Sunday, February 04, 2007

Transit Material




G-force for a Year Arbitrarily choose duration of one year for acceleration phase. One year of g-force acceleration brings ship to velocity of .6443 c (observed from Earth). Exhaust particle speed of .99 c and fuel load of .50% TOGW gives ship sufficient range to do this. Incidentally, it's possible that one time a year, Earth is in best position to send spacecraft to a particular stellar destination. Thus, it could be possible to make this an annual event, and one year shuttles become more reasonable.
Total DistAccel TimeFinal
Velocity
Acceleration distanceCruise distanceCruise timeDecel timeTotal Time
DtAccVFindAccdCrutCrutDecT
LYdaysAU/day% cAULYLYYearsDaysYears
1 365.26 111.56 64.43% 23,824 0.38 0.25 0.38 365.26 2.38
2 365.26 111.56 64.43% 23,824 0.38 1.25 1.93 365.26 3.93
3 365.26 111.56 64.43% 23,824 0.38 2.25 3.49 365.26 5.49
4 365.26 111.56 64.43% 23,824 0.38 3.25 5.04 365.26 7.04
5 365.26 111.56 64.43% 23,824 0.38 4.25 6.59 365.26 8.59
6 365.26 111.56 64.43% 23,824 0.38 5.25 8.14 365.26 10.14
7 365.26 111.56 64.43% 23,824 0.38 6.25 9.70 365.26 11.70
8 365.26 111.56 64.43% 23,824 0.38 7.25 11.25 365.26 13.25
9 365.26 111.56 64.43% 23,824 0.38 8.25 12.80 365.26 14.80
10 365.26 111.56 64.43% 23,824 0.38 9.25 14.35 365.26 16.35
IVGivenc[1 - (1 - Δ)tAcc]
ct +v(t)

ln(1-Δ)
DTtl - dAcc - dDec
dCru
VFin
tAcctAcc + tCru + tDec
Definitions
  • D is total distance from our star, Sol, to destination.
  • tAcc is acceleration duration from departure til start of cruise. This case study proposes one year (365.26 days) for all destinations.
  • Δ - Daily difference in spaceship's velocity is due to acceleration caused by constant g-force. We approximate this value: Δ = 86,400 g / c = .2826% c
  • VFin is final velocity achieved after applying g-force propulsion for tAcc duration.
    • vFin is also the maximum velocity achieved during the flight.
    • vFin is also cruise velocity; for this case study, it is .6443 c for all examples.
  • dAcc is acceleration distance.1 light year (LY) = 63,241 AU.
  • dDec is deceleration distance; it equals acceleration distance.
  • dCru is cruise distance; it equals total distance minus distances for acceleration and deceleration.
  • tCru is cruise time as observed from the Earth.
  • tDec is deceleration time. Assuming consistent g-force, deceleration time equals acceleration time.
  • T is total time: acceleration + cruise + deceleration

  • AXIOM. Light speed is absolute and puts limits on interstellar travel. Even at light speed, interstellar flights take years for photons, virtually massless particles. Since human spaceships will contain large quantities of mass, the best we can hope for is to approach light speed; we can never attain it and certainly never surpass it.

    ASSUMPTION-1. Self Contained Fuel. Prior to departure from Sol, notional spaceship will collect and carry sufficient fuel for planned propulsion phases to destination.

    ASSUMPTION-2. Earthlike Gravity. We currently know two methods to achieve Earth like gravity on an interstellar vessel.
    • Constant G-force Acceleration. If an onboard propulsion system can increase ship's velocity by 9.80665 m/s for every second of "powered" flight, then ship's contents will feel a force equivalent to Terran gravity in the direction opposite to propulsion vector.
    • Centrifugal Force. If ship is not able to maintain g-force for entire flight, then the ship must spin so that contents feel forced against the inside of the outer hull. Thus, ship's shape should be cylindrical and rotate around its longitudinal axis; spin rate (usually given in degrees per second) will be inversely proportional to radius (as cylinder size increases, less spin rate is needed to maintain centripetal acceleration of 9.80665 m/s/s). Other pieces will present further details. (idea: insert figure with two g-force ships)
    ASSUMPTION-3. Cruise Phase. Initial calculations indicate that any interstellar voyage would require fuel consumption greater than 100% of ship's mass to power entire flight. Thus, TE assumes following flight profile.
    • Acceleration Phase. Ship starts off trip by accelerating at g-force for 365.26 days, this will bring it to a velocity of .6443c (64.43% of light speed). Occupants will feel a gravity like force drawing them back to departure, Solar System; thus, "up" will be toward destination, and "down" will be toward Sol, departure star.
    • Cruise Phase. Due to fuel considerations, ship will stop propulsion after 1 year and lose g-force from back of ship. Thus, ship will maintain constant velocity of 64.43c for entire cruise phase (majority of voyage). To maintain Earth like gravity, ship will then have to reconfigure to gain g-force against inside of outer hull by starting sufficient spin to gain g-force.
    • Deceleration Phase. Ship will need to end this trip by slowing down from 64.43c to an operational speed. Thus, at 1 year prior to arrival, ship will apply propulsion vector against direction of flight. While acceleration phase directed exhaust particles toward Sol, departure; the deceleration propulsion vector will point in opposite direction, toward destination. Now, "up" will now be in the direction of Sol which is retreating from the ship, and "down" will be toward destination, which is getting closer.
    Closest Destinations.
    DestinationAccel TimeFinal
    Velocity
    Acceleration distanceCruise distanceCruise timeDecel timeTotal Time
    StarDtAccVFindAccdCrutCrutDecT
    NameLYdaysAU/day% cAULYLYYearsDaysYears
    Alpha Centauri 4.365
    365.26
    111.56
    64.43%
    23,824
    0.38
    3.61
    5.61
    365.26
    7.61
    Barnard's Star 5.963
    365.26
    111.56
    64.43%
    23,824
    0.38
    5.21
    8.09
    365.26
    10.09
    Wolf 7.786
    365.26
    111.56
    64.43%
    23,824
    0.38
    7.03
    10.91
    365.26
    12.91
    Lalande 8.291
    365.26
    111.56
    64.43%
    23,824
    0.38
    7.54
    11.70
    365.26
    13.70
    Sirius 8.583
    365.26
    111.56
    64.43%
    23,824
    0.38
    7.83
    12.15
    365.26
    14.15
    Luyten 8.728
    365.26
    111.56
    64.43%
    23,824
    0.38
    7.97
    12.38
    365.26
    14.38
    Ross 9.681
    365.26
    111.56
    64.43%
    23,824
    0.38
    8.93
    13.86
    365.26
    15.86
    Observed
    Given
    c[1 - (1 - Δ)tAcc]

    c= 173.15 AU/dy
    ct +v(t)

    ln(1-Δ)
    DTtl - dAcc - dDec
    dCru
    VFin
    tAcc
    tAcc + tCru + tDec

    Cruise Profile to Nearest Star
    Total DistAccel TimeFinal
    Velocity
    Accel
    Dist
    Cruise DistanceCruise TimeDecel TimeTotal Time
    DtAccVFindAccdCrutCrutDecT
    LYdaysAU/day% cAULYLYYearsDaysYears
    4.3365111.5664.5%23,6720.373.565.523657.52
    IVGiven
    c[1-(1-Δ)tAcc]
    ct +v(t)

    ln(1-Δ)
    DTtl - dAcc - dDec
    dCru 
    VFin
    tAcctAcc + tCru + tDec
    Definitions

    0 Comments:

    Post a Comment

    Links to this post:

    Create a Link

    << Home