User's Manual for AeroFcn: A FORTRAN Program to
Contents
1. 11 SUPPLEMENTARY NOTES 12a DISTRIBUTION AVAILABILITY STATEMENT 12b DISTRIBUTION CODE Unclassified Unlimited Subject Category 61 13 ABSTRACT Maximum 200 words This report documents the computer program AeroFcn a utility program that computes the following 18 aerodynamic parameters geopotential altitude Mach number true velocity dynamic pressure calibrated airspeed equivalent airspeed impact pressure total pressure total temperature Reynolds number speed of sound static density static pressure static temperature coefficient of dynamic viscosity kinematic viscosity geometric altitude and specific energy for a standard or a modified standard day atmosphere using compressible flow and normal shock relations Any two parameters that define a unique flight condition are selected and their values are entered interactively The remaining parameters are computed and the solutions stored in an output file Multiple cases can be run and the multiple case solutions can be stored in another output file for plotting Parameter units the output format and primary constants in the atmospheric and aerodynamic equations can also be changed 14 SUBJECT TERMS Aerodynamic equations relations atmospheric equations relations compressible flow normal shock equations relations aerodynamic functions parameters 15 NUMBER OF PAGES 23 16 PRICE CODE A02 17 SECURITY CLASSIFICATION2. 28 96440 4 Reynolds number characteristic length l 1 00000 ft 5 Coefficient of viscosity constant 8 7 3025000E 07 Ibrv ft s deg R 6 Sutherland s constant S 198 72000 deg R 7 Number of atmospheric layers nal 8 8 Geopotential altitude breakpoints H ft 9 Temperature atmospheric breakpoints Tua deg R 10 Pressure atmospheric breakpoints P Ibf ft 11 Temperature gradients in atmosphere Lu deg R ft 12 Effective Earth radius ro 13 Acceleration due to gravity sea level go 14 Geopotential gravity length constant 9 2 0855532E 07 ft 32 17410 ft s 32 17410 ft s 15 Convert to Metric units 16 Examine atmospheric breakpoints 17 Reset to original values 18 Return to Program Options Menu Changing these constants will change the corresponding values in the atmospheric and aerodynamic equations The primary constants can be displayed and modified in either English or metric units by choosing option 15 Primary constant units are changed as a set not individually Therefore the menu label for option 15 is set to Convert to Metric units when English units are in use and set to Convert to English units when metric units are used The atmospheric model can be modified by changing the number of layers or the breakpoints altitude temper ature pressure and temperature gradient using options 7 through 11 The standard day model presented in the Atmospheric Model sect
3. The function is set to false if an error is detected The problem is described in an error message and allows the parameters to be reselected If a zero velocity condition is entered a solution is computed from the current geopotential altitude and zero Mach number Because the selected parameters which may be different from the current geopotential altitude and Mach number are retained in the solution inconsistencies may appear in these solutions Zero velocity conditions are detected and a caution is issued but it is not considered to be an error The atmospheric and aerodynamic functions described in Atmospheric Model and Aerodynamic Equations are mostly smooth and well behaved The equation solver almost always converges quickly to a solution if one exists Occasionally there exists more than one solution for a given pair of selected parameters In this case the program will simply converge to the nearest solution If a solution does not exist or the equation solver does not converge within the proper tolerance or the maximum number of iterations specified an error message is displayed In addition many of the functions will restart the search algorithm with a different initial estimate if the equation solver fails to converge in an attempt to circumvent local minima and convergence problems 19 CONCLUDING REMARKS This report documents the utility and limitations of the computer program AeroFen A section on program operations descri
4. 18 SECURITY CLASSIFICATION 119 SECURITY CLASSIFICATION 20 LIMITATION OF ABSTRACT OF REPORT OF THIS PAGE OF ABSTRACT Unclassified Unclassified Unclassified Unlimited NSN 7540 01 280 5500 Standard Form 298 Rev 2 89 Prescribed by ANS Sid 730 18 208 102
5. described previously also change the parameter values Option 3 Compute Solution Once the parameters are selected and their values entered the Compute solution option number 3 on the main menu will compute the values of the remaining 16 parameters in the current units For example Case 1 Parameter Values selected parameters Geopotential altitude 30000 0 ft x Mach number 800 True velocity 471 5 knots Dynamic pressure 281 5 Ibf ft Calibrated airspeed 303 9 knots Equivalent airspeed 288 4 knots Impact pressure 329 5 Ibf ft Total pressure 957 9 IbfAt Total temperature 464 4 deg R Reynolds number 2 27828E 06 Speed of sound 589 3 knots Static density 8 89272E 04 slug ft Static pressure 628 4 Ibf ft Static temperature 411 7 deg R Coefficient of viscosity 3 10595E 07 slug ft s Kinematic viscosity 349269F 04 ft s Geometric altitude 30043 2 ft Specific energy 39868 4 ft Computed solutions are numbered sequentially and are called cases Parameter values are displayed to the terminal screen in either the default standard format or scientific notation see Option 6 Change output format The computed solution in the given example was the first case from the output file aro dat The parameters were displayed in the standard format The selected parameters were geopotential altitude and Mach number with values of 30 000 ft and 0 8 resp
6. is then selected and geopotential altitude is calculated The geopotential altitude ranges for isothermal atmospheric layers are also displayed but cannot be selected The multiple case option uses a logical Iplt that prevents having to choose the desired geopotential altitude range for each iteration when the multiple case option is chosen The logical Iplt is set true after the first case of a multiple case run is computed and the geopotential altitude range is stored as the variable nhrng and used for each case in the multiple case solution These plotting variables are contained in the following common blocks H Hy 30 common aroplt conpar xplt kplt common nlplt nplt ipit nhrng Program Structure The AeroFcn FORTRAN code is divided into three subprograms AerolO f AeroEgns f and AeroAuxf Routines that execute the program logic sequencing and provide for the user interface are contained in AerolO f The software that describes the aerodynamic equations and mathematical relationships of the atmospheric model is contained in AeroEqns f AeroAux f consists of auxiliary code such as interpolation routines and character String manipulation functions The software package is written in American National Standards Institute ANSD FORTRAN 77 except for the following items e lowercase letters were used extensively throughout the program and e double precision constants were often written in single precision for example 20 0 instead
7. units and with a prompt for a new value If a number is entered followed by a lt cr gt then that number becomes the current value for that selected parameter If just a lt cr gt is entered then the default value is retained Any other type of input will not be accepted and an error message will appear There are four ways to change the parameter values the first two are straightforward whereas the third and fourth ways are more subtle The first is to select option 2 from the main menu and change the parameter values as described in the previous paragraph The second way is to choose option 3 from the main menu and compute the parameter values see Option 3 Compute Solution This will change the values of the parameters not selected only if the values of the selected parameters have changed since the last time solutions were computed The third way to change the parameter values is to select option 5 from the main menu convert the units of one or more parameters and choose the corresponding parameter value s to be converted to the new units as described in Option 5 Change parameter units The fourth way is to again select option 5 from the main menu and convert the units of one or both the selected parameters without converting the corresponding values Then choosing option 3 from the main menu will compute the remaining 16 parameters based on the old parameter values that now have new units Obviously any combination of the four methods
8. 0 0 and amch le 1 0 then cl gam gam 1 0 c2 1 0 gam 1 0 2 0 amch 2 c1 f 1 pt pa c2 gam 1 0 2 0 amch 2 pa c2 gam 1 0 2 amch 2 c3 4 0 gam amch 2 2 0 gam 1 0 f 1 pt cl c2 c3 1 0 gam 1 0 endif c return end Notice that a penalty function is employed for Mach numbers less than zero Penalty functions are implemented in all subroutines called by the equation solver to limit the algorithm to a search space appropriate to the atmospheric model and aerodynamic equations Since computational speed was not a problem terms such as gam gam 1 were not computed outside the iterative process Derivations of Geopotential Altitude Anexplicit solution was derived for many of the selected parameters without the use of the equation solver The equations presented in this section represent the more complicated derivations all of which consist of geopotential altitude as a function of an atmospheric parameter The remaining explicit solutions are trivial and can be found in the subroutine solve or in functions that are called within solve The following equations derived from the atmospheric and aerodynamic equations from the previous sections are expressions of geopotential altitude as a function of one atmospheric parameter and various primary constants From equation 3 geopotential altitude can be expressed as a function of static temperature for a nonisot
9. End Program Option 9 from the main menu terminates the program after allowing the entire session to be saved If the case information is saved single and multiple cases are stored sequentially in the output file aro dat The plotting output file aroplt dat is written whenever that option is chosen under the Multiple Case Plot File Menu as described in the previous section There is no default to the End Program Menu since a mistake at this point could mean a significant loss of data PROGRAMMER S REFERENCE GUIDE The purpose of the program was to solve for 16 atmospheric and aerodynamic parameters given the values of any 2 selected parameters that define a unique flight condition The problem was divided into two parts The first 11 part used subroutine solve to compute geopotential altitude and Mach number from two selected parameters The second part used subroutine exprss to compute the remaining 16 parameters from geopotential altitude and Mach number The following sections discuss the atmospheric model aerodynamic equations equation solver derivations of geopotential altitude program structure and error protection Atmospheric Model The 1976 U S Standard Atmosphere was used as the reference for the atmospheric model in AeroFen Six atmospheric parameters are functions of geopotential altitude static temperature static pressure static density speed of sound coefficient of dynamic viscosity and kinematic viscosity The accel
10. Fcn FORTRAN code AeroEqns f subprogram of AeroFcn FORTRAN code AeroFen aerodynamic function FORTRAN program AerolOf subprogram of AeroFcn FORTRAN code altfun subroutine ampchp function ANSI American National Standards Institute aro dat Output file aropltdat output file badstr variable brkfn logical function choose subroutine chrchk subroutine cmp3 compressed data file format lt cr gt carriage return exprss subroutine fnalt subroutine FORTRAN formula translation fstchk subroutine initil subroutine inpchk subroutine iod subroutine lis1 ASCII data file format Ipalt variable Jplt variable nhrng variable ntrplz selchk solve zamchp Symbols mg H V U Po Pi de R To TMb To Ti Ve interpolation subroutine logical function subroutine subroutine speed of sound sea level speed of sound specific energy acceleration due to gravity geopotential gravity length constant geopotential altitude breakpoints for geopotential altitude breakpoints for temperature gradient characteristic length Mach number molecular air mean weight molecular air mean weight at sea level mass potential energy geopotential meter static pressure breakpoints for static pressure sea level static pressure total pressure dynamic pressure impact pressure gas constant Reynolds number effective Earth radius Sutherland s constant Static temperature breakpoints for static temperature sea le
11. NASA Technical Memorandum 104237 User s Manual for AeroFcn A FORTRAN Program to Compute Aerodynamic Parameters Joseph L Conley April 1992 NASA National Aeronautics and Space Administration NASA Technical Memorandum 104237 User s Manual for AeroFcn A FORTRAN Program to Compute Aerodynamic Parameters Joseph L Conley NASA Dryden Flight Research Facility Edwards California 1992 NASA National Aeronautics and Space Administration Dryden Flight Research Facility Edwards California 93523 0273 CONTENTS ABSTRACT 1 NOMENCLATURE 1 INTRODUCTION 3 PROGRAM OVERVIEW 3 PROGRAM OPERATION E 3 Option 1 Select Parameters a ee eee 4 Option 2 Enter Change Parameter Values 5 Option 3 Compute Solution a a 6 Option 4 Examine Parameter Values o 7 Option 5 Change Parameter Units ROS A is o a EN 7 Option 6 Change Output Format a a 9 Option 7 Change Primary Constants eee eee eee ee eee 10 Option 8 Multiple Case Plot File ee ee eee ee ee ee eee 11 Option 9 End Program ee ee ee ee ee ee ee 11 PROGRAMMER S REFERENCE GUIDE 11 Atmospheric Model 3 32 08 desi dee a heck ew hw Ge Mod a ae te Aa es 12 Aerodynamic Equations 00 00 ee ee ee ee ee ee 14 EQUADON SOLVED cia Se bs a be Gd ee ade Ws ee hd ee ne ee Less 15 Derivations of Geop
12. Reynolds number characteristic length constant Energy height or specific energy E is the sum of potential energy mg H and kinetic energy m V divided by unit weight Es BH 3 24 where m is mass Equation Solver To solve the transcendental equations inherent in computing many of the parameters a nonlinear equation solver was used The equation solver varies a single parameter to zero a general function The routine that calls the equation solver specifies the convergence criteria the parameter to be varied along with an initial estimate and any auxiliary parameters that are necessary in solving the atmospheric and aerodynamic equations The following routine amchp which computes Mach number given total and static pressure demonstrates how the equation solver is implemented Double precision function amchp pt pa c Cig function computes Mach number given total and static pressure c implicit double precision a h implicit double precision o z c double precision x 1 wk 182 par 2 logical lofile 1stfmt c common outfil nunit1 lofile lstfmt nunit2 nunit3 c external zamchp c C equation solver variables c nsig 5 neqns 1 itmax 500 c c total and static pressure are passed as parameters par 1 par 2 pt pa c C initial estimate for Mach number c 15 x 1 1 0 c C nonlinear equation solver c call zsent zamchp nsig neqns itmax par x fnorm wk ier c C Solu
13. bes the various menu options and overall capabilities A section for programmers is included that documents the atmospheric model aerodynamic relations and how the FORTRAN code is structured to solve for the unknown variables Comments on error protection are also included in this section In summary AeroFen is a flexible FORTRAN software package wherein commonly used aerodynamic and atmospheric variables are related to each other using well known compressible flow and normal shock equations and a modifiable standard day atmospheric model Once two unique variables are selected from interactive menus and their values entered the remaining variables are computed and the solutions stored in an output file Further options allow multiple cases to be run and the solutions to be stored in an output file for plotting as well as options that change parameter units the output format and primary constants Dryden Flight Research Facility National Aeronautics and Space Administration Edwards California March 15 1991 REFERENCES 1 U S Standard Atmosphere 1976 National Oceanic and Atmospheric Administration NASA United States Air Force Washington D C Oct 1976 2 Garbinski Charles Paul C Redin and Gerald D Budd User s Manual for EZPLOT Version 5 5 A FORTRAN Program for Two dimensional Graphics Display of Data NASA TM 88293 1988 3 Maine Richard E Manual for GetData Version 3 1 A FORTRAN Utility Program for Time History Da
14. ectively The units for the parameter values are the default units and can be modified using option 5 of the main menu see Option 5 Change parameter units Certain parameter pairs require the selection of a geopotential altitude range from which geopotential altitude is computed see Derivations of Geopotential Altitude For these cases appropriate geopotential altitude ranges are dis played a range is selected and the geopotential altitude corresponding to the specified flight condition is calculated 6 Option 4 Examine Parameter Values By choosing option 4 from the main menu Examine parameter values the selected parameters the parameter values and the parameter units can be conveniently examined The information displayed is the same as a computed solution except for the menu title Option 5 Change Parameter Units Choosing option 5 from the main menu leads to the following menu where the units of any or all the parameters can be changed x x Change Parameter Units Menu Select parameters for unit change default 22 1 Geopotential altitude ft 2 Mach number 3 True velocity knots 4 Dynamic pressure Ibf t2 5 Calibrated airspeed knots 6 Equivalent airspeed knots 7 Impact pressure IDf ft 8 Total pressure Ibf ft 9 Total temperature deg R 10 Reynolds number 11 Speed of sound knots 12 Static density slug ft 13 Static pressure Ibf ft2 14 Static temperature deg R 15 Coefficient
15. eration due to gravity and geometric altitude are also functions of geopotential altitude and are included in this section The standard day atmospheric model is divided into a series of spherical layers of air Equations describing the atmospheric properties inside each layer are based on breakpoints of geopotential altitude H static temperature Tu p static pressure P and temperature gradient L Mb Where the subscript b represents the layer number The following equations are implemented in AeroFen and are valid for the geopotential altitude range from 5 0 kilo meters below sea level to 84 5 kilometers above sea level Molecular scale temperature Ty is a function of geopotential altitude H T Tmb Lu H Hp 1 Molecular scale temperature Ty is related to kinetic static temperature T by a ratio of the molecular air mean weight at sea level Mp and the molecular air mean weight M Mo Tu T 2 ET 2 From sea level to 79 km geopotential altitude the molecular air mean weight is constant and equal to Mo From 79 to 84 5 km geopotential altitude the molecular air mean weight is virtually equal to the sea level value Therefore the molecular scale temperature and static temperature are treated as equivalent in this atmospheric model Static temperature can then be expressed as a function of geopotential altitude using equations 1 and 2 T Tm Lusp H Ap 3 For an isothermal atmospheric layer where te
16. her mal layer T Tu Lu From equation 5 geopotential altitude can be expressed as a function of static pressure for a nonisothermal layer H H 25 R Lu b H Hy 0 com 1 26 From equation 6 geopotential altitude can be expressed as a function of static pressure for an isothermal layer R T us H H en 21 From equations 3 5 and 7 geopotential altitude can be expressed as a function of static density for a non isothermal layer nn aif iM Mo R L H Hy 142 LR a 24 28 P Mo Lu 17 From equations 3 6 and 7 geopotential altitude can be expressed as a function of static density for an iso thermal layer R Tys pR Tu s H Hy Ln 29 Mo eee sd From equations 3 and 8 geopotential altitude can be expressed as a function of atmospheric speed of sound for a nonisothermal layer a Mo 7R T us 1R Lu b From equation 12 geopotential altitude can be expressed as a function of gravitational acceleration H Tro 1 2 31 Three parameters are not monotonic functions of geopotential altitude static temperature atmospheric speed of sound and coefficient of dynamic viscosity To compute geopotential altitude from one of these three parameters geopotential altitude ranges based on the atmospheric layers where the parameter to be found is either Strictly increas ing or decreasing are displayed A geopotential altitude range
17. ion is defined by the atmospheric equations and the breakpoints for the eight atmospheric layers between sea level and 84 5 kilometers Option 16 allows the atmospheric breakpoints to be examined All the primary constants except Reynolds number characteristic length affect the atmospheric model In addition option 17 will restore all the primary constants including the atmospheric breakpoints to their original values The sea level constants po Po and ay that appear in the aerodynamic equations are defined as the value of that parameter at an altitude of 0 ft Therefore changing the primary constants can change the corresponding value of the sea level parameters 10 Option 8 Multiple Case Plot File The Multiple case Plot file option from the main menu produces the following menu which allows multiple cases to be run The output from multiple cases can be stored in a file for plotting Multiple Case Plot File Menu default 8 Select constant parameter Select varying parameter input constant parameter value Input varying parameter min max and delta Compute multiple cases only Compute multiple cases and Create plot file NO OM amp ON Change plot file format 8 Retum to Program Options Menu A constant and a varying parameter are selected to run multiple cases These parameters are selected by choos ing option 1 or 2 from the menu shown above and entering the corresponding values The constant and varying para
18. meters are chosen in the same way the individual case parameters were chosen as described in Option 1 Se lecting Parameters A parameter cannot be selected to be both the constant and varying parameter The varying parameter values require a minimum maximum and delta value creating a parameter array from which solutions are computed Options 5 and 6 from the Multiple Case Plot File Menu compute the parameter solutions for the multiple cases Option 5 displays the multiple case solutions to the terminal screen Multiple case sets are numbered sequentiall y as well as the individual cases inside each multiple case set Option 6 writes the multiple case solutions to the plot file aroplt dat and will also display a message asking whether or not to display the solutions to the terminal screen Each time option 6 is chosen a file name for the multiple case set should be entered Different file names for each set of multiple cases are necessary to prevent the data sets from being overwritten Option 7 from this menu allows the output format to be specified for the plotting output file aroplt dat The first format cmp3 is a compressed format read by the plotting program Ezplot ref 2 The second format type lis is a less efficient but more readable ASCII format that may be desirable for viewing data or for other plotting routines Reading and writing data in cmp3 and lis1 formats are documented in the GetData reference manual ref 3 Option 9
19. metric altitude 9157 2 m Specific energy 12151 9 m Note that Case 2 is equivalent to Case 1 from the Option 3 Compute Solution section Parameter units can also be changed individually by selecting the corresponding parameter from the menu The parameters that have dimensions of length geopotential altitude geometric altitude and specific energy E can be expressed in feet meters miles nautical miles or kilometers The parameters that have dimensions of velocity true velocity calibrated airspeed equivalent airspeed and speed of sound can be expressed in nautical miles per hour knots feet per second miles per hour meters per second or kilometers per hour The parameters that have dimensions of pressure dynamic pressure 3 impact pressure q lt total pressure P and static pressure P can be expressed in pounds force per foot pounds force per inch atmospheres newtons per meter inches of mercury in Hg centimeters of mercury cm Hg inches of water in H2 O or millibars newtons per 100 0 meters The parameters that have dimensions of temperature total temperature T and static temperature 7 can be expressed in degrees Rankine degrees Fahrenheit degrees Kelvin or degrees Celsius Static density p can be expressed in slugs per foot kilograms per meter or pounds mass per foot The coefficient of dynamic viscosity uz can be expressed in slugs per foot second pounds mass per foot sec
20. mperature gradient equals zero static temperature reduces to T TMb 4 Static pressure P is also a function of geopotential altitude For a nonisothermal layer static pressure can be expressed as gh Mo e n _ TMb oi E Phu Ho where R is the gas constant and g is the geopotential gravity length constant The units of R differ in this and the following equations from those in the primary constant menu see Option 7 Change Primary Constant by a Ibm slug conversion factor If the atmospheric layer is isothermal then static pressure is defined as 6 P Pr E R T 5 12 From the perfect gas law static density p can be expressed as a function of static pressure to static temperature _PMo P RT ve Speed of sound in the atmosphere a is a function of the square root of static temperature R T 8 a 4 Mo 8 where y is the ratio of specific heats of air constant Coefficient of dynamic viscosity u is a function of static temperature art L Fas 9 where S is Sutherland s constant and is a primary constant The units of also differ in this equation from those in the primary constant menu by a Ibm slug conversion factor Kinematic viscosity 7 is defined as the ratio of coefficient of dynamic viscosity to static density j Tr 10 The standard day atmosphere between sea level and 84 5 km or 277230 97 ft is divided into 8 layers The Standard day breakpoints in English units fo
21. of 2 0D 01 The nonstandard code was used to increase the readability of the code The output files aro dat and aroplt dat use the file unit numbers 13 and 14 respectively A scratch file is used by the program and is assigned the file unit number 15 The program was written in a modular style with the assumption that some of the subroutines and functions would probably be modified or replaced in the future Program dimension limits described in the following can easily be changed through parameter statements The following is a list of the dimension limit names brief descriptions and sizes that set the size of the arrays used in AeroFcn 18 kc Number of primary constants 14 kdu Default units 1 flight test 2 English 3 metric 1 kp Number of atmospheric and aerodynamic parameters 18 kplt Maximum number of elements in varying parameter 10001 kal Maximum number of atmospheric layers 20 The parameter kdu specifies to which set of default units the program initializes in subroutine initil English flight test or metric units can be set as the default by modifying kdu to 1 2 or 3 respectively Of course the units can also be changed interactively as described in Option 5 Change Parameter Units Error Protection Error protection is built into the code to protect against improper input The types of error protection include user interface errors unreasonable numerical values nonunique parameter selection and numerical compu
22. of viscosity slug ft s 16 Kinematic viscosity ft s 17 Geometric altitude ft 18 Specific energy ft 19 Flight test units 21 Metric units 20 English units 22 Return to Program Options Menu Parameter units remain fixed until changed by using options from this menu The units shown are option 19 flight test units English and metric units are also offered as options 20 and 21 on this menu These three options will globally change the units of all the parameters to the chosen type English units differ from flight test units in the velocity parameters The velocity parameters are defined as ft s in English units and knots in flight test units The metric units option configures the parameters in the international system or SI units Case 2 shows a solution in metric units for the selected parameters impact pressure and Reynolds number Case 2 Parameter Values selected parameters Geopotential altitude 9144 0 m Mach number 800 True velocity 242 5 ms Dynamic pressure 13480 1 N m Calibrated airspeed 156 3 ms Equivalent airspeed 148 4 ms Impact pressure 15777 1 N m Total pressure 45866 7 N m Total temperature 258 0 deg K Reynolds number 2 27828E 06 Speed of sound 303 2 ms Static density 458313E 01 kg m Static pressure 30089 5 N m Static temperature 228 7 deg K Coefficient of viscosity 1 48714E 05 kg m s Kinematic viscosity 3 24482E 05 m s Geo
23. ond or kilograms per meter second Kinematic viscosity n can be expressed in feet per second inches per second meters per second or centimeters per second Mach number and Reynolds number are dimensionless quantities Changing the parameter units either globally or individually does not directly change the parameter values Once the units have been changed the current parameter values can be retained or multiplied by a conversion factor corresponding to the new units If the units are changed globally a message appears asking if the parameter values should be converted to the new units When the units of a single parameter are changed a message is displayed showing the current parameter value and the value if it were to be converted to the new units A selection is made between the current value and the converted value Generally values should be converted when units are changed Option 6 Change Output Format Option 6 from the main menu Change output format controls the format in the output file aro dat and the format displayed to the terminal screen The Change Output Format Menu is as follows x Change Output Format Menu x current value 1 1 Standard format 2 Scientific notation The default standard format is based on the default units for the atmospheric and aerodynamic parameters for most input values If more precision is required the output can be displayed in scientific notation by choosing the Scientific n
24. ong with the remaining aerodynamic parameters in many standard aerodynamic texts Total pressure P is defined as the sum of static pressure P and impact pressure ge P P dec 14 Dynamic pressure 7 is defined as one half the product of static density p and true airspeed V squared 1 q gt Pp y 15 Mach number M is defined as the ratio of true airspeed V to the speed of sound a M 16 Total pressure can also be defined as a function of static pressure and Mach number The total pressure equation for M lt lis l P P 1 TM 17 Total pressure for M gt 1 is 18 4 qM 2 9 1 1 7 M 2 1 P 2 M P Equivalent airspeed V is a function of the product of true airspeed and the square root of static density Ve v f 19 po where po is the sea level static density constant Impact pressure is a complicated function of calibrated airspeed Ve For V lt ao impact pressure is defined as de Po 1 27 y 1 20 where Po and ao are sea level constants of static pressure and speed of sound respectively The impact pressure equation for V gt ap is 1 Vo y y 1 sl I a O A 21 47 2 1 D 14 Total temperature 7 is a function of static temperature and Mach number T T 1 12M 22 Reynolds number Re can be expressed as the ratio of static density and true airspeed to coefficient of dynamic viscosity i Res Pu 23 j where lis the
25. osity 17 Geometric altitude 18 Specific energy 19 Erase selections 20 Return to Program Options Menu Two parameters are selected to describe a flight condition Geopotential altitude and Mach number are shown in the previous menu as the currently selected parameters and remain so until chosen otherwise Parameters are selected one at a time and the currently selected parameters are marked by an asterisk and surrounded by square brackets The following pairs of parameters do not describe a unique flight condition impact pressure qe and calibrated airspeed V dynamic pressure 7 and equivalent airspeed V and any combination of geopotential altitude geometric altitude and the atmospheric parameters parameters 1 11 12 13 14 15 16 and 17 If a nonunique pair has been selected an error message appears If a third parameter is selected while two parameters are currently selected the first two selections are erased and the third choice becomes the only selected parameter In addition option 19 erases the currently selected parameter s Option 20 the default option on this menu is used to return to the main menu This menu is displayed until two unique parameters have been selected Option 2 Enter Change Parameter Values Values for the selected parameters can be entered or changed by choosing the Enter Change parameter values option from the main menu The default value for the selected parameter is displayed with the current
26. otation option as shown in the following example Case 3 Case 3 Parameter Values selected parameters Geopotential altitude 1 50000E 05 ft Mach number 1 20000E 01 True velocity 7 64183E 03 knots Dynamic pressure 2 74722E 02 Ibf ft Calibrated airspeed 3 1015E 02 knots Equivalent airspeed 2 84861E 02 knots Impact pressure 5 03845E 02 Ibf ft Total pressure 06571E 02 Ibf ft Total temperature 1 43254E 04 deg R Reynolds number 1 20990F 05 Speed of sound 6 36819F 02 knots Static density 3 30279E 06 slug ft Static pressure 2 72541E 00 Ibf ft Static temperature 4 80719E 02 deg R Coefficient of viscosity 3 52088E 07 slug ft s Kinematic viscosity 1 06603E 01 ft s Geometric altitude 1 51087E 05 ft Specific energy 2 77286E 06 ft The current format type is displayed and retained until the other format is chosen Option 7 Change Primary Constants This option modifies the constants that appear in the atmospheric and aerodynamic equations described in the At mospheric Model and Aerodynamic Equations sections When option 7 is chosen from the main menu the following menu will appear Change Primary Constants Menu default 18 Constants are currently defined in English units Ratio of specific heats of air y 1 40000 2 Gas constant R 1545 31812 ft lbm Ibm mol deg R 3 Molecular air mean weight sea level Mo
27. otential Altitude Oe Aiea et el uk 17 Fogra SUCE ici o oss So Fee DB he ng aris RO Se Danby we mw Realy a aci 18 a AAA 2k free ook ae a ees fees eek oh Se Boe Beas Se A es 19 CONCLUDING REMARKS 20 REFERENCES 20 To obtain a copy of this code please call Joe Conley at FTS 415 464 3677 or write to Joe Conley Ames Research Center Mail Stop 269 4 Moffett Field CA 94035 ABSTRACT This report documents the computer program AeroF cn a utility program that computes the following 18 aerody namic parameters geopotential altitude Mach number true velocity dynamic pressure calibrated airspeed equiv alent airspeed impact pressure total pressure total temperature Reynolds number speed of sound static density Static pressure static temperature coefficient of dynamic viscosity kinematic viscosity geometric altitude and specific energy for a standard or a modified standard day atmosphere using compressible flow and normal shock relations Any two parameters that define a unique flight condition are selected and their values are entered interac tively The remaining parameters are computed and the solutions stored in an output file Multiple cases can be run and the multiple case solutions can be stored in another output file for plotting Parameter units the output format and primary constants in the atmospheric and aerodynamic equations can also be changed NOMENCLATURE AeroAuxf subprogram of Aero
28. r the eight atmospheric layers are Atmospheric Breakpoints Geopotential Layer b altitude H Temperature Tas Pressure P Temp gradient Lay ft deg R Ibf ft deg R ft 1 0 0000000 518 6700 2116 2199995 0 0035662 2 36089 2388450 389 9700 472 6799016 0 0000000 3 65616 7979000 389 9700 114 3437577 0 0005486 4 104986 8766400 411 5700 18 1287947 0 0015362 5 154199 4750650 487 1700 2 3161984 0 0000000 6 167322 8346450 487 1700 1 3980314 0 0015362 7 232939 6325450 386 3700 0 0826313 0 0010973 8 277230 9711275 337 7700 0 0083153 0 0010973 Note that the breakpoints are defined at the bottom of each layer and in the atmospheric reference b is defined as 0 for the first layer Two other functions of geopotential altitude are also presented in this section Geometric altitude 7 can be expressed as a function of geopotential altitude roH de 11 Pro H 11 where ro is the effective Earth radius constant The conversion constant T is defined as pan 12 Jo 13 where go is the sea level acceleration due to gravity constant Gravitational acceleration g can be expressed as a function of geometric altitude or geopotential altitude by using equation 11 9 90 gt o EY 13 To Z T ro Aerodynamic Equations The aerodynamic parameters are defined in equations 14 through 24 Equations 14 through 21 were taken from reference 4 and can be found in various forms al
29. ram introduction appears on the screen This is followed by the program s main menu Program Options Menu x default 1 Select parameters Enter Change parameter values Compute solution Examine parameter values Change parameter units Change output format Change primary constants Multiple case Plot file on O oO Bb O N a 9 End program Any option can be chosen at any time from this menu The normal sequence is to choose option 1 and select 2 parameters such as Reynolds number Re and dynamic pressure 7 from the list of 18 Next option 2 is chosen and the values for the selected parameters are entered Then option 3 is chosen and the remaining parameters are computed The solutions are displayed on the terminal screen and can be saved in an output file with the default name aro dat at the end of the session The default menu choice changes from 1 to 2 and then to 3 respectively to reflect this sequence Whenever option 3 is chosen a solution will be computed based on the current values of selected parameters The program initializes Mach number M and geopotential altitude h as the selected parameters with values of 1 0 and 0 0 ft respectively The parameter values can be examined at any time by choosing option 4 from the main menu In addition the parameter units can be changed by choosing option 5 Option 6 allows the format of the information displayed to the terminal screen and output file to be altered The value
30. s and programmer s guide to the formula translation FORTRAN program AeroFen The aerodynamic equations incorporated in the program are compressible flow and normal shock relations for subsonic and supersonic conditions Modifications to the atmospheric and aerodynamic equations can be made by changing the primary constants found in those equations PROGRAM OVERVIEW The AeroFen is a menu driven interactive FORTRAN program that computes 16 aerodynamic parameters from 2 specified parameters that define a unique flight condition The user interface provides a flexible structure that allows for the easy manipulation of the atmospheric and aerodynamic equations output units and Output formats including provisions for plotting multiple cases The FORTRAN code for AeroFen may be obtained upon request Menu options are selected by typing the number corresponding to the desired option followed by a carriage return lt cr gt Normally 2 parameters are selected the units and output formats defined the values entered and the remaining 16 parameters are computed In addition primary constants that exist in the atmospheric and aero dynamic equations e g ratio of specific heats of air y can be changed Each set of 18 parameters along with the corresponding primary constants define a single case Single cases and multiple parameter variation cases for plotting can be run and stored in output files PROGRAM OPERATION After typing AeroFcn the prog
31. s of the primary constants that appear in the atmospheric and aerodynamic equations can be modified by choosing option 7 Option 8 introduces the Multiple Case Plot Option Menu where multiple cases are run and the solutions can be stored in an output file for plotting called aroplt dat The two output files are referred to as aro dat and aroplt dat However these files can be assigned any name assuming they are legal file names as defined by the local operating system Option 9 terminates the program after giving the option to save the computed solutions in the output file aro dat The program prevents information from scrolling past the screen s available window by requiring a lt cr gt The places where a lt cr gt is necessary should be obvious The main menu options are described in more detail in the following sections Option 1 Select Parameters The atmospheric and aerodynamic parameters are selected from the following menu by choosing option 1 on the main menu x x Parameter Selection Menu default 20 Select individually 2 known parameters x currently chosen parameter s 1 Geopotential altitude 2 Mach number 3 True velocity Total pressure 4 Dynamic pressure 5 Calibrated airspeed 6 Equivalent airspeed 7 Impact pressure 8 9 Total temperature 10 Reynolds number 11 Speed of sound 12 Static density 13 Static pressure 14 Static temperature 15 Coefficient of viscosity 16 Kinematic visc
32. ta NASA TM 88288 1987 4 Gracey William Measurement of Aircraft Speed and Altitude NASA RP 1046 1980 REPORT DOCUMENTATION PAGE Public reponing burden for this collection of information is estimated to average 1 hour per response including the time for reviewing instructions searching existing dala sources gathering and the data ne K completing and reviewing the collection of information Send comments regarding this burden estimate or any other aspect of this collection of information ing suggestions for reducing this burden to Washington ptr reta Services Directorate for information Operations and Reports 1215 Jefferson Davis Highway Suke 1204 Arlington VA 22202 4302 and to the Office of Management and Budget Paperwork Reduction Project 0704 0188 Washington DC 20503 1 AGENCY USE ONLY Leave blank 2 REPORT DATE 3 REPORT TYPE AND DATES COVERED May 1992 Technical Memorandum 4 TITLE AND SUBTITLE User s Manual for AeroFcn A FORTRAN Program to Compute Aerodynamic Parameters RTOP 533 02 36 8 PERFORMING ORGANIZATION REPORT NUMBER 7 PERFORMING ORGANIZATION NAME S AND ADDRESS ES NASA Dryden Flight Research Facility PO Box 273 Edwards CA 93523 0273 H 1675 9 SPONSORING MONITORING AGENCY NAME S AND ADDRESS ES 10 SPONSORING MONITORING AGENCY REPORT NUMBER National Aeronautics and Space Administration Washington DC 20546 0001 NASA TM 104237
33. ting problems Unless otherwise specified error messages describe the problems in this section and allow recovery Every input that is read interactively by the program is passed through subroutine iod which ensures that the variable type read was the type expected Menu choices are protected by the subroutine choose which allows only the options available on the current menu Filenames for the output files are checked for illegal characters in subroutines chrchk and fstchk This error protection is highly dependent on the operating system where Aerofen is installed Currently there are no characters that are specified as illegal This however can be changed as shown in the following example where the number of illegal characters is the dimension of variable badstr and the data statement contains the following illegal characters character 27 badstr data badstr amp _ gt lt I The local compiler however may not allow some of these nonstandard characters in the character string Values of the selected parameters are checked in subroutine inpchk for unreasonable inputs such as negative Mach numbers The minimum maximum and delta values that create the vector for the multiple case option is created and checked in logical function brkfn The selected parameters are checked in logical function selchk This function insures that there are two param eters selected and that the pair defines a unique flight condition
34. tion for Mach number c amchp x 1 C error protection c if ier ne 0 then write 1000 pt pa write nunit3 1000 pt pa read endif c 1000 format 2x ZSCNT did not converge The values given for the input parameters may 2x not produce a physically realizable system 2X Total pressure 1pe15 5 lbf ft 2 2x Static pressure lpel5 5 1bf ft 2 return end A corresponding subroutine is called by the equation solver that contains the nonlinear function to be set to zero For this example the equation solver calls the subroutine zamchp and varies Mach number x 1 given total pressure par 1 and static pressure par 2 until the function f 1 converges to zero Therefore the Mach number at convergence is the Mach number which satisfies the flight condition determined by the selected parameters The code for subroutine zamchp is as follows Subroutine zamchp x f n par c C routine finds the Mach number for a given static and total pressure C implicit double precision a h implicit double precision o z c double precision x 1 f 1 par 2 double precision MO c common prmcon gam Rstar MO Rel beta S ro g0 g0prm c C set Mach number and pressure parameters c amch x 1 pt par 1 pa par 2 c C employ penalty function for Mach less than zero 16 if amch le 0 0 then 1 10 0 amch pt elseif amch gt
35. vel static temperature total temperature true airspeed calibrated airspeed Ve equivalent airspeed Z geometric altitude mV kinetic energy B primary constant used in coefficient of viscosity formula y ratio of specific heats 7 kinematic viscosity ratio of coefficient of dynamic viscosity and density m coefficient of dynamic viscosity p Static density po sea level static density r conversion constant INTRODUCTION Aerospace engineers scientists and students are often confronted with many highly interrelated aerodynamic parameters such as Mach number M calibrated airspeed V and dynamic pressure 7 The tables graphs and formulas used by the aerospace community frequently do not contain the desired parameters or the relationships between parameters in a tractable form Furthermore computing a particular parameter is often complicated by inconvenient units and conversion factors Therefore the computer program AeroFcn was written to compute aerodynamic parameters easily in a convenient set of units given an independent pair of parameters The AeroFen program incorporates a flexible model of the U S Standard Atmosphere 1976 ref 1 that de scribes the atmospheric parameters as a function of geopotential altitude A accurately from sea level to 84 5 kilometers A nonlinear equation solver was implemented to solve the transcendental relationships that occur in computing many of the parameters This report presents a user
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