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A simple estimate for coilgun performance

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  • Luke
    Here s a quick method to estimate what kind of performance you can get out of a coilgun. Some folks here might find it interesting. First, decide on the
    Message 1 of 51 , Dec 2, 2010
      Here's a quick method to estimate what kind of performance you can get out of a coilgun. Some folks here might find it interesting.

      First, decide on the efficiency of your coilgun. Coilguns are linear brushless electric motors, and brushless electric motors have demonstrated efficiencies of 90% to 95%. Superconductive electric motors might have efficiencies of 98% to 99%. Denote this as a decimal, and call it e; that is e = 0.9 to e = 0.95.

      Next, decide on the length and radius of your projectile. Decide on what your projectile is made of and find its mass (mass = density * length * radius^2 * pi, and remember to use consistent units). Also find the projectile cross-sectional area (area = radius^2 * pi). Decide how fast you want your projectile to be going and find its final kinetic energy (kinetic energy = 0.5 * mass * velocity^2, again remember to use consistent units).

      Given the efficiency of your coilgun, you can find out how much your projectile heats up. You might figure that half of the wasted energy goes into the projectile, and thus your projectile will gain a heat energy of 0.5 * (1/e - 1) * (kinetic energy). Look up the specific heat of the material your projectile is made of, commonly called C. Then your projectile reaches a temperature of (heat energy)/(C * mass) - again make sure your units are consistent. If you are using a synchronous coilgun with a permanent magnet in the projectile, this temperature needs to be less than the Curie point or the projectile will become non-magnetic. If your coilgun projectile is made of superconductors and you are using Meissner effect repulsion, this temperature will need to be less than the critical temperature of the superconductor or your superconductor will become non-superconducting. If you are using an asynchronous coilgun which uses inductive forces on conductive loops, this temperature will need to be less than the melting temperature of your projectile. If the temperature is too high, you will either need to use a material that can handle higher temperatures, make the coilgun more efficient, or accept a lower velocity for the projectile.

      Decide the maximum magnetic field your coilgun can handle. If you are using a synchronous coilgun with permanent magnets (probably in the projectile, with the field coils along the barrel) you are limited by a saturation field of around 0.2 to 2 tesla beyond which your efficiency falls off rapidly. If you are using superconductors, your field is limited by the critical field of the superconductor. For conventional BCS-type superconductors this limits you to fields of several tens of tesla or less, for high Tc superconductors you might be able to get to 100 to 200 tesla. If using an asynchronous coilgun that uses induction to launch normally conductive projectiles there is no obvious physical upper limit to the magnetic field strength, although high field strengths will require massive bracing to keep the barrel from exploding.

      Now assume that the barrel is filled with field, and that the projectile sweeps the field out of the barrel, turning the field energy into kinetic energy (this is not actually how coilguns work, but it gives the physical upper limit based on energy conservation). The energy density is about 400 kJ/m^3/T^2 times the square of the magnetic field strength (398,098 J/m^3/T^2 to six significant figures). Call this value K (K = 400 kJ/m^3/T^2). You now know the volume needed in the barrel based on how much energy the projectile ends up with (volume = kinetic energy / (K * (magnetic field)^2)). since you know the cross-sectional area of the projectile and thus of the barrel, you know how long the barrel needs to be (length = volume / area). If the barrel is unacceptably long, you will either need to figure out how to get a stronger field in the barrel, make the projectile shorter (if you do the math, you can see that the barrel length will be a multiple of the projectile length for a given field, material, efficiency, and final velocity) or make due with a lower velocity of the projectile.

      As an example, suppose we have a synchronous coilgun, and that the coilgun can generate 1 tesla fields (a good number that will not saturate the ferromagnet). Our presumed ferromagnet is probably mostly iron, with about 8000 kg/m^3. To reach 100 km/s, you will need 40 TJ per cubic meter of projectile. Since this is 100 million times the energy density of the field, you will need the projectile to sweep out 100 million times its volume in order to accelerate up to the desired speed. This means you need an accelerating track 100 million times the length of your projectile. If the projectile is the size of a dime, with 1mm thickness, you will need a 100 km long track. If 2.5% of the energy goes into the projectile as heat as a result of inefficiencies, you get 100 GJ of heat per cubic meter of projectile, or 12 MJ/kg. This is three times the specific energy liberated by detonating high explosives, so you can expect your projectile to explode like a bomb inside your coilgun barrel. Consequently, this appears to be an unworkable design.

      Luke
    • tsz52
      ... Just another approach suggestion, as a tool for focus:- Optimal point designs ( in the middle ) are the interesting ones, but it s best to get the extremes
      Message 51 of 51 , Jan 19, 2011
        --- In sfconsim-l@yahoogroups.com, "krakonfour" <krakonfour@...> wrote:
        >
        > > Frankly, it sounds like practically the same thing,
        > > to me. Coilguns, magical fusion drives, lasers,
        > > etc...
        >
        > That's depressing. That's like telling me Battlestar galactica was not much different from Star Wars...I mean, they both had space fighters, carriers, blasters and planet slagging, right? Come on! I went from a laser battle from a tenth of a lightsecond to a kinetics exhchange at a third of the distance...The laser are practically useless at long range here, and instead of a wearing down battle, I have elements of first-hit one kill...
        >

        Just another approach suggestion, as a tool for focus:-

        Optimal point designs ('in the middle') are the interesting ones, but it's best to get the extremes sorted first, as reference points.

        [I've had a similar problem with my 'bit of everything' Frigates - after many years, I've realised that I need to nail down my Cutters and BBs first.]

        It's a bit cheesy and well-worn but as a focusing tool only, try the min-maxing archetypes: The Dreadnought Battlebrick; and the Agile Needleship.

        Battlebrick: Doesn't jink (except for at vast range) and is ponderous, can take a beating but shouldn't have to given all of Mr Kuo's excellent suggestions (rotating multi-layered Whipple shields and drones etc). [I should just mention that re the Dreadnought vibe in the other thread, I meant 'Steam turbine and screw propulsion'....]

        There'll be multiple redundancy - try and design it such that it can still fight even if half of it is blown away.

        Agile Needle: With the kinetics that you want, unless you're a leviathan, if you're hit, you're toast - so it's all acceleration and jinking (with minimal AMMs/drones too, since you'll need some).

        It's all lightness and drive (select its weapons accordingly) - it can also be numerous in comparison to BB. If it's dead if it gets hit anyway, it might as well have some kind of AM Drive.

        You might find (for a quick and dirty first approximation) tweaking existing games useful here: (Battlefleet Gothic) Space Marine Battlebarge vs Eldar Corsairs (consider the Holofield save to be a jink save, and change the Eldar Drive); or quickly knock up a few ideas using a Full Thrust or Colonial Battlefleet spreadsheet (again, Shields are jink drive etc) etc.

        In most discussions that I've come across, BB seems to win, but I've never found any units in any game ever that I could make dance and sing as well as my Eldar Corsairs, so I keep trying to get that archetype to work in my settings (remember that acceration/speed is a strategic weapon in addition to a tactical one, and that these approaches favour different worldviews and resource/tech/economic bases).

        It might give you a better idea of what you want your factions to be able to do in your uni, and be a better foundation for designing the *tricky* ships somewhere in the middle (generally turn out worst of both worlds rather than best... but the odd good one that you manage to devise will make your heart burst with accomplishment and joy).
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