Burnout Velocity Research Articles

Optimal midcourse guidance law for the exo-atmospheric interceptor with solid-propellant booster

This paper focuses on the midcourse guidance law for the exo-atmospheric interceptor with solid-propellant booster to intercept a target in the Keplerian orbit, in which the thrust direction command is provided under the typical framework of predictor-corrector algorithm. Firstly, an analytical solution is derived to predict the burnout velocity and position vectors, in which the thrust vector is assumed to be along the velocity vector. Secondly, the predicted values are used to formulate a set of nonlinear algebraic equations to determine the desired burnout velocity direction to impact the target. Actually, those equations are transcendental because Lambert's problem with unspecified time-of-flight is involved. Then, Newton-Raphson method is used to solve the problem. In the calculation process, the Jacobian matrix corresponding to the equations is derived in an analytical manner, which significantly improves the computational efficiency. Thirdly, an optimal correction guidance law is constructed to steer the interceptor to achieve the desired burnout velocity direction. Finally, convergence evaluation, optimality verification, and Monte Carlo simulations are carried out to test the performance of the proposed guidance law. The results show that it not only performs well in providing the optimal guidance command, but also has high computational efficiency and guidance accuracy. Moreover, it has great robustness even in large dispersions and uncertainties.

A numerical investigation of radiation feedback in different regimes of opposed flow flame spread

Radiation has been found to play an important role in opposed-flow flame spread, especially in the low-velocity microgravity environment. To explore the various aspects of flame radiation, an existing comprehensive 2D computational model including gas and surface radiation as well as radiation feedback to the solid is utilized. The comprehensive radiation model is simplified into a number of sub-models: no radiation, gas losses, surface loss, uncoupled (gas and surface losses without feedback). The sub-models are evaluated over the kinetic, thermal, and radiative regimes for a thin PMMA fuel. The resulting spread rates, flame and vaporization temperatures, and flame structures are compared to the comprehensive fully coupled model. The computational results reveal that gas-to-surface feedback moderately enhances spread rate and may affect the critical burnout velocity but has little effect on flame and vaporization temperatures.

A Novel Approach for Optimizing Two-Phase Flow in Water Rockets: Part I

The main objective of enhancing the water rocket performance is nothing but to achieve the maximum possible burnout velocity and maximum altitude. As reported by previous researchers, the presence of the two-phase flow deteriorates the performance of water rockets. This article is the first in a series of articles that aim at a new design of the rocket nozzle that makes the presence of the two-phase flow an advantage that enhances the water rocket performance. The aim of this article is to introduce an energy balance analysis that investigates the optimum liquid water to gas mass ratio that achieves the optimum performance (the maximum possible burnout velocity) for a water rocket. In this energy balance analysis, the liquid water to the gas mass ratio is to be optimized using the reservoir pressure as the independent variable during the expansion process to avoid the complexity of the transient nature of the flow process.

Trajectory Design for Space Missions to Libration Point L2

This work is focused on the detection and computation of "free" transfer trajectories from parking orbits around the Earth to quasiperiodic orbits around the collinear libration point L(2), in the Sun-Earth system; no correction or insertion maneuvers into the final orbits have been considered. The circular restricted three-body problem is the mathematical model used to describe the motion of a spacecraft, in the gravitational field of the two primaries, computed by integrating the nonlinearized equations of motion. A shooting method has been designed and developed to determine the increment of velocity required for the perigee maneuver, which injects a spacecraft into its transfer trajectory: first the velocity boundary for the Earth escape/capture condition is detected and then an iterative bisection method is applied until the burnout velocity, tangential to the parking orbit, leads the spacecraft to its final Lissajous orbit. For a launch from Kourou at local noon, Ariane5 GTO and Soyuz GTO "equivalent" have been studied and compared, considering fuel minimization for the transfer maneuver and general mission constraints, as maximum excursion of the final Lissajous orbit from the ecliptic plane and eclipses avoidance during the mission. This analysis highlights advantages and drawbacks of various parking orbits. Mission goals are the key factor for the tradeoff among orbit selection, launch options, and the other constraints, fixed by mission requirements.

Influence of products of combustion and addition of water vapor on the turbulent combustion of methane mixtures

An experimental and theoretical study of the effects of the combustion products and water vapor on the turbulent combustion of methane mixtures in engines with spark ignition is presented. In order to compare experimental data for a spherical mock-up chamber, with known turbulent field, with the conditions at the end of the compression stroke of an actual engine running with an initial pressure of ~i.0 MPa and a temperature of 550-650~ the air was replaced by a mixture of 02 + 1.6N 2. The initial temperature in all cases was 385~ Because of the selected gas composition, the velocity of the experimental laminar flame was the same as that in the combustion chamber of the engine, under the specified conditions at the end of the compression stroke. The correctness of this procedure has been confirmed by [i] from measurements of the laminar velocity on rapid compression rigs. Systems involving partial engine loading and recirculation of the residual gases require a knowledge of the combustion properties of mixtures with specific proportions of the combustion products. Data on the effect of water vapor concentration on the normal combustion velocity and the turbulent burnout velocity can also be obtained by the constant volume method. For the study of the combustion of mixtures diluted with the combustion products, a predetermined portion of the fuel mixture was burned and the combustion products mixed with the remaining portion of the unburnt fuel mixture. Water vapor was produced in the combustion chamber by burning a stoichiometric mixture of hydrogen and oxygen at the selected pressure and subsequently mixing the combustion products with the unburnt fuel mixture. The experimental results for three groups of fuel mixtures with different coefficients of excess oxygen (~) are shown in Fig. i, where the velocity of turbulent burnout (w) is plotted against the root mean square pulsating velocity u' E. The normal velocities of the laminar flames (u n) are given by the points of intersection on the ordinate axis. As will be seen from Fig. i, the dilution of any initial mixture of CH 4 + 2=(O= + 1.6N=) by the combustion products or by water vapor decreases the velocities of both laminar and turbulent combustion. This can be explained by the lower combustion temperature after dilution. The decrease in the turbulent velocity caused by dilution of the fuel mixture with the combustion products is constant throughout the entire range of the values of =, whereas dilution with water vapor has the greatest effect on nonstoichiometric the effect being smallest when ~ = I.i. An important trend, illustrating the effect of the diffusion-thermal structure of the flame front on turbulent combustion, is apparent from a comparison of the w(u'z) curves for mixtures of the same dilution with values of = equal to 1.4 and 0.8. When ~ = 1.4, the

Constant thrust programming for a multistage rocket flown in vacuum with a given initial/final thrust-to-weight ratio in an arbitrary stage

The burn time and burnout velocity of a multistage rocket flown vertically in vacuum with constant thrust tangential to the flight path and a prescribed initial/final thrust-to-weight ratio in an arbitrary stage have been determined.The present paper also deals with optimal staging under given conditions of flight.

Orbit plane change by external burning aerocruise.

plication to modern engineering problems/' Douglas Aircraft Co., Santa Monica, Calif. (1957); unpublished lecture notes. 8 Miele, A., General variational theory of the flight paths of rocket powered aircraft, missiles and satellite carriers, Astronaut. Acta 4, 264-288 (1958). 9 Bauer, A. B. and Thelander, J. A., A variational method for finding the flight path which gives the maximum burnout velocity for a multistaged rocket vehicle, Douglas Aircraft Co., Long Beach, Calif., Engineering Rept. LB-25956 (June 1959). 10 Stewart, C. E. and Thelander, J. A., Optimum trajectory analysis, Ford Motor Co., Aeronutronic Div., Tech. Rept. 11-1435(1961).

Comment on ''relative variation of rocket vehicle specific impulse and structural weight fraction for constant burnout velocity

I Ref 1, which is concerned with optimum rocket flight performance, a discussion of the relative influence of changes in propulsion system design or propellant capability is presented An equation, (3 23b) of Ref 1, which expresses the ratio AIsp/ As, is derived for conditions of constant burnout velocity and zero-gr flight in vacuum The final equation is in error, as are the curves of Fig 3-9, p 3-15 of Ref 1 The correct results are derived by writing the equation for burnout velocity

NUCLEAR ROCKET THRUST OPTIMIZATION USING DYNAMIC PROGRAMMING

The problem considered is that of maximizing the burnout velocity of a solid core nuclear rocket. The optimal thrust schedule was shown, for a range of realistic parameter values, to differ from the well-known result for chemical systems because of the necessity to remove core fission product decay afterheat. This afterheat, which must be removed if the core is to remain intact, is a function of the reactor operating power schedule. The criterion of optimality is the maximization of the rocket final velocity under the constraints of a maximum and minimum allowable reactor power level corresponding to engine throttleable limits and a fixed initial propellant loading that is to be allocated either as useful thrust-producing propellant or as a core afterheat removal coolant yielding no useful thrust. The method of dynamic programming is used to perform the optimization. Numerical results are presented for an example problem that considers vertical, drag-free liftoff from a stationary earth with a uniform gravitational field. Means to relax all of these restrictions, along with other important extensions, are discussed. The effect of varying the problem parameters also is indicated, and implications thereof are pointed out.

Characteristic Control Requirements for Nuclear Rocket Engines and Vehicles

Because efficiert staging of rocket vehicles, in general, requires a rapid thrust buildup, a rapid startup will be essential in nuclear rocket engines. However, the startup and staging methods selected must not compromise system reliability or safety. The minimum startup time depends for the most part on the maximum allowable fuel element tempetature rise rates. In addition, the relatively long interstage section and the thrust buildup characteristics presert unique, if not complex, problems for the analysis of the staging sequence. The two thrust vector cortrol systems, although reflecting some degradation in over- all performance, do not exhibit enough advantage of one over the other to select the optimum system for the early phase of a nuclear vehicle program. Further evaluation, for proper selection, is highly dependent on the engine development approach and study of the engine environments and operational requirements. The instantaneous and sharp cutoff of thrust, experienced in the chemical engine, is not feasible in the nuclear rocket engine since the fission product heat must be removed to prevent material temperatures from subsequertly reaching unacceptable levels if engine integrity is to be mairtained with all componerts in operating condition. The tail-off performance produced by after-coo.,ng must be factored intomore » the determination of the final burnout velocity, but it must certainly be predictable and repeatable, in both magnitude and time, in order to establish acceptable vehicle performance, stability, and control. (auth)« less

Optimum Maneuvers for Launching Satellites Into Circular Orbits of Arbitrary Radius and Inclination

2 Miele, A., A Survey of the Problems of Optimizing Flight Paths of Aircraft and Missiles, ARS preprint 1219-60. 3 Breakwell, J. V., The Optimization of Trajectories, J. Soc. Indust. Appl. Math., vol. 7, no. 2, June 1959, pp. 215-247. 4 Kelley, H. J., Gradient Theory of Optimal Flight Paths, ARS preprint 1230-60. 5 Kulakowski, L. J. and Stancil, R. T., Boost Trajectories for Maximum Burn-Out Velocity, ARS JOURNAL, vol. 30, no. 7, July 1960, pp. 612-618. 6 Bliss. G. A., Lectures on the Calculus of Variations, University of Chicago Press, Chicago, First Ed., 1946, Chap. 7. 7 Cicala, C. and Miele, A., Brachistochronic Maneuvers of a Variable Mass Aircraft in a Vertical Plane, J. Aero. Sci., vol. 22, no. 8, Aug. 1955, pp. 577-578. 8 Wheelon, A. D., Free Flight of a Ballistic Missile, ARS JOURNAL, vol. 29, no. 12, Dec. 1959, pp. 915-926. 9 Leitmann, G., On a Class of Variational Problems in Rocket Flight, J. Aero/Space Sci., vol. 26, no. 9, 1959. 10 Leitmann, G., Minimum Transfer Time for a Power-Limited Rocket, XI Int. Astronautical Congress, Stockholm, 1960. 11 Fried, B. D., On the Powered Flight Trajectory of an Earth Satellite, J E T PROPULSION, vol. 27, no. 6, June 1957, pp. 641-643.

Optimum Pay-Load-Ratio Relation for Multiple-Stage Rockets

The principle of the multiple-stage rocket is reviewed. It is shown that the burn-out velocity of a multiple-stage rocket is higher than that of a single-stage rocket of the same over-all mass ratio. It is also shown that the over-all pay-load ratio of a multiple-stage rocket required to reach a given velocity is minimum when the pay-load ratios of all stages are equal. Departure from this equality is demonstrated to have little effect on the over-all pay-load ratio.

On the Optimization of Two-Stage Rockets

Abstract : Equations useful in design studies are derived for determining the optimum weight distribution for two-stage tandem rockets for the case of different structural factors and propellant specific impulses in each stage. Minimization of gross weight for a given required burnout velocity and payload is the criterion of optimization used. For illustrative purposes an example is included in which the optimum distribution is found for a hypothetical chemically-boosted atomic rocket. (Author)