{
  "export": {
    "source": "https://urth.darkrealm.vip/thread/whorl/1471",
    "note": "Exported from an unofficial mirror of a public mailing list. Copyright in each message remains with the person who wrote it.  Email addresses are obscured as `user at host`, the form the original archive published. This file was rebuilt from parsed fields rather than retained headers, so it is faithful in content but not byte-exact.",
    "addresses": "obscured as 'user at host'"
  },
  "archive": "whorl",
  "thread": {
    "id": 1471,
    "subject": "Voyage of the Whorl: Calculations of Thrust, Distance and Peak Velocity",
    "messages": 1,
    "voices": 1,
    "first": "2001-09-04T07:32:55+00:00",
    "last": "2001-09-04T07:32:55+00:00"
  },
  "messages": [
    {
      "message_id": "<whorl-v0012-0915@digest.urth.net>",
      "from": {
        "name": "Talarican",
        "address": "exultnttalarican at mindspring.com"
      },
      "date": "2001-09-04T07:32:55+00:00",
      "subject": "(whorl) Voyage of the Whorl: Calculations of Thrust, Distance and Peak Velocity",
      "in_reply_to": null,
      "reply_link": null,
      "blocks": [
        {
          "kind": "text",
          "depth": 0,
          "text": "Assuming a \"Bussard ramjet-style\" 1/2 continuous acceleration, 1/2\ncontinuous deceleration flight profile, to calculate the necessary\nacceleration/deceleration and actual distance covered, the elapsed times\nwere divided in half, as the acceleration and deceleration phases are (ah,\nso Wolfean!) symmetrical.\n\nBruce Bowden, a.k.a. \"Dr. Matrix\", has been kind enough to post various\nforms of the Lorentz equations for relativistic motion on his \"Starships of\nthe Mind\" website. (scientium.com/essays/startrip/startrip.html)\n\nAssume a value for {a'}, the subjective acceleration, and set half the\nelapsed Urth time {t} to 550 yr. Calculate elapsed subjective time {t'} for\neither the accelerating or decelerating leg:\n\nt' = c / a' * arcsinh(a' t / c)              (*1)\n\nKeep iteratively adjusting {a'} until close enough to that value for which\n{t'} = 150 yr, half the subjective voyage time. (A process of \"relaxation\",\nif you will)\n\nHaving approximated {a'}, calculate x, 1/2 the distance to B&G, for either\nthe accelerating or decelerating leg\nx = c^2 /a' (cosh(a't'/c) - 1)\n\nThen peak velocity (at turnover) can be calculated\nv[peak] = c * sqrt(1- (1/(1 + a'x/c^2)^2)\n\nIt is of course convenient to perform all the actual calculations in SI\nunits. The following constant values and conversion factors were used.\n\nc = 299792458 m/s     (*2)\n1 year = 31556926 s      (*2)(*4)\n1 parsec = 3.08573 * 10^16m     (*3)\n1 light-year = 9.46055 * 10^15m     (*3)\n1 std. gee = 9.80665 m/s^2     (*2)\n\nUsing that most wondrous of software inventions, the spreadsheet    (*5), a\nvalue of {a'} was found, by trial and error, which fulfilled the two elapsed\ntime conditions {t} and {t'}. Then {d} and {v[peak]} could be directly\ncalculated.\n\n{a'} was found to be equal to about 0.02026 gee, which gets you within about\na fortnight of exact. And if _that's_ not close enough, there's no more\nhelp, hope, or comfort _I_ can offer you. (especially since {t} and {t'}\naren't known to the nearest year anyway).\n\nTherefore, {d}= 2*{x} was 9.54 * 10^18 meters, or 309 parsecs, or 1008\nlight-years (as we'd expect);\nand {v[peak]} at turnover was 2.99 * 10^8 m/s, or 0.996 c.\n\nby way of comparison, using 2*{t} = 1000yr,\n{a'} ~ .0194 gee, {d} = 277 psc, {v[peak]} = 0.995c.\n\nThe slight acceleration required, about one fiftieth gee, should hardly be\nnoticeable to ordinary Cargo except possibly a few physicists, and it could\nbe that the interior of the Whorl is slightly sloped forward in such a\nfashion as to compensate. Perhaps the \"mountains\" which divide segments of\n_Whorl's_ interior longitudinally (_Exodus_ ch 15) are actually escarpments\nat the edges of sections tilted slightly forward (\"eastward\")?\n\nOf course, presumably \"turnaround\" took place some 180 years prior to the\nevents in BLS; were any strange perturbations in _Whorl's_ perceived gravity\nnoticed by the Cargo at that time, and recorded in history, as the\nstarcrosser executed its maneuver? Unfortunately, there are no indications\nin the text that I could find.\n\nThe Bussard Ramjet, unfortunately, has one glaring limitation, provided you\ngrant that they and their vast \"ramscoops\" are even possible. A Bussard\nramjet's terminal velocity is said to limited by the resistance of the\ninterstellar gas against the ramscoop to about 0.90 c. This unfortunately\nlimits the maximum time dilation to about 40%, and the effective actual time\ndilation, given that the Whorl had to gradually accelerate and then\ndecelerate, to quite a bit less; i.e. subjective trip time had to be well\nover 400 years minimum. That just isn't going to fit well with the textual\nevidence.\n\nPerhaps the starcrosser reached 0.90 c using Bussard ramjets, and then\naccelerated without the ramscoop using matter-antimatter annihilation.\n\nNotes:\n(*1) Note my \"spreadsheet style\" notation: ^ is of course an exponent\noperator. Since ASCII includes no radical sign, the FOTRAN-like\npseudo-function \"sqrt\" is used to indicate a square root.\n(*2) source: CRC Handbook of Chemistry, 63rd ed.\n(*3) source: CRC Mathematical Tables, 26th ed.\n(*4) standard 20th century Earth year used in satellite orbit calculations.\nPossibly the second weakest assumption in the whole analysis, after the\nvalue of {t}.\n(*5) \"Excel\", ported with enormous trouble from your \"Very Small-Pliable\nPortals\" environment to that of the great thinking engine that allows me to\ncommunicate down the Corridors of Time with your Internet. The thinking\nengine now reports an overwhelming urge to display an endless blue expanse\nthen lapse into a comatose state. Furthermore, it has generated a most\nannoying aquastor that appears to be a piece of bent wire with eyes.\n\nThe Mad Exultant with red eyes.\n\n\n\n*This is WHORL, for discussion of Gene Wolfe's Book of the Long Sun."
        }
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}