Subject: Space-tech Digest #118
Contents:
Magnetic Sails (11 msgs)
------------------------------------------------------------
From: Christopher Neufeld
To: space-tech@cs.cmu.edu
Subject: Re: Magnetic Sails
Cc: PUSCHG@crl.aecl.ca
Date: Thu, 23 Apr 1992 13:55:39 -0400
This might be straying a bit from space-tech, but since it started
here, I might as well round things up a bit.
On Apr 22, 5:25pm, "GORDON D. PUSCH" wrote:
>
>> There exists in low temperature physics a thermal 'switch', a device
>> which can connect two objects thermally, and disconnect them, without
>> moving parts ... You put your sample and your heat source/sink at
>> opposite >ends of a piece of superconductor below its critical temperature.
>> By applying a magnetic field you drive it normal, or let it remain
>> superconducting by removing the field. In the normal state the ends are
>> in good thermal contact. In the superconducting state it acts as a
>> reasonably good thermal insulator ...
>>
>I'm afraid I don't understand that at *all*. While I agree that Niven's
>wrong, I thought that heat propagrated through a superconductor the same
>way it does through any *other* superfluid: by ballistic phonon transport
>(so-called ``second sound''). How the heck does this thingy work? What's
>the physics behind it?
>
My reference is Mackinnon's _Experimental Physics at Low
Temperatures_, copyright 1966 Wayne State University Press, Library of
Congress Catalog Card Number 65-14928.
On page 94 is a graph of "Possible form of observed thermal
conductivities of a metal" versus temperature, with a cusp at Tc where it
goes superconducting and the conductivity drops. Quoting from page 99:
"The two-fluid concept is useful for the qualitative explanation of
other properties. Thermal conductivity is an example of one. The
thermal conductivity, \kappa, for a metal may be expressed as
\kappa = \kappa_e + \kappa_l
where \kappa_e is the electronic contribution to the conductivity and
\kappa_l the lattice contribution. In a pure metal at low temperatures,
\kappa_e >> \kappa_l. The superconducting electrons carry no heat (no
entropy) so, as the number of normal electrons decreases, \kappa_e, and
hence \kappa decreases - as observed. One should note that this
explanation allows for no internal convection process, as is suggested
for liquid helium II."
As for comparing this process with liquid helium II convection and
second sound, that's a bit out of my expertise. Mackinnon's book goes
into internal convection and second sound on p 57 et seq.
--
Christopher Neufeld....Just a graduate student | alien: n. a being who
neufeld@helios.physics.utoronto.ca Ad astra | travels great distances
cneufeld@terranet.cts.com | to molest our cattle
"Don't edit reality for the sake of simplicity" | and trample our grain
------------------------------
From: henry@zoo.toronto.edu
Date: Thu, 23 Apr 92 14:46:03 EDT
Subject: Re: Magnetic sails
Cc: Christopher Neufeld
To: space-tech@cs.cmu.edu
>In interstellar space, ambient is 2.7 degrees Kelvin...
No it's not. They've forgotten that there are stars out there.
Henry Spencer at U of Toronto Zoology
henry@zoo.toronto.edu utzoo!henry
------------------------------
Date: Fri, 24 Apr 1992 17:33 EDT
From: "GORDON D. PUSCH"
Subject: Magsail sketch
To: space-tech@cs.cmu.edu, Bradford@maccs.McMaster.CA,
brand <@cunyvm.cuny.edu:brand@vtcc1.BITNET>
I've made up ``ASCIIgraphic-classic(tm)'' sketch of a magsail in ``axial''
attitude i.e., sail loop's plane perpendicular to wind) --- just so everybody
here can be sure about what a magsail *looks* like :-).
Note that Zubrin also refers to the ``normal'' attitude, which means
the *normal* to the sail loop's plane is *perpendicular* to the wind.
(As far as I can tell, ``normal'' is not the *normal* attitude of a magsail;
rather, it is ``axial'' is the normal attitude of a magsail ... %-T.)
(Replace ``solar wind'' w/ ``geomagnetic field lines'' for surface-launch.)
MagSail Sketch
================
#
----> S /#
----> O Shrouds --> / #
----> L / #
----> A / #
----> R $$$ #
----> PayLoad ;-) $$$ # <-- SuperConducting Unobtanium Loop :-T
----> (14 tonnes) $$$ # (64 km diameter;
----> W \ # 50 kAmp current;
----> I \ # 5 tonnes mass)
----> N \ #
----> D \# (1 tone misc. hardware and avionics)
#
/
/======== T H I S E N D
\======== D O W N !!!!!
\
Gordon D. Pusch
------------------------------
Date: Fri, 24 Apr 1992 18:38 EDT
From: "GORDON D. PUSCH"
Subject: Magsail Equation Summary (long -- 5K)
To: space-tech@cs.cmu.edu
X-VMS-To: SPACE-TECH
X-VMS-Cc: PUSCHG
Below is a compendium of magsail equations, taken from Zubrin's article,
and from my own doodlings ... They are in psuedo-TeX; sorry!!!
Symbol glossary:
==================
Symbol glossary, together with estimated values (I'm not sure if I've done
the english-to-metric conversions correctly; if an english unit is given,
it's the original from Zubrin's article).
%
$ rho_s := {solar-wind mass-density} \simeq 8.31e-21 kg/m^3 @ 1 AU $
$ V_s := {solar-wind velocity} \simeq 400--600 km/sec @ 1 AU $
$ B_e := {Earth's avg. field at the equator} = 3.05e-5 Tesla, $
$ R_e := {Earth's mean radius} = 6.378e6 m, $
$ r := {spacecraft distance from Earth's center}, $
$ R_s := {spacecraft distance from Solar center}, $
$ \theta := {spacecraft angle from north pole}, $
$ I := {magsail loop total current} \simeq 50 kAmp, $
$ A := {magsail loop area} = \pi R_m^2, $
$ R_m := {magsail loop radius}, \simeq 32 km, $
$ r_m := {magsail loop conductor radius} \simeq 1.26 mm, $
$ J_c := {superconductor critical current-density} \sim 1e10 Amp/m^2, $
$ \rho_m := {superconductor mass-density} \sim 5000 kg/m^3), $
$ M_m := {magsail mass} \simeq \rho_m \pi r_m^2 R_m = 5 tonnes $
$ T_m := {superconductor tension} = 90.8 lbs = 403 Newtons (?) $
$ \tau_m := {superconductor hoop-stress} \simeq 11760 psi = 81 MPa(?) $
$ \mu_0 := {``permiability of free space''} := 4\pie-7 Newtons/Amp^2. $
%
M A G S A I L E Q U A T I O N S
=====================================
Solar Wind Density:
=====================
Zubrin assumes an inverse-square law for solar-wind density:
$$
\rho_s := (8.35e-21 kg/m^3) (R_s/(1 AU))^{-2}
$$
I'm not convinced it's correct, but I'm including it anyway ...
Drag/Mass ratio:
==================
Formula given by Zubrin in _Analog_ article (was in my first post;
included again for completeness):
$$
D/M = (0.6) * (J_c/rho_m) * ( mu_0 * R_m * (rho_s * V_s^2)^2 / I )^(1/3).
$$
(I am somewhat puzzled by the numerical factor of ``0.6'' ... perhaps it is
an estimated coefficient of drag they got from their hypersonic aerodynamics
code; if so, I wouldn't trust it --- I'd expect significant additional
contributions from Alfven-wave production, for example.)
Magsail in Geomagnetic Field:
===============================
Zubrin gives the following for the force on a magsail with magnetic-moment
aligned w/the local geomagnetic field:
$$
\vec{F} = - 3 IA (B_e/R_e) (r/R_e)^{-4}
{ [ \hat{r} + \onehalf \sin( 2 \theta ) \hat{\theta} ]
\over
[ 1 + 3 {\cos^2}( \theta ) ]^2 }.
$$
For some reason, he chooses *not* to express this as ``force per unit
coil-mass'' normalized by his fundamental ``material-parameter,''
$J_c/\rho_m,$ as he did for $D/M$; I do so here:
$$
F/M = - 3 \pi (J_c/\rho_m) R_m
(B_e/R_e) (r/R_e)^{-4}
{ [ \hat{r} + \onehalf \sin( 2 \theta ) \hat{\theta} ]
\over
[ 1 + 3 {\cos^2}( \theta ) ]^2 }.
$$
Note that again, for fixed $J_c/\rho_m$, one wants $R_m$ to be as large
as practicable; Zubrin mentions this in the text, but does not make it
clear why. Note that a magsail's ``lift-ratio'' is *linearly proportional
to its radius*.
Superconductor tension:
=========================
I have not managed to find or derive a formula for the self-tension of a
current-carrying loop; however dimensional analysis shows it must be of
the form:
$$
T_m = {\mu_0/4\pi} I^2 f( r_m / R_m ),
$$
where $f(r_m/R_m) \equiv f(x)$ is a dimensionless function. My experience
in calculating the magnetic fields in our cyclotron over the past two years
causes me to strongly suspect that $f$ is some sort of horrid elliptic
integral. My preliminary analysis bears this intuition out; also that
$f$ should *probably* go like $x$ for small $x$ (but I'm not so sure of
this yet; it might go like some other positive power --- but it *should*
be postive, because an *infinitely* large loop should have zero tension).
The tension Zubrin gives is quite small --- about 90lbs (I wonder why they
picked *that* value? ;-).
Superconductor Hoop-Stress:
=============================
The hoop-stress is:
$$
\tau_m = {\mu_0/4\pi} {\pi r_m^2} (I/{\pi r_m^2})^2 f( r_m / R_m )
= {\mu_0 J_c^2 / 4\pi} {\pi r_m^2} f( r_m / R_m )
$$
(where I have optimistically substituted $J_c$ for the current-density;
one should probably include some safety-factor).
MagSail-Loop Mass:
====================
If I have correctly estimated the small-$x$ behavior of $f$, then for
$\tau_m$ fixed (say, to 80% of $\tau_max$ for the material in question),
the magsail's mass scales as
$$
M_m \sim \rho_m R_m^{1/3}.
$$
Thus, the magsail's mass scales very slowly with its radius. As previously
noted, its surface lift capacity scales *linearly* with radius.
Gordon D. Pusch
------------------------------
Date: Fri, 24 Apr 1992 20:23 EDT
From: "GORDON D. PUSCH"
Subject: Re: Magsails
To: space-tech@cs.cmu.edu
X-VMS-To: SPACE-TECH
X-VMS-Cc: PUSCHG
I have just sent a long summary of most of the relevent equations from
Zubrin's article, RE: magsails plus some I doodled up myself. To summarize
my summary :-T
o for *fixed material*, a magsail's geomagnetic lift is linearly
proportional to its radius;
o The tension in the magsail loop is *very small* --- Zubrin gives
about 90 lbs for his canonical model (I wonder why they picked *that*
value? :-)
o I tentatively conclude that the loop-tension scales with the *square*
of the current, *inversely* with the sail's radius R_m, and *directly*
with the conductor thickness r_m (for R_m >> r_m).
o Therefore the loop's hoop-stress also scales inversely with the sail's
radius, and directly with the *cube* of the conductor thickness.
o The magsail's mass scales only as the *CUBE ROOT* of its radius,
so its payload/structure ratio rapidly improves with radius.
o The previous three points suggest that magsails should be built really,
really *BIG* ...
Paul Dietz's arguments RE: need for ``superconducting Unobtanium'' have
convinced me that an onboard power-supply *IS* needed for surface launches.
I disaggree, however, that:
>
> ... For a 5 ton vehicle accelerating at 3 gees at 7 km/s (say),
> the required power is about 1 gigawatt ...
>
for three reasons:
1) The magsail's acceleration declines as (r/R_e)^{-4}, so by the time
it's up to 7 kps, its acceleration (and the power required) should have
dropped substantially.
2) If one can efficiently couple power *inductively* into the supercon-
ducting loop, i.e., w/out running the main loop-current through a resistive
device, one can in principle accelerate as gently (and with as little
power consumption) as one wishes (modulo things like power consumed by
the cryo-coolers that will *DEFINATELY* be required for launch from
Earth's surface --- even if departing from ``Port Bathurst'' ;-) ...
I remember reading in high-school about just such a device: a supercon-
ducting doohickey called a ``flux-pump'' --- basically the Josephson-device
equivalent of a switching power-supply, if I understood it correctly ---
that was supposed to do just that. Unfortunately, I didn't need one at
the time, and since then, I haven't been able to relocate a reference,
despite almost twenty years of trying :-(.
3) Finally, from the formulas I derived, I believe that ``surface-escape''
and ``interplanetary'' gaussjammers will have rawther diff'rent designs.
Rather than having an ``all-in-one space-truck,'' I suspect that one would
instead want two different types of vehicles --- call them ``tugboats''
and ``clippers'' --- for the two jobs. (Think of it as being something
like a two-stage rocket, only moreso ;-). The rather more sturdy ``tugboats''
will carry cargo from ground out to a (magsail-levitated?) transfer station;
from there, it will be transhipped to the rather more aetherial ``clippers''
for Earth-escape ... ``Tugboats'' will have big onboard power-supplies,
stiff superinsulating sheathing on their sails, and hefty active cryocoolers.
``Clippers'' will be designed for the absolute minimum of mass, in order
to run efficiently before the (admittedly feeble) solar wind ...
One thing Zubrin doesn't disscuss (although *you* sort of brought it up
for a different reason, Paul, and I flippently dismissed it :-): one should
allow a substantial current-density safety-margin --- because every time a
solar-flare or coronal-mass-ejection hits this one of these flimsy things,
it's going to induce big transient current fluctuations, much like those
occuring in a geomagnetic storm! Unless there's a substantial safety-
margin, one risks the possibilty of part of the loop ``quenching'' ---
i.e., going ``normal'' --- in which section shortly after, 80MJ of heat
will appear! 8-[.
I don't *think* there's *MUCH* risk of ``whiffing'' the wire ---
2.62 mm is pretty heavy-gauge stuff; but this underscores a need I've
already commented on: copper or aluminum cladding to thermally-stabilize
and quench-protect the loop. *ALL* well-designed superconducting magnets
use cladding; for example, the coils in the superconducting cyclotron
I work with are *very* conservative ---- almost 95% copper, only 5%
superconductor --- and almost certainly because of that, we've *never*
had a quench; the SSC's magnets, on the other hand, use (IMHO) far too
little copper or iron, and have had quench-problems from the very begining
(the SSC's Central Design Committee apparently failed to learn from ISABEL's
mistakes --- but enough poltical science :-(.
Next round of objections, please? :->
Gordon D. Pusch
------------------------------
Date: Fri, 24 Apr 92 21:54:11 -0400
From: dietz@cs.rochester.edu
To: PUSCHG@crl.aecl.ca
Subject: Re: Magsails
Cc: space-tech@cs.cmu.edu
Gordon suggested coupling energy into the loop inductively...
This has actually already been tried, with normal materials. A device
was built at MIT that dumped a massive current pulse into a stationary
coil. A single turn coil of copper, resting on this, was accelerated
to 1 km/s in about one centimeter. Melted it, too. The purpose
was to build a kind of EM thruster using disposable coils as
reaction mass.
Scaled up, something like this would enable the launcher to
experience stronger fields, and therefore have weaker currents.
It could also launch from more convenient locations. But mariners
would object when the compasses stopped working. Maybe it could
be sold as an energy storage device when not being used for
launches.
Even more grandiose, one could augment the Earth's magnetic field with
an equatorial coil. The energy stored in the part of the earth's
field beyond the atmosphere is only about 30 GW-years (about 200
megatons TNT), not an impossibly large amount. The coil had better
be in many segments so that faults didn't cause catastrophe.
Paul F. Dietz
dietz@cs.rochester.edu
------------------------------
Date: Sun, 26 Apr 1992 02:02 EDT
From: "GORDON D. PUSCH"
Subject: More MagSail formulas ...
To: space-tech@cs.cmu.edu
X-VMS-To: SPACE-TECH
X-VMS-Cc: PUSCHG
Since my post of yesterday, I have found and derived some additional
formulas --- one of which appears to drastically change one of my
conclusions ...
Magsail in Geomagnetic Field:
===============================
I have derived the following formula for estimating the minimum magsail
radius needed to just support a given weight in the Earth's geomagnetic
field over a geomagnetic pole:
$$
R_m
\geq
(10.88 km) W (r / R_e)^2 (\rho_m / 10^3 kg/m^3)
\over (J_c / 10^10 Amp/m^2)
$$
Here, W is Zubrin's ``weight factor,'' i.e., the total vehicle mass
divided by the magsail loop's mass alone. I assume a mass-density
\rho_m and current-density J_c for the loop; as I mentioned earlier,
both quantities probably need ``safety factors'' to include cladding-mass
and critical-current margin.
(Note: assuming a multiturn coil does not help, because only the *total*
current matters.)
Absolute Ceiling:
===================
If I solve instead for $r$, I find that statically-levitating magsails
have an ``absolute ceiling,'' because the dipole-dipole force is inverse-
*fourth*-power, while gravity is inverse-square. This ceiling is given by:
$$
(r / R_e)
\leq
(.3032) \sqrt[ (R_m / 1 km) * (J_c / 10^10 Amp/m^2)
\over (\rho_m / 10^3 kg/m^3) ],
$$
If I plug in Zubrin's values, I find that his magsail's absolute ceiling
is about 0.38 R_e, i.e., his sail can't ``hover'' at *any* altitude
--- it has to orbit.
Superconductor tension:
=========================
I found an approximation for the self-inductance of a current-loop in
Smythe's _Static and Dynamic Electricity_. I believe the tension should
be given by $\partial E / \partial C$, where $E$ is the stored energy,
and $C$ is the loop's circumference. The somewhat surprising result for
the tension is:
$$
T_m = {\mu_0/4\pi} I^2 [ \ln( 8 R_m / r_m ) - 3/4 ]
$$
i.e., the tension appears to *logarithmically diverge* with the loop-radius!
Plugging in Zubrin's numbers, I get $ T_m = 4591 N = 1032 lbs $, in poor
agreement with the value of 90 lbs I computed from the hoop-stress and
wire-diameter he gives in the _Analog_ article. I doubt I will be able to
reconcile my results with Zubrin's until I get copies of the actual papers,
so I can see where his numbers came from --- by any chance, does one of you
out there already have them? George Herbert, maybe?
Superconductor Hoop-Stress:
=============================
The hoop-stress becomes:
$$
\tau_m = {\mu_0 {J_c r_m}^2 / 4 } [ \ln( 8 R_m / r_m ) - 3/4 ]
$$
or 916 MPa = 133000 psi for Zubrin's values --- which I find distressingly
large ...
MagSail-Loop Mass:
====================
Since the ``log'' makes \tau_m insensitive to R_m, the magsail's mass
now appears to (very crudely) scale as:
$$
M_m \sim R_m,
$$
because r_m is now bounded from above by the breaking-stress of the wire
(up to logarithmic factors). Since the magsail's geomagnetic lift also
scales like R_m, it looks as if a magsail's ``weight factor'' is essentially
independent of its size, rather than improving with size, as I stated before ...
Gordon D. Pusch
------------------------------
Date: Sun, 26 Apr 1992 01:58 EDT
From: "GORDON D. PUSCH"
Subject: Re: Magsail
To: space-tech@cs.cmu.edu
Since my post of yesterday, I have found and derived some additional
formulas --- one of which appears to drastically change some of my
conclusions ...
o Magsails capable of ground launches will have to be *VERY* big,
unless superconductors with a significantly higher J_c/\rho_m can be
developed (organic? buckyball-based?), or Paul Deitz's idea of
ground-launch-assist coils works out.
o Statically-levitating magsails have an ``absolute ceiling,'' because
the dipole-dipole force is inverse-*fourth*-power, while gravity is
inverse-square. Zubrin's canonical magsail's ceiling is *0.38 R_earth*
--- it can't hover; it has to orbit.
o I *think* I've found a formula for the tension and hoop-stress, and
it doesn't look good --- I differ from Zubrin's quoted hoop-stress and
tension by more than an *order of magnitude*. If I'm right, the tension
*diverges logarithmically* as R_m increases, while the hoop-stress places
an (almost R_m-independent) upper-bound on the superconducting loop's
thickness, r_m. I doubt I will be able to reconcile my results with
Zubrin's until I get copies of the actually papers, so I can see where
his numbers came from --- by any chance, does one of you out there
already have them? George Herbert, maybe?
o The new results mean that (modulo logarithmic factors) a magsail's
mass is essentially proportional to its radius, while its ``weight factor''
is (almost) independent of radius, contrary to what I said before.
None of the above results *necessarily* invalidate my notion of
``tugboats'' --- actually, the term ``coasters'' or ``tenders'' would
probably be a better nautical analogy) --- but it *does* require that the
``tugboats'' need to have orbit-matching capability with the transfer-
station. I imagine they would do this by ``tacking'' and ``jibing:''
tilting to use their their excess-lift capacity at their instantaneous
altitude to tangentially accelerate, and also periodically reversing their
polarity, in order to ``pump'' up their velocity (think of it as a *REALLY*
big electric motor ;-). I haven't studied the dipole-dipole interaction
potential and force enough yet to figure out what the lift and thrust
polars look like (beyond deducing that they're elliptical), or whether
one needs to reverse polarity twice or four times per orbit, but I'm
confident it's *possible*. It'll just be bloody complicated shiphandling ...
An alternative strategy would be to do something straight out of
Douglas Adams: ascend to one's absolute ceiling, then tip ship for
maximum tangential thrust ... In other words: ``... fling yourself
at the ground, and --- at the very last second --- *miss* ...'' 8-)
Gordon D. Pusch
------------------------------
From: fils@iastate.edu
To: space-tech@cs.cmu.edu
Subject: Re: Magsail
Date: Sun, 26 Apr 92 19:43:59 CDT
In reply to the letter by: Gordon D. Pusch
>I will be able to reconcile my results with
>Zubrin's until I get copies of the actually papers, so I can see where
>his numbers came from --- by any chance, does one of you out there
>already have them? George Herbert, maybe?
You may want to try:
Magnetic Sails and Interplanetary Travel
AIAA-89-2441
published in Journal of Spacecraft and Rockets, March/April 1991
I wish I could read it, our library has this issue out being bound.
Douglas Fils fils@iastate.edu | Ego vos hortor tantum possum ut amicitiam
Dept. of Physics and Astronomy | omnibus rebus humanis anteponatis.
Iowa State University (ISU) | Cicero, On Friendship V.17
------------------------------
Date: Sun, 26 Apr 1992 21:23 EDT
From: "GORDON D. PUSCH"
Subject: Re: Magsail
To: fils@iastate.edu, space-tech@cs.cmu.edu
I *also* wish I could read it, but I'll have to *order* a copy first;
our tech-library is so relentlessly nuclear-engineering oriented that
we don't even get _Aviation Leak_!!! Furthermore, Chalk River is darned
isolated; I suspect the nearest copies of J.S.&R. must be at *least* as
far away as the Technical Document Centre in Ottawa (250 km) --- I might
even have to go as far as U. Toronto or Syracuse (ca. 600 km) ... *sigh*
Gordon D. Pusch ! BITnet:
AECL Research !
Chalk River Laboratories ! Phone: (613) 584-3311, X-4107 (off.)
Chalk River, Ont. CANADA ! (613) 584-2368 (hm.)
K0J 1P0 !
------------------------------
Date: Sun, 26 Apr 92 23:34:01 -0500
From: pgf@srl03.cacs.usl.edu (Phil G. Fraering)
To: PUSCHG@crl.aecl.ca, fils@iastate.edu, space-tech@cs.cmu.edu
Subject: Re: Magsail
I know what you mean; JSR was discontinued at the USL library due
to budgetary pressures... I think I'm the only one there who's ever
used it recently...
pgf
------------------------------
End of Space-tech Digest #118
*******************