Moonfall is a movie coming out in 2022. It creates a scenario where the Moon’s orbit is changed and set on a collision course with the Earth. It is fun to work out the orbital mechanics.
Let us assume that the Moon is in a circular orbit around the Earth. It is actually more influenced by the Sun than the Earth, but the circular orbit approximation is sufficient for our purposes. A mysterious force changes the orbit from circular to elliptical so that at closest approach it hits the Earth. The transfer orbit has an eccentricity of 0.9673 and a semi-major axis of 195000 km. The new orbital period is 9.9 days so it will hit the Earth in 5 days!
What kind of force is needed? The required velocity change is 0.83 km/s so a force of 6 x 1016 N applied over 10 seconds is required. To get an idea of how large that force really is, the Space Launch System (SLS) Block 2 vehicle produces about 10 million pounds of thrust , which is approximately 50 x 106 N (50 MN). Hence it would take 1.2 billion SLS rockets firing for 10 seconds to perform such a re-direction of the Moon! An image of the SLS is shown below (image from ).
As the Moon approaches the Earth it is going to raise the tides. A simple formula (really only valid when the Moon is far from the Earth) is
where is the gravitational constant for the moon, is the gravitational constant for the Earth, r is the distance between the Earth and Moon and a is the radius of the Earth. The distance during the approach and the wave height are shown in the following plot.
By around 3 days the tides started getting really big! We’d expect the Moon’s gravitational force also to pull on the solid part of the Earth’s surface, causing all sorts of trouble.
This summer I worked on the design of a millisecond pulse generator as part of the ARPA-E GAMOW grant. The goal of this project was to supply pulses of very high current to a fusion reactor’s plasma control antenna using solid-state power electronics. Some key design considerations were the ability to parallelize the pulse generator to scale to many power levels, to operate at high voltages, and to minimize the current rise time through the load antenna. I spent most of my time working in LTspice XVII to simulate the circuit and its response to rapid pulses of current. I wanted to make sure the circuit performed as desired, while also remaining safe for both the devices in the circuit and the operators controlling the circuit.
We based the design of the circuit on a load switch developed previously at Princeton Satellite Systems by Cindy Li and Eric Ham. Our biggest progress was in the selection of switching devices and the improvement of the gate drive circuitry. Because our goal is to switch current as quickly as possible, we did not want to rely on outdated klystrons as our switches. We decided to use many parallel MOSFETs to switch the current. The device we chose was a 650 V silicon carbide cascode JFET from UnitedSiC. This FET has low on-state resistance, meaning that it does not heat up as much when pulling large amounts of current. By using many devices in parallel, we can pull more total current while keeping each individual FET below its current capacity. Then by using multiple boards in parallel, we can reach different power levels for different fusion reactors.
Implementing safe gate driver circuitry was another important step. The power MOSFETs used to switch the current cannot be turned on directly from a computer control signal, due to both power and safety concerns. A logic-level signal is not powerful enough to activate the FET, and directly connecting the computer to the high-voltage circuitry is unsafe. To solve both problems, I designed a galvanically-isolated gate drive circuit based on an Infineon gate driving IC. The intermediate circuit takes the computer control signal and steps it up to an intermediate voltage level high enough to activate the MOSFET, while keeping the both sections electrically isolated from each other. Each MOSFET has its own gate drive circuit, enabling independent control.
Working on the millisecond pulse generator was a great experience as an intern. I gained lots of practice working with team members across organizations and disciplines. I became much more proficient in LTspice, and I learned how to rigorously approach challenging engineering problems.
As a Summer 2021 intern, my first project was to complete the structural design of a 1U CubeSat that will fly in orbit with and observe the NASA Solar Cruiser. The 1U CubeSat needed to follow the CubeSat design specifications set by the California Polytechnic State University; it needed to have specific dimensions, needed to weigh a certain amount, and needed to be able withstand structural loads and natural frequency/vibrational loads. In order to design and test the CubeSat, I used Fusion360’s design and simulation softwares. I based my design of the CubeSat off of the engineering drawing provided by the California Polytechnic State University’s “CubeSat Design Specification” manual.
I designed the initial model in Fusion360 as one part made up of different components, as shown below:
The top of the CubeSat faces the positive z-direction, while the front faces the negative y-direction and the right side faces the positive x-direction. The CubeSat also needed four deployable solar panels attached by hinge mechanisms to the four edges of the top face. The panels needed to start parallel to the walls and then, when deployed by some mechanism, needed to swing upward in the positive z-direction.
After designing the idealized CubeSat, I ran multiple modal frequency analyses and structural analyses in order to make sure the CubeSat could withstand the proper loads. First, I ran modal frequency analyses, with fixed boundary conditions for a cantilever beam. The natural frequencies for the first four modes of the CubeSat are shown in the following table:
CubeSat natural frequencies for the first four modes, calculated by Fusion360
The above natural frequencies calculated in Fusion360 are very similar to the theoretical natural frequencies of a cantilever beam, given by the formula:
Where “E” is the modulus of elasticity (also known as Young’s Modulus), and “I” is the area moment of inertia. This formula can be used to find the natural frequencies of a cantilever beam for any mode of vibration, “n”.
These results are from the following study: https://www.hindawi.com/journals/ijae/2018/9724263/
These results are similar to the ones I found in my modal frequency analyses.
After running the modal frequency analyses, I ran a few structural load analyses. The CubeSat frame had a honeycomb structure, which I modeled in Fusion360, and was made up of Aluminum 7075 material. The CubeSat needed to be able to withstand a maximum pressure differential of 15.2 psi (0.104 MPa) created by the Space Launch System (SLS) ascent into space, according to NASA’s Space Launch System Program’s White paper.
The maximum displacement of the CubeSat’s structure due to the applied force was 0.009 m, which is very low. Fusion360 calculates Von Mises stresses, and the maximum stress was 16.08 MPa, which is well under Young’s Modulus of Aluminum 7075 (71.7 GPa). The safety factor of the structure was 8+ everywhere on the structure, meaning the structure is much stronger than the 15.2 psi (0.104 MPa) load applied.
After running the modal frequency and static stress analyses in Fusion360 and getting the desired results, the CubeSat was ready to be modeled as 3D printable parts and 3D printed with PLA on the FlashForge Creator Pro printer:
The initial CubeSat design in Fusion360 had to be modified and broken up into different parts that were each 3D printable; after printing each part, I assembled them to form the whole CubeSat. I decided to break the initial design up into the following 3D printable parts: the top, the bottom, four separate side walls, four separate side rails, four deployable solar panels; finally, I needed to add four hinges plus four rods to attach each of the solar panels to the main structure (similar to a door hinge mechanism). This allowed the solar panels to rotate on a hinge from their initial position up to 180 degrees upward and back. Photos of the different 3D printed parts are shown below:
After 3D printing all the necessary parts, I needed to assemble them. I modeled screw holes in Fusion360 on each 3D printed part in specific locations, so that I would not need to bore holes manually after the parts were printed. I ordered screws for plastic from McMaster Carr, so I knew the correct diameter and length for the screw holes I modeled in Fusion360. This way, the parts were ready to be assembled immediately after 3D printing. Images of the final assembled 1U CubeSat are shown below:
3D printing the final product was an iterative process, so I ended up assembling two different CubeSats entirely and printing a multitude of different versions of each part until I assembled the final product correctly. During the printing process I ran into many problems with the design of the parts, as well as issues with the printer itself. Some design problems included incorrect part sizes, incorrect screw hole placement, incorrect screw hole tolerancing/sizing, and incorrect dimensions of the overall assembled cube. Some printer issues included warping and two nozzle clogs. Some of my parts warped due to a lack of adhesion between the printer bed and the filament coming out of the nozzle, meaning the corners of these parts bent upward and were no longer usable. I solved this problem by reducing the heat of the 3D print bed to make sure the filament could cool down correctly on the bed. On a couple of occasions, parts would not print at all or the filament would come out tangled and would not stick to the bed; I solved this problem by taking apart the nozzle and manually unclogging it so that the filament could come out correctly. I also re-leveled the bed, to make sure the nozzle was close enough to the printer bed so that when the filament initially came out of the nozzle it would stick to the bed immediately. Photos of intermediate designs are shown below:
Overall, this project was educational, challenging, and fun! I learned a new CAD software, Fusion360, which will be useful in the future, and I practiced my engineering design and 3D printing skills!
Overall, this project was educational, challenging, and fun! I learned a new CAD software, Fusion360, which will be useful in the future, and I practiced my engineering design and 3D printing skills!
We just started our latest project for ARPA-E under the ARPA-E GAMOW program in which we will be build power amplifiers for fusion reactors. The goal is to lower the cost and increase the reliability of fusion reactor power electronics. We currently have grants under the DOE INFUSE program and another ARPA-E project that is part of the ARPA-E OPEN 2018 program. We just finished a NASA STTR grant to study the effects of plasma pulses on low temperature superconducting coils.
For those who have been following our work, you know that there are many articles and videos about our work. For your convenience, we’ve collected many of the URLs for them in this blog post.
Space optical navigation employs a camera for attitude determination and a second high dynamic range camera on a pan/track mount for terrain and celestial body tracking. Navigation and attitude determination are performed in a Bayesian framework using anUnscented Kalman Filter with an IMU as the navigation and attitude base. The Optical Navigation Module provides MATLAB code for implementing optical navigation. Additional measurements can be added including a sun sensor for sun distance measurements in interplanetary space, Global Positioning System (GPS) measurements near the Earth, and range and range rate from ground stations or other spacecraft in deep space. The system is suitable for both lunar and Mars landing missions and icy moon and asteroid orbital missions such as Artemis, Lunar Orbital Platform Gateway, Orion Multi-Purpose Crew Vehicle, Europa Clipper, Lucy, Psyche. It is also applicable to any situation where GPS is not available.
The Optical Navigation Module allows you to implement an optical navigation system for any of these applications. It includes dynamical models for cis-lunar and deep space missions along with measurement models for all of these sensors. Several scripts provide examples to get you going quickly.
This picture shows the camera aimed at the horizon and the stars that it can see during Earth reentry. The step counter gives the integration step. The star numbers are sequential from the file of stars but the stars come from the Hipparcos catalog.
This pictures shows the laboratory hardware for an optical navigation camera on a pan/tilt mount. Flexible cables eliminate the need for slip rings simplifying the design. The platform is driven by orthogonal stepping motors with harmonic drives.
Note the size. As with all of our toolboxes, full source code is provided.
PSS just finished up a research contract for NASA in which we discovered some surprising and useful ways in which Low Temperature Superconductors (LTS) may be more suitable than High Temperature Superconductors (HTS) for making light, efficient electric motors.
In short, they’re cheaper. They’re much, much easier to design, manufacture, and use. Unlike HTS, it’s easy to make LTS electrical joints that are just as superconducting as the coils. LTS experience less heating when their internal current is changed. Crucially, you can make a “persistent switch” in which an LTS magnet is charged once and the current is trapped in the coil, persisting without the need to constantly supply current. Our LTS of choice is NbTi, the “workhorse” of the LTS family.
Interested in knowing more? Then read on!
There are several big pushes toward electric aircraft. Air travel accounts for 2.5% of our carbon emissions. So what’s preventing us from electrifying aircraft like we did with cars? The problem is weight. An extra pound of motor or batteries costs much more in an aircraft than it does in a car.
That being said, there are dozens of research groups, companies, and agencies working on hybrid electric and fully electric aircraft. There are even serious advantages to having the freedom to place propulsion units (motors rather than jet turbines) wherever you want within the aircraft, concepts called Boundary Layer Ingestion and Distributed Electric Propulsion. The aerodynamics is complicated, but the gist is that you can get huge emissions savings even if you’re still using jet fuel and turbines, if those turbines are powering lots of little motors rather than one big jet engine.
As we said earlier, all parts of the propulsion powertrain need to be lightweight in order to make a practical electric aircraft. For decades now, superconductivity has been known as a phenomenon with the potential to decrease the weight and increase the efficiency of motors. The idea goes back to the 1960s, with several experimental LTS rotors being tested in the 1970s and 1980s before the programs ended.
But what happened in the 1980s that shifted focus away from LTS motors? The answer is the discovery of HTS. On paper, HTS looks wonderful. It is superconducting at more achievable temperatures, ~100 K versus ~8 K for LTS. It can create magnetic fields much higher than LTS. Plus, it can carry much more current than LTS, meaning the same motor can weigh significantly less if made of HTS.
Yet despite research programs going back to the 1980s and continuing today, there are still no HTS motors on the market. Why is that?
The LTS difference
It turns out HTS is expensive and extremely hard to use. A magnet made of HTS would cost 20 times more than one made of LTS. HTS is weak, and when it’s under strain it can’t carry as much current. It can’t be flexed in one direction. To join two cables of HTS together into one superconducting piece, you have to grow more superconductor between them; you can’t just snap them together like extension cords.
On the other hand, LTS magnets have matured since the 1980s. Most hospitals now have an LTS magnet in the form of their MRI machine. Thousands of tons of LTS are produced yearly. LTS is cheaper, stronger, more flexible, and easier to work with. Its so-called AC losses (heating that occurs when the current is changed) are lower. Two LTS cables can be joined together to make one long LTS cable.
This latter property allows the so-called persistent mode of LTS magnets. In this mode, no external current is required to power the magnet. You charge the magnet up once, then you can disconnect it and walk away. Our LTS magnet vendor, Superconducting Systems, Inc. (SSI) of Billerica MA, has magnets that have sat persistently charged for decades.
How this affects a motor design
As part of our Phase I NASA SBIR, we designed a motor using LTS. The motor design targets small aircraft like Cessna Denali or regional airliners like Beechcraft 1900. The motor’s output power is 1 MW. The total target system weight is 100 kg. The target efficiency is 99.5%.
One of the challenges of using superconducting materials is keeping them cold. Because of the low AC losses and persistent mode of LTS, we were able to cut the heat leak down from dozens of Watts to less than 1 Watt. We were able to completely eliminate the charging subsystem and cryocooler of HTS designs. We have identified four innovative technologies that are enabled by and instrumental to the use of LTS in motors. We will be developing this technology in the coming years.
One of our innovations came from the significantly reduced heat leak into the cold rotor. Rather than use heavy, expensive cryocoolers to cool the rotor, the design suddenly came into the realm of Liquid Helium (LHe) reservoirs. Our SSI partners liken it to the difference between a refrigerator and a cooler. Use the refrigerator (cryocooler) when keeping food cold for weeks or months, but use a cooler (LHe) when making a day trip to the beach.
The journey of the LTS motor has just begun. Work continues at PSS. Contact us for more information or partnering opportunities.
Watch this space! Some day soon, perhaps sooner than you think, you could be flying across the country in an aircraft as renewably powered as your electric car.
Professor Michael Littman of Princeton University, who is a consultant on our Neural Space Navigator NASA Phase I SBIR, has the gimbaled camera in action! Check out the video.
The high dynamic range camera is mounted on a pan/tilt mechanism that uses stepping motors with harmonic drives. Harmonic drives have zero backlash. The camera assembly is 17 cm tall.
The Neural Space Navigator uses a neural network for terrain relative navigation during landings or takeoffs. Otherwise it uses the angles between planetary horizons or centers and stars combined with planetary chord widths for navigation measurements. The system uses an Unscented Kalman Filter and an Inertial Measurement Unit for both navigation and attitude determination. Contact us for more information!
A DC motor is the core of all momentum and reaction wheels. If you apply a voltage a, current will be produced which will cause the wheel to change speed. At the same time, the back electromotive force (EMF) will build up, eventually driving the motor torque to zero.
This is evident from the dynamical equation for a DC motor.
is the inertia, is the torque constant, the voltage, the friction torque, the motor impedance and is the angular rate of the shaft.
You can turn this into a reaction wheel by adding current feedback as shown in the following block diagram.
is the forward gain. The input is the desired torque. This is divided by the torque constant to get the desired current. The difference between the motor current and the desired current is integrated. How do you pick the gain? If you work through the equations you will get this equation for the voltage,
is the time constant. The response is shown in the following plot. Even as the speed increases, the difference between the desired torque and motor torque is nearly zero.
The thesis gives an excellent overview of nuclear fusion technology and space propulsion. The author then goes on to do trajectory analysis for the Titan mission using STK. He presents three different mission strategies using Direct Fusion Drive. He includes all of the orbital maneuvering needed to get into a Titan orbit. His mission designs would get a spacecraft to Titan in two years.
Dr. Gary Pajer, Yosef Razin and Michael Paluszek of Princeton Satellite Systems and Dr. Samuel Cohen of the Princeton Plasma Physics Laboratory were awarded a 2020 Thomas Edison Patent Award for U.S. Patent 9,822,769, “Method and Apparatus to Produce High Specific Impulse and Moderate Thrust from a Fusion- Powered Rocket Engine.” This patent is for a new type of nuclear fusion reactor that is compact, making it suitable for mobile power, emergency power, space propulsion and power. Images of a mobile version of the reactor, and a version used for a rocket engine are shown below. The work is currently funded by an ARPA-E OPEN grant. NASA has also funded this work through the NASA NIAC program.
The 41st Edison Patent Awards Ceremony, themed “Transforming Hope into Action” will take place virtually on November 12th. Contact Vanessa Johnson for more information about the event.