An abstract idea came to mind in this past hour which seemed to present any number of ideas. Firstly, the idea of using an alternative to rocket fuel for extremely high altitude orbital point to point transport, and secondly getting away from conventional fuel sources as a propellant in doing so. For the reader, whom it weren't so obvious to conventional fuel sources such as gas are used primarily for the reason that typically aerodynamic properties change quite significantly in the context of extremely high altitude orbits. For this reason a fixed wing craft such as plane would no longer have the lift of air on the wings allowing for a craft to stay aloft at conventional speeds at such altitudes. Here in the rub, is the application of Newton's Third Law. Here the departure of ignited rocket exits gas which forms a thrust for the vehicle providing necessary lift, which achieving higher orbital speeds provisions the craft with a lengthier orbital stay (taking advantage of centripetal acceleration) in this equation which counter acts the gravitational central force on such craft. Thus in the case, of extremely high orbital physics, little to none of the properties of aerodynamic flight apply in so far as keeping a crafts altitude. Now the fun stuff. Firstly it should be stated that the ideas aren't necessarily bounded in the context of practical engineering by today's standards. More so, I'd view this with a degree of abstraction.
The ring. How to keep a ring aloft spanning the arc length of one earth revolution without rotating it for centripetal acceleration. Is it possible? I thought of this in the context of summation of ring whose mass were continuously distributed exactly the same throughout the entirety of the ring track itself. Thus if placed at a certain high orbital altitude the tendency of gravity to pull the ring into a state of contraction would provide equal and opposite translated force at on diametric point opposite of such point whose force would equally cause contraction force. It would seem if such ring were perfectly equally balanced in so far as mass distribution in theory the ring could stay aloft without rotated motion. Or in other words the ring could remain stationary.
The track system. If the ring could generate electricity in some fashion it would seem even if earth's rotation itself viewed from the standpoint of an electromagnetic generator relative the ring, then something of electricity could be provisioned in some way. The problem with fixing mass transport systems would be in the most obvious case, in equality of mass distribution. A car or ship system tethered to the ring would cause an imbalance of mass distribution. This could disturb the ring orbital altitude which would lead to translated motion in the ring. Thus it would seem two solutions would suffice. The transport craft would need apply some contrary force normal burn to ensure equality in mass distribution alongside the ring, or a counter mass moving exactly diametrically opposite the craft (of equal mass to the craft and payload) would need be applied to balance the mass load on the ring.
Now practical considerations to this:
It would seem engineering an integral structure to span great arc distance as mentioned would be exceeding to today's standards in engineering. Consider that the world's tallest buildings are no more then 5000 ft high, and then consider the arc length across the globe at such altitude and there is no comparison in the required engineering necessary to build a system of this type. Secondly, how to sequentially build the structure without huge thrust payload expense to balanced completion, and then considering the tolerance for error and management for corrections to the system. Nothing built is ever exactly perfect, but built within allowable tolerances. Likely such a system would need feasibly have corrections applied to the system?! Additive and Subtractive solutions to the rings mass could provide solution to translation of the ring. It seems this at least shouldn't be the greatest obstacle to management. Structural integrity and building the structure is another problem. Other disadvantages to this system, is the very fixed nature of transport service. Obviously the ring is unlikely to be translated in orbital normal alignments since this would require huge amounts of applied force. Thus ring itself say at an equatorial alignment could be far from servicing a flight from LA to Paris. Here you'd be dropped off at some position in the Pacific centered thousands of miles south of LA, and your launch from Paris would require a docking in the Atlantic west of Gabon. In other words, something of short hop high orbital flight would apply, or conventional flight required just to get into position. Even if the ring were aligned in degrees of tilt the same would be true.
The even more advanced solution a network high altitude grid ring grid. Now imagine abstractly building a grid like structure whose mesh structure were an earth only scaled outward even greater such that the grid had a mass distribution applied equally throughout. It would seem something of logistical transports problem could be solved and made more practically as in the an interconnecting track grid structure. The simplest solution to the connection problem then could be described neither moving in scaled equatorial based arc lengths, but moving in scaled mid latitude arc lengths alongside a longitudinal arc length traverse. It would seem the greatest obstacle and potential downfall of this structure were the sheer out of this world feat in construction (in terms of cost), and in terms of engineering complexity. The more complex a system is the more problems there are likely to arise in such system. A caveat to the alternative single ring track. It would seem, at least a disconnection once have reach peak orbital velocity could mitigate the necessity for re entry slower longitudinal point to point connections problem. Once the craft has achieved maximum orbital velocity, it could be disengaged from the track and then native rocket systems could provide normal burn thrust for orbital realignments. Thus at least when coming from Paris, one wouldn't need to have to traverse thousands of miles north for the jaunt, if the obit normal burns were provided to the craft then disengaged from the track. So what additionally advantages of extremely high orbital altitude track system aside from other stuffs mentioned? Firstly the lack of atmosphere makes for extremely high speed travel (as in the case using conventional rocketry) where air drag is generally non existent. Secondly, the track system provisions alternatives to rocketry for propulsion. Since it is that the Newton's third law can be applied without kinetic motion through exhaust (via burned fuel). It seems to me that energy use for propulsion here could be applied cheaply (outside of holistic considerations to overall maintenance and building/design/materials/labor/management costs). Ideally if structural mass could be scaled in such a way, problems of building could be solved here? Consider, a track centrally no greater then the diametric radius of a flag pole or less, and hollow core in design, the added problem is computing structural load throughout the system?
Building the equatorial ring:
The immediate and easiest solution that I could think of actually does make use of centripetal acceleration to mitigate fuel load costs, and provisions less problems for design engineering integrity here. In this problem since centripetal acceleration mitigates load on the structure load balance can be considered. Here, an automated assembler could fashion the structures. I imagined something as simple as a machine fed materials and doing this in the process of something like a pipe extrusion for a given desired arc measured appropriately for desired arc curvature. Additionally the lift cost problem could be solved if manufacture of raw materials were done on Earth's moon (where propulsion materials lift cost were lessened). Building longitudinal rings for the mesh structure seems more difficult in the engineering sense, and more so rings designed at various degrees of orbital angles an easy to achieve prospect. This also frames a difference in terms of the point to point travel by docking windows, since a rotating ring system that were defined hub spoke at two equatorial points. Ideally it would seem if launch windows for docking were introduced into the system, neither would a craft be required to provision additional fuel burn to achieve the orbital speed of the ring track at a desired latitude. Thus at least achieving orbital alignment on the part of the craft, and then having a system for docking the track without the necessity of achieving the tracks orbital velocity in reducing conventional fuel costs. Once having connected to the track, alternative propulsion is applied to match the tracks orbital speed. Systems management of a non geo stationary track system does add, however, added consequences of travel launches in meeting to optimal considerations for docking.
The additional problem physics of motion of the ring is that its circular having no elliptic eccentricity, mass load imbalance of the ring should lead to consequences, however, of differences potentially overtime in altitude periapsis (PE) and apoapsis (AP). Re balancing the ring in theory means translating the ring by applying correction mass at apoapsis (or translated normal thrust...applied in the direction of the gravitational force) in this case..
The biggest obstacles in space flight/navigation here, were low velocity transfers (well below the velocities necessary to maintain orbit or even intercontinental sub orbital extremely high altitude flights), also bearing to the craft's stability. Ideally point to point transfer here aims to utilize ring transport neither as a total solution in the terrestrial sense, since it neither considers the ground to orbital docking problem, but adds to the ranged enhancement of long distance/semi permanent/permanent orbital flight. Here if conventional rockets could be designed needing less fuel payload, the ring would enhance satellite flight by providing intermediary to final sequence lift staging for orbital transfers. In simulated experience, however, it seems much easier to achieve orbital plane transfers once orbit were established but neither under combined circumstances of navigation and lift together.
Other ideas in design of simpler construction involve shorter arc lengths as opposed to entire arc rings of global span. Here one would need compute the desired arc length so as to provision (in the case of human transport) comfortable acceleration, and then necessary to achieve reasonable sub orbital to orbital flight. This would be equivalent to the arc distance typified for burn accelerations ranging for sub orbital to orbital flights, since the track itself were the primary energy source for acceleration. In terms of altitude management, the problem is changed, since the arc spans means the tracks structure were as a great. The track could also be used, for instance, a re entry jettison, which simultaneously provides aid to management of AP/PE altitudes. Certainly the cost for materials in construction would drop here even, but disadvantages to such a system also means that tracks of lesser lengths would translate into less frequent transfer windows. Permanent orbital payloads transfers compound to the difficulties of AP/PE altitudes management likewise. It would seem problematic to all this were Newton's third law, since translation of kinetic energy inevitably leads to the consequence of the partial track having lost altitude and some manner conventional thrust/lift necessary to re balance permanent orbital flight for such structure. In other words, a partial track could be seen in this light as being merely equivalent to as nothing more then energy storage (or something like a electro magnetic to kinetic battery), served to limited purpose without some means of kinetically recharging. Ring AP/PE altitude management, on the other hand it seems at first thought in theory to mitigate the problems associated in the partials case. The track could potential develop negative delta velocities, but all these problems could be solved involving negative delta v intercontinental flights balanced with respect to positive delta v flights the same could be true in the partial rings case? If you've ever simulated negative at low extremely high altitudes, however, energy use is much greater for negative delta travel alongside additional problems owing to Earth's relative angular momentum.
Other potential uses: Other potential uses are lift assist systems. Unlike terrestrial stationary towers. Moving cranes could be attached at diametrically opposite points where mass load balancing were applied for lift, or in other words using the ring as a space crane. Important here since imbalanced mass loads would lead to some measure of AP/PE altitude loss. Here the attached crane would be tracking to earth's equatorial rotation speed (assuming the ring were perfectly situated such that all points of the ring were intersecting Earth's equatorial plane), otherwise, one would need track terrestrial rotation by latitude to ensure that both cranes were situated diametrically opposite for mass lifts...or in other words schemes where intersections with the equatorial plane were intersecting by 2 points, would require more complex rotation tracking models. Inter stellar and intra stellar staging possibilities? It seems if a ring could be designed to move in a staging alignment plane, devising a system of three g-balanced mass rings with two rings made to be moved to a given alignment and mirror alignment plane, potentially the outer track of the ring could be staged for launching craft, albeit at the moment one would need to simultaneously jettison two mass loads, one counter mass load that were stage launched simultaneous to a given craft. Ideally I imagined such mass could be anything as long as its distributions were approximately uniform to that of the launched craft. Technically one could devise something of a recapture system here I'd imagine albeit reaching high centripetal acceleration speeds could make more problematic for the amount of input energy into the mass recapture system on the dummy mass load. What makes this interesting is that, in theory, one could build (as long as the ring were strong enough with stand the mass load at any given point on the track of radial force applied) ejection velocities. Both masses would need to travel again at equal rates of speed positioned radially diametrically opposite and ejected at the same time. Potentially, this could serve of enormous benefit to reduction of fuel costs (saving the rest for correction burns or a return trip home) assuming another such ring hadn't already been built on a receiving celestial body. Additionally, two other counter mass loads would need be synchronized similarly on the the mirror plane, and launched simultaneously as well. All such mass would need be applied in equal relation balancing gravitational load on the ring so as neither inflecting AP/PE altitude loss. Obvious advantages to such a system, were reduction of fuel mass payloads on a given craft, albeit at the expense of requiring several times the initial input energy for launching a given craft, if it were possible to create recapture systems which convert kinetic mass energy back into the system, however, perhaps energy recovery could be done here?
Leading to a final conclusion: It would seem interesting if a future of space flight were defined neither the albeit common use of propellant gases, combinations of electric lift systems, coupled with electric high altitude orbit lift staging systems, one should hope a diversity of travel technology solutions should exist...while at the moment space flight is not something given to the ordinary everyday human experience, a potential future may consider alternative technologies to conventional rocketry an important step with respect to mass space flight transportation especially in consideration to environmental concerns, I believe, conventional rocketry as a mass transport system for larger planetary populations will always be limiting especially with respect to climate management issues.
Extensions of these ideas: Inter stellar staging systems could be built at some place in solar system, or potentially at extremely high altitude Earth orbits and so forth, or built around moons, for instance, that have re scaled rings of very diametric sizes. I imagined a cheaper one that wouldn't be unlike particle accelerator systems found here on Earth, for example, that applied in principle the same type of acceleration principles. Advantages here being that less input energy required in orienting a given structure to a respective alignment plane, and then secondly, allowing for low cost maintenance and building in general. The idea that a myriad of power sources could be used in launching the craft...for instance, consider fusion/solar/ sources which are converted to kinetic propulsion. Again, this removes the need of load bearing a given craft with significant fuel mass for a given journey, but for payloads carrying humans, gravitational load experienced under centripetal acceleration is a significant problem since.
Some interesting basic physics here to consider. We neglect mass in the computation of the ejection velocity, but we will use in principle gravitation experienced at sea level here. I'll use meters here for computation then given the km/h conversion. First g at sea level on Earth is around 9.8 m/s^2. The centripetal acceleration can be found using the formula a = v^2 / r. Let's assume our launch ring is 100 km in radius which has a radius 100,000 m. Lets assume our launch is given at a discomfort of no more then 3 g or 29.4 m/s^2, then our equation becomes 29.4 m/s^2 * 100,000 m = v^2 which means v = 1714.6 m/s or at an ejection of 6172.56 km/hr. Now let's set our ring at Earth's radius which is 6371 km or 6371000 m in radial length. Then we have v^2 = 187307400 m^2/s^2 and v = 13686 m/s or v = 49269 km/hr. Thus we can see the bigger the radial armature of the ring, the more instantaneous velocity we can be build more comfortably into our given system without causing as much passenger discomfort. The maximum gravitational load human occupants (through training and screening) can receiving is generally around 9 g 's...we'd like to more ideally keep this to no more then 2 or 3 g's and preferably 1 g, however for load. For an Earth based ring, but at 100 km above Earth, we'd have a maximum ejection velocity of around (for human occupants) 49655 km/hr or 13.8 km/s...here escape velocities from Earth is given at 11.186 km/s which is defined as the necessary velocity from the surface of the Earth.
So what sort of ring structure would be needed to bring a craft up to the speed of light in terms of radial distance? We'd assume a comfortable acceleration load that were at a maximum of 1 g would be approximately
61389.065412275515 AU or 1256 times greater then the distance from the Sun to Pluto at Aphelion, or in other words, your turn radius is far from being on a dime!
Now a very crude volumetric, materials construction analysis!
Just how much material might be needed for our track. Without further estimations on the stength of materials but some crude renderings here, we'll use the geometry of the torus for our approximation.
The interior volume of a torus is given by the formula, 2 pi^2 R * r^2 where R is the 'Major" Radius (e.g., the altitude from Earth's center to the center point of the rotating torus track), and r is "minor" Radius (e.g. the cross sectional radius of the rotating torus track). Neither computed, however, for the effects of length contraction approaching relativistic speeds....the effects of a moving length, for example of an object 1 m in length at 3x10^7 m/s is 99.5 cm. Formulation here l = l_0 (1 - v^2/c^2) where l_0 is the stationary length of such object and v is the velocity of the object and c is the speed of light (2.998 x 10^8 m/s). Noticeable effects of time dilation and length contraction occur when speeds are in the order 10^8 m/s...on my part wholly speculative, or at least not considering a complete treatment, or in other words, I am not sure if the effects of length contraction can be wholly neglected in the scope of this problem at higher orders of velocities. We'd also note the craft were also technically moving in a non inertial frame of reference (non rectilinear motion).
Here we'll actually compute the volume for a hollow core torus structure, assuming that the track neither need be completely solid. In this case, we can compute the total volume for a 1 meter "minor" radius cross section, with interior walls approximately 1 feet thick.
our total volume is given by
19.739208802178717237668981999752m^2 *6478100m = 127872568.5413939481373434322926 m^3
our hollow volume is given by
9.5400196212877326642658215141854 m^2 *6478100m = 61801201.108664060972380418351045 m^3
where 0.6952 m hollow "minor" radius
subtracting the second volume from the first yields
66071367.432729887164963013941555 m^3 for this design
pure titanium is at a solid density of 4.506 g·cm−3
which is 4506 kg/m^3
this would require 297,717,579,702 kg of titanium for our construction (I hadn't considered the density for alloys which would likely be the case)...very crude approximations here.
or in other words
328177455.566548 short tons of titanium for this project!
Total world production here on earth in tonnes for Titanium runs at
6700000 tonnes per year
If all world titanium resources were devoted to this track, it would take us 49 years to amass enough titanium! Maybe its still feasible...still have to deal with the cost for getting this stuff aloft! :)
If you wanted to do a bit more research on the alloys (likely used) you'd likely want to look up density informations of the respective materials for Grade 6 Titanium Alloy (common aircraft and possibly? spacecraft materials manufacturing). This contains 5% Aluminum and 2.5% tin.
Aluminum density is 2.70 g·cm−3
Tin density ranges from
5.769 g·cm−3 to
7.365 g·cm−3
depending on the type of tin used.
or an overall density around 4.48 g/cc
The following link provides some additional materials information if you wanted to get more comprehensive with materials study and determine what minimum materials were needed according to any number of potential load rigors that would apply to the structure.
http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MTA520
Other materials ideas include
carbon nanotubes. Which could significantly reduce materials requirement for production, and likewise are formed from more common elements...meaning more abundant base of carbon exists relative to titanium. It would be noted that
its specific strength of up to 48,000 kN·m·kg−1 is the best of known materials, compared to high-carbon steel's 154 kN·m·kg−1.
Likely a structure of this type might be represented in a torus of honey comb like lattice work, its also interesting to note that it has a high magnetic moment (read the torus section) for potentials in power generation.
Some additional thoughts: If it were possible to extend the radial launch armature extending out from the torus itself. The pervasive problem with sending humans in flight is centripetal force load on the occupants here. This will always limit the scope of such a launch assists in building escape momentum
at extremely high velocities. Thus for near speed of light travel, likely the process of building velocity for inter stellar travel would likely require on board propulsion systems which would be cheaper...even in the other cases, it may be less expensive in housing large propulsion and fuel systems, but it seems tantalizing at least in so far as building high ejection velocities for crafts that aren't carrying humans. The end problem is orbital insertion, likely integrated capture insertion systems would need be developed on a receiving end, or again making use of in housed propulsion methods would avail as a likely conventional solution. In theory if building high velocities weren't a problem to damaging equipment and craft, there is still the problem that conventional propulsion systems would lack necessary fuel on a receiving end for the insertion braking...likely resorted to the same methods used for insertion capture on a receiving end, where on board propulsion systems are used as navigational guidance to the capture system.
