Launch Azimuth Research Articles

Launch parameters of a lunar ice payload traveling via electromagnetic mass accelerator

This paper describes a solution for procuring propellent needed for future space exploration missions based on the Lunar Electromagnetic Mass Accelerator (LEMMA) concept analyzed by McNab and McGlasson. This study examined the feasibility of using an electromagnetic launcher (EML) to transport raw materials used in propellent production from the lunar south pole to the National Aeronautics and Space Administration's (NASA) Lunar Gateway. The proposed Gateway space station, to be located in a lunar near-rectilinear halo orbit (NRHO), is a critical part of NASA's Artemis program. Cheaply and efficiently sourcing lunar hydrogen from surface ice to the Gateway would benefit the program's success and future exploration of the solar system. Our study of the launch requirements for a lunar EML payload are described here. AGI Inc's Systems Tool Kit (STK) was used to calculate the required launch azimuth, elevation, magnitude, epoch, and trip duration for a payload launched from the Moon to rendezvous with Gateway. The study shows that it is feasible to conduct a single launch from the lunar south pole that can intercept any point along the Gateway's orbit with variable launch conditions.

Efficient Estimation of a Thrusting/Ballistic Trajectory Using a Single Passive Sensor

The state of a thrusting/ballistic object moving in a 3-D space can be determined uniquely by a 4-D parameter vector (launch azimuth and elevation angles, drag coefficient, and specific thrust, with the latter two assumed constant) given the location of the launch point (LP). Using the first line-of-sight (LoS) measurement and the known launch altitude, one can reconstruct the LP, which, if taken as the true LP, can be used to estimate the above parameter vector. However, the resulting estimate ignores the fact that the LP based on the first LoS measurement is noisy. To make the estimate account for the LP location uncertainty, we augment the parameter vector with the ground coordinates of the LP, yielding a 6-D vector to be estimated. The estimation errors of the resulting maximum likelihood estimates are shown to meet the Cramer–Rao lower bound, i.e., they are efficient.

On the Non-coplanar Transfer of Type II between Two Circular Orbits

The paper regards two-impulse transfer from a low parking orbit into a circular orbit with the altitude less than 36 000 km, while the inclination correction is carried out with each maneuver. An approximate formula is proposed capable of evaluating analytically the optimal value of the first correction of inclination; the corresponding accuracy data are given. Examples are provided to show the operational efficiency of an optimal non-coplanar transfer of the type II with injections of satellites into various target orbits from Russian launch sites with due account of the available launch azimuths.

Trajectory characteristic analysis influenced by initial state errors for long-range vehicles

The initial state errors, caused by the Earth’s un-homogeneity through the leveling and alignment of an inertial platform before launching a long-range vehicle, will bring about remarkable flight state deviations and fall point deviations by flight dynamics. In order to analyze the propagation characteristics of the initial state errors and rapidly estimate their influence magnitude, an analytical propagation model of trajectory design is deduced by employing state space perturbation theory in nominal launch coordinate system. Then, propagation matrices of engine-cutoff state deviations and fall point deviations are obtained. In the simulations, deviations of engine-cutoff and fall point are computed in the case of a fixed launch azimuth, different launch azimuths and different launch points. Next, propagation regularities of the initial state errors are analyzed from the launch point to the engine-cutoff as well as to fall point. Conclusions are as follows: (1) the estimation accuracy of flight states deviations during boost phase will be distinctly enhanced when considering the force term deviations; (2) in the case of different launch azimuths, position and velocity deviations of engine-cutoff in the x, y directions and longitudinal deviation of fall point are symmetrical at the azimuth of 45° where these deviations are maximum. Comparatively, position and velocity deviations of engine-cutoff in the z direction and lateral deviation of fall point are symmetrical at the azimuth of −45°; (3) the proposed analytical propagation model of the initial state errors has a high estimation accuracy within the error percentage of 2%, which can improve computational efficiency by 100 times and is more suitable for multiple simulation scenarios.

Evaluation and selection of missile's optimal initial launch azimuth under side window detection using a hybrid decision making method

Initial launch azimuth of missile is a key factor that affects the guidance performance, especially for missile with side window seeker. The aim of this study is to select the optimal initial launch azimuth of missile with side window seeker to achieve a high hit rate by using a hybrid multi-attribute decision making (MADM) method. The hybrid decision-making method combines interval numbers and combination weight with Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The specific innovations of the hybrid MADM method includes developing a new method to measure the distance between interval numbers, a new normalization method based on ideal interval for attributes, and a new combination weight method based on attribute importance. It is found that the decision results are robust, have a reliability of up to 90% or even 95%, and the best azimuths of missile can achieve a hit rate as high as 90% or even 100%. This indicates that there is a great possibility of solving the guidance problem of side window detection based on proportional navigation by applying the optimal initial launch azimuth of missile. The optimal results can provide reference for the fire control system.

A rapid compensation method for launch data of long-range rockets under influence of the Earth's disturbing gravity field

Regarding the rapid compensation of the influence of the Earth’ s disturbing gravity field upon trajectory calculation, the key point lies in how to derive the analytical solutions to the partial derivatives of the state of burnout point with respect to the launch data. In view of this, this paper mainly expounds on two issues: one is based on the approximate analytical solution to the motion equation for the vacuum flight section of a long-range rocket, deriving the analytical solutions to the partial derivatives of the state of burnout point with respect to the changing rate of the final-stage pitch program; the other is based on the initial positioning and orientation error propagation mechanism, proposing the analytical calculation formula for the partial derivatives of the state of burnout point with respect to the launch azimuth. The calculation results of correction data are simulated and verified under different circumstances. The simulation results are as follows: (1) the accuracy of approximation between the analytical solutions and the results attained via the difference method is higher than 90%, and the ratio of calculation time between them is lower than 0.2%, thus demonstrating the accuracy of calculation of data corrections and advantages in calculation speed; (2) after the analytical solutions are compensated, the longitudinal landing deviation of the rocket is less than 20m and the lateral landing deviation of the rocket is less than 10m, demonstrating that the corrected data can meet the requirements for the hit accuracy of a long-range rocket.

Propagation mechanism analysis of navigation errors caused by initial state errors for long-range vehicles

The inertial navigation system is aligned and leveled before the launch of a long-range vehicle. However, the non-uniformity of the Earth can lead to initial state errors including initial positioning errors and initial orientation errors, causing navigation errors in flight dynamics and eventually impact-point deviations up to approximately 1 km. In order to analyze the propagation mechanisms of initial state errors and rapidly estimate their influence magnitudes, navigation perturbation equation subject to apparent acceleration coupling is established based on state space perturbation theory in the launch inertial coordinate system. Afterwards, a series of analytical form of deviations are derived including gravitational acceleration deviation, apparent acceleration projection deviation, apparent acceleration coupling deviation, initial velocity errors and initial position errors. Then, the analytical propagation model of engine-cutoff state deviations and impact-point deviations are acquired by solving the navigation perturbation equation. In the simulations, computer codes are programmed to calculate the propagation matrices of engine-cutoff state deviations and impact-point deviations in the case of fixed launch azimuth, followed by the propagation mechanism analyses of initial state errors. Next, two more scenarios of different launch azimuths and different launch points are simulated to further verify the reliability of the proposed analytical propagation model. The results show that analytical solutions of the propagation model proposed in this paper can well coincide with numerical solutions, with relative errors being all less than 1%, which is also suitable for multiple distinct simulation scenarios compared with previous methods.

A Rapid Gun Firing Correction Algorithm Using Discrete Time Transfer Matrix Method

To improve the next shot hit accuracy, a firing angle correction algorithm will be developed using the distance error computed between the impact and target coordinates to determine the launch azimuth and quadrant elevation angles for artillery projectiles. This correction method will be developed using the discrete time transfer matrix method of the projectile modified point mass model DTTMM-4DOF to improve correction method performance. To validate the proposed algorithm, a spin-stabilized 155mm-HE projectile flight trajectory will be used, assuming that wind magnitude and direction with the down range are changing as function of projectile altitude.

직접 전이궤적을 이용한 한국형 달 궤도선 임무설계 및 분석

달 궤도선은 한국형발사체(KSLV-II)에 실려 지구 저궤도에 투입된 후, 지상 안테나를 이용한 달 궤도선의 추적데이터 획득 및 궤도결정 과정을 거쳐 적절한 시점에서 TLI(Trans Lunar Injection) 엔진을 점화시켜야 한다. 본 논문은 달 궤도선을 나로우주센터에서 발사하여 달 궤도에 진입하기까지 여러 단계로 나누고 발사 방위각 및 발사창 분석부터 TLI 및 LOI(Lunar Orbit Insertion) 분사 위치에 따른 속도증분(<TEX>${\Delta}V$</TEX>) 그리고 가시성 및 식 기간 분석까지 수행하여 직접 전이궤적의 전반적인 특성을 분석하였다. 본 논문은 향후 달 임무 설계 시 관성비행 기간 및 전이기간에 따라 속도증분이 어떻게 변하는지에 대한 전반적인 내용을 파악하는데 도움이 되고, 발사 시각 선정과 연료소모를 줄일 수 있는 파라미터 선정에 도움을 줄 것으로 판단된다. The Lunar orbiter is expected to be inserted into a ~300km low Earth orbit using Korea Space Launch Vehicle-II(KSLV-II). After the states are successfully determined with obtained tracking data, the Trans Lunar Injection(TLI) burn has to be done at appropriate epoch to send the lunar orbiter to the Moon. In this study, we describe in detail the mission scenario of the Korean lunar orbiter from the launch at NARO Space Center to lunar orbit insertion(LOI) stage following direct transfer trajectory. We investigate the launch window including launch azimuth, delta-V profile according to TLI and LOI burn positions. We also depict the visibility conditions of ground stations and solar eclipse duration to understand the characteristics of the direct transfer trajectory. This paper can be also helpful not only for overall understanding of <TEX>${\Delta}V$</TEX> trend by changing TOF and coasting time but for selecting launch epoch and control parameters to decrease fuel consumption.

Surface Corridor Requirements for Space Launches over the Black Sea

Romanian space project NERVA develops the small rocket launcher for injecting nanosatellites into a very LEO. The launching area security first requires establishing a safe launch corridor on the ground. The first candidate for the experiments with the orbital rocket prototype is the western coast of the Black Sea in Romania. Optimal flight considerations immediately show that the best launch azimuth is on west-east direction, which defines a launching corridor along the Black Sea with the similar orientation. Do to the dense population of the sea shore area and to the rather agglomerated condition on the Black Sea, serious concerns arise regarding the safety measures to be solved, before any space activity above the Black Sea should begin. The main challenge is the safe prediction of the impact point of the space launcher in every moment of the atmospheric ascent, in case of unavoidable failure of the propulsion system. This task is assumed and presented as developed within a recent research activity of the NERVA team.

A Simplified Guidance for Target Missiles Used in Ballistic Missile Defence Evaluation

A simplified guidance scheme for the target missiles used in Ballistic Missile Defence is presented in this paper. The proposed method has two major components, a Ground Guidance Computation (GGC) and an In-Flight Guidance Computation. The GGC which runs on the ground uses a missile model to generate attitude history in pitch plane and computes launch azimuth of the missile to compensate for the effect of earth rotation. The vehicle follows the pre launch computed attitude (theta) history in pitch plane and also applies the course correction in azimuth plane based on its deviation from the pre launch computed azimuth plane. This scheme requires less computations and counters In-flight disturbances such as wind, gust etc. quite efficiently. The simulation results show that the proposed method provides the satisfactory performance and robustness.

Doppler-inferred launch angles of global acoustic ray paths

Doppler measured at Ascension Island from a moving acoustic source at Heard Island is used to compute the azimuth of the acoustic path at the source. This method yields a launch angle of 268.06±0.1° as compared to the geodesically derived launch angle (allowing for Earth flattening and horizontal refraction) of 268.05°. Although the Doppler-derived launch azimuths should theoretically be able to resolve the small angular differences between acoustic paths to hydrophones to the West and East of Ascension, this proved not to be the case.

Sonic boom measurement for space shuttle

Sonic boom measurements have been obtained during six flights of the Space Transportation System (STS). Information regarding sonic boom signature characteristics that include overpressure, period, and shock‐rise‐time will be discussed and some comparisons with predictions will be shown. Measurements of the sonic boom generated by the orbiter during descent flight phases were made on STS‐1, STS‐2, STS‐4, and STS‐11. Ascent measurements were obtained during STS‐5 and STS‐7 launches. The objectives were (1) to define sonic boom characteristics of the STS during both launch and entry, and (2) to assess the validity of a semi‐empirical method used previously to predict 2, 4, and 11 entries into Edwards Air Force Base or Kennedy Space Center. Sonic booms during descent are of particular interest to NASA because of the population centers exposed. During ascent from the Kennedy, no land masses are impacted by the pressure wave. However, ascent booms for STS launches are important to the Air Force because of their plan to launch the Shuttle from Vandenberg Air Force Base. From Vandenberg, the launch boom may impact (for some launch azimuths) the Channel Islands and, under some conditions, the California coast itself.

INVESTIGATION OF MAXIMUM STRESSES IN LONG, PRESSURIZED, CYLINDRICAL SHELLS

mum launch azimuths, since for this launch time the optimum azimuth is due-east. The entire trajectory is seen to lie in the reference plane, and where the trajectory terminates, the reference plane is extended by the dashed curve. For the other two launch times, the reference plane is translated and drawn through the launch site in order to yield a visualization of two-dimensional motion. Some understanding of the variation of launch azimuth can be obtained from this figure. Consider, for example, the trajectories shown for Afo = +1 hr. For the due-east launch azimuth, the trajectory is S shaped. There are two turnings or bendings of the trajectory. Near the launch site, the flight plane is turned southerly to bring the motion toward the desired plane. Towards the injection point, a second turning is necessary to bring the velocity vector as well as the position vector into the plane. Optimization of the launch azimuth is seen to alleviate the necessity for the bending around the launch site. Thus, the bending of the trajectory, i.e., its three-dimensionality, can be equated roughly with energy expenditure. This would leave one with a final conjecture. The initial bending of the plane seen for the due-east launch azimuth is necessary to direct the motion toward the desired plane, and if this were not done, burnout would occur at some point relatively remote from the reference plane. But if a coast were introduced at a sufficiently high energy level to avoid excessive descent, and if the coast were of a sufficiently long duration to allow a displacement of the order of 180°, the vehicle would approach automatically the reference plane from the other side of the earth. This may improve performance in much the same manner as did optimization of the launch azimuth.