On Thursday, November 10, 2022 at 8:38:11 AM UTC-6, Wolffan wrote:
> On 10 Nov 2022, David Brown wrote
> (in article<657e2ac8-4184-43f2...@googlegroups.com>):
> > On Wednesday, November 9, 2022 at 4:21:59 PM UTC-7, Wolffan wrote:
> > > On 09 Nov 2022, David Brown wrote
> > > (in article<d672798f-3b06-4d93...@googlegroups.com>):
> > > > Here's something I've been working on for a retro future project with hard
> > > > sci fi elements. It calls for a gigantic 300+ meter ship
> > > that’s aircraft carrier size. I hope that you’re starting from orbit, or
> > > there’s likely to be a problem.
> > >
> > > Also, that’s one dimension. What shape is it? It’s one thing if it’s a
> > > 300 metre long cylinder, with a diameter of, oh, 30 metres. It’s something
> > > else if it’s a 30-metre thick disk with a diameter of 300 metres. It’s a
> > > whole other thing if it’s a 300-metre radius sphere.
> > > > to accelerate to
> > > > 250,000 miles
> > > 250,000 miles per what?
> > > > for a trip to the outer solar system, which I arm waved to
> > > > maybe +12,000 miles of acceleration per day.
> > > you don’t do acceleration in miles per day. Personally, I work best in SI
> > > units: metres, kilogrammes, seconds, joules, watts, newtons, that kind of
> > > thing. The acceleration due to gravity, one gee, is approximately 9.81
> > > metres
> > > per second per second. (that last ‘per second’ is kind of important) One
> > > gee is a rather significant acceleration. I usually just round up to a nice
> > > even 10 m/s/s, it’s easier to work with.
> > >
> > > Some basic concepts:
> > >
> > > delta-vee is the total mission change in velocity. It’s rather
> > > significant.
> > >
> > > the mission delta-vee for a rocket-propelled vehicle is equal to the
> > > rocket's
> > > exhaust velocity times the natural log of the mass ratio, where the mass
> > > ratio is the total mass of rocket, payload, reaction mass, and everything
> > > else at the start of the flight (m1) divided my the mass of whatever is left
> > > at the end of the flight (m2). Note that that’s for the _total_ mission,
> > > you usually need to get there and back.
> > >
> > > v = u + at. That is, the final velocity equals the intial velocity plus the
> > > acceleration times the time spent under acceleration.
> > >
> > > s = ut + 0.5at^2. That is, the displacement equals the inital velocity times
> > > the time under acceleration plus half the acceleration times the square of
> > > the time.
> > >
> > > So let’s do an example: we want to go to the Moon. We want to do it at one
> > > gee continuous accel. We want to get back.
> > >
> > > So... the distance from the Earth to the Moon is 380,000 kilomtres, or 380
> > > million mtres. That’s 3.8 x 10^8 metres. We have to get there and back.
> > > That’s 7.6 x 10^8 metres. (It’s not really 380 million metres. See
> > > below)
> > >
> > > Ok... problem. We need to arrive at the Moon with velocity of zero relative
> > > to the Moon. We need to get back to Earth, or at least Earth orbit, with
> > > velocity zero. (well, we have to make lunar orbit and Earth orbit, but we
> > > can
> > > worry about that later.) This means that we can’t just boost all the way,
> > > we must boost half way, turn around, slow down. We must do this twice to
> > > make
> > > the round trip. As we need to fiddle around a little, let’s say that
> > > it’s
> > > 400,000 km to the Moon. Our total displacement is now 800,000 km.
> > >
> > > Ok, so the displacement we have to calculate is one quarter of 800,000 km,
> > > or
> > > 200,000 km (there’s a reason why I picked 400,000 km...) So s = 2 x 10^8
> > > m.
> > >
> > > We simplify where possible, and set u to zero. As will be seen later, actual
> > > values of u won’t make much difference.
> > >
> > > So... 2 x 10^8 = 0 + 0.5at^2. Cool. at^2 = 4 x 10^8.
> > >
> > > Now, a =10. (keep things simple...) which means that
> > >
> > > 10t^2 = 4 x 10^8
> > >
> > > so... t^2 = 4 x 10 ^7.
> > >
> > > hmm. My calculator says that t must equal 6325 seconds, (105.4 minutes, 1.76
> > > hours) approximately. Hmm, We must do this four times (once accel going to
> > > the Moon, once delec to zero, once accel going back to Earth, once decel to
> > > zero) so that’s 25300 seconds, approximately.
> > >
> > > hmm. v = u + at. u = 0. v = at. a =10, t = 25300. So... your total mission
> > > delta vee is... 253,000 metres per second, 253 km/s. So... how much reaction
> > > mass are you going to need? delta-vee = ve x ln mr. The best chemical
> > > rockets
> > > have a ve on the order of 4 km/s. The natural log of the mass ratio is going
> > > to be... 63.25. You’re gonna need a who lot of go-juice. And now you know
> > > why NASA didn’t try to use continuous accel in the Apollo moonships.
> > > Either
> > > you’re going to need something hotter than a chemical rocket, or you
> > > can’t accel all the way. Hot-jet nukes might, in theory, get to 100 km/s
> > > ve... that at least gives a managable mr. Still not good, though. You need
> > > better. Fusion rockets would be a lot better. Photon rockets would be nice.
> > > Neither one is likely to be available for the near future, if at all.
> > > You’re gonna need to think carefully about what kind of trajectories you
> > > want to use, continuous accel is off the table. It’d be nice; 3.5 hours to
> > > the Moon, 7 hours for a round trip, a few days to Mars, a few weeks, at
> > > most,
> > > for anywhere in the system... Not happening without magic tech.
> > >
> > > Jerry Pournelle went into great detail about this kind of thing in his A
> > > Step
> > > Further Out columns in Galaxy, some of which were collected into a nice big
> > > paperback. Look it up.
> > > > Here's the weird thing. Regular
> > > > terrestrial cars can accelerate 0-60
> > > that’s miles per hour. Call it 100 km per hour. It’s 400,000 km to the
> > > Moon. That’s 4000 hours, assuming that the car could achieve escape
> > > velocity, which it can’t. (it’s worse than that, you have to flip and
> > > decel, so it’s gonna take longer)
> > > > in 10 seconds without even being
> > > > considered that fast, which comes out at 1 mile per second
> > > one mile per minute. 3600 mph is one mile per second. An SR-71 spy plane
> > > could hit 2000 to 2400 mph before atmospheric friction would heat it up and
> > > destroy it.
> > > > . That means if all
> > > > conventional limitations were removed (friction, cooling, controllability,
> > > > fuel supply, etc), the car could accelerate to 86,400 mph in 24 hours
> > > nope.
> > > > . The
> > > > monkey wrench is, 1 G of acceleration amounts to a change of only 35 kph or
> > > > 21 miles per hour,
> > > no. 1 gee is 10 m/s/s (approximately). That’s 10 metres per second per
> > > second. At the end of the first second, that’s 10 metres per second, 36000
> > > metres per hour, a.k.a. 360 km/s. At the end of the second second, that’s
> > > 20 m/s. At the end of the third, 30 m/s. Ten seconds in, 100 m/s.
> > > > and people aren't supposed to be able survive 10 G of
> > > > acceleration for more than a few seconds.
> > > it ain’t the people you should be concerned about, it’s the structure of
> > > your vehicle. Very few vehicles can take 10 gees.
> > > > Therefore, a manned vehicle
> > > > accelerating at +5040 miles per hour every 24 hours would already kill the
> > > > crew many times over. What am I missing here???
> > > yes. You accel at, say, 1 gee, and you get to anywhere in the system in
> > > under
> > > a month and a half. One gee. You’re mixing up velocity and acceleration.
> > >
> > > May I suggest a basic course on statics and dynamics?
> > > >
> > > >
> > > > David N. Brown
> > > > Mesa, Arizona
> > I have ridiculously detailed and probably incoherent specs for the ship in
> > chapters posted on my blog. It's called the Janus, and my head description is
> > Tinker Toy ship. My specs have been 360 m long (cut down from my very first
> > ideas) and 40-60 meters wide at one or two places including a Von Braun style
> > ring for artificial gravity. There's also supposed to be a fusion reactor and
> > a space shuttle-sized landing craft up front. The general idea was always
> > something long and skinny that could be simply lined with fuel. After putting
> > things down and getting feedback here, I recalculated the speed as 400,000
> > kph, to be reached with acceleration of +800 kph per hour. I now believe the
> > G count would come out as something like 0.022, which would be completely
> > pitiful for anything that wasn't in the size range of the Empire State
> > Building. It really would be a "different" approach to spaceship design.. It
> > could be called the Space Yugo, except the timeline would diverge before
> > communist Yugoslavia existed. Hope this makes a little more sense; I might
> > put up a link or so tomorrow.
> You still have a problem with ‘acceleration’ and ‘velocity’. I
> suspect that you’re making the Star Trek/Wars Error and have the decks
> parallel to the thrust. Won’t work. When under accel, down is aft.. When
> spinning, down is out. Spinning while under accel is a Bad Idea(™), as it
> will tend to induce nausea.
>
> So... here’s my first cut at Ship Fit To Rule The System: Manifest Destiny.
> ‘Cause the manifest destiny of anyone who gets in Manny Dee’s way is to
> become plasma.
>
> Manny Dee masses 500,000 tonnes, with crew, supplies, ammunition, etc., but
> no reaction mass for her main motors. She normally carries another 500,000
> tonnes of reaction mass: water. No, I don’t ship water up from Earth,
> there’s lots of water in comets, various asteroids, Saturn’s rings, and
> assorted other objects in Jupiter and Saturn orbit. This gives her a mass
> ratio of 2, and the natural log og 2 is 0.6931. Manny Dee has four main
> motors, with an exhaust velocity of 100,000 km/s (one third of lightspeed)
> ‘cause they’re really great fusion rocket thingies with lots of
> handwavium tech. And that number is easy to work with. Hmm. Manny Dee has a
> mission delta vee of 69,300 or so km/s. She can go anywhere in the solar
> system and get back on one tank of reaction mass.
>

What nuclear reaction are you assuming to get an exhaust velocity
of 100,000,000 meters per second (1/3 C) for a fusion rocket? Using
values of 1.00784 atomic mass units for the mass of hydrogen and
4.002602 AMU for helium, I calculate an exhaust velocity of about
36,000,000 meters per second (.12 C) for four atoms of hydrogen
fusing to form one atom of helium.

Peter Wezeman
anti-social Darwinist