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No abstract available
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.
The problem of trajectory optimization is important in all space missions. The solution of this problem enables one to specify the optimum thrust steering program which should be followed to achieve a specified mission objective, simultaneously satisfying the constraints.1 It is well known that whether or not the ascent trajectory is optimal can have a significant impact on propellant usage for a given payload, or on payload weight for the same gross vehicle weight.2 Consequently, ascent guidance commands are usually optimized in some fashion. Multi-stage vehicles add complexity to this analysis process as changes in vehicle properties in one stage propagate to the other stages through gear ratios and changes in the optimal trajectory. These effects can cause an increase in analysis time as more variables are added and convergence of the optimizer to system closure requires more analysis iterations. In this paper, an approach to simplifying this multi-stage problem through the creation of an upper stage capability boundary is presented. This work was completed as part of a larger study focused on trade space exploration for the advanced booster system that will eventually form a part of NASA s new Space Launch System.3 The approach developed leverages Design of Experiments and Surrogate Modeling4 techniques to create a predictive model of the SLS upper stage performance. The design of the SLS core stages is considered fixed for the purposes of this study, which results in trajectory parameters such as staging conditions being the only variables relevant to the upper stage. Through the creation of a surrogate model, which takes staging conditions as inputs and predicts the payload mass delivered by the SLS upper stage to a reference orbit as the response, it is possible to identify a "surface" of staging conditions which all satisfy the SLS requirement of placing 130 metric tons into low-Earth orbit (LEO).3 This identified surface represents the 130 metric ton capability boundary for the upper stage, such that if the combined first stage and boosters can achieve any one staging point on that surface, then the design is identified as feasible. With the surrogate model created, design and analysis of advanced booster concepts is streamlined, as optimization of the upper stage trajectory is no longer required in every design loop.
Traditional azimuth-elevation ("az-el") stages are used to point a variety of devices ranging from large optical telescopes to tank guns. Such a stage typically has an elevation stage having a horizontal axis mounted on an azimuth stage with a vertical axis. Both stages are often motorized. Optical communications transceivers often require two-axis motorized control, as when the communications link is between a ground station and an aircraft or satellite. In such applications, the traditional azimuth-elevation stage has two important drawbacks: a gimbal lock exclusion zone at zenith and susceptibility to pointing errors caused by backlash. Az-el stages in which the azimuth stage cannot rotate a full 360deg have the additional drawback of an azimuth exclusion zone. The diagonal-axes stage described here mitigates or eliminates all of these problems. Instead of one vertical axis and one horizontal axis, a diagonal-axes stage has two horizontal axes, both oriented at 45 to the trajectory of the target. For example, a ground station located on the equator tracking a satellite with an equatorial orbit would have one axis parallel to northeast and southwest, and the other axis parallel to northwest and southeast. The diagonal-axes stage is considerably less vulnerable to backlash. If it is correctly oriented, its axes rotate in only one direction during an overhead pass by a satellite. As a result, the effects of backlash may be inherently eliminated. If the gravity-induced torque on either axis changes during the pass, then backlash may become important during the part of the pass where the gravity torque, instead of opposing the motion of the stage, pushes the stage in the direction of motion. This can result in the loss of gear-to-gear contact in one or more stages of the gear reduction mechanism. In this case, a preload spring used to eliminate backlash need only be sufficiently strong to overcome the gravity torque, i.e. it need not overcome friction in the gear train. The diagonal-axes stage is not backlash-free for arbitrary target trajectories such as an aircraft might execute. If properly oriented for any particular satellite, however, it is backlash-free for all passes of that satellite, which will trace out parallel paths on the sky, and for all passes of any other satellite that are perpendicular to the first. It will also be backlash-free for some fraction of other satellite trajectories.
This viewgraph presentation describes the modeling and simulation of the Ares Upper Stage Transportation, lifting, stacking, and mating operations within the Vehicle Assembly Building (VAB) at Kennedy Space Center (KSC). An aerial view of KSC Launch Shuttle Complex, two views of the Delmia process control layout, and an upper stage move subroutine and breakdown are shown. An overhead image of the VAB and the turning basin along with the Pegasus barge at the turning basin are also shown. This viewgraph presentation also shows the actual design and the removal of the mid-section spring tensioners, the removal of the AFT rear and forward tensioners tie downs, and removing the AFT hold down post and mount. US leaving the Pegasus Barge, the upper stage arriving at transfer aisle, upper stage receiving/inspection in transfer aisle, and an overhead view of upper stage receiving/inspection in transfer aisle are depicted. Five views of the actual connection of the cabling to the upper stage aft lifting hardware are shown. The upper stage transporter forward connector, two views of the rotation horizontal to vertical, the disconnection of the rear bolt ring cabling, the lowering of the upper stage to the inspection stand, disconnection of the rear bolt ring from the upper stage, the lifting of the upper stage and inspection of AFT fange, and the transfer of upper stage in an integrated stack are shown. Six views of the mating of the upper stage to the first stage are depicted. The preparation, inspection, and removal of the forward dome are shown. The upper stage mated on the integrated stack and crawler is also shown. This presentation concludes with A Rapid Upper Limb Assessment (RULA) utilizing male and female models for assessing risk factors to the upper extremities of human beings in an actual physical environment.
A program was conducted to evaluate the effects of scaling, tip clearance, and IGV reset on the performance of a low aspect ratio compressor stage. Stage design was obtained by scaling an existing single stage compressor by a linear factor of 0.304. The design objective was to maintain the meanline velocity field of the base machine in the smaller size. Adjustments were made to account for predicted blockage differences and to chord lengths and airfoil edge radii to obtain reasonable blade geometries. Meanline velocity diagrams of the base stage were not maintained at the scaled size. At design speed and flowrate the scaled stage achieved a pressure ratio of 1.423, adiabatic efficiency of 0.822, and surge margin of 18.5%. The corresponding performance parameters for the base stage were 1.480, 0.872, and 25.2%, respectively. The base stage demonstrated a peak efficiency at design speed of 0.872; the scaled stage achieved a level of 0.838. When the scaled stage rotor and stator tip clearances were doubled, the stage achieved a pressure ratio of 1.413, efficiency of 0.799, and surge margin of 16.0% at the design flowrate. The peak stage efficiency at design speed was 0.825 with the increased clearance. Increased prewhirl lowered the stage pressure ratio as expected. Stage efficiency was maintained with ten degrees of increased prewhirl and then decreased substantially with ten additional degrees of reset.