Theory of Flight of the Sounding Rocket

1959 ◽  
Vol 26 (1) ◽  
pp. 127-129
Author(s):  
V. C. Liu
Keyword(s):  
Close Agreement ◽  
Equations Of Motion ◽  
Sounding Rocket ◽  
Performance Parameters ◽  
Atmospheric Density ◽  
Free Flight ◽  
Sounding Rockets ◽  
Definite Pattern ◽  
Transcendental Functions ◽  
Rocket Performance

Abstract Solutions of the equations of motion of vertically ascending rockets (both in power flight and in free flight) are given in closed form. Atmospheric density is assumed to vary exponentially with altitude, and the variation of the drag coefficient of the rocket with Mach number is assumed to follow a definite pattern. (The validity of the latter assumption is established by its close agreement with measured results.) These solutions, given in terms of special transcendental functions, can be used for the rapid estimation of sounding-rocket performance, eliminating the often-used laborious process of stepwise integration. The general rocket-performance parameters prescribed in the analysis also can be used to advantage in comparing and selecting multistage sounding rockets.

scholarly journals Approximately permanent electronic orbits and the origin of spectral series

1915 ◽  
Vol 91 (626) ◽  
pp. 156-170
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Experimental Work ◽  
Close Agreement ◽  
Equations Of Motion ◽  
Electronic Systems ◽  
Spectral Series ◽  
Simplifying Assumptions

The electrodynamical theory which we owe to Lorentz and Larmor provides theoretically a logical and consistent scheme whereby the equations of motion of electronic systems may be formulated. But, unfortunately, even most simple cases lead to equations of such complexity that the attempt to deduce exact solutions must at present be abandoned since there is no mathematical machinery available for the purpose. We have accordingly to make some simplifying assumptions, not strictly true, in order to obtain an approximate solution. In many cases, results are thus obtained which give a very close agreement with observation, and this is so far gratifying. But modern experimental work in radiation makes it clear that the phenomena have not yet been co-ordinated with the electrodynamical theory of electrons. It is reasonable to enquire if this is due to the failure of mathematicians to provide an explanation, whether because the approximations used are not accurate enough, or because the conception of the electronic systems considered is not sufficiently general ?

Calculations for anemometry with fine hot wires

1968 ◽  
Vol 32 (1) ◽  
pp. 9-19 ◽  
Author(s):  
W. W. Wood
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Close Agreement ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Measured Data ◽  
Hot Wire ◽  
Linear Equations Of Motion ◽  
Hot Wires ◽  
Non Linear Equations

The heat transfer appropriate to low Reynolds number hot-wire anemometry is calculated from the full non-linear equations of motion and of heat transfer by an iterative method starting with the Oseen solution and its heat flux analogue. The second and third iterates yield close agreement with measured data.

Auroral electrodynamics---investigation by a dual sounding rocket experiment

2020 ◽  
Author(s):  
Hassanali Akbari ◽  
Robert Pfaff ◽  
Keyword(s):  
Electric Fields ◽  
Sounding Rocket ◽  
Sounding Rockets ◽  
Neutral Winds ◽  
Incoherent Scatter ◽  
Ac Electric Fields ◽  
Numerical Studies ◽  
Rocket Experiment ◽  
N Wave

<p>We present results from a 2017 sounding rocket experiment in which two NASA sounding rockets were simultaneously launched into the auroral ionosphere. The rockets included comprehensive instrumentation to measure DC and AC electric fields, magnetic fields, energetic particles, plasma density, and neutral winds, among other parameters, and achieved apogees of 190 and 330 km. This unprecedented collection of in-situ measurements obtained at two altitudes over an auroral arc, along with conjugate ground-based measurements by the Poker Flat incoherent scatter radar and all-sky cameras, enable us to investigate the behavior of an aurora arc and its associated electrodynamics. A prominent feature of our observations is the presence of localized, large-amplitude Alfvén wave structures observed in both the electric field and magnetometers at altitudes as low as 190 km in the vicinity of up- and down-ward current regions. The observations are discussed in the context of ionospheric feedback instability. The results are compared to predictions of previously published numerical studies and other sounding rocket observations.</p>

Rocket attitude determination by a Fourier method

1979 ◽  
Vol 57 (5) ◽  
pp. 728-732 ◽  
Author(s):  
D. W. Green ◽  
B. G. Wilson
Keyword(s):  
Optical Sensor ◽  
Additional Data ◽  
Attitude Determination ◽  
Fourier Method ◽  
Angular Motion ◽  
Sounding Rocket ◽  
Free Flight ◽  
Transverse Axis ◽  
Magnetometer Data

It is shown that the parameters completely specifying the angular motion of a symmetrical sounding rocket in torque-free flight may in general be determined from a Fourier-transformed segment of transverse-axis magnetometer data, with limited additional data from an auxiliary optical sensor. The method is simple and rapid, and an example is worked out.

Some Stability Problems of Ground Effect Wing Vehicles in Forward Motion

1972 ◽  
Vol 23 (1) ◽  
pp. 41-52 ◽  
Author(s):  
P E Kumar
Keyword(s):  
Equations Of Motion ◽  
Longitudinal Mode ◽  
Ground Effect ◽  
Rate Of Change ◽  
Free Flight ◽  
Slender Bodies ◽  
Lateral Mode ◽  
The Stability ◽  
Future Work ◽  
Flight Model

SummaryRecent advances in the development of ground cushion vehicles have indicated the need for a more efficient means of providing lift at the higher speeds envisaged in the future. A wing operating in ground effect could provide this lift and might be far more attractive economically than the “Hovercraft”. This note investigates some of the stability aspects of such a “Ground Effect Wing” Vehicle, using linear analysis, by developing the relevant equations of motion and examining the characteristic equations using quasi-steady derivatives, at fixed heights, obtained from wind-tunnel tests. In addition comparison is made between an analogue simulation of a GEW and the flight paths obtained from a free-flight model. This investigation showed that the longitudinal mode of oscillation for both single and tandem-wings with endplates was unstable and artificial stability was necessary. The lateral mode of oscillation for a single wing was stable in both roll and yaw, the latter being subject to fin and endplate configurations. The effects of the force, and moment, rate of change of height derivatives were not considered, as values for these derivatives were not available. Some proposals for future work include the development of suitable aerofoil sections for operation near the ground and the investigation of slender bodies in ground effect.

A New Method for the Solution of a Differential Equation with Two-Point Boundary Conditions Applied to the Compressible Boundary Layer on a Yawed Infinite Wing

1956 ◽  
Vol 60 (552) ◽  
pp. 808-809
Author(s):  
L. F. Crabtree ◽  
E.R. Woollett
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Exact Solution ◽  
Stagnation Point ◽  
Close Agreement ◽  
Equations Of Motion ◽  
New Method ◽  
Compressible Boundary Layer ◽  
Point Boundary ◽  
Direct Solution

The compressible laminar boundary layer on a yawed infinite wing is considered in Ref. 1, where it is shown that the problem may be solved by a direct solution of the linearised equations of motion under certain assumptions. As an example of this procedure the boundary layer near a stagnation point was calculated. Tinkler has published solutions of the exact equations for the general Falkner-Skan case (Ref. 1) obtained on the M.I.T. differential analyser for several values of the parameter involved. It has been found that the numerical results of Ref. 1 were in error and the corrected results obtained by a new method are tabulated below. Tinkler's exact solution of the stagnation point flow for ω = 0·10 is also given for comparison, and it will be seen that there is close agreement

scholarly journals A reactive control system for a partially guided small sounding rocket

2019 ◽  
Vol 304 ◽  
pp. 07011
Author(s):  
Cristian Emil Constantinescu
Keyword(s):  
Flight Control ◽  
Sounding Rocket ◽  
Reactive Control ◽  
Dead Weight ◽  
Sounding Rockets ◽  
Stability And Control ◽  
Second Stage ◽  
Upper Stage ◽  
The Stability ◽  
And Control

Most small sounding rockets are unguided vehicle. Stability is solved aerodynamically using fins and/or rapidly spinning the vehicle and trajectory is determined by the azimuth and elevation of the launch pad as the rocket usually fly a gravity turn. Access to upper atmosphere usually require two or three stages and the presence of fins on the upper stages inflict a penalty on the stability of the launcher in the start configuration. The paper presents a modification made to an existing launcher suggested by the need to add dead weight for stability when flying small payloads. By eliminating the fins from the second stage and using a RCS for active stability and control of the upper stage several opportunities arise: the aerodynamic configuration is simpler and the stability in the start configuration improved, drag is reduced a bit, non-gravity turn evolutions are possible and special payload requested attitudes (mainly orienting a camera towards ground) are conceivable. Of course, this require a new OBC with enhanced sensors and new navigation and flight control algorithms.

scholarly journals Solidification Furnace Developed for Sounding Rockets: Rio Verde Mission

2019 ◽  
Author(s):  
Rafael Cardoso Toledo ◽  
Manuel Francisco Ribeiro ◽  
Irajá Newton Bandeira ◽  
Chen Ying An
Keyword(s):  
Parabolic Flight ◽  
Space Research ◽  
Metal Alloys ◽  
Sounding Rocket ◽  
Sounding Rockets ◽  
Space Research Institute ◽  
Solidification Furnace ◽  
Research Institute

Brazil has a Microgravity Program mainly based on experiments using sounding rockets. Up to now, four missions have been carried out with approximately 35 experiments submitted in total. In all flights, the Associate Laboratory of Sensors and Materials of the Brazilian Space Research Institute (LABAS/INPE) participated with a fast solidification furnace, capable of producing temperatures up to 900 °C, which was tested with semiconductor and metal alloys. This paper describes the construction and the performance of that furnace during the last parabolic flight, Rio Verde Mission, occurred in 2016. The solidification furnace is now qualified and ready to be used by other institutions in sounding rocket flights.

Modeling and Validation of a Roll Simulator for Recreational Off-Highway Vehicles

2011 ◽  
Author(s):  
Scott B. Zagorski ◽  
Dennis A. Guenther ◽  
Gary J. Heydinger ◽  
Anmol S. Sidhu ◽  
Dale A. Andreatta
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Excellent Correlation ◽  
Motor Systems ◽  
Non Linear ◽  
Entrapped Air ◽  
Three Degrees Of Freedom

A model of a roll simulator for recreational off-highway vehicles (ROV) is presented. Models of each sub-system are described including the equations of motion, the braking, hydraulic and roll motor systems. Derivation of the equations of motion, obtained using Lagrange’s energy equation, demonstrates that they have three degrees-of-freedom (two dynamic, one static) and are coupled and highly non-linear. Results from the hydraulic sub-system illustrated that the amount of entrapped air in the system can significantly influence the response. Comparisons of the model with experimental data from the actual roll simulator showed close agreement. The greatest difference was with motor pressure. The acceleration levels and roll motions for both the model and experimental data showed excellent correlation.

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