In this paper a new method of speeding a projectile to orbital
velocities is introduced. This method is based on utilizing the power
of an Explosively Pumped Flux Compression Generator. Due to
great magnetic fields generated by the EPFCG, thrusts in the order of
1 x 108 N can be produced using
its direct application on a target.
The projectile in ECCG has a circuit that is also be powered by the
EPFCG through induction. Sample calculations showed that a 6.1 kg
projectile could be accelerated to 14.3 km/s within 0.001 seconds
and a length of 4.67 m, well enough to launch it into space.

We propose a payload launcher called the Explosively Compressed Coil Gun (“ECCG”) that can accelerate payloads to velocities sufficient to escape Earth’s gravity. The ECCG is composed of a Helical Generator, which has proven to produce magnetic fields in excess of 200 Teslas. The center of the Helical Generator proposed is empty, as shown in Figure 1. There is a metal armature under the solenoid and explosives, such as TNT, in the metal armature. The target is to be sent at an initial speed of 10 m/s using a conventional gun.

The operation of the ECCG involves a preliminary current in the metal ring on the projectile supplied by a small capacitor on the projectile. Once the projectile passes the center point of the helical generator, the explosives are ignited. This causes the solenoid to be short-circuited by the metal armature, thereby increasing the current. As the circuit shortens, it strives to conserve the magnetic field. This in turn increases the current flowing in the solenoid.
The target circuit experiences rapid magnetic flux changes. Therefore, a current that is reverse to that in the solenoid is generated in the ring. This creates a repulsive force between the solenoid and projectile. As the projectile moves towards the exit of the helical generator, so does the explosion head. The explosion is controlled so that center of the solenoid is always behind the projectile, as shown in Figure 3. Since the solenoid is not restricted by the resistance of a conductive wire, very large currents can be generated in the solenoid and induced in the ring.
The electromotive force in the ring is proportional to the rate of change of the magnetic field, which in turn is proportional to the rate of explosion of the metal armature. In this paper, example calculations will be given to show the potential of the ECCG method. In the next section, the equations used for this example and results of the calculations will be explained.

The calculations are based on equations the following equations:
(1)

where is the EMF in volts, ÖN is the net magnetic flux through the circuit in webers, and t is time is seconds.
The current generated in the target ring is from Ohm’s law:

(2)

The force on the ring is calculated using the magnetic force expression:
(3)
Once force is determined, acceleration, velocity, and position are calculated using Newton’s standard equations:

(4)

(5)

(6)

3. NUMERICAL CALCULATIONS
In order to see if we could reach orbital speeds using ECCG, we performed the calculations on an example case of a 6.1 kg projectile with a radius of 0.25 m. A helical generator with a 200 Tesla/m2 maximum flux was examined. For simplicity and being conservative, the projectile was assumed to be at rest when the generator was ignited and the resistance of the projectile ring was assumed to be constant at 0.07 ohms/m.
Assuming the rate of change of magnetic flux as constant at 200,000 Teslas/second, the result of induced current calculation is 560,714 Amps flowing through the ring. Since the rate of magnetic flux increase is also constant, the force on the projectile linearly increases from 0 to 1.78 x 108 N in 0.001 seconds. Given the mass of the projectile at 6.1 kg, the projectile speed at the time the flux is 200T is 14.287 km/s, as shown in Figure 4. All this happens within a total distance of 4.67 meters as calculated from Equation 6.

Yeah look it all sounds very interesting, but given the simplistic approach you've taken to modelling it, I'd brace for dissapointment if I were you, as you're about to get cut to shreds by people pointing out all of the things you're not taking into account.

This is 622 megajoules of energy. At whatever incredibly low efficiency you're going to be operating at here, that's going to be a hell of a lot of TNT.

Also, what're you going to have the 6.1kg do, anyway. Are you wanting to shoot holes in orbital space stations?

What hardware aboard your projectile will survive the 22 million G's?

Lastly, I'm pretty sure it's hard if not impossible to achieve orbit from a ballistic trajectory, because of the requirement for more horizontal velocity than vertical. So, what's this thing meant to do, anyway?

//it's hard if not impossible to achieve orbit from
a ballistic trajectory//

That is true. Gravitationally speaking, a ballistic
launch is equivalent to firing something from the
surface of an infinite, flat plain (or, indeed, plane)
- just that the whole trajectory gets curled
around.

So, if you launch ballistically, there are only three
options:

(1) You exceed escape velocity, and just keep on
going forever

(2) Your projectile completes an orbit that brings
it right back through the launch point or

(3) Your orbit is intercepted by the earth.

You cannot launch something purely ballistically
into orbit. You might be able to do something
fancy with aerodynamics to deflect the projectile
away from its purely ballistic trajectory; or you
can of course use additional thrust to alter the
trajectory.

All of which could be discerned by watching a few 1960's/70's era cartoons. Throw something up, it comes back down. Throw something hard enough horizontally and it flies around the earth to hit you in the back of the head.

I welcome all the attacks. Not as much fun here without them.
So, it is not that inefficient, or at least no more than a rail gun.
Good thing is it does not require expensive capacitors.

I do not intend to send monkies in those obviously. It is meant
for payload, basic electronics, etc.

I would be worried about G if Darpa had not achieved putting a
guiding system in a bullet. The G in a 50 caliber is
comparable. It goes to 0.3km/s in 0.5m. You can put a guide
system to put it in orbit or have a space shuttle catch it.

//It seems like a lot of trouble just to build a gigantic PIAT.// Didn't the PIAT have a reputation of being as or more dangerous to the operators, as it was to the enemy?

...Probably an apt analogy. Look, I'm not saying the idea's a bad one - I suppose I'm just having a bit of fun here. But I am curious whether you think the science here should be taken seriously, as I think there's some gaps in the analysis.

I've even posted a superficially similar idea, called the explosively confined gun barrel. Which was my idea for concentrating explosive energy into a projectile, but without switching to, and then back from, electrical/magnetic energy.

There is no science here. There are assumptions and
calculations. This is the simplest analysis for this concept. The
details are I am sure more than any theory can handle. It would
have to be tested.

Concentrating explosion is nice, but you will be limited to mach
speed, 0.3 - 1.5 km/s dependibg on gas.

//but you will be limited to mach speed, 0.3 - 1.5 km/s dependibg on gas// - Ah, no. Even bullets in barrels aren't confined to that.

An EFP (we've done this before on this site, go look up explosively formed penetrators/projectiles, the wiki article is good enough for a start) can easily achieve 4+ km/sec, do so reliably, and are reasonably efficient at putting holes in things specifically designed to be hole resistant.

Similarly, the payload of a rocket is not limited to the exhaust velocity of the propellant - it's the compounding nature of the rocket equation that limits velocity.

I would contend that some clever arrangement of EFP's/rockets, explosively confined gun barrels, etc ie directly mechanical means would be simpler, cheaper, more efficient and more likely to work, as opposed to a system such as you are proposing, which exchanges mechanical energy into electrical and magnetic, and then back to mechanical.

Hmmm interesting. It does say the EFP launched a 6 pounder at
2km/s. Imagine the G on that one. That conflicts with what I
know and what Wiki writes on light gas guns. Heck, maybe thete
is some quantum physics going on.

Either way, I think 4km/s is your limit with an EFP. At least until
proven otherwise. I do not claim mine is more efficient, but it is
one option out there. There is always the HARP cannon too.

I don't see how an unpowered projectile could ever be launched into space. The drag from the thick atmosphere near the surface (even from a tall mountain) would so large that the initial velocity would need to be insane. In all the projectile launch proposals I've seen, I've never seen any discussion of this issue, besides maybe a cursory note hat they'll need to improve heat shield technology. Considering that an orbital vehcle reentering the atmosphere rapidly decelerates and get extremely hot when hitting the upper atmosphere, makes any attempt to penetrate the lower atmosphere at a much higher speed seem completely ludicrous to me. It seems like you've got to traverse the lower atmosphere relatively slowly then accelerate as it thins out.

I think that, if the described process did manage to get something moving at 14 km/sec, tidal forces and induced heat from magnetic flux would ensure that what came out would be a not-particularly-well-directed plasma stream.

//you will be limited to mach speed, 0.3 - 1.5 km/s dependibg on gas//

Velocity is indeed limited by the speed of sound in the propelling gas, but that gas may be *very hot*. The speed of sound is proportional to the square root of temperature.

/The speed of sound is proportional to the square root of temperature./

Perhaps one could induce a lightning bolt, then use the plasma channel as a track for the projectile. The gas/plasma should be much less dense and so offer less resistance.

The bolt might serve double duty in that it could also fill the role of the capacitor in providing juice.

Science is solving the wave equation for the thousand something
particles that erupt during the collision of nuclei at near the
speed of light and trying to discern never seen before patterns
in a universe of data or figuring out the meanings of dna
sequences etc. There is no science here or anywhere else except
a
few institutes. The rest is technoogy, a much different
avenue.

I eat at the same place as Yelon Muzk. They have burgers with magic mushrooms.

Technoogy. That's right. What new technology has there been in the last two decades that were truly novel?

Lightning bolt is an interesting idea. I had a similar one. Or you could point 100 lasers from different directions that intersect right before the nose of the rocket to heat up the air. There is a chance you might hit the rocket tho.

The navy slug had about 3% of the kinetic energy that you want to imbue yours with and came out of a timed energy-release, ie: much more efficient process, railgun.