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 *******************