Monday, July 8, 2013

Augmented Back Pack and Other Clothing

During an evening of booze and hockey in the background my friend Andrew and I started to chatting about  an idea for a hackable smart backpack intended to move the backpack from a passive container to a dynamic tool.

In an era of ever cheaper tools for embedding smart tools into watches, glasses, and t-shirts why have backpacks generally been left out of the realm of innovation.  The HackPack would serve as a dynamic platform for makers and users to have access to smart tools.  The minimum components in the HackPack would include an onboard battery, computer or microcontroller capable of bluetooth communication, and readily accessible ports for distributing data/power.  The key feature of the HackPack package is the ability for the tools of the backpack to communicate with smart phones and other devices. The basic kit could be made into a small package according to set standards and intended to augment existing backpacks.  A more consumer friendly version of this concept would come pre-built with a collection of sensors and displays to communicate with the owner.
Figure 1

In figure 1 you see a visual outline of what the HackPack's exterior could feature.  The red lines indicate the placement of EL wire intended to display simple information, ex. someone going for a bike ride at night could have their changes in direction displayed by the character display on the back.  The lights on the strap could be used to alert the user of useful information about the state of the HackPack, whether they have an appointment, etc..  In the side view of the HackPack there are 3 blue squares indicating where vibration pads could be placed in the straps of the back pack.  The pattern and intensity of the pad's vibration would communicate any number of set messages, ranging from telling a hiker where they should be looking for their next course correction, to working with a social networking app to let you know a friend is nearby.  The straps should also have simple button pads to allow users to communicate with the on board micro-controller with out requiring access to an additional tool.  These basic features would be complimented by a collection of attachment points placed on the exterior and interior of the backpack, allowing users to add speakers, electrical generators, environmental quality sensors, the limits would be the imaginations of accessory engineers.

The Spec sheet for this backpack would look something like this

On-Board Computer:  Arduino micro-controller with bluetooth shield, Rasberry Pi computer
Battery Pack:  Capable of keeping computer and accessories online for at least 24 hours and charging a standard 2100 mAh cellphone battery at least 2 times
Communication Points:  USB or 3 wire PWM compatible
Weight: 3 lbs or less for all basic kit components

Additional attachments could include.
Infrared communication system for laser tag and mesh networking
Geiger Counter
Wirelessly accessible hard-drive
Speakers
Electrical generators
Moisture Sensors
Video Camera
Projectors
RFID/NFC sensors for keeping track of interior elements (this idea was taken from here)


http://www.kickstarter.com/projects/phorce/phorce-the-worlds-first-smart-bag
battery and tells you how much battery life is left via bluetooth

http://www.talk2myshirt.com/blog/archives/4197 weight sensing pack

http://gajitz.com/green-to-go-sustainable-multi-talented-electronic-backpack/ artsy fartsy deal

http://www.ubergizmo.com/2010/05/aniomagic-weight-sensitive-backpack/ weight sensing

http://www.treehugger.com/renewable-energy/energy-generating-backpack.html energy generating backpack

http://www.treehugger.com/gadgets/rechargeable-led-backpack-totes-your-stuff-keeps-cyclists-safe.html  illuminated pack

http://www.digitaltrends.com/lifestyle/new-smart-clothes-will-be-able-to-adjust-to-your-moods/ smart clothes

http://thinkmag.net/think/tag/smart-clothes/ more smart clothes

http://healthinformatics.wikispaces.com/Smart+Clothes

Cool Ben Heck design hack for making a turn signal backpack attachment
http://www.engadget.com/2013/07/30/ben-heck-bicycle-turn-signal/


Smarter Jacket
Dynamic EL wiring that "knows"  when the user wants to be seen and when not

bluetooth accessible for easy finding

Saturday, June 29, 2013

Bag Bowl Water for your Dog where ever you need it

Making sure your pet remains well hydrated on a hot day can be a difficult affair, doubly so if you want to pack light for a simple walk around town.  For those fortunate enough to live in neighborhoods that have pet watering stations this isn't much of a concern, for the rest of us, I suggest "Bag Bowl" (totally not TM).  The basic idea came to me while taking my sister's dog for a walk around the Boston Commons.  While there are water fountains it's a little difficult to get a 50 lbs puppy to the fountain's level and I think people would complain if the pup, Georgia, licked the fountain.  My temporary solution was to take a spare waste disposal bag and fold it into a shape that Georgia could drink from.  This worked rather well but it had some faults, namely the weird hand configuration I needed to fill the bag.  The "Bag Bowl" would serve as a light weight frame to support a dog's waste bag, unused of course, for when you wanted to fill it with water or food.  
(Drawings to come)


I realize that it would probably make more sense to have some kind of pouch deal that had a pocket for the poo bags separately, but I like the idea a bit when I came up with it this afternoon and wanted to update my blog.

Wednesday, June 26, 2013

Orbital Rings as a Means of Altering Asteroid Trajectories

Guys seriously guys, I love the idea of mining space.  I mean not like a little serial, I'm being super serial.  Like super duper serial.   

Space resource utilization is something that has started to move from the fields of speculative fiction, to the early stages of corporate development, firms like Planetary Resources and Deep Space Industries are starting to put tangible efforts into advancing the goal of many futurists, moving humanity beyond our earthly bounds.  One critical challenge of space mining developments stem from the need to minimize the energy required to extract a given unit of mass from a celestial body. What this introductory outline would like to propose is a unique means of which to alter the course of a given asteroid or comet to a location that would be useful for future human use, including but not limited to one of the Earth's five Lagrangian Points, Lunar orbit, or high orbit around the Earth.  In the Wandering Across Asteroids article I discussed one potential approach for modifying the orbital trajectory of an asteroid enough to eliminate potential threats to human civilization on Earth, by means of having a large walking robot to serve as a gravitational tug.  I would now like to suggest creating a child design of the gravitational tug walker and the orbital ring concept.
 
Totally Not to Scale Front View


The rationale behind building an orbital ring around an asteroid is very similar to the logic of using the walker approach.  The system would allow for the dynamic application of a significant enough mass near the center of gravity of an asteroid to alter the orbit.  Placing the gravity tug relatively close to the surface of the selected asteroid would be achieved by building and/or deploying a magnetic levitation (maglev) track  at slightly above the maximum radius of the asteroid.  The maglev track allows the counter mass to rapidly position itself along any point of the circumference. The more rapid the ability to reposition the greater the degree of control of the asteroid.  The major differentiation between using an orbital ring versus a walker style close proximity gravity tug stems from the number of moving components required for motion (once the system has been deployed).  A walker would have any number of moving components while an orbital ring, and how ever many cars riding on its track way, could have as few as zero moving parts. * 





*The asterisk here is to let me quickly say that while zero moving parts is nice and all, there is no guarantee that doing so would actually make any real engineering sense, seeing as there are a range of unknown variables that still need to be accommodated. 



Research Stuff


Kinetic Impact Analysis using traditional launch means
http://www.princeton.edu/sgs/publications/sgs/archive/15_1-Koenig-Chyba.pdf

ESA call for deflection ideas
http://www.nbcnews.com/id/50499682/ns/technology_and_science-space/t/got-good-idea-how-bash-asteroids-they-want-hear-it/#.UcamwvnVBsk
(physorg version)
http://phys.org/news/2013-01-asteroid-deflection-mission-ideas.html



NASA proposal for Lassoing asteroids

http://www.nbcnews.com/id/50398762/ns/technology_and_science-space/t/nasa-might-lasso-asteroid-drag-it-orbit-near-moon/#.UcamyvnVBsk

Asteroid capture article (potentially for mars mission)

http://www.euronews.com/2013/04/11/nasa-unveils-plan-to-catch-asteroid-as-step-to-mars-flight/


Asteroid tug boat, giant engine that will strap on an asteroid to change its orbit http://b612foundation.org/wp-content/uploads/2013/02/Asteroid_Tugboat.pdf

wikipedia list of asteroid avoidance tech
http://en.wikipedia.org/wiki/Asteroid_impact_avoidance

another paper on asteroid deflection
http://www.gps.caltech.edu/~sue/TJA_LindhurstLabWebsite/ListPublications/Papers_pdf/Seismo_1621.pdf

http://en.wikipedia.org/wiki/Gravitational_tractor
http://en.wikipedia.org/wiki/Ion_Beam_Shepherd

more deflection options
http://theweek.com/article/index/239846/6-clever-ways-to-avoid-getting-hit-by-an-asteroid

Asteroid capture animation
http://www.dailymail.co.uk/sciencetech/article-2308660/Animation-released-shows-Nasa-intends-CAPTURE-asteroid.html


nuking an asteroid for deflection
http://www.adrc.iastate.edu/files/2011/09/AAS-11-403.pdf

I need to reread this, I don't think this is the same idea as mine, but it might be
http://www.centauri-dreams.org/?p=7431


http://arc.aiaa.org/doi/pdf/10.2514/6.2008-6254




Thursday, June 20, 2013

Knock off Nerf Idea

Fig 1 Nerf N-Strike Elite Rayven
Source:Hasbro corporate page
One of the minor frustrations of many traditional nerf gun designs is the potential for darts jamming.  While newer designs have added special access ports for clearing darts that have folded in on each other I felt it would be cool to put forth my own concept for a dart gun that eliminates the potential for jams and allows for easier reloading to boot.  Instead of utilizing the more common spring clip design used in toys like the Nerf Rayven (figure 1) this design would have each round placed in their own specialized chamber (fig 2)
(I will try to add some more details but right now I need to just get this out the door before I get back to job applications)
One of my favorite ideas in this design is the small magnets embedded in the pink side wall of the clip.  They serve as  way for whoever is using the toy to expand their clip as they are still firing their first clip.  During normal operation the magnets will keep the clips attached with enough force that normal jostling won't allow them to come apart and as each round is fired the next cell in the clip is chambered with the firing mechanism.  As the clip is pulled through and about to expire, a small amount of pressure is applied to the pink arms, forcing the magnets far enough apart that they upper clip can simply fall off.  On the right hand side of Figure 2 you will see the turquoise linear gear teetj that would allow for a worm gear to power the clips through the gun.
Figure 2
So while I like where I am going with this idea, I am going to call this a very basic early draft as there are about 20 things I would like to rethink/redesign for a system that would probably make a lot more sense

Monday, June 10, 2013

Wave Energy Concentration Via Metamaterials

One of the most interesting (for engineering and physics nerds) technologies to come out of the 1990's, while they were first theorized in 1968 it took over 30 years before researchers could develop the first application of a metamaterial, altering the magnetic properties of a material.  As our understanding of metamaterials grows the number of potential uses have skyrocketed.  Articles dealing with creating "The Cloak of Invisibility" have received some of the greatest attention, but some of the other uses should not be ignored.  Researchers have created so called superlenses, earning the name as a result of their ability to see at resolutions once considered impossible  ex. viewing a protein under an optical microscope.  While metamaterials that work within the electromagnetic spectrum receive more press coverage, researchers are also utilizing the underlying physics of the technology to guide the energy of physical waves, including seismic, acoustic, and hydraulic wave-forms.

The ability to guide the energies of ocean waves has tremendous implications, from the DoD's efforts to eliminate energy lost to wave action on Naval vessels to cloaking ocean structures from tsunamis.  What I would like to suggest is utilizing these wave guide technologies into ocean energy production.

The available wave energy from the world's oceans has been estimated to be roughly 2 trillion watts, or enough power to help 8 Del'Oreans to travel back to 1955 (in non-science fiction terms this would be the equivalent of powering 800 Million American households)  While the available ocean energy is tremendous, the sea is also one of the harshest environments for energy production, the technologies needed to provide an affordable generating platform are still being developed.

What I would suggest is using a network of structures intended to focus the energy of waveforms that occur most frequently in a given area.  By concentrating the energy of the waves onto a single point engineers would minimize the number of moving parts and consequently critical failure points.  (see figure 1 below) The site of the concentrated wave action could utilize any number of suggested wave capture technologies.  The concentrated energy of the wave system would also allow for additional safety features on the generating element, further increasing the systems life expectancy.  The likely ecological benefits of using a complex structure as opposed to the guide wall approach used by the Wave Dragon would stem from allowing organisms to flow more naturally around the structure as needed.
Fig 1:  Potential appearance of a the wave generator, (lacking a deep understanding of geometric requirements of a meta material lens the configuration above is arbitrary (my bad))

 The primary rational for having the metamaterial configuration for energy concentration versus the solid wall approach being implemented by the Wave Dragon platform (besides the fact that it would be awesome), is based off a personal theory as to the robustness of a walled approach for a floating platform, it is my belief that a metamaterial structure would allow for more redundancy in the structure, increasing survivability.  Additionally conversations at an MREC conference in 2012 highlighted that the more variable the wave forms a given generator would have to accommodate, the greater the potential cost of the system through outs a given life expectancy.  A metamaterial wave guide would concentrate the force of some of the most common wave frequencies while (hopefully) more chaotic elements would only minimally interact with the platform.  In Figure 2 you can see how the amplitude of the wave grows as it comes closer to the focal point of energy production.
Fig 2 Cutaway view of the metamaterial wave power plant.

The largest concern for this wave generator proposal is that of cost efficacy, while the design is intended to reduce the quantity of moving parts for a given production capacity, the installation of the wave guides is far from a non-trivial component of the overall cost.  That being said with the huge reliability and availability of wave power for coastal communities, it is my opinion that at least some degree of research would be worth the investment.  Accounting for the maintenance of the guide pylons is another consideration as bio-fouling has the ability to drastically alter the geometry of a given wave guide.

The wave generator system should be thought of as a renewable energy deployment platform, not just a hydro-kinetic generator.  The tops of the wave guide pylons could have wind turbines or solar panels mounted on them, transforming them from simple inert structures to more surface area for offshore energy production.  The interior volume of the pylons might also be considered for pumped air energy storage, (an slightly different version of the idea, and one more) as proposed by the MIT Energy Initiative or pumped hydro-electric.  The two storage mechanisms could work in tandem with the pumped hydro being utilized during low tide and the pumped air energy storage being utilized during high tide.  The interior volume of the pylons might also be considered for a micro-server farm, being in  a location with relatively constant sea temperatures (or at minimum cold enough to benefit processor cooling), while not necessarily optimal for all applications, it could serve as a very remote back up location for important data.

TL:DR (what I was trying to say was) energy developers could use crazy geometries to build a structure intended to concentrate the energy of ocean waves onto a small point, theoretically lowering the cost of producing energy from ocean waves

During my research I cam across a selection of articles I didn't necessarily fit into this narrative but they either informed comments to one degree or another or might be useful for further reading
people actually researching into the idea.
This groupd of post docs based in France is doing some work associated with water based metamaterials, but not for wave form concentration (as I can barely understand from their abstracts)


List of other Wave generating technologies

http://mhk.pnnl.gov/wiki/images/5/58/Wave_Energy_Utilization.pdf

http://en.wikipedia.org/wiki/Wave_power

http://www.icrepq.com/icrepq-08/380-leao.pdf

http://www.oceanrenewable.com/wp-content/uploads/2007/03/futuremarineenergy.pdf

Using Metamaterials for Hiding sea craft from ocean waves
http://news.sciencemag.org/sciencenow/2011/07/a-submarine-that-doesnt-make-wav.html

http://news.softpedia.com/news/Invisibility-Cloaks-Could-Hide-Ships-from-Waves-256723.shtml


Alternative wave generator
http://www.sciencedirect.com/science/article/pii/S0141118712000648
http://en.wikipedia.org/wiki/Cycloidal_Wave_Energy_Converter

The Metamaterial that I used as a reference (now I realize as it was a cloak design it was probably a poor choice, but you know... I was making it up)
http://nanopatentsandinnovations.blogspot.com/2011/01/newly-developed-cloak-hides-underwater.html

Background research on wave energy
http://www.see.ed.ac.uk/~shs/Wave%20Energy/thorpe%20review%20.pdf



Friday, June 7, 2013

A Kit of Parts for Front-line Manufacturing

The various branches of the United States Department of Defense have all started to make large pushes into developing unique capabilities in rapid prototyping capabilities.  In entry, Wise Welding Warriors, I noted how rapid-prototyping was being used to drastically reduce the turn around time between war-fighters finding critical problems in their ability to operate effectively and developing material solutions for that problem.  The logistical benefits of being able to build and repair components closer to the front-line are already impressive and will only become more useful as the capabilities of the various technologies mature.  Currently relatively simple mechanical solutions can be created by Rapid Equipping Force's  ELM facilities, the ability to integrate electronic components into design solutions will undoubtedly serve as capability multiplier.

Open source electronics platforms including the Arduino and Rasberry Pi have taken the maker community by storm allowing amateur inventors to create technologies ranging from automatic plant watering systems, to  pens that work in 3-D, to prosthetic prototypes, and semi-autonomous vehicles.  The consistent characteristics of these platforms, working in tandem with their opensource nature allows for creative talents to avoid reinventing the wheel, but instead refining a technology for a given need.  The Lego Mindstorms platorm has also unleashed unimaginable levels of creativity from its user base, by being both open ended in use and reliable.  This kind of open source creativity/capability added to ELM style operations could allow engineers anywhere in the world to develop advanced solutions for conflict regions around the world.

Within the realm of robotics technologies creators could know that they would have access to a micro-controller and assorted components that from the get go would be capable of being formed into traditional small scale land based robots or quadcopters.  As efforts were added to the platforms engineers might develop additional remote sensing capabilities or robots intended to aid local farmers in optimizing water usage for irrigation, aiding in good will missions to counter insurgent activities.

 A set database of standardized components as well as a shared database of tips and tricks would mirror current open source civilian projects.  This similarity would be extremely intentional, ideally the components used would also share traits with products already available to civilians.  For sake of security concerns there would be some rather significant differences between the platforms used by the Department of Defense and its allies and more traditional open source ecosystems.  The development community would need to be multi-tiered with increasing levels of security needed to access more sensitive aspects of the community portal, extremely general community work would work through a civilian accessible web host, while moderated the platform would most likely benefit from minimizing any heavy handed oversight by military command (voiding extreme scenarios).  At a higher tier, only recognized academic groups, contracting firms, and military personal would have access, sharing would be less immediate but still reasonably open.  The highest tiers would likely only need to concern a vetted group of developers who would be responsible for communication protocols and the source code of the devices.  This tiered system of development would work to prevent potential hazards highlighted in the Armed Forces Journal article "Print when ready, Gridley", where the author voiced concerns of design databases being hacked and mobile factories are transformed into a digital fifth column.

The hardware utilized by military personal would ideally be as similar in design as possible to the platforms available to the public, with key exceptions in the ability for components to communicate on military channels, which for obvious reasons should not be put out for general access, unlike many drone transmissions in Afghanistan.
DARPA has already begun work on developing open platforms for organizations to have a common base package for building a product around, the ADAPT sensor system is serving as the flagship technology.  The sensor package has already been used as a ground sensor and the control module for a quad-copter.



Monday, May 27, 2013

Mobus Bridge: A(n) (Im)Possible City in the Sky

Mobius Bridge is a mega-construction structure for the 31st century, built above the Earth's equator Mobius Bridge would be ring structure serving as a habitat platform.  Unlike many space rings proposed in science fiction works like Larry Niven's Ringworld the Mobius Bridge would not use centripetal force to provide the source of gravity, instead the Earth's gravity well would provide the attraction force.  For the Earth to provide the pull of gravity more naturally to the body of the Mobius Bridge, the structure of the Bridge would need to orbit around the Earth with the same angular velocity as the Earth's natural rotation.

What the the Orbital Rings might look like
Source: http://io9.com/if-earth-had-a-ring-like-saturn-508750253
Traditional approaches to placing objects in Earth Orbit would make it impossible for a space based structure to provide a gravity force not provided by some kind of additional acceleration put on a selected object.  The design of the Mobius Bridge would require some unique solutions to keep the ring structure both in orbit and having objects placed on the Bridge still feeling the downward tug of gravity.  Several potential solutions could be considered for keeping the Bridge suspended.  The first potential solution considered would involve using a collection of tethers linking up with counterweights, similar to the solutions suggested for building a space elevator.

        For a sufficiently low mass bridge designs a massive collection of thrusters would provide the necessary counter forces to keep the Bridge in orbit.  Unfortunately by the time the station got big enough to allow for a proper habitat the energy requirements to keep it suspended in space would only make sense for a species with near god like levels of energy production and control.  The most likely solution for keeping the Mobius Bridge in orbit would be to have the structure be made from two primary components.  The habitat segments of the Bridge would lazily drift over the Earth's equator maintaining the same day night cycle as the ground below.  Within the frame of the habitat would be one or more massive magnetic orbiting rings.  Each of these orbiting rings would serve as a track-way for the habitat structure to ride on, similar to magnetic levitation trains here on Earth.  The dynamic interaction of the forces between the inner rings and the habitat ring create a situation where the net balance leaves residents of the habitat ring experiencing the slightly reduced pull of the Earth's gravity, several hundred kilometers above the ground.

Roughly speaking the force of gravity on the Bridge would be a result of the tangential velocity of the ring and  its distance from the center of the Earth.  (for those who aren't power nerds, this means you are accounting for the tendency of objects being spun to pull outwards and that the force of gravity gets weaker at a distance)  To make the calculations easier, the primary sources of accelerations can be separated into two primary equations.  The biggest impact on the gravity felt by objects in the habitat ring of the Bridge would be the distance between the bridge and the Earth.  The force of gravity between two objects can be calculated using Newton's Law of Universal Gravitation, (see Fig 1)
Figure 1:  Newton's Law of Universal Gravitation
In this equation the variables are defined as follows
Figure 1A
F is the force of gravitational attraction.
G sub c is the gravitational constant (Fig 1A).
M1 and M2 are the respective masses of the objects                                                     being analyzed.
r is the distance between the center of mass of the objects

               While the above form is the most universal form of the Law of Gravitation for cases where M1 is much larger than M2 a slightly different version is used, where only the mass of the major body really needs to be considered.
Figure 2:  Acceleration of Gravity Near the Surface of a large body
Where g represents the rate of acceleration between the two objects, Gsubc is still the same and MEarth is the mass of the Earth, which is roughly 5.9736E+24kg and r represents the distance from the center of mass of the Earth to the center of mass to the object.  On the surface of the Earth r averages roughly 6370 km, for the Mobius Bridge that value will most likely fall between 6500 km and 6900+ kilometers from the Earth's center.

For the station being built at 130 km above the Earth's surface, or just 30 km above the line that defines what is legally space, the force of gravity would work out to be roughly 9.44 m/s^2.  At 530 km above the average surface of the Earth, gravity would still be an acceptable 8.37 m/s^2.   (note that these values don't yet factor in the centripetal force)
The second major influencing variable for determining the acceleration of gravity on objects on the Mobius bridge is the centripetal force caused by station rotating with the same angular velocity as the ground below. 
The relation of centripetal force to net acceleration would be a negative resultant of the equation 
Figure 3:  Acceleration of Gravity at the Equator
Reference:  Western Washington University
ω^2*r.  Where ω is equal to to the angular velocity of the planet Earth.  The value of is ω equal to 2*π/1day or 2*π/86,400s.  Putting all of these variables back into a single equation we get the equation to the right.  Using this equation we can create a rather useful table (Fig 4) on how much acceleration would be felt at different target orbits.  (A curve showing the estimated gravitational force at various altitudes will be found further down, useful detail the platform would experience roughly 0.5 g's around 2600 km above the Earth's surface)


Figure 4:  Force of gravity at 130, 330, 530, and 1000 km above the Earth

             Another consideration for making the Mobius Bridge would the trade off of habitable surface area vs how much of the sky would be blocked out by the station.  Making the Bridge too large would cause tremendous environmental impacts, affecting the amount of sunlight reaching plants, migratory patterns of regional fauna, and more.  To limit the impact of building a Mobius Bridge around the Earth, engineers would need to determine how much of the sun and moon could conceivably be blocked by the structure  before being problematic.  According to these sources NASA and Wikipedia the Sun and Moon are both roughly 0.5 degrees or 1800 arc seconds across from the perspective of an Earth bound observer (the decision to use angles allows for consideration of the perceived size of objects with respect to a terrestrial observer as opposed to the absolute size which will be constrained the most by this).  As this document deals with estimated values, we will roughly constrain the relative width of the station to between 1/100th and 1/10th the angular diameter of the Sun and Moon (between 0.005 and 0.05 degrees across).
Courtesy of Wikipedia.com: Angular Diameter
Fig 5 A geometric representation of the angular diameter
Courtesy of Wikipedia.com: Angular Diameter 





where d is the actual width of a selected object and D is the distance between the observer and the body and δ is the resultant angle. (see Fig 5)

Ex:  If engineers decide that they want to make a station that keeps its inhabitants at roughly 0.9 g's they would need to build it at an altitude of about 330km.  (See Fig 4) at that altitude and with the given constraints of keeping the station from not blocking the Sun excessively we get the equation shown in Fig 6
Fig 6 Angular Diameter with constraints
Solving for d @ D=330km we get the range 28.77m < d < 287.7 m

The final design would need to be a careful balance between the width constraints required for ecologically sustainable properties, maximizing internal working space, and a host of other variables.  One fortunate trait of the Mobius Bridge is that you are not limited to making a single structure around a planet, given enough time and patience by an advanced civilization a planet might be found with a collection of archologies that would rival the ring's of Saturn in beauty.

Follow Up Materials
One additional means of maintaining the operational altitude of the Mobius Bridge would be the use of electromagnetic tethers as a means of using the Earth's magnetic field to gently counter the pull of gravity and compensate for uneven mass distribution, both within the archology and the outside universe.  These tethers work by utilizing the Lorentz Force within the Earth's magnetic field. (I will try to add a less physics cut and paste explanation, once I understand this enough to do so)

Figure X  G force curve with respect to altitude (in meters)













Disclaimer Bit
It turns out the idea for building a Mobius Bridge was suggested at least as early as the 1870's by many geek's favorite inventors Nikola Tesla.  Wikipedia has a cool entry on Orbital Rings that provides a host of additional details.  A group called the Alna Space Program seems to have done an incredible amount of research into the design requirements of building an Orbital Ring, but I think I'm still going to call it a Mobius Bridge (seems sexier)  The author/engineer Paul Birch published a paper in the 80's into creating an orbital ring and other dependent structures, including a lightsail wind mill, and an orbital sphere built around a planet.
Other outlandish engineering proposals can be found on the Wikipedia entry for Megastructures, although something as large as the Mobius Bridge, you might as well go grandiose and call it a giga-structure.  Developing an orbital ring platform for planets like Venus could be integral in long term attempts to terraform the planet.

Other Stuff
Using the Lorentz Force for crazy orbits 
Further Reading on Tether Propulsion