About Michael Paluszek

Michael Paluszek is President of Princeton Satellite Systems. He graduated from MIT with a degree in electrical engineering in 1976 and followed that with an Engineer's degree in Aeronautics and Astronautics from MIT in 1979. He worked at MIT for a year as a research engineer then worked at Draper Laboratory for 6 years on GN&C for human space missions. He worked at GE Astro Space from 1986 to 1992 on a variety of satellite projects including GPS IIR, Inmarsat 3 and Mars Observer. In 1992 he founded Princeton Satellite Systems.

Pluto Orbiter – the Next Step after New Horizons

The spectacular success of the NASA New Horizons mission has led to many new discoveries about Pluto. The next step would be to send an orbiter. That isn’t easy to do with chemical propulsion but could be done with Direct Fusion Drive.

We’ve done a preliminary mission analysis for a Pluto orbital mission. We are baselining a Delta IV Heavy that can put up to 9,306 kg into interplanetary orbits. These plots show various parameters versus mission duration. The maximum duration is the same as the New Horizons mission, 10 years.

PlutoMission2MW4Yr

Let’s use the 4 year mission as a baseline. It would use a 2 MW DFD engine to reach Pluto in about 4 years and go into orbit. The engine would thrust for 270 days out of the 4 year mission producing 110 km/s delta-V. The trajectory is shown below

PlutoTraj2MW4Yr

Once there, almost 2 MW of power would be available for the science mission, over 10000 times as much power as is available to New Horizons! The New Horizons bit rate is no more than 3000 bits per second. The high power would allow for a bit rate of over 135 Mbps for data transmission back to Earth using the JPL Deep Space Optical Communications System and a 30 kW laser transmitter. The time in transit is much shorter than New Horizons and would produce significant savings on operations costs. Launch times would be more flexible since gravity assists would not be needed.

DFD would use deuterium and helium-3 as fuels. Only 1700 L of helium-3 would be needed for this project. Current U.S. production of helium-3 is 60000 L per year.

Since we would be going all the way to Pluto it would make sense to include a lander. One way to power the lander is using laser power beamed from the orbiter. Here are results for a possible system, beaming over 30 Wh per pass from a 200 km orbital altitude.

LaserPower

Currently, experiments are taking place in the Princeton Field Reversed Configuration laboratory. Here is the machine in operation at the Princeton Plasma Physics Laboratory:

Experiment

The next step is to build a slightly larger machine to demonstrate fusion. Fusion power generation has been demonstrated in the Princeton Plasma Physics Laboratory Tokamak Fusion Test Reactor and the Joint European Torus but never in a machine using helium-3. A flight engine would follow. Its small size would keep the development and production costs down.

DFD would enable many challenging missions include human exploration of Mars, Europa landers and interstellar probes.

Lunar Topography

If you are sending a spacecraft to the moon, you will be interested in lunar topography. A new function in the Spacecraft Control Toolbox lets you superimpose a height map onto any sphere.

MoonTopoThe function RSHMoon.m gives you the Clementine spacecraft topographic data using a spherical harmonic expansion of the rangefinder data.

 

A new function, PlanetWithTerrain.m, lets you superimpose this data onto a sphere.

 

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Fission Powered Lunar Lander

Settlements on the moon, for mining and scientific research, will require routine travel between lunar orbit and the lunar surface. One idea is to use a lunar shuttle with a nuclear fission rocket engine. The hydrogen fuel would come from water on the moon. Fission rockets have twice the specific impulse of the best chemical rockets leading to low fuel consumption. In addition, they would leave the oxygen from the electrolysis of water available for the lunar settlements.

Stanley Borowski of NASA/GRC is co-author of a paper giving the status of nuclear fission rockets:

NTR Technology Development and Key Activities Supporting a Human Mars Mission in the Early-2030 Timeframe

Fission rockets were developed in the 1970’s but the technology was never tested in flight. We used his paper to create a fission rocket. A 3D model based on a drawing the paper is shown below:

NTP

We built the launch vehicle using a single script in the Spacecraft Control Toolbox for MATLAB:

Spacecraft Control Toolbox 2015.1

The script uses a bilinear tangent steering law to estimate the required two way delta-v. The lander flies to 12 km where it meets a freighter. The crew is housed in an Orion spacecraft. The vehicle is shown below:

FissionNL

The landing legs are based on the Apollo Lunar Module. The liquid hydrogen is stored in the 4 spherical tanks. The nuclear thermal engine is hidden by the box to which the legs are attached. The lander lifts the Orion spacecraft and 6000 kg more of payload which would include helium-3 mined on the moon.

The Orion model was created by Amazing3DGraphics. Amazing3D is really good at creating low polygon count models that are useful for simulation and disturbance modeling.

The script and new supporting functions will be available as part of SCT Release v2015.2.

Maximum Achievable Velocity Change



The rocket equation gives the ratio of the initial mass to the final mass given a velocity change and an exhaust velocity.

$$\frac{m_i}{m_f} = e^\frac{\Delta V}{V_e}$$

This seems to say that given enough fuel we could get an infinite velocity change! To see what the maximum possible velocity change could be we need to account for the structural fraction. The structural fraction multiplied by the mass of fuel gives the mass of the structure needed to support and contain the fuel. The rocket equation now is as follows

$$\frac{m_h + (1+f)m_p}{m_h + fm_p} = e^\frac{\Delta V}{V_e}$$

where m_p is the mass of propellant, f is the structural fraction, and m_h is the mass of all other hardware. If we let the mass of propellant go to infinity, and solve for the velocity change, we get:

$$ \frac{\Delta V}{V_e} = \log{\frac{1+f}{f}}$$

The following plot shows the ratio of velocity change to exhaust velocity for a range of structural fractions.
VelocityRatio

Reaction Wheel Friction Models

Reaction wheels are used in many spacecraft for attitude control. A reaction wheel is a momentum exchange device because it controls the spacecraft by exchanging momentum with the rest of the spacecraft. Momentum is exchanged via a motor that is fixed to the spacecraft. As with all rotating parts it is subject to friction. Friction needs to be modeled as part of the design process.

The standard way to model friction is with three terms. One is damping which is proportional to wheel speed. The faster the wheel spins the more friction torque is produced. Ultimately, this limits the net control torque. At some speed the motor is just balancing the friction torque. The second component is Coulomb friction that is constant but flips signs when the wheel speed changes sign. the third is static friction. It is like Coulomb friction but only exists at zero speed.

An alternative friction model is known as the bristle friction model. This models friction as bristles that bend. It also has the same friction components described above but they are applied though the bristle state.

Both models can be made to produce similar results as shown in the following figure.

FrictionComparison

The static friction is clearly seen. The wheel speeds are nearly the same. The middle plot is of the bristle state. The problem with these models is when the torque is low and the wheel speed passes through zero. We then get limit cycling as shown below.

LimitCycle

This is due to numerical error.

We can eliminate the limit cycling by using a very small integration time step with the bristle friction model. An alternative approach is to use the first model and multiply the sum of the static and Coulomb friction with a sigmoid, or s function.

Friction

The coefficient of the sigmoid function is beta. Very small betas remove the static friction, and all Coulomb friction, near zero speed. The large betas retain the form of the friction and eliminate the limit cycling!

HighBeta

These models can be found in the Spacecraft Control Toolbox 2015.1 . This particular script will be available in 2015.2 which will be released in July.

Two Stage to Orbit with the Launch Vehicle Toolbox

The Launch Vehicle Toolbox (LVT) combines the Spacecraft Control Toolbox, the Aircraft Control Toolbox and additional libraries of launch vehicle functions and scripts. We’ve used it internally to support a number of contracts.

We have studied two stage to orbit vehicles for a number of years. Our design, known as Space Rapid Transit, uses an aircraft first stage (the Ferry) with a turbo-ramjet engine to take the launch vehicle to 40 km and Mach 6.5. The turbo-ramjet engine is dual fuel using jet fuel for the turbofan and hydrogen for the ramjet. The turbofan core would be based on an existing modern jet engine. A hydrogen fueled turbo-ramjet was tested by MBB for their Sanger launch vehicle. Hydrogen fueled ramjets have been tested by NASA. The SR-71 engine was an early operational turbo-ramjet.

The Orbiter uses a cryogenic hydrogen/oxygen engine to enter the transfer ellipse and then circularize the orbit. The Ferry engine can operate in pure turbofan mode for efficient low-speed operations such as moving the Orbiter between airfields.

TSTODemo.m is a LVT script that models the trajectory from takeoff through circular orbit insertion. The TSTO stack starts on the runway in takeoff mode. When it is moving at the takeoff speed it pulls up and climbs. It transitions from turbofan to ramjet and climbs to the separation altitude and velocity. The simulation works with flight path and heading angles. You can try flying the vehicle in a variety of trajectories. The following figure shows the trajectory up to Ferry/Orbiter separation.

SRTTrajectory

The Space Rapid Transit vehicle is documented in this paper:

Paluszek, M. and J. Mueller, Space Rapid Transit – A Two Stage to Orbit
Fully Reusable Launch Vehicle, IAC-14,C4,6.2, International Astronautical Congress, Toronto, Ontario Canada, October 2014.

The Orbiter starts at the termination condition. The script computes a transfer orbit and the necessary velocity changes to get the Orbiter into an ISS altitude orbit. Part of the delta-V is the drag loss. The Orbiter trajectory is not simulated. The architecture of LVT makes it easy to build these kind of analysis and simulation scripts. Your aren’t locked into a specific design path as can happen with GUI based tools.

For more information go to Launch Vehicle Toolbox for MATLAB.

SolidWorks Interface in SCT 2015.1

Version 2015.1 will have a new DXF file format exporter to export CAD models built in the Spacecraft Control Toolbox into SolidWorks. The following figure shows the Lunar Lander model in the Spacecraft Control Toolbox CAD window.

LunarLander

Exporting requires just two lines of code:

g = BuildCADModel( 'get model' );
ExportDXF(g,'LunarLander');

Rodger Stephens of Prism Engineering provided SolidWorks models from the DXF file. The file opened in SolidWorks with 7 parts creating an assembly called LunarLander-1.

SolidWorks1

Each part contains planes, sketches, and surfaces.

SolidWorks2

The Spacecraft Control Toolbox has always had DXF import capability but now it can export in a format that is supported by most CAD packages. This will speed the process of going from conceptual designs in the Spacecraft Control Toolbox to detailed designs in SolidWorks and other CAD packages.

Patched Conics

Patched conics are a useful approximation when dealing with orbits that are under the influence of multiple planets or moons. The idea is that only one planet’s or moon’s gravitational field is active at any one time. For example, at the start of a mission from Earth orbit to the Moon, we assume that only the Earth’s gravity acts on the spacecraft. For each planet or moon we define a sphere of influence where that body’s gravity is greater than all other sources. In the Earth/Moon system the Moon’s sphere of influence extends to about 66,000 km from the moon.

A new function in the Spacecraft Control Toolbox Release 2015.1 is PatchedConicPlanner.m. It allows you to explore trajectories in a two-body system. The following figure shows the trajectory of the spacecraft and the orbit of the Moon in the Earth-centered frame. The trajectories assume that the spacecraft is only under the influence of the Earth. The spacecraft is in an elliptical orbit designed to have its apogee just behind the Moon.

PCC1

The next figure shows the spacecraft in the Moon centered frame. The blue line is the trajectory of the spacecraft assuming that the Moon was not there. The green line is the hyperbolic trajectory of the spacecraft starting from the patch point computed assuming the Earth’s gravity had no influence on the trajectory. Notice the sharp turn due to the Moon’s gravity. The function returns the Moon-centered orbital elements along with other useful quantities.

PCC2

The following shows a closeup of the trajectory. The miss distance, as expected, is less for the hyperbolic trajectory. The plot clearly shows a good place for a delta-v maneuver to put the spacecraft into lunar orbit.

PCC3

This function allows you quickly explore the effect of different patch points and to try different spacecraft transfer orbits. While a “high-fidelity” analysis requires numerical orbit propagation that includes the Moon, Sun and Earth’s gravitational fields, PatchedConicPlanner.m, let’s you generate good starting trajectories for mission planning.

Heading to the Moon

We have transitioned our lunar lander work from the Spacecraft Control Toolbox to VisualCommander. Here is a simulation of the lander heading to the moon on the elliptical transfer orbit designed in our Landing on the Moon blog post.

Lunar Transfer

The model was discussed in our Moon Lander Design blog post. We exported it from the Spacecraft Control Toolbox as a Wavefront obj file. The textures were applied by Amazing3D Graphics. Amazing 3D Graphics builds very high quality models with low polygon counts that are ideal for simulation and games.

The attitude control system is our Precision ACS system. In the next few weeks we’ll be adding software to perform mid-course corrections, lunar orbit insertion and lunar landing. Say tuned!