A study of accuracy in selected numerical-analysis integration techniques

Report discusses several methods of performing numerical integration with computer. When data can be expressed as state vector that is dependent variable in a differential equation, self-starting integrators can be used to predict future data

Space shuttle navigation filter development

Problems encountered in developing a high speed trajectory data processor for the shuttle ascent and entry phases are described. The development of a 19 state acceleration filter for the processor is reported

Pocket nickel cadmium cell and battery evaluation

The Nickel Cadmium 129-ampere hour cell was tested in order to characterize the cell under controlled conditions. Results of charge characterization and discharge characterization are reported. Ampere hour efficiency, open circuit stand, and cycle life operation results are included. The battery is briefly described

Refraction corrections for surveying

Optical measurements of range and elevation angle are distorted by the earth's atmosphere. High precision refraction correction equations are presented which are ideally suited for surveying because their inputs are optically measured range and optically measured elevation angle. The outputs are true straight line range and true geometric elevation angle. The 'short distances' used in surveying allow the calculations of true range and true elevation angle to be quickly made using a programmable pocket calculator. Topics covered include the spherical form of Snell's Law; ray path equations; and integrating the equations. Short-, medium-, and long-range refraction corrections are presented in tables

Least squares polynomial fits and their accuracy

Equations are presented which attempt to fit least squares polynomials to tables of date. It is concluded that much data are needed to reduce the measurement error standard deviation by a significant amount, however at certain points great accuracy is attained

Inversion and approximation of Laplace transforms

A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator

Development of single-cell protectors for sealed silver-zinc cells

Three design approaches to cell-level protection were developed, fabricated, and tested. These systems are referred to as the single-cell protector (SCP), multiplexed-cell protector(MCP). To evaluate the systems 18-cell battery packs without cell level control were subjected to cycle life test. A total of five batteries were subjected to simulate synchronous orbit cycling at 40% depth of discharge at 22C. Batteries without cell-level protection failed between 345 and 255 cycles. Cell failure in the cell level protected batteries occurred between 412 and 540. It was determined that the cell-level monitoring and protection is necessary to attain the long cycle life of a AgZn battery. The best method of providing control and protection of the AgZn cells depends on the specific application and capability of the user

Shuttle program: Ground tracking data program document shuttle OFT launch/landing

The equations for processing ground tracking data during a space shuttle ascent or entry, or any nonfree flight phase of a shuttle mission are given. The resulting computer program processes data from up to three stations simultaneously: C-band station number 1; C-band station number 2; and an S-band station. The C-band data consists of range, azimuth, and elevation angle measurements. The S-band data consists of range, two angles, and integrated Doppler data in the form of cycle counts. A nineteen element state vector is used in Kalman filter to process the measurements. The acceleration components of the shuttle are taken to be independent exponentially-correlated random variables. Nine elements of the state vector are the measurement bias errors associated with range and two angles for each tracking station. The biases are all modeled as exponentially-correlated random variables with a typical time constant of 108 seconds. All time constants are taken to be the same for all nine state variables. This simplifies the logic in propagating the state error covariance matrix ahead in time

Some new nystrom integrators

Nystrom integrators were self starting integrators used to integrate the second order, vector, differential equations the second derivative of x factorial = f factorial (t, x factorial) and the second derivative of x factorial = f factorial (t, x factorial, first derivative of x factorial). Nystrom integrator parameters were defined by a set of nonlinear constraint equations and frequently there were more parameters than there were equations. Additions are included for higher order integrations when the second derivative of x factorial = f factorial (t)

Shuttle program: Computing atmospheric scale height for refraction corrections

Methods for computing the atmospheric scale height to determine radio wave refraction were investigated for different atmospheres, and different angles of elevation. Tables of refractivity versus altitude are included. The equations used to compute the refraction corrections are given. It is concluded that very accurate corrections are determined with the assumption of an exponential atmosphere