	41.49% c	7,459.5 AU	0.1180 LY	22.38% GW0
177 dy	71.55 AU/dy	41.32% c	7,387.5 AU	0.1168 LY	22.42% GW0
178 dy	71.26 AU/dy	41.16% c	7,315.8 AU	0.1157 LY	22.45% GW0
179 dy	70.97 AU/dy	40.99% c	7,244.4 AU	0.1146 LY	22.49% GW0
180 dy	70.68 AU/dy	40.82% c	7,173.3 AU	0.1134 LY	22.53% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT FUEL FACTORS OVERVIEW Let EXHAUST PARTICLE SPEED = .99c. Thus, RELATIVISTIC GROWTH impacts fuel flow. Increase ∇ by EFFICIENCY FACTOR:  ε = 1.362,to compensate for inevitable inefficiencies. Daily Fuel CONSUMPTION RATE: ε∇ =0.000485 = .0485% GW/day. DAILY GROSS WEIGHT REMAINDER:1-ε∇ = 0.99951 = 99.951% GW.
181 dy	70.39 AU/dy	40.65% c	7,102.4 AU	0.1123 LY	22.56% GW0
182 dy	70.10 AU/dy	40.49% c	7,031.9 AU	0.1112 LY	22.60% GW0
183 dy	69.81 AU/dy	40.32% c	6,961.6 AU	0.1101 LY	22.64% GW0
184 dy	69.51 AU/dy	40.15% c	6,891.7 AU	0.1090 LY	22.67% GW0
185 dy	69.22 AU/dy	39.98% c	6,822.0 AU	0.1079 LY	22.71% GW0
186 dy	68.93 AU/dy	39.81% c	6,752.6 AU	0.1068 LY	22.74% GW0
187 dy	68.63 AU/dy	39.64% c	6,683.5 AU	0.1057 LY	22.78% GW0
188 dy	68.33 AU/dy	39.47% c	6,614.7 AU	0.1046 LY	22.82% GW0
189 dy	68.04 AU/dy	39.29% c	6,546.2 AU	0.1035 LY	22.85% GW0
190 dy	67.74 AU/dy	39.12% c	6,478.1 AU	0.1024 LY	22.89% GW0
191 dy	67.44 AU/dy	38.95% c	6,410.2 AU	0.1014 LY	22.92% GW0
192 dy	67.14 AU/dy	38.78% c	6,342.6 AU	0.1003 LY	22.96% GW0
193 dy	66.84 AU/dy	38.60% c	6,275.3 AU	0.0992 LY	23.00% GW0
194 dy	66.54 AU/dy	38.43% c	6,208.3 AU	0.0982 LY	23.03% GW0
195 dy	66.24 AU/dy	38¼% c	6,141.6 AU	0.0971 LY	23.07% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT CONSIDER CLASSICAL MOMENTUM Conserve momentum. Mship × Vship = mfuel × vExh Divide each side by one second. Mship × Vship 1 sec = mfuel 1 sec × vExh Introduce g, "fuel flow per sec (ffsec)" and decimal light speed (dc × c). Mship = ffsec g × dc × c Solve for ffsec. ffsec = g dc × c × MShip Insert values: g = 9.8065 m/s/s dc×c=.99c=296,794,533m/s ffsec = 0.00000330% MShip Convert to ffday. Recall 1 day = 86,400 sec Thus, ffday = 86,400 ffsec ffday = 0.2854% MShip
196 dy	65.93 AU/dy	38.08% c	6,075.2 AU	0.0961 LY	23.10% GW0
197 dy	65.63 AU/dy	37.90% c	6,009.1 AU	0.0950 LY	23.14% GW0
198 dy	65.32 AU/dy	37.73% c	5,943.3 AU	0.0940 LY	23.18% GW0
199 dy	65.02 AU/dy	37.55% c	5,877.9 AU	0.0929 LY	23.21% GW0
200 dy	64.71 AU/dy	37.37% c	5,812.7 AU	0.0919 LY	23.25% GW0
201 dy	64.40 AU/dy	37.20% c	5,747.8 AU	0.0909 LY	23.28% GW0
202 dy	64.10 AU/dy	37.02% c	5,683.3 AU	0.0899 LY	23.32% GW0
203 dy	63.79 AU/dy	36.84% c	5,619.0 AU	0.0889 LY	23.36% GW0
204 dy	63.48 AU/dy	36.66% c	5,555.1 AU	0.0878 LY	23.39% GW0
205 dy	63.16 AU/dy	36.48% c	5,491.5 AU	0.0868 LY	23.43% GW0
206 dy	62.85 AU/dy	36.30% c	5,428.1 AU	0.0858 LY	23.46% GW0
207 dy	62.54 AU/dy	36.12% c	5,365.1 AU	0.0848 LY	23.50% GW0
208 dy	62.23 AU/dy	35.94% c	5,302.5 AU	0.0838 LY	23.54% GW0
209 dy	61.91 AU/dy	35.76% c	5,240.1 AU	0.0829 LY	23.57% GW0
210 dy	61.60 AU/dy	35.58% c	5,178.0 AU	0.0819 LY	23.61% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT RELATIVISTIC MASS GROWTH  Lorentz Transform quantifies the relativistic growth due to particle speed.  ffExh = ffsec √(1 - dc²) = ffsec √(1 - (.99)²) = ffsec √(1 - 0.9801) Decimal "c" (dc) is particle speed as decimal light speed, c. ffExh = ffsec √(0.0199) = ffsec 0.141 = 7  ffsec TE BRAINSTORM: Let fuel flow per second (ffsec) be the original mass at rest.  Let exhaust fuel flow (ffExh) be the relativistic particle mass at an accelerated, very high velocity, perhaps 99% c for 7x growth.ffExh = 7 × ffsec
211 dy	61.28 AU/dy	35.39% c	5,116.3 AU	0.0809 LY	23.64% GW0
212 dy	60.96 AU/dy	35.21% c	5,054.9 AU	0.0799 LY	23.68% GW0
213 dy	60.64 AU/dy	35.03% c	4,993.7 AU	0.0790 LY	23.71% GW0
214 dy	60.33 AU/dy	34.84% c	4,933.0 AU	0.0780 LY	23.75% GW0
215 dy	60.01 AU/dy	34.66% c	4,872.5 AU	0.0770 LY	23.79% GW0
216 dy	59.68 AU/dy	34.47% c	4,812.3 AU	0.0761 LY	23.82% GW0
217 dy	59.36 AU/dy	34.29% c	4,752.5 AU	0.0752 LY	23.86% GW0
218 dy	59.04 AU/dy	34.10% c	4,693.0 AU	0.0742 LY	23.89% GW0
219 dy	58.72 AU/dy	33.91% c	4,633.8 AU	0.0733 LY	23.93% GW0
220 dy	58.39 AU/dy	33.72% c	4,575.0 AU	0.0723 LY	23.96% GW0
221 dy	58.07 AU/dy	33.54% c	4,516.4 AU	0.0714 LY	24.00% GW0
222 dy	57.74 AU/dy	33.35% c	4,458.2 AU	0.0705 LY	24.03% GW0
223 dy	57.41 AU/dy	33.16% c	4,400.3 AU	0.0696 LY	24.07% GW0
224 dy	57.08 AU/dy	32.97% c	4,342.8 AU	0.0687 LY	24.11% GW0
225 dy	56.76 AU/dy	32.78% c	4,285.5 AU	0.0678 LY	24.14% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT EFFICIENCY Vessel must consume more fuel than needed for just theoretical G-force propulsion. More fuel is needed to overcome design flaws and power peripheral systems such as life support, navigation, communications and even entertainment. We know propulsion efficiency improves as engineers design ever better  systems. Thus, Thought Experiment (TE) arbitrarily assumes a dynamic efficiency model starting much less than 100% but trending toward 100% over time.
226 dy	56.43 AU/dy	32.59% c	4,228.7 AU	0.0669 LY	24.18% GW0
227 dy	56.09 AU/dy	32.40% c	4,172.1 AU	0.0660 LY	24.21% GW0
228 dy	55.76 AU/dy	32.21% c	4,115.9 AU	0.0651 LY	24.25% GW0
229 dy	55.43 AU/dy	32.01% c	4,060.0 AU	0.0642 LY	24.28% GW0
230 dy	55.10 AU/dy	31.82% c	4,004.4 AU	0.0633 LY	24.32% GW0
231 dy	54.76 AU/dy	31.63% c	3,949.2 AU	0.0624 LY	24.35% GW0
232 dy	54.43 AU/dy	31.43% c	3,894.3 AU	0.0616 LY	24.39% GW0
233 dy	54.09 AU/dy	31.24% c	3,839.7 AU	0.0607 LY	24.43% GW0
234 dy	53.75 AU/dy	31.04% c	3,785.5 AU	0.0599 LY	24.46% GW0
235 dy	53.41 AU/dy	30.85% c	3,731.6 AU	0.0590 LY	24.50% GW0
236 dy	53.07 AU/dy	30.65% c	3,678.0 AU	0.0582 LY	24.53% GW0
237 dy	52.73 AU/dy	30.46% c	3,624.8 AU	0.0573 LY	24.57% GW0
238 dy	52.39 AU/dy	30.26% c	3,572.0 AU	0.0565 LY	24.60% GW0
239 dy	52.05 AU/dy	30.06% c	3,519.4 AU	0.0557 LY	24.64% GW0
240 dy	51.70 AU/dy	29.86% c	3,467.3 AU	0.0548 LY	24.67% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT ADJUST DAILY FUEL FLOW (ffDay)for relativistic growth and inevitable inefficiency.BEST GUESS BRAINSTORM for daily fuel consumption first involves downsizing fuel estimate due to relativistic mass growth.  Recall: fuel particles at .99c velocity should grow 7x!!  Formula uses ∇ to designate daily relativistic fuel. A good thing too, cuz propulsion efficiency will likely start out very low; thus, we upsize estimate for fuel consumed to make up for vessel's inefficiency. Following formula uses efficiency factor,  ε, to increase estimate of daily fuel. After all this brainstorming, TE proposes a daily decrement of ε∇ = 0.047% of vessel's initial Gross Weight (GW0) .  Compute each day's cumulative fuel consumption as % of GW0.  Recall total G-force time includes 1 year of acceleration plus deceleration days.ft = 1 - (1-ε∇)t = 1 -(1-.00047)t+365¼ GW0 EXAMPLE: 241 days      Let GW0 = 100 tons.f241 = 1 - (0.99953)241+365¼ = 1 - (0.7520) GW0f241= (100-75.20)% GW0 ≈ 24.71% GW0= 24.71 tons
241 dy	51.36 AU/dy	29.66% c	3,415.4 AU	0.0540 LY	24.71% GW0
242 dy	51.02 AU/dy	29.46% c	3,363.9 AU	0.0532 LY	24.74% GW0
243 dy	50.67 AU/dy	29.26% c	3,312.8 AU	0.0524 LY	24.78% GW0
244 dy	50.32 AU/dy	29.06% c	3,262.0 AU	0.0516 LY	24.81% GW0
245 dy	49.97 AU/dy	28.86% c	3,211.5 AU	0.0508 LY	24.85% GW0
246 dy	49.62 AU/dy	28.66% c	3,161.4 AU	0.0500 LY	24.88% GW0
247 dy	49.27 AU/dy	28.46% c	3,111.7 AU	0.0492 LY	24.92% GW0
248 dy	48.92 AU/dy	28.26% c	3,062.3 AU	0.0484 LY	24.95% GW0
249 dy	48.57 AU/dy	28.05% c	3,013.2 AU	0.0476 LY	24.99% GW0
250 dy	48.22 AU/dy	27.85% c	2,964.5 AU	0.0469 LY	25.02% GW0
251 dy	47.86 AU/dy	27.64% c	2,916.2 AU	0.0461 LY	25.06% GW0
252 dy	47.51 AU/dy	27.44% c	2,868.2 AU	0.0454 LY	25.09% GW0
253 dy	47.15 AU/dy	27.23% c	2,820.5 AU	0.0446 LY	25.09% GW0
254 dy	46.79 AU/dy	27.03% c	2,773.3 AU	0.0439 LY	25.13% GW0
255 dy	46.44 AU/dy	26.82% c	2,726.3 AU	0.0431 LY	25.20% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT HOW FAST, SO FAR???After 256 days of G-force propulsion, Thot Exp (TE) brainstorms that interstellar vessel velocity is at 26.61% c as measured by our friends way back on Earth.
256 dy	46.08 AU/dy	26.61% c	2,679.8 AU	0.0424 LY	25.23% GW0
257 dy	45.72 AU/dy	26.40% c	2,633.6 AU	0.0416 LY	25.27% GW0
258 dy	45.35 AU/dy	26.19% c	2,587.7 AU	0.0409 LY	25.30% GW0
259 dy	44.99 AU/dy	25.98% c	2,542.3 AU	0.0402 LY	25.34% GW0
260 dy	44.63 AU/dy	25.77% c	2,497.2 AU	0.0395 LY	25.37% GW0
261 dy	44.26 AU/dy	25.56% c	2,452.4 AU	0.0388 LY	25.41% GW0
262 dy	43.90 AU/dy	25.35% c	2,408.0 AU	0.0381 LY	25.44% GW0
263 dy	43.53 AU/dy	25.14% c	2,364.0 AU	0.0374 LY	25.48% GW0
264 dy	43.16 AU/dy	24.93% c	2,320.3 AU	0.0367 LY	25.51% GW0
265 dy	42.80 AU/dy	24.72% c	2,277.1 AU	0.0360 LY	25.55% GW0
266 dy	42.43 AU/dy	24.50% c	2,234.1 AU	0.0353 LY	25.58% GW0
267 dy	42.05 AU/dy	24.29% c	2,191.6 AU	0.0347 LY	25.62% GW0
268 dy	41.68 AU/dy	24.07% c	2,149.4 AU	0.0340 LY	25.65% GW0
269 dy	41.31 AU/dy	23.86% c	2,107.6 AU	0.0333 LY	25.69% GW0
270 dy	40.94 AU/dy	23.64% c	2,066.2 AU	0.0327 LY	25.72% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT HOW FAR, SO FAR???After 271 days of G-force deceleration, Thot Exp (TE) brainstorms that distance to destination is at 0.0320 LY which equals 2,025.1 AUcounting down ever closer.
271 dy	40.56 AU/dy	23.43% c	2,025.1 AU	0.0320 LY	25.76% GW0
272 dy	40.19 AU/dy	23.21% c	1,984.5 AU	0.0314 LY	25.79% GW0
273 dy	39.81 AU/dy	22.99% c	1,944.2 AU	0.0307 LY	25.83% GW0
274 dy	9.43 AU/dy	22.77% c	1,904.2 AU	0.0301 LY	25.86% GW0
275 dy	39.05 AU/dy	22.55% c	1,864.7 AU	0.0295 LY	25.90% GW0
276 dy	38.67 AU/dy	22.33% c	1,825.5 AU	0.0289 LY	25.93% GW0
277 dy	38.29 AU/dy	22.11% c	1,786.7 AU	0.0283 LY	25.97% GW0
278 dy	37.91 AU/dy	21.89% c	1,748.3 AU	0.0276 LY	26.00% GW0
279 dy	37.52 AU/dy	21.67% c	1,710.3 AU	0.0270 LY	26.04% GW0
280 dy	37.14 AU/dy	21.45% c	1,672.7 AU	0.0264 LY	26.07% GW0
281 dy	36.75 AU/dy	21.23% c	1,635.4 AU	0.0259 LY	26.10% GW0
282 dy	36.37 AU/dy	21.00% c	1,598.6 AU	0.0253 LY	26.14% GW0
283 dy	35.98 AU/dy	20.78% c	1,562.1 AU	0.0247 LY	26.17% GW0
284 dy	35.59 AU/dy	20.55% c	1,526.0 AU	0.0241 LY	26.21% GW0
285 dy	35.20 AU/dy	20.33% c	1,490.3 AU	0.0236 LY	26.24% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c×(365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT HOW MUCH FUEL, SO FAR???After 286 days of G-force deceleration, Thot Exp (TE) brainstorms that vessel gross weight decreases to 73.71% GW0. THEREFORE, remaining (26.28% GW0) was total fuel consumed (ft) to propel our vessel.
286 dy	34.81 AU/dy	20.10% c	1,455.0 AU	0.0230 LY	26.28% GW0
287 dy	34.42 AU/dy	19.88% c	1,420.1 AU	0.0225 LY	26.31% GW0
288 dy	34.02 AU/dy	19.65% c	1,385.5 AU	0.0219 LY	26.35% GW0
289 dy	33.63 AU/dy	19.42% c	1,351.4 AU	0.0214 LY	26.38% GW0
290 dy	33.23 AU/dy	19.19% c	1,317.7 AU	0.0208 LY	26.41% GW0
291 dy	32.84 AU/dy	18.96% c	1,284.3 AU	0.0203 LY	26.45% GW0
292 dy	32.44 AU/dy	18.73% c	1,251.4 AU	0.0198 LY	26.48% GW0
293 dy	32.04 AU/dy	18.50% c	1,218.9 AU	0.0193 LY	26.52% GW0
294 dy	31.64 AU/dy	18.27% c	1,186.7 AU	0.0188 LY	26.55% GW0
295 dy	31.24 AU/dy	18.04% c	1,155.0 AU	0.0183 LY	26.59% GW0
296 dy	30.83 AU/dy	17.81% c	1,123.6 AU	0.0178 LY	26.62% GW0
297 dy	30.43 AU/dy	17.58% c	1,092.7 AU	0.0173 LY	26.66% GW0
298 dy	30.03 AU/dy	17.34% c	1,062.2 AU	0.0168 LY	26.69% GW0
299 dy	29.62 AU/dy	17.11% c	1,032.0 AU	0.0163 LY	26.72% GW0
300 dy	29.21 AU/dy	16.87% c	1,002.3 AU	0.0158 LY	26.76% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT INITIAL GROSS WEIGHT (GW0)Empty vessel has no pax, no cargo and no fuel (aka "dry"). Thus, empty vessel's GW is mass of vessel's structure and equipment. HOWEVER, vessel's function is transporting pax and cargo.  FURTHERMORE, much like today's airliners in the sky, G-force vessel requires considerable initial fuel which could = ½ GW0. EXAMPLE: If vessel's total mass = 100 tons, fuel could = 50 tons!!! INITIAL GROSS WEIGHT (GW0) is vessel's total mass at very beginning of Phase I. Acceleration.  This includes considerable fuel which decreases throughout powered flight.
301 dy	28.80 AU/dy	16.64% c	973.0 AU	0.0154 LY	26.79% GW0
302 dy	28.40 AU/dy	16.40% c	944.1 AU	0.0149 LY	26.83% GW0
303 dy	27.98 AU/dy	16.16% c	915.6 AU	0.0145 LY	26.86% GW0
304 dy	27.57 AU/dy	15.92% c	887.5 AU	0.0140 LY	26.90% GW0
305 dy	27.16 AU/dy	15.69% c	859.8 AU	0.0136 LY	26.93% GW0
306 dy	26.75 AU/dy	15.45% c	832.6 AU	0.0132 LY	26.96% GW0
307 dy	26.33 AU/dy	15.21% c	805.7 AU	0.0127 LY	27.00% GW0
308 dy	25.91 AU/dy	14.97% c	779.3 AU	0.0123 LY	27.03% GW0
309 dy	25.50 AU/dy	14.73% c	753.3 AU	0.0119 LY	27.07% GW0
310 dy	25.08 AU/dy	14.48% c	727.7 AU	0.0115 LY	27.10% GW0
311 dy	24.66 AU/dy	14.24% c	702.5 AU	0.0111 LY	27.13% GW0
312 dy	24.24 AU/dy	14.00% c	677.8 AU	0.0107 LY	27.17% GW0
313 dy	23.82 AU/dy	13.75% c	653.4 AU	0.0103 LY	27.20% GW0
314 dy	23.39 AU/dy	13.51% c	629.5 AU	0.0100 LY	27.24% GW0
315 dy	22.97 AU/dy	13.26% c	606.1 AU	0.0096 LY	27.27% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT DAILY GROSS WEIGHT (GWt) FUEL CONSUMPTION: ε∇ =  .0485% GW/day.For each day of G-force, compute daily gross weight via:EXPONENTIAL EQUATION: GWt =  (1-ε∇)t =(.99515)t INITIAL GROSS WEIGHT:  GW0 =  (1-ε∇)0 = 1.000 GW0 G-force propulsion consumes fuel (both acceleration and deceleration), and ship's gross weight continually decreases.  THUS, after 1 year of acceleration GW1-year =  (1-ε∇)365¼ = 84.28% GW0 Table counts days of deceleration (t) from 0 to 365¼.GWt =  (1-ε∇)t+365¼ GW0EXAMPLE:  GW316 =  (.99515)316+365¼ GW0 =  72.69% GW0
316 dy	22.54 AU/dy	13.02% c	583.0 AU	0.0092 LY	27.31% GW0
317 dy	22.11 AU/dy	12.77% c	560.4 AU	0.0089 LY	27.34% GW0
318 dy	21.69 AU/dy	12.52% c	538.2 AU	0.0085 LY	27.37% GW0
319 dy	21.26 AU/dy	12.28% c	516.4 AU	0.0082 LY	27.41% GW0
320 dy	20.83 AU/dy	12.03% c	495.0 AU	0.0078 LY	27.44% GW0
321 dy	20.39 AU/dy	11.78% c	474.1 AU	0.0075 LY	27.48% GW0
322 dy	19.96 AU/dy	11.53% c	453.6 AU	0.0072 LY	27.51% GW0
323 dy	19.53 AU/dy	11.28% c	433.6 AU	0.0069 LY	27.54% GW0
324 dy	19.09 AU/dy	11.03% c	414.0 AU	0.0065 LY	27.58% GW0
325 dy	18.65 AU/dy	10.77% c	394.8 AU	0.0062 LY	27.61% GW0
326 dy	18.22 AU/dy	10.52% c	376.1 AU	0.0059 LY	27.64% GW0
327 dy	17.78 AU/dy	10.27% c	357.8 AU	0.0057 LY	27.68% GW0
328 dy	17.34 AU/dy	10.01% c	339.9 AU	0.0054 LY	27.71% GW0
329 dy	16.89 AU/dy	9.76% c	322.5 AU	0.0051 LY	27.75% GW0
330 dy	16.45 AU/dy	9.50% c	305.5 AU	0.0048 LY	27.78% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ Next⇓ BOT TE BRAINSTORMS CLASSICAL FUEL ASSUME EXHAUST PARTICLE VEL = .99c Routinely achieved by today's synchrotrons. MShip  × VShip = mfuel × vfuel Rearrange and substitute: ffday = MShip .99c × g × 86,400 sec day Values for light speed, c, & Earth gravity, g. ffday = MShip 296,794,533m/s × 9.8065 m/s sec × 86,400 sec day Classical daily fuel consumption computed: ffday  = 0.2854% ship's mass (MShip) HOWEVER, needs adjusting for relativistic mass growth & inevitable inefficiency.
331 dy	16.01 AU/dy	9.24% c	289.0 AU	0.0046 LY	27.81% GW0
332 dy	15.56 AU/dy	8.99% c	272.9 AU	0.0043 LY	27.85% GW0
333 dy	15.11 AU/dy	8.73% c	257.2 AU	0.0041 LY	27.88% GW0
334 dy	14.66 AU/dy	8.47% c	242.0 AU	0.0038 LY	27.92% GW0
335 dy	14.22 AU/dy	8.21% c	227.3 AU	0.0036 LY	27.95% GW0
336 dy	13.76 AU/dy	7.95% c	213.0 AU	0.0034 LY	27.98% GW0
337 dy	13.31 AU/dy	7.69% c	199.2 AU	0.0031 LY	28.02% GW0
338 dy	12.86 AU/dy	7.43% c	185.8 AU	0.0029 LY	28.05% GW0
339 dy	12.40 AU/dy	7.16% c	172.8 AU	0.0027 LY	28.08% GW0
340 dy	11.95 AU/dy	6.90% c	160.4 AU	0.0025 LY	28.12% GW0
341 dy	11.49 AU/dy	6.64% c	148.3 AU	0.0023 LY	28.15% GW0
342 dy	11.03 AU/dy	6.37% c	136.8 AU	0.0022 LY	28.18% GW0
343 dy	10.57 AU/dy	6.11% c	125.7 AU	0.0020 LY	28.22% GW0
344 dy	10.11 AU/dy	5.84% c	115.0 AU	0.0018 LY	28.25% GW0
345 dy	9.65 AU/dy	5.57% c	104.8 AU	0.0017 LY	28.29% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼	1G Acc 7G Acc 7G Dec 1G Dec TOP Prev⇑ Next⇓ BOT TE BRAINSTORMS PRACTICAL FUEL ASSUME EXHAUST PARTICLE VEL = .99c CONSIDER RELATIVISTIC GROWTH which decreases daily fuel requirement. Divide ffday by Lorentz Transform. ∇ = 0.2854% MShip 1 / √(1 - 0.99²) = 0.2854% MShip 7 CONSIDER INEVITABLE INEFFICIENCY which increases daily requirement. TE brainstorms an arbitrary Efficiency Factor, ε. ε∇ = 0.2854% MShip 7 × ε = .0485% GW day Adjust for relativity & inefficiency:  ADJUSTED DAILY FUEL:  ffAdj  = ε∇ =  .0485% GW/day NOTE: Due to constant fuel consumption,  ship's  mass shrinks constantly. but above percentage persists on and on for every G-force day. Let initial Gross Weight (GW0)= 100 tonnes. EXAMPLE: From 99 to 101 days of G-force deceleration, note  slight decreases in daily fuel consumption due to decreasing GW. 'F' is cumulative fuel consumed; 'f' is incremental fuel.
346 dy	9.19 AU/dy	5.31% c	95.1 AU	0.0015 LY	28.32% GW0
347 dy	8.72 AU/dy	5.04% c	85.8 AU	0.0014 LY	28.35% GW0
348 dy	8.26 AU/dy	4.77% c	77.0 AU	0.0012 LY	28.39% GW0
349 dy	7.79 AU/dy	4.50% c	68.7 AU	0.0011 LY	28.42% GW0
350 dy	7.32 AU/dy	4.23% c	60.9 AU	0.0010 LY	28.45% GW0
351 dy	6.85 AU/dy	3.96% c	53.5 AU	0.0008 LY	28.49% GW0
352 dy	6.38 AU/dy	3.68% c	46.6 AU	0.0007 LY	28.52% GW0
353 dy	5.90 AU/dy	3.41% c	40.1 AU	0.0006 LY	28.55% GW0
354 dy	5.43 AU/dy	3.14% c	34.1 AU	0.0005 LY	28.59% GW0
355 dy	4.95 AU/dy	2.86% c	28.6 AU	0.0005 LY	28.62% GW0
356 dy	4.48 AU/dy	2.59% c	23.6 AU	0.0004 LY	28.65% GW0
357 dy	4.00 AU/dy	2.31% c	19.1 AU	0.0003 LY	28.69% GW0
358 dy	3.52 AU/dy	2.03% c	15.0 AU	0.0002 LY	28.72% GW0
359 dy	3.04 AU/dy	1.75% c	11.4 AU	0.0002 LY	28.75% GW0
360 dy	2.56 AU/dy	1.48% c	8.3 AU	0.0001 LY	28.79% GW0
time (t)	Spot Velocity (Vt)		Countdown Distance (dt)		Total Fuel (ft)	1G Acc 7G Acc 7G Dec 1G Dec TC Prev⇑ CONSUMPTION CONCLUSION Compare one year's fuel consumption (due to G-force acceleration) with two years' fuel consumption (both acceleration & deceleration).Intuition initially compels one to conclude that two years of G-force takes twice as much fuel as one year.  However, constant consumption requires exponentiation to more accurately determine correct values. SURPRISE!!!   THOT EXP confesses to a small prank on the readers!  TE used an efficiency factor, ε, for Deceleration Fuel values of 1.000 (very unlikely cuz 1.0 indicates perfect efficiency). This means Table's fuel consumption values are minimums.  Actual values will likely start higher!!!
360 dy	2.56 AU/dy	1.48% c	8.3 AU	0.0001 LY	28.79% GW0
361 dy	2.07 AU/dy	1.20% c	5.7 AU	0.0001 LY	28.82% GW0
362 dy	1.59 AU/dy	0.92% c	3.6 AU	0.0001 LY	28.85% GW0
363 dy	1.10 AU/dy	0.64% c	1.9 AU	0.0000 LY	28.89% GW0
364 dy	0.61 AU/dy	0.35% c	0.8 AU	0.0000 LY	28.92% GW0
365 dy	0.12 AU/dy	0.07% c	0.1 AU	0.0000 LY	28.95% GW0
365¼ d	0.00 AU/dy	0.00% c	0.0 AU	0.0000 LY	29.00% GW0
Given	(1-(1-Δ)365¼-t)× c		dt=c × (365¼-t) + Vt ln(1-Δ)		1-(1-ε∇)t+365¼

SUMMARY

PHASE I. G-force Acceleration  consumes fuel in an exponentially decreasing way. SIMPLE SUM: 4.57 tons + 8.94 tons = 13.51 tons HOWEVER: 13.51 tons > 13.10 tons; fuel actually consumed.	PHASE II.  Cruise at Constant Velocity (.6457 c). Pause G-force propulsion for a few years to save fuel; HOWEVER, life support, navigation, communication, etc. still need power; perhaps, supplied by onboard fusion reactor.	PHASE III. G-force Deceleration Vessel velocity must decrease back to near zero velocity precisely at destination. Thus, decelerate for exactly same distance & duration as Phase I.  Crew must carefully navigate to precise location to reinitiate G-force propulsion.

VOLUME 0: ELEVATIONAL VOLUME I: ASTEROIDAL VOLUME II: INTERPLANETARY VOLUME III: INTERSTELLAR	SLIDESHOW	1G Acceleration for 1 year. 7G Acceleration for 100 days. 7G Deceleration for 48¼ days. 1G Deceleration for 1 year.