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At least 19 records

From the Rocket Equation to Maxwell's Equations: Electrodynamic Tether Propulsion Nears Space Test

The US space program is facing a growing challenge to its decades-long, global leadership position, as current launch costs consume valuable resources and limit achievements in science, exploration, and commercial development. More than 40% of projected launches over the next 10 years have payloads with intended destinations beyond low-Earth orbit. Therefore, more cost-effective upper stages and on-board propulsion systems are critical elements in reducing total space transportation costs. A new type of space propulsion, using electrodynamic tethers, may be capable of performing multiple sequential missions without resupply and have a potential usable lifetime of several years. They may provide an in-space infrastructure that has a very low life cycle cost and greatly enhanced mission flexibility, thus supporting the goal of reducing the cost of access to space. Electrodynamic tether thrusters work by virtue of the force the Earth's magnetic field exerts on a wire carrying an electrical current. The effect is the basis for electric motors and generators. The Propulsive Small Expendable Deployer System (ProSEDS) experiment, planned for launch in the summer of 2000, will demonstrate the use electrodynamic tether thrust by lowering the altitude of a Delta-H rocket's upper stage on which it will be flying. Applications of the technology include a passive deorbit system for spacecraft at their end-of-life, reusable Orbit Transfer Vehicles, propellantless reboost of the International Space Station, and propulsion and power generation for future missions to Jupiter.

Johnson, Les

Exergy Analysis of Rocket Systems

Exergy is defined as the useful work available from a system in a specified environment. Exergy analysis allows for comparison between different system designs, and allows for comparison of subsystem efficiencies within system designs. The proposed paper explores the relationship between the fundamental rocket equation and an exergy balance equation. A previously derived exergy equation related to rocket systems is investigated, and a higher fidelity analysis will be derived. The exergy assessments will enable informed, value-based decision making when comparing alternative rocket system designs, and will allow the most efficient configuration among candidate configurations to be determined.

Gilbert, Andrew

Comet Hitchhiker: NIAC Phase 1 Final Report

Summary of Activities-Developed the Comet Hitchhiker concept, which is to hitch rides on small bodies (asteroids and comets) using a tethered spacecraft. (Section 2)-Identified five scientifically important missions that would be enabled or significantly benefited by the Comet Hitchhiker concept.The five mission concepts are: KBO rendezvous, Centaur rendezvous, Trojan rendezvous, Damocloid rendezvous, and Main asteroid belt tour to rendezvous with multiple (10) objects. (Section 3)-Derived the Space Hitchhike Equation, or "the rocket equation for hitchhiker", which relates the specific strength of tether, mass ratio, and V. (Section 4.1)-Performed in-depth feasibility analysis of the critical components of the concept through: Finite-element simulations of tether and spacecraft dynamics, as shown in Figure 1 (Section 4.4); Supercomputer simulations of the hypervelocity impact of harpoon on a small body, as shown in Figure 2. (Section 6)-Performed public outreach activities including the collaboration with a concept artist of the Museum of Science Fiction, exposure to media, and public presentations. (Section 8)

Deep Space

Exploring Mars: the Ares Payload Service (APS)

In last year's Mars Society convention we introduced the results of five years of studies of space launch capability for the second millennium. We concluded that Single Stage to Orbit (SSTO) vehicles such as the Delta Clipper X33, and X34 cannot make it to orbit from the Earth's surface. Whether taking off vertically or horizontally or landing vertically or horizontally, the rocket equations, the performance of available fuels, and the realities of the weight and strength of materials leave no margin for payload. The promised savings from SSTO systems are illusory. However, a configuration that is able to deliver useful payload to orbit is the Single step to Orbit, SsTO, a rocket plane that is released fully fueled, from 35,000 to 40,000 feet altitude. Three approaches have been proposed. The Hot'l and Molnya Corporation designs carry the fueled rocket plane to altitude on the back of a carrier aircraft. In this design the carrier aircraft is Russia's Antonov 225 the world's largest cargo plane. The rocket plane is a modified version of the Buran, Russia's own space shuttle. Another configuration is Kelly Aviation's concept in which the fully fueled rocket plane is towed to altitude by the cargo plane and then released. A third approach is based on the early "X" planes, which were dropped from the belly of the carrier plane. While the rocket equations indicate that these three concepts can deliver useful payloads, the Stanford review found significant advantages to the approach of Pioneer Rocket, in which the rocket plane flies up to the carrier plane with conventional jet engines, docks, and then loads on the oxidizer for the flight to orbit. This architecture has more reasonable abort modes in case of system failure in either aircraft and can deliver a larger final payload to orbit for a given sized carrier. The Stanford recommendation is that the carrier aircraft be the Antonov 225. A design based on this was presented in a report last year. Refinements to the design notably an improved re-entry cooling system and fueling stability analysis were done this year. More technical detail and a proposed international consortium to develop the SSTO is presented in another session of this year's Mars convention. We believe that there will be no human exploration of Mars based on the Shuttle or Expendable launch vehicles, and no resources available except for a cooperative international program. However, just as the world is learning to cooperate in peacekeeping, we hold out the hope that similar cooperation will develop for Mars exploration. With that in mind, this year we asked the question- "How will the human mission get to Mars if it has to use the SsTO for transportation?"

Bowen, Justin

Estimating Basic Preliminary Design Performances of Aerospace Vehicles

Aerodynamics and Performance Estimation Toolset is a collection of four software programs for rapidly estimating the preliminary design performance of aerospace vehicles represented by doing simplified calculations based on ballistic trajectories, the ideal rocket equation, and supersonic wedges through standard atmosphere. The program consists of a set of Microsoft Excel worksheet subprograms. The input and output data are presented in a user-friendly format, and calculations are performed rapidly enough that the user can iterate among different trajectories and/or shapes to perform "what-if" studies. Estimates that can be computed by these programs include: 1. Ballistic trajectories as a function of departure angles, initial velocities, initial positions, and target altitudes; assuming point masses and no atmosphere. The program plots the trajectory in two-dimensions and outputs the position, pitch, and velocity along the trajectory. 2. The "Rocket Equation" program calculates and plots the trade space for a vehicle s propellant mass fraction over a range of specific impulse and mission velocity values, propellant mass fractions as functions of specific impulses and velocities. 3. "Standard Atmosphere" will estimate the temperature, speed of sound, pressure, and air density as a function of altitude in a standard atmosphere, properties of a standard atmosphere as functions of altitude. 4. "Supersonic Wedges" will calculate the free-stream, normal-shock, oblique-shock, and isentropic flow properties for a wedge-shaped body flying supersonically through a standard atmosphere. It will also calculate the maximum angle for which a shock remains attached, and the minimum Mach number for which a shock becomes attached, all as functions of the wedge angle, altitude, and Mach number.

Luz, Paul L.

Separating Propulsive Mass and Energy for Space Applications

Initially and traditionally, space access and in-space propulsion utilized combustion and expulsion of chemical “fuels” carried on board, with performance governed by the rocket equation. These chemicals produced energy, and after combustion, constituted the propulsive mass/momentum. The best such chemicals in terms of Isp that are deemed safe engineering/mission wise are hydrogen and oxygen, producing some 450 seconds of Isp. There are more reactive chemicals, such as fluorine, which have higher Isp, but also have serious safety issues. Propulsion in atmospheres can ingest atmospheric constituents (aka “airbreathing propulsion”) which provide additional propulsive mass when heated and a component of the combustion/energy generation process. This utilization of non-stored/carried propulsive mass provides partial separation of propulsive mass and energy and produces higher Isp. The other approach to separating propulsive mass and energy is to, either on board or added from offboard, supply additional energy, such as from nuclear or solar sources. This is the approach for fission nuclear thermal and electric propulsion, which can provide an Isp in excess of 800 seconds of Isp. Other processes or in addition to thermal expansion, such as electro-magnetics, can be employed to increase exit velocity and Isp. Separating propulsive mass and energy for space faring is commonly referred to as a means to circumvent the rocket equation and is capable of producing major benefits for the development of commercial deep space and space faring in general including affordable fast transits to mitigate the human health impacts of galactic cosmic radiation (GCR) and microG. The key to higher than chemical Isp, beyond H2-O2, and beyond the radiated energy and systems limitations of solar for space faring, is a light weight, high energy density source, either on board or via utilization of energy beaming to the vehicle. Traditional energy sources include chemical, heat, electrics, mechanical, photons, and nuclear. Propulsive mass can be carried on board, sourced beyond the surface of Earth via in-situ resource utilization (ISRU), and includes harvesting from atmospheres. High Isp via electromagnetic related propulsive mass acceleration requires sufficient ionization and conductivity. The major metrics for space propulsion are costs, safety, Isp, weight, and thrust level, the latter dependent upon mission requirements. High thrust for human missions is needed to reduce time exposed to radiation and microG and high thrust is required for space access. Costs of space access are reducing via reusability, printing manufacture, and robotization of manufacturing and operation. Chemical rockets provide high thrust from the expansion of the heated mass constituents at high mass flow. The other high thrust propulsion approach is magnetohydrodynamics (MHD), which, in addition to high thrust, has a high Isp of over 2,000 seconds of Isp. The VASIMIR engine offers some 5,000 seconds of Isp at high thrust [ref. 3]. Electric propulsion cycles are capable of Isp much higher than that but at low thrust levels using available energy sources. With cost as a major metric, reusable rockets and improved manufacturing and operations are rapidly greatly lowering the costs of space access, which could provide/supply in space fuel depots and affordable chemical propulsion for the desired human fast transits (e.g., some 200-day round trips to Mars). The other option for fast transits is VASIMIR, given a nuclear on-board energy source that has the requisite many megawatts of power and an alpha, kgs of weight/kW of energy produced, on the order of one (i.e., a light weight, high energy density energy source). The purpose of this report is to examine the options beyond traditional rocket engines, where propulsive mass and energy are combined, specifically the separation of propulsive mass and energy. This report considers the spectrum of advanced energetics, sources of propulsive mass, conductivity enhancement approaches, energy beaming possibilities, and candidate propulsion cycles. Suggestions are made for various combinatorial, system level, beyond traditional combustion rocket, space propulsion approaches for human deep space missions given the changing conditions of increased knowledge of deep space resources for ISRU, revolutionary energetics, and technology advancements writ large.

Dennis M. Bushnell

The Trailblazer Program

This paper presents the "Three Pillars of Success" for the Trailblazer Program. The topics include: 1) The "Rocket Equation" for SSTO (Single Stage To Orbit); 2) The Rocket I* Barrier; 3) Rocket-Based Combined-Cycle Engine; 4) Potential for Reusability; 5) Factors Mitigating RBCC Performance; 6) The "Trailblazer" Program; 7) Trailblazer Performance Goals; 8) Trailblazer Reference Vehicle; and 9) Trailblazer Program Architecture.

Trefney, Charles J.

Design of a Nozzle for the Spyder 2nd Stage Solid Rocket Motor

During the 2019 summer term, the author worked with a group of four interns to complete the preliminary design of a 2nd stage solid rocket motor for Up Aerospace’s Spyder Launch Vehicle. The Spyder vehicle is a four stage, solid fuel rocket designed as part of collaboration between NASA and Up Aerospace to develop a vehicle capable of delivering a 10 kg, 6U CubeSat into a 350 km, circular, low Earth orbit. As part of the agreement, NASA is tasked with designing high performance 2nd, 3rd, and 4th stages while Up Aerospace will provide the 1st stage, derived from the first stage of the company’s sub-orbital Spaceloft XL vehicle. Previous intern teams have designed the 3rd and 4th stages, which left the preliminary design of the 2nd stage motor to be completed this summer. The purpose of this report is to highlight a trade study which the author conducted to determine the nozzle geometry which would most benefit the performance of the 2nd stage motor. In this study, various nozzle parameters such as throat radius (RSI), expansion ratio, mass and their effects on the Isp and Delta V of the 2nd Stage were investigated. From this study, a nozzle geometry providing the necessary performance was chosen and implemented as part of the preliminary design of the 2nd stage motor. To mature the 2nd stage motor design, a trade space was needed to determine the nozzle configuration which would most benefit the performance of the 2nd stage. The trade space established did not only evaluate different expansion ratios for the same throat radius, but also investigated the possible performance gained from decreasing the throat radius to increase the expansion ratio and Isp capable of being delivered by the nozzle. Decreasing the throat radius would cause the chamber pressure to increase, consequently increasing the case and insulation mass required to safely operate a motor at higher pressures. To account for this factor, accurate estimates of inert mass first needed to be established. After doing so, the effects of varying nozzle expansion ratios, exit half angles, and subsequently length and mass were evaluated against motor and nozzle performance factors such as delta V and Isp. For this study, four throat radii ranging from 1.75” to 2.375” and consequently four different chamber pressures ranging 550 psia to 1200 psia were investigated. BACKGROUND To launch into Low Earth Orbit, a payload needs to be accelerated to the orbital velocity necessary to keep it from falling back to Earth. The change in velocity required between launch and orbital insertion is known as Delta V. The Delta V which a rocket or stage can deliver can be calculated using the Ideal Rocket equation, 𝛥𝑉=−𝑔0∗𝐼𝑠𝑝∗ln(𝑀𝑓𝑀𝑖) (3) Where 𝑔0 is the acceleration due to gravity at the earth’s surface, 𝐼𝑠𝑝 is the specific impulse of the rocket, 𝑀𝑖 is the initial mass of the rocket, and 𝑀𝑓 is the final mass of the rocket after burnout. From preliminary calculations beyond the scope of this paper, it was determined that 30500 ft/s of delta V would be required for a payload to be inserted into a 350 km circular orbit around the Earth. Using the known masses and Isp values of the 1st, 3rd, and 4th stages and equation 3, the delta V of each stage was calculated. The delta V required by the 2nd stage could then be found by taking the difference between the total delta V required and the delta V of the 1st, 3rd, and 4th stages. From this, the required delta V of the 2nd Stage was calculated to be 7340 ft/s. Specific impulse is an efficiency factor of the nozzle which defines the impulse delivered by the motor per unit of propellant weight. The main variables of a nozzle’s specific impulse investigated in this trade were exit cone half angle, throat radius, and expansion ratio which is affected by the throat radius. The expansion ratio, ε, of a nozzle is defined as the ratio between the nozzle exit area and throat area, and can be calculated using the equation, ε=𝑅𝑒𝑥𝑖𝑡2𝑅𝑠𝑖2 (2) Where 𝑅𝑒𝑥𝑖𝑡 is the radius of the nozzle’s exit and 𝑅𝑠𝑖 is the radius of the nozzle’s throat. A larger expansion ratio and smaller exit half angle will increase the Isp of a nozzle by allowing the gas to expand more and by allowing more of the exhaust gas to produce thrust in the direction of the motor’s central axis. A cross section view of the 2nd Stage motor with the major components annotated is provided in figure 1.

Bennett, Daniel

Space Resource Utilization and Extending Human Presence Across the Solar System

The Presidents Vision for Exploration is not a single mission, but an open ended journey that seeks to answer "How can we live on other worlds?" Using space resources is the only known approach for affordable, sustained, flexible, and self sufficient, human occupation beyond Earth orbit. Earth is a large planet. A simple analysis using the rocket equation shows that if Earth were a bit larger, chemical propulsion as a mechanism to access space would become impractical. Thus, even with the most efficient chemical rocket launch capability, the cost of lifting massive payloads into space will remain very steep (currently about $l00k/lb to the Moon and greater than $500k/lb to Mars). Space resource utilization should begin with an aggressive broad based demonstration program as afforded by the precursor missions implementation of the President's Vision of Exploration. Ion engine upper stages, for example, were studied for over 30 years, but only implemented in design after the Deep Space 1 in space demonstration. These demonstrations should include: extraction of elements from lunar regolith, and Martian soil and atmosphere, demonstration of power break even and growth from lunar or Mars moons derived photovoltaics, oxygen extraction for life support and propellant, and metals and alloys for in space repair and the production of habits and radiation shielding. Space resource utilization yields operational dividends through the subsequent programs including: propellant from lunar oxygen which could cut transportation costs from Earth in half, mega watts per year of power grown from lunar photovoltaics at decreasing cost per kW, decreased cost for human Mars missions by a factor of 10 by using propellant derived from Mars atmosphere for return, and in space manufacturing and food production with space resources yielding safe sustained and eventually self sufficient human presence in space. After the demonstration and implementation, the space resource utilization investment enables commercial and private viability beyond Earth orbit. For example, analysis has shown the lunar oxygen production for propellant becomes commercially viable after the exploration program completes the R&D, and power from lunar derived photovoltaics could, according to past NASA sponsored studies, pay for themselves while supplying most of Earth's electrical energy after about 17 years. Besides the Moon and Mars the resources of the near Earth asteroids enable the building of large space structures and science payloads. Analysis has shown that one of the thousands of these objects (some as easily accessible in space as the Moon and Mars), 2 km dia, the size of a typical open pit mine, would cost the total global financial product of Earth for 30,000 years if we were to launch it from Earth. Beyond Mars, the belt asteroids have been calculated to contain enough materials for habitat and life to support 10 quadrillion people. Thus, the development and use of space resources enables the extension of human life through the solar system allowing humanity to move from a planetary to a solar system society.

Curreri, Peter A.

Multi-Objective Hybrid Optimal Control for Multiple-Flyby Interplanetary Mission Design using Chemical Propulsion

Preliminary design of high‐thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys and the bodies at which those flybys are performed. For some missions, such as surveys of small bodies, the mission designer also contributes to target selection. In addition, real‐valued decision variables, such as launch epoch, flight times, maneuver and flyby epochs, and flyby altitudes must be chosen. There are often many thousands of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the impulsive mission design problem as a multi‐objective hybrid optimal control problem. The method is demonstrated on several real‐world problems. Two assumptions are frequently made to simplify the modeling of an interplanetary high‐thrust trajectory during the preliminary design phase. The first assumption is that because the available thrust is high, any maneuvers performed by the spacecraft can be modeled as discrete changes in velocity. This assumption removes the need to integrate the equations of motion governing the motion of a spacecraft under thrust and allows the change in velocity to be modeled as an impulse and the expenditure of propellant to be modeled using the time‐independent solution to Tsiolkovsky's rocket equation [1]. The second assumption is that the spacecraft moves primarily under the influence of the central body, i.e. the sun, and all other perturbing forces may be neglected in preliminary design. The path of the spacecraft may then be modeled as a series of conic sections. When a spacecraft performs a close approach to a planet, the central body switches from the sun to that planet and the trajectory is modeled as a hyperbola with respect to the planet. This is known as the method of patched conics. The impulsive and patched‐conic assumptions significantly simplify the preliminary design problem.

Optimization

A review of interstellar rocketry fundamentals

To reach even the nearest stars in a human lifetime requires a ship speed that is a substantial fraction of the speed of light. This means an enormous kinetic energy investment in the ship and suggests that maximizing the efficiency may be more important than minimizing the mass ratio. This paper develops the pertinent relativistic rocket equations and finds the conditions for high kinematic efficiency. Using the limiting efficiency of percent, the minimum energy needed for one-way and for round trip voyages, and to explore all 'good' suns out to a given distance, using prefueled rockets, is determined. Savings due to refueling the rocket (and reloading propellant) at the destination and in flight are both somewhat greater than 2:1.

Oliver, B. M.

Rho-Isp Revisited and Basic Stage Mass Estimating for Launch Vehicle Conceptual Sizing Studies

The ideal rocket equation is manipulated to demonstrate the essential link between propellant density and specific impulse as the two primary stage performance drivers for a launch vehicle. This is illustrated by examining volume-limited stages such as first stages and boosters. This proves to be a good approximation for first-order or Phase A vehicle design studies for solid rocket motors and for liquid stages, except when comparing to hydrogen-fueled stages. A next-order mass model is developed that is able to model the mass differences between hydrogen-fueled and other stages. Propellants considered range in density from liquid methane to inhibited red fuming nitric acid. Calculated comparisons are shown for solid rocket boosters, liquid first stages, liquid upper stages, and a balloon-deployed single-stage-to-orbit concept. The derived relationships are ripe for inclusion in a multi-stage design space exploration and optimization algorithm, as well as for single-parameter comparisons such as those shown herein.

Kibbey, Timothy P.

Mass driver reaction engine characteristics and performance in earth orbital transfer missions

Configurations of a typical mass driver reaction engine (MDRE) are presented and its use for delivery of payloads to geosynchronous orbit (GEO) from low earth orbit (LEO) is discussed. Basic rocket equations are developed for LEO to GEO round-trip missions using a single exhaust velocity. It is shown that exhaust velocities in the 5-10 km/sec range (specific impulse of 500-1000 sec) are well suited for mass drivers, minimizing the overall cost of missions. Payload delivery rate fractions show that there is little to be gained by stretching out LEO to GEO transfer times from 90 to 180 days. It therefore pays to use the shorter trip time, approximately doubling the amount of delivered payload during any fixed time of use of the MDRE.

Snow, W. R.

Fast round-trip Mars trajectories

This paper is concerned with the effect of limiting the overall duration or else the one-way flight time of a round trip to Mars, as reflected in the sum of impulsive velocity increments required of the spacecraft propulsion system. Ignition-to-burnout mass ratios for a hypothetical single stage spacecraft, obtained from the rocket equation by combining these delta-V sums with appropriate values of specific impulse, are used to evaluate the relative effectiveness of four high-thrust propulsion alternatives. If the flight crew goes to the surface of Mars and stays there for the duration of their stopover, it is much cheaper (in terms of delta-V) to minimize their zero-g exposure by limiting the interplanetary transit time of a conjunction-class mission (round trip time = 800-1000 days, Mars stopover = 450-700 days) than to impose the same limit on an opposition-class mission (round trip time less than 600 days, stopover = 40 days). Using solid-core nuclear thermal propulsion to fly a conjunction-class mission, for a moderate mass penalty the interplanetary transit time (each way) probably could be limited to something in the range of 4 to 6 months, depending on the launch year.

Wilson, Sam