A Reply to "Can Hyperloop Be Adapted As Launch Loop?"
- Most recent revision Saturday May 14 1100am US Pacific time (1900 GMT)
The simple answer to this simple question is NO.
Hyperloop is Elon Musk's idea for running hyperspeed trains between San Francisco and Los Angeles in a vacuum tunnel.
Hyperloop won't work as described, for many reasons; the main reason is turn radius. There are a lot of east-west mountain ranges between SF and LA, seismically unstable, so it will not be practical to drill through them. Going around them involves a lot of wiggles to avoid terrain, and the maximum turn radius of those wiggles limits speed to well below Shinkansen speed. The idea might be patched by running the tunnels off the coast, underwater, but to the average reader that sounds crazy. Unless the northern terminus is Gilroy and the southern terminus is Fresno, hyperspeed trains are incompatible with California topography.
The maximum Shinkansen speed is 320 km/h (89 m/s) and the minimum turn radius is 4000 m. If those occur simultaneously (probably not, the trains probably go slower on track segments with curves) the radial acceleration is 1.98 m/s² or 0.2 gees. That's accommodated by banking the track, and tracks could be banked more for higher gee acceleration. The tightest turn in I5 is a 600 meter radius near milepost 207 at Lebec, though it looks like it could be gentled to 1200 meters with some digging. The average speed of the hyperloop is claimed to be 670 km/h (186 m/s) , top speed 1200 km/h (333 m/s); the gee forces would be 2.9 and 9.4 gees respectively. Of course the pods must slow way down for these curves, but that adds to the trip time and reduces average speed. With a 1 gee limit through the turns (that would be back and forth and up and down, very barfogenic), the speed would be limited to 108 m/s. From milepost 215 at Grapevine to the south end of the mountains at milepost 161 is 54 miles or 87 km, so travel time through this section alone would be 13.5 minutes.
Ignore the twisty mountains south of the Bay area, and assume the other 480 km are straight, with 1 gee acceleration and deceleration to speeds up to 333 m/s; total delta V time = (333.3x4-108x2/19.8 = 78 seconds added onto the 480km/.33km/s = 1440 second trip time. Total time 1440 + 68 + 805 = 2313 seconds = 39.5 minutes. That is only 10% longer than the claimed 35 minutes, but it involves double the gee force and "jerk" of a roller coaster. Planes take longer, they also make much slower turns, 2 to 3 minutes to turn 180 degrees. The 1200 m radius turn at 108 m/s is 35 seconds, which is more than 10 times "jerkier". Somebody was sleeping through physics class.
Besides, as we transition from the Combustion Age to the Second Information Age, we will use predictive-adaptive telepresence to get around, at the speed of light, not at the speed of weight.
Surface Coilgun Launch
The first good technical description of a coilgun space launcher was in Edwin Fitch Northrup's Zero to Eighty, published by Princeton's Scientific Press in 1937. Northrup built some formidable prototypes, much more impressive than O'Neill and Kolm's benchtop "mass driver" forty years later. Earth-to-space coilgun launchers have 4 big fails:
1) Atmospheric density is exponential with height. Air at the Earth's surface is a trillion times denser ( click here for diagram ) than the air at 400 km ISS altitude, and ISS orbit drag is inconveniently high there. Imagine trying to dive through 10 feet of rock at mach 30. Air drag is halved at the top of the tallest mountains ... 5 meters of rock. You will need a very dense vehicle to penetrate that, even with substantial velocity loss. Rockets climb to very high altitudes before going full throttle, and lose about 1000 meters per second doing so; a full-velocity-from mountaintop launch might lose "only" 2000 m/s IF the vehicle is very long and skinny and dense.
- air density at 80 km altitude, where vehicles exit the launch loop, is 10 ppm of surface density, and 30 ppm of Everest summit air density. Vehicles slow down a few meters per second exiting the Earth's atmosphere at 80 km altitude, a few milligees of acceleration. At 8 km mountaintop altitudes, similar vehicles would be smashed to shreds by horrendous gee forces and insane turbulence. Reentry occurs at much higher altitudes.
2) curving up the slope of any mountain will subject you to horrendous gee forces, far worse than a hyperspeed train. The centrifugal acceleration formula is V2/R - for a 30 degree exit angle at 8000 meters altitude, the turn radius is 75 km. V = 10000 m/s, R = 75000, so the acceleration is 13300 m/s2, of 13 hundred gees.
- 3) Coilgun electronics cost scales as the payload mass times the velocity cubed - the electronic drivers at the end must pulse with enormous power levels. If a 1 kilogram 100 m/s benchtop coilgun costs $1000 (WAG numbers for the Kolm/O'Neill 1974 Princeton model), then a 10000 m/s 10 tonne mass driver would cost 1e13 dollars.
- 4) If you did manage to get to orbital velocity at a 30 degree angle to the earth, you will be in an elliptical orbit with a high apogee, and a perigee deep below the earth's surface. You need to carry a rocket for apogee insertion into a higher, more circular orbit, somewhere in the van Allen Belt. If that rocket fails, you will slam into the ground about 2 hours later. Horizontal launch means horizontal reentry, much gentler though still challenging.
Why is Rocket Launch Expensive, Anyway?
Rocket Launch is very difficult, at the bleeding edge of mechanical possibility. Rocket launch involves the hard work of thousands of clever specialists, who want to be paid. If rockets fail and fall on a city, they can kill many people, so a big chunk of launch cost is insurance. We launch about 400,000 kilograms to orbit per year. Divide salaries and other costs by kilograms, and you get a huge $/kg number, even larger than what launch customers actually pay. The difference is paid by government subsidy, because domestic launch contributes to national prestige. If you want cheaper launch, go to India or Russia, where the clever specialists work for tiny wages.
Or, increase launch volume. 10x the volume does not need 10x the specialists, more like 5x. That cuts the cost per kilogram in half. It also adds experience and reduces accident rates, lowering insurance costs. If you can't imagine 10x more applications for expensive space launch, get a better imagination, or go to http://server-sky.com and borrow mine.
That said, while I would love to have cheap rockets. I would also like free ice cream and a pony.
Developing practical and reliable rockets cost the world trillions of dollars ... and thousands of murdered prisoners in the Nordhausen V2 factory. Millions of prisoners starved in concentration camps, because harvests were turned into alcohol to fuel the V2s. If we had started with coilguns in the 1940s, we would have evolved to launchloops half a century later, and we would be launching billions of kilograms into orbit per year in 2016. We are paying dearly for our war-making belligerence and spiteful 1918 Armistice, the ghosts of millions of murdered slaves, and our slavish devotion to the ideas of the Nazi monsters who murdered them.
Launch loop provides altitude, momentum, and energy, using kinetic energy and momentum stored in a 5 centimeter diameter iron rotor (3 kg/m ) moving at 14 km/s inside an evacuated sheath. The payload drags magnetically on the rotor, and wastes more than 60% of the energy, which heats the rotor to a dull red. Launch energy can be restored over minutes to hours with high-efficiency linear motors on the surface, from ordinary power plants, so even with the waste, the energy cost of launch is under $10/kg.
However, launch loop is an enormous, expensive machine, costing tens of billions to build and develop, and it is militarily vulnerable, so the military won't pay for it. Launch loops (and other more fanciful and physics-challenged ideas) won't happen until we build a market, which means paying attention to what people want. In addition to physics, many space enthusiasts are unable to pay attention to other people, and will die of old age without the resources to accomplish much, sigh.
Similar loop technology can also be used for very inexpensive power storage and high efficiency intercontinental power transmission, see PowerLoop . That is how loop technology will be developed, storing the intermittent off-peak-demand power produced by solar farms and windmills. The Power Loop will tie together the world's power grids, so that an attack on any nation involved will damage the economies of all other nations involved. That Pax Energia will help create a world peaceful enough for launch loops to survive.
But that will be insufficient. Yes, launch loops will launch megatons per year, cheaply. However, they make no economic sense in a world that launches less than a kiloton per year. Find new applications for rockets first, for example, http://server-sky.com. The best way to accomodate high cost per kilogram to orbit is to develop products that produce high value per kilogram in orbit. Server sky is a proposal for modern solid state satellites, 1000 times lighter per value produced than a (profitable) state-of-the-art GEO communication satellite. If the value is high, and the market is large, a 1000 times lighter satellite might be launched in quantities millions or trillions of times higher. That will stimulate the total launch market enough to drive strong cost competition. That will create opportunities for other new space products. Until we have much higher near-term demand, we will not earn the resources to address supply side improvements, and get on a healthy cost reduction curve.
Another option is space sourced bistatic airspaced radar. Starry eyed futurists have yammered about space based solar power for half a century, but the first step to a practical system is vastly larger than any other first step that humanity has ever accomplished. Radar illumination levels are tiny compared to a rectenna, and radar pulses sourced from orbit make radar receivers vastly easier. From there, we can scale up; first lighting up the entire global airspace (no more missing airliners!), then when we DO start shipping grid power from space, the sidelobe radar interference (now mostly ignored) will become a welcome necessity, not a showstopper.
When we are launching millions of tons to orbit per year, when there is enough total market to support many launch loops (so a few can break or be taken out of service for maintenance), and when there is a global powerloop grid to bring power to launch loops or distribute power from space solar power satellites, then (and only then) will it make sense to build launch loops. If we are serious about a space-based civilization, and move more cargo between earth and space than we do between seaports now, we must have non-combustion alternatives to rockets. Until then ... rockets work.
Yes, it will take a while to do all that. It took 4 billion years for life to conquer the earth. It will take more than a few generations for life to conquer the solar system. We've wasted three generations pretending rockets would get a lot cheaper, and that we can do it without an inclusive global effort. Want cheap launch? Invite the rest of the world to participate, share what we know, and listen to their wise suggestions.
Added note about Startram
This is a coilgun in the sky. Making a coilgun lightweight, and placing it tens of kilometers above the power source, does not make it cheaper.
Any "gun" must keep the projectile/payload on a very straight path. A payload moving at 8000 meters per second encounters 8000 meters of track deviation (from perfectly straight) per second. Consider a 100 meter wavelength, 5 millimeter sinusoidal lateral or vertical path variance (deviance δ = +/- 2.5 e-3m) is an 80 Hz vibration, angular frequency ω = 2 π f = 500 radians/second, acceleration a = ω² δ = 625 m/s² = 64 gees. Somehow, the stiffness of the tube and the guy wires must keep the system laser straight while the vehicle passes through. Launch loop has a similar requirement, of course, but a built-in solution; the rotor is moving at 14 km/s, and extremely difficult to deflect. Indeed it can: segment A can be moving upwards a few micrometers per second, and neighboring segment B downwards, and that can integrate into a large ripple over the 140 second transit from west to east station. However, by adjusting forces to the spacing magnets to the track. vertical and lateral momentum may be exchanged with the track, and with the guy wires as the moving system center of mass passes by them. Both systems will require extremely accurate laser distance measurements to maintain trajectory and stability, and a prodigious amount of digital calculation to compute stabilization strategies, but the Startram lacks a rotor to carry transverse and vertical momentum laterally down the track. It must do these fine-control movements entirely with guy wires, passing through a turbulent atmosphere.
The Gen 2 Startram makes some ignorant assumptions about magnetic fields and superconductors. If the field is 30 gauss (3 millitesla) at 20 kilometers altitude, then it is 12 Tesla at the edge of a 10 meter diameter superconducting wire on the surface - Ampere's law, freshman electromagnetics. Real superconductors fail near such fields - LHC runs at 8 Tesla, and they would run higher fields if they could. Yes, some lab experiments run as high as 30 Tesla, but only briefly, at centimeter scales. Read a freshman physics book, please!