05-18-2019, 06:09 PM

An extract from Airplane Stability Calculations with a Card Programmable Pocket Calculator, NASA {Scientific and Technical Information Office} Technical Memorandum 78678, 1978

SUMMARY

Programs are presented for calculating airplane stability characteristics with a card programmable pocket calculator. These calculations include eigenvalues of the characteristic equations of lateral and longitudinal motion as well as stability parameters such as the time to damp to one-half amplitude or the damping ratio. The effects of wind shear are included. Background information and the equations programmed are given. The programs are written for the International System of Units, the dimensional form for the stability derivatives, and stability axes. In addition to the programs for stability calculations, an unusual and short program is included for the Euler transformation of coordinates used in airplane motions. The programs have been written for a Hewlett Packard HP-67 calculator.

INTRODUCTION

Over the past several years, the programmable pocket calculator has developed into a highly sophisticated device that has almost computer characteristics. Because of its sophistication, the newer models are capable of being programmed to make very complicated calculations. Since different logics are used in programmable calculators and since the available keyboard instructions vary with models of different manufacturers, it is necessary to identify the make and model of the calculator for which a program is written. The airplane stability programs presented in this paper were written for a Hewlett Packard HP-67 card programmable calculator; however, its use and identification in this report does not constitute an endorsement of the product by the National Aeronautics and Space Administration.

Programs are given for the calculation of the coefficients of the airplane lateral and longitudinal characteristic equations, the eigenvalues, and the stability parameters such as the time to damp to one-half amplitude or the damping ratio. In addition, a unique coordinate transformation program is given for transformations between inertial axes and airplane body axes. This program requires very few program steps and may be useful as part of a larger program. The equations on which the programs are based are given so that the programs can be readily adapted to other calculators that have sufficient program capacity.

The programs presented herein evolved during the study of wind shear and its effect on airplane stability and control. These programs proved useful in making stability calculations in this study and should be of use in other investigations.

Please note the additional information contained in the AUG & SEP 1978 errata at the beginning of the publication.

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SUMMARY

Programs are presented for calculating airplane stability characteristics with a card programmable pocket calculator. These calculations include eigenvalues of the characteristic equations of lateral and longitudinal motion as well as stability parameters such as the time to damp to one-half amplitude or the damping ratio. The effects of wind shear are included. Background information and the equations programmed are given. The programs are written for the International System of Units, the dimensional form for the stability derivatives, and stability axes. In addition to the programs for stability calculations, an unusual and short program is included for the Euler transformation of coordinates used in airplane motions. The programs have been written for a Hewlett Packard HP-67 calculator.

INTRODUCTION

Over the past several years, the programmable pocket calculator has developed into a highly sophisticated device that has almost computer characteristics. Because of its sophistication, the newer models are capable of being programmed to make very complicated calculations. Since different logics are used in programmable calculators and since the available keyboard instructions vary with models of different manufacturers, it is necessary to identify the make and model of the calculator for which a program is written. The airplane stability programs presented in this paper were written for a Hewlett Packard HP-67 card programmable calculator; however, its use and identification in this report does not constitute an endorsement of the product by the National Aeronautics and Space Administration.

Programs are given for the calculation of the coefficients of the airplane lateral and longitudinal characteristic equations, the eigenvalues, and the stability parameters such as the time to damp to one-half amplitude or the damping ratio. In addition, a unique coordinate transformation program is given for transformations between inertial axes and airplane body axes. This program requires very few program steps and may be useful as part of a larger program. The equations on which the programs are based are given so that the programs can be readily adapted to other calculators that have sufficient program capacity.

The programs presented herein evolved during the study of wind shear and its effect on airplane stability and control. These programs proved useful in making stability calculations in this study and should be of use in other investigations.

Please note the additional information contained in the AUG & SEP 1978 errata at the beginning of the publication.

BEST!

SlideRule