04-12-2024, 08:47 PM

An excerpt from Zen & the Art of Airplane Sizing, Anthony P. Hays, Lockheed Aeronautical Systems Company, 1993 SAE General, Corporate, & Regional Aviation Meeting & Exposition, Wichita KS, May 18-20,1993, 5 pages {ISSN 0148-7191}

ABSTRACT

This paper describes the development of a set of algorithms that find the takeoff gross weight of an aircraft for given vehicle and engine characteristics, and mission requirements. A major objective was to find the most elementary set that would still yield useful answers. The result was a set that could be encoded on an inexpensive programmable pocket calculator with only 24 lines of code. Results are compared with actual characteristics of an executive jet and its' derivative versions.

1. INTRODUCTION

All the major airframe (and aero-engine) companies have large computer programs for airplane sizing and trade studies. In essence each program consists of two parts, mission analysis and weight buildup. …

…

The weight buildup program calculates the empty weight using empirical component weight equations. …

…

The difficulty with these computer programs is that they need large amounts of input data before they can be used. …

…

At the beginning of a design project this information is unknown to the designer. It is also quite possible that some "what if?" questions are asked concerning, say, the effect of fuel consumption on range, or the effect of additional payload on takeoff gross weight. Large computer programs are just too unwieldy to answer these questions quickly. A simple program was needed that would answer these questions and would run on a pocket calculator. An objective was to find the most simple set of algorithms that would still yield useful results; the Zen philosophy espouses a certain minimalist approach to life, and hence the title to this paper.

2. METHOD

The algorithms described here were programmed on a pocket calculator with a root-finder. That is, an equation can be encoded in a form such that first the user declares the unknown variable, then the calculator requests values for the known variables, and solves iteratively for the unknown variable. This feature can be used on a mission sizing program by writing an equation for the difference between the empty weight of an airplane from flying the mission, and the empty weight from empirical weight buildup. If this difference is set to zero, then the calculator is performing the same functions as a large mission sizing program. …

…

3. RESULTS

Equations 7 and 8 can be put into a Hewlett Packard HP-32s calculator in only 24 lines of code, and it may be possible to encode them in fewer. A listing of the program is shown in Figure 8. Once the coding is keyed in, parametric analyses can be performed to find, for example, the impact of cruise sfc, cruise LID, or range on takeoff gross weight. A list of inputs is shown in Figure 6. …

…

Step Keys Comments (or content of X register)

M01 LBLM Label this routine

M02 INPUT R Input range [n.mi.l

M03 INPUT P Input payload [lb]

M04 INPUT V Input cruise speed m]

M05 INPUT F Input reserve fraction

M06 INPUT L Input cruise L/D

M07 INPUT C Input cruise sfc [lb/lb/hr]

M08 INPUT W Input TOGW [lb]

M09 1 1

MI0 RCL+F (1+F)

M11 RCL R R

MI2 RCLxC R*C

M13 RCL+V R * W

M14 RCL+L R*U(V*L)

MI5 e

M16 + (1 +F)m(R*U(V*L))

M17 RCL - F (1+F)/EXP(R*U(V*L))-F

M18 RCL x W W((1+F)/EXP(R*U(V*L))-F

MI9 RCL - P W((1+F)/(EXP(R*U(V*L))-F)-P

M20 RCLW W

M21 RCLxA A*W

M22 RCL+B A*W+B

M23 - (W((l+F)/EXP(R*C/(V*L))-F)-P-

(A*W+B-(A*W+B)

M24 RTN End routine

Put values in storage locations A and B for the vehicle being designed.

BEST!

SlideRule

ps: sorry, NO URL (happy hunting)

ABSTRACT

This paper describes the development of a set of algorithms that find the takeoff gross weight of an aircraft for given vehicle and engine characteristics, and mission requirements. A major objective was to find the most elementary set that would still yield useful answers. The result was a set that could be encoded on an inexpensive programmable pocket calculator with only 24 lines of code. Results are compared with actual characteristics of an executive jet and its' derivative versions.

1. INTRODUCTION

All the major airframe (and aero-engine) companies have large computer programs for airplane sizing and trade studies. In essence each program consists of two parts, mission analysis and weight buildup. …

…

The weight buildup program calculates the empty weight using empirical component weight equations. …

…

The difficulty with these computer programs is that they need large amounts of input data before they can be used. …

…

At the beginning of a design project this information is unknown to the designer. It is also quite possible that some "what if?" questions are asked concerning, say, the effect of fuel consumption on range, or the effect of additional payload on takeoff gross weight. Large computer programs are just too unwieldy to answer these questions quickly. A simple program was needed that would answer these questions and would run on a pocket calculator. An objective was to find the most simple set of algorithms that would still yield useful results; the Zen philosophy espouses a certain minimalist approach to life, and hence the title to this paper.

2. METHOD

The algorithms described here were programmed on a pocket calculator with a root-finder. That is, an equation can be encoded in a form such that first the user declares the unknown variable, then the calculator requests values for the known variables, and solves iteratively for the unknown variable. This feature can be used on a mission sizing program by writing an equation for the difference between the empty weight of an airplane from flying the mission, and the empty weight from empirical weight buildup. If this difference is set to zero, then the calculator is performing the same functions as a large mission sizing program. …

…

3. RESULTS

Equations 7 and 8 can be put into a Hewlett Packard HP-32s calculator in only 24 lines of code, and it may be possible to encode them in fewer. A listing of the program is shown in Figure 8. Once the coding is keyed in, parametric analyses can be performed to find, for example, the impact of cruise sfc, cruise LID, or range on takeoff gross weight. A list of inputs is shown in Figure 6. …

…

Step Keys Comments (or content of X register)

M01 LBLM Label this routine

M02 INPUT R Input range [n.mi.l

M03 INPUT P Input payload [lb]

M04 INPUT V Input cruise speed m]

M05 INPUT F Input reserve fraction

M06 INPUT L Input cruise L/D

M07 INPUT C Input cruise sfc [lb/lb/hr]

M08 INPUT W Input TOGW [lb]

M09 1 1

MI0 RCL+F (1+F)

M11 RCL R R

MI2 RCLxC R*C

M13 RCL+V R * W

M14 RCL+L R*U(V*L)

MI5 e

^{x}EXP(R*U(V*L))M16 + (1 +F)m(R*U(V*L))

M17 RCL - F (1+F)/EXP(R*U(V*L))-F

M18 RCL x W W((1+F)/EXP(R*U(V*L))-F

MI9 RCL - P W((1+F)/(EXP(R*U(V*L))-F)-P

M20 RCLW W

M21 RCLxA A*W

M22 RCL+B A*W+B

M23 - (W((l+F)/EXP(R*C/(V*L))-F)-P-

(A*W+B-(A*W+B)

M24 RTN End routine

Put values in storage locations A and B for the vehicle being designed.

BEST!

SlideRule

ps: sorry, NO URL (happy hunting)