Questions:

1. How does power change with distance from the sun?
2. Name 1 of our potential methods of transmitting the energy from space to the earth, along with 1 con.


Members:
  • Aly Lodge
  • Greg Bergdoll
  • Matt Stumbo
  • Ben Norris

Project Description:


In this project we aim to research the viability of, and methodology for, harnessing solar energy from the sun using a Dyson Sphere (i.e. - Dyson Cloud). A Dyson Sphere is a mega structure which encompases a star to harness its energy. In this project, we will analyze a Proto-Dyson Sphere- a partial covering of a star. Perfect grey body mirrors totaling 30,000 km^2 will orbit around the Sun 150e6 km (1 AU) away. The mirrors will be located at the L4 and L5 Lagrange points. These mirrors will concentrate sunlight to a solar tower. A Rankin cycle will be used, as the heat of the sunlight boils water and thus steam turns a turbine. The electricity produced will be transmitted via tethering to the Earth for use.The primary goal of this project is to eliminate our dependency on non-renewable sources of electricity (e.g. - oil, coal, etc.).

Objectives:


1. Investigate the different proposed Dyson Sphere implementations and their associated pros/cons.
2. Develop energy production capable of meeting the 17TW global demand using the superstructure.
3. Identify repercussions of different methods of Energy transmission to the earth
4. Determine monetary cost requirements for such a project.


Status Quo:


Currently, the world has a large dependence on non-sustainable energy sources-- most of which have an increasingly devastating impact on our environment. Energy generation emits some of the highest concentrations of greenhouse gasses. Increasing the concentration of greenhouse gasses will increase the temperature of the world. Increasing temperatures can cause increased hurricane severity and frequency, ocean acidification, increased sea levels, as well as endangerment/extinction of species.This project targets energy generation as a means of significantly reducing greenhouse gas emissions, specifically carbon dioxide. Recently, the globe has just reached carbon dioxide concentrations of 400ppm. Since 2000, concentrations of been increasing at a rate of 2ppm/year.

As we begin to realize the effects of our technological advances and consumerist economy, the necessity of a new source of "clean" energy is clear. With natural resources like currently accessible oil half depleted, and the methods of extraction becoming more costly and detrimental to our environment, the science community had been fraught with debate over the next breakthrough in energy production. Currently, the world consumes about 17TW of energy per year. A Proto-Dyson sphere is suggested to produce some of this power and eliminate our reliance on harmful methods of energy generation. To ensure diversity, we would rely on the Proto-Dyson Sphere's energy generation as well as nuclear energy generation. We know that nuclear energy provides about 17TW annually, meaning the proposed Proto-Dyson Sphere would have to generate 16TW.

Recognized Concept Designs:

Several concepts were analyzed for the creation of this proposal. Among them were the Dyson Sphere, Dyson Ring, and Dyson Bubble.
external image dysonsphere.jpg

Figure 1: Dyson Sphere

This method seemed implausible -- as can be viewed from this cartoon illustration. The design is improbable, but it was the early concept that was later generalized. This deign is impossible because there is no way to get the sphere to stay in position; it would collide with the planet it is generating energy for. The dyson sphere would also heat up and cook the inner planet.


ring.png

Figure 2: Dyson Ring

The Dyson Ring is one of the more plausible designs; it has less demand on resources and requires less maintenance.

external image Dyson_Sphere_by_capnhack.jpg

Figure 3: Dyson Bubble

This design implements several Dyson Rings for maximum efficiency. It seemed a little unnecessary for the project.

Proto-Dyson Sphere--Space Components



Figure 4 below demonstrates the most ideal design for the Proto-Dyson Sphere. This model utilizes two mirrors placed at the Earth-Sun L4 and L5 points--it is a modification of the Dyson Ring idea. It utilizes a solar tower and a high temperature super conductor cable placed on a space elevator to transmit the energy back to earth.
photo.JPG
Figure 4: Proto-Dyson Sphere Initial Concept


Mirrors:


The mirrors for the solar concentration would be located at the Earth-Sun L4 and L5 points which can be seen in Figure 5 below. These points were chosen because they are stable. The mirrors will always be 60 degrees ahead or behind the Earth in the Earth's orbit around the sun. The benefit of this is that the Earth will not move relative to the mirrors, simplifying the accuracy of the mirrors beaming the energy to the solar tower tethered to earth. Figure 6 describes how the power density changes as a function of the distance from the sun. It is clear that the power changes as a function of 1/R2. There are a myriad of hurdles that must be over come to get the mirrors into position. The largest of these hurdles is transferring the mirrors to L4/L5 because of the amount of fuel required; it will take approximately 1 km/s to do the transfer. What this means is that velocity of the mass of mirrors needs to be changed 1 km/s over the course of the transfer. This amounts to 1e8 kg of fuel if a biprop thruster system is used (Isp ~ 300 s). If a more efficient engine, such as an ion engine is used (Isp ~ 3000 s), then the fuel mass is 1e6 kg. Both of these fuel masses prohibit this mission.




external image 704px-Lagrange_points2.svg.png
external image 2R4qrg4xici6ZDgr-Rl7YFP6qGX3heCrQo7V6xFzOsx1DkJ85TeZ6vfu12mKW7-2etQewBAHCmA_ld7IdfyE0Qeg0tIv2SswbDfkm-3SwaRjNrwWYh94NBNuGSo
Figure 5: Earth-Sun Lagrange Points
Figure 6: Power Density as a Function of Distance


Ideally, perfect grey body mirrors would be used as they would enable total reflection, prohibiting the material from getting hot. As this material would be 150 e6 km from the sun, as determined by the black dot in Figure 6, the temperature would be incredibly hot. It was determined that 30,000 km^2 of mirror would be necessary. Each mirror would also need to be slightly concave, which would allow more accurate reflection of sunlight to its designated solar tower. A mirror of 1 by 1.5 meters costs approximately $76.00 according to home depot. Using this cost as a baseline estimation, this project would require $1.5 trillion for the required mirrors. The total mass of these mirrors is 72e6 kg. This is massive, compared to the largest man made object in space: the International Space Station. This has a mass of 420,000 kg and is in a low earth orbit, which requires much less energy to attain versus an Earth-Sun L4/L5 position. This part of the project assumes a working space elevator, so the cost of getting the materials into space would be zero.

Black Body Turbine:

A solar tower was determined to effectively represent the Black Body Turbine. A solar tower is shown in Figure 7 below for reference.
power_tower.gif
Figure 7: Solar Tower Design

In Figure 7, the mirrors are on the Earth and are reflecting their light to the receiver. In the Proto-Dyson Sphere, the two mirror described in the Mirrors section, would sit at the L4 and L5 positions and reflect the light to the tower. This concentrated sunlight would be aimed at a container of salt. The salt would thus liquify and become molten, which would heat water and cause it to boil in the steam drum. Salt was chosen to receive the high concentrations of sunlight because it has a high heat capacity (0.88 KJ/KgK) meaning it has an inherent ability to store heat.

Once the water turns to steam, a closed loop system with the rate of water evaporation equal to the rate of water condensation would prohibit the water from increasing in its equilibrium temperature and the water level from decreasing. In space, the lack of material would mean the water would be condescended via heat lost from radiation. This means that we need to analyze the rate of heat being reflected at the solar tower and the rate of heat leaving the radiator. This is the limiting factor to how much sunlight the solar tower can handle. According to baseline solar tower information from Wikipedia, each solar tower is capable of accepting 773K of heat. We can control how much heat the towers are getting by controlling the light that hits the solar tower via different angle placements of the mirrors. The heat being absorbed by the solar tower is 392MW, according to the highest capacity these turbines can handle. This would mean we would need about 38,500 turbines to generate our 16TW goal. To calculate the rate of heat being radiated, we used this equation: P=sigma(Thot^4-Tcold^4)A. Assuming the temperature of cold space is 2.7K, we calculated 20245.29W/m^2. This number is left in terms of area so we could calculate how much area the cooling pipes would require. Dividing the input power by the output power yielded an area of about 19,500m^2. To acquire this much area, the cooling tubes which hold the steam would have to be flat. The metal pipes themselves would have to be anodized. Anodized metal describes metal which has been colored black. It is important to have these pipes as close to an ideal black body as possible so they radiate more efficiently. Shields would be necessary to eliminate other sources of radiation, besides background cosmic radiation.


Proto-Dyson Sphere--Earth Components


Choosing the most effective and least harmful method of transmitting the energy back to earth was thought provoking. We identified the different pros and cons of three methods of transmission: funneling the energy to earth, wirelessly transmitting the energy to earth, and tethering the energy to earth.

Direct Funneling Energy

This method does not require using the solar turbines in space, as the concentrated sunlight would be directed to Earth. The concept is illustrated in Figure 8 below. The problem with this idea is that it can be extremely dangerous. If the sunlight misses its destination and does not hit the receiver on Earth, it could cause mass damage and threaten the area around the receiver along with any humans or animals. Another problem with this transmission method is that the sunlight would burn a hole through the atmosphere. This would cause massive global sunburn, as the concentrated light diminishes the ozone and allows more sunlight in earth.The risk associated with this method of transmission led us to omit it as a possible option.



external image CYnag4xw4Fuo4uUrUIVGpwRbZ018KvV_LuK6zTRO9w5dsiocMlyFh0fHcyIdqNDHqyNTst5vng54Zf08FrZhKZSbgiVbBzjoKd7PfrzeqUq314SFIcYU_uOzGYM
Figure 8: Laser Transmission to Earth

Wireless Transmission:

This method of energy transmission involves broadcasting high energy radio waves. These waves would be created via the energy from turbine. Radio waves were chosen as best form of transmission as they are absorbed the least by the environment as demonstrated in Figure 9. This would allow the best efficiency when transmitting through the atmosphere. An advantage to this method is the availability of free energy! Each electrical device on earth can be designed with a wireless charging device that absorbs these radio waves when the battery is low. Unfortunately, there are several problems with this method. Transmitting electricity wirelessly was found to have severe health effects for humans over time. These high energy waves would also flood out most means of communications. Again, the issue of human health led us to omit this as a viable transmission method.

external image n2V-p9rx6yKk3nnECJfjEOuPD88OWsBrFEymJmJ02l5dI-eZuRmI53rWgKXgjdcqJcUPMzDB80usTPpvVDKV-7rk1dPqwvcf5r3LbcLRIFnnaAEJsVltmHCZHs0
Figure 9: Absorption of Electromagnetic Radiation in the Atmosphere

Tethering:

This method involves hard wiring the electricity generated from the solar turbine down to a central station at earth. After analysis of alternative methods to getting the electricity to earth, it was decided that tethering was the best method because it was the only issue without a serious safety factor. The main limitation with this method is the efficiency of the cable, and our fear of losing the energy we created.

The most efficient type of cable is the High Temperature Superconductor. As it is a super conductor, we are going to assume 100% efficiency. HTS Triax is implementing a 55GW, 300m long, 7kg/m cable in New York this year. The information for our project will be based off of this design. We are going to assume that the nature of a high temperature super conductor allows 100% efficiency of 55GW throughout the length of the entire cable. An image of this superconductor is provided in Figure 10 below.

external image OAFidJMoMb3935wLMw9FWYGzd288xY9rImB1_ZqciuumSkw_FUR9MXT_LiHpv4b1wRcErb-1hFw0QvUMC50m8GcPL6t-LDKByB1grKk3W2HtQQ3RnY_2pZXuBW0
Figure 10: NKT Cable High Temperature Super Conductor
This concept would require the use of a space elevator as the fundamental structure which holds the cables from space to the earth.Thus, information was used from the Space Elevator Group. They're group calculated a length of 50,000km from their base on earth to their max peak in space. This means, we'd need 50,000km of our superconductor cable to attach to the outside of the space elevator structure. We know that each line is capable of holding 55GW of energy, meaning we'd need approximately 300 lines to provide 16TW to the world. If one line, stretches 50,000km and weighs 7kg/m, we can calculate that one line weighs 350 million tons. This means that 300 lines would weigh 105 billion tons.According to the space elevator group, a counter weight is required to keep their design taut. They estimated this weight would need to be 10 trillion tons. As our cables weigh 105 billion tons, and would be attached to the space elevator, we would alleviate some of the weight required as a counter weight. The counter weight would only need to be about 10 trillion tons if our cable weight was attached. Not only do our high temperature super conductors require cooling, but the space elevator requires cooling as well. A uniformly distributed temperature is necessary for a functional elevator. As our cables would be attached to the elevator, we will assume our cables will maintain a uniformly cool temperature due to conduction. According to Wikipedia, 100,000 tons of high temperature super conductor material costs around 550 million dollars. Using this estimate, we concluded that all 300 cables would cost 16 quadrillion dollars. It appears that transmitting electricity from space to earth, with around 100% efficiency, is very costly.

Once the energy arrives at Earth, High Voltage DC transformers will distribute the energy where it is necessary in the world. High Voltage DC transformers are implemented over High Voltage AC transformers because High Voltage DC transformers lose less energy over long distances.

Conclusion:

There are some important assumptions that were necessary in the design of this project. Included in these assumptions were the construction of a functional Space Elevator, and using perfect grey body materials to direct the sun's energy. As these assumptions are highly complex, the project itself seems unreasonable. Another problem with this design is that the fuel masses are too long. Although a Proto-Dyson Sphere would alleviate our dependency on fossil fuels, the assumptions required for this project are too complex and unfortunately, this project is not feasible.

Cost Summary Table:


Cost (dollars)
Mirror Production
1.5 Trillion
Space Elevator
10.6 Trillion
Black Body Turbine
90 Million, 3 Million for O&M/year
Tether Cable
16 quadrillion

The lifetimes for these prodicts are mostly unknown, as their lifetime depends on whether or not they are hit by debris in space.







external image dysonswarm.png














References:

1. Fermilab
http://home.fnal.gov/~carrigan/infrared_astronomy/infrared_astronomy_master.htm

2. Freeman Dyson
http://en.wikipedia.org/wiki/Freeman_Dyson

3.Dyson Sphere FAQ
http://www.aleph.se/Nada/dysonFAQ.html#BUILT

5. International Space Station
http://www.nasa.gov/mission_pages/station/main/onthestation/facts_and_figures.html

6. Home Depot Mirror Cost
http://www.homedepot.com/p/36-in-x-48-in-Acrylic-Mirror-5-Sheet-Contractor-Value-Pack-AM3648S-5/202509289#.UaJWnLWcf4I)

8. Superconductors
http://www.htstriax.com/manhattan.html
http://www.nktcables.com/support/download/catalogues-and-brochures/high-voltage-and-offshore/~/media/Files/NktCables/download%20files/com/HTS-Triax_engl_061108.ashx

9. Space Elevators
Space Elevator Spring 2013 group