SUBSONIC RELATIONSHIPS BETWEEN PRESSURE …

1 SUBSONIC RELATIONSHIPS BETWEEN PRESSURE altitude , calibrated AIRSPEED, AND MACH NUMBER FFRRAANNKK BBRROOWWNN AAiirrccrraafftt PPeerrffoorrmmaannccee EEnnggiinneeeerr SEPTEMBER 2012 TECHNICAL INFORMATION HANDBOOK AFFTC-TIH-10-01 Approved for public release; distribution is unlimited. (412TW-PA-12762) AFFTC AIR FORCE FLIGHT TEST CENTER EDWARDS AIR FORCE BASE, CALIFORNIA AIR FORCE MATERIEL COMMAND UNITED STATES AIR FORCE 13 September 2012 REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information.

2 Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it DOEs not display a currently valid OMB control number.

3 PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 13-09-2012 2. REPORT TYPE Final 3. DATES COVERED (From - To) N/A 4. TITLE AND SUBTITLE SUBSONIC RELATIONSHIPS BETWEEN PRESSURE altitude , calibrated Airspeed, and Mach Number 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Frank S. Brown, Aircraft Performance Technical Expert 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) AND ADDRESS(ES) Air Force Flight Test Center Edwards AFB CA 93524 8.

4 PERFORMING ORGANIZATION REPORT NUMBER AFFTC-TIH-10-01 9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 773 TS/ENF 307 E Popson Ave Edwards AFB CA 93524-6841 10. SPONSOR/MONITOR S ACRONYM(S) 11. SPONSOR/MONITOR S REPORT NUMBER(S) N/A 12. DISTRIBUTION / AVAILABILITY STATEMENT Approved for public release; distribution is unlimited. Refer other requests for this document to 773 TS/ENF, Edwards AFB, California 93524-6841. 13. SUPPLEMENTARY NOTES SC: 012100 CA: Air Force Flight Test Center, Edwards AFB 14. ABSTRACT This handbook derives equations for PRESSURE altitude , calibrated airspeed, and Mach number valid for SUBSONIC Mach numbers in the troposphere and the stratosphere using the 1976 standard atmosphere.

5 Equations are also developed for equivalent airspeed, true airspeed, local speed of sound, and incompressible dynamic PRESSURE . Numerical examples are presented solving for PRESSURE altitude , calibrated airspeed, or Mach number using the other two parameters. 15. SUBJECT TERMS calibrated airspeed 1976 standard atmosphere Pitot statics PRESSURE altitude (ICAO)International Civil Aviation Organization Mach number 1993 ICAO international standard atmosphere 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OFABSTRACT Same as Report 18.

6 NO. OF PAGES 174 19a. NAME OF RESPONSIBLE PERSON 412 TENG/Tech Pubs a. REPORT Unclassified b. ABSTRACT Unclassified c. THIS PAGE Unclassified 19b. TELEPHONE NUMBER (include area code) DSN 527-8615 Standard Form 298 (Rev. 8-98)Prescribed by ANSI Std. page was intentionally left blank. iii EXECUTIVE SUMMARY The purpose of this handbook is twofold: 1. Present the SUBSONIC RELATIONSHIPS among PRESSURE altitude , calibrated airspeed, and Mach number, and 2. Show that the RELATIONSHIPS BETWEEN calibrated airspeed and Mach number at a given PRESSURE altitude are independent of the ambient air temperature or the total air temperature.

7 Equations relating ambient air PRESSURE and PRESSURE altitude were derived for the 1976 standard atmosphere. The equation for Mach number as a function of the ratio of total air PRESSURE to ambient air PRESSURE comes from classical gas dynamics. The equation for the speed of sound as a function of ambient air temperature and the sea level, standard day value were obtained from the 1976 standard atmosphere. The equation for true airspeed was based on the definition of Mach number, true airspeed divided by the local speed of sound. The equations for equivalent airspeed and for calibrated airspeed were developed from the true airspeed equation by setting selected local parameter values to their sea level, standard day equivalents.

8 Numerical examples are presented solving for PRESSURE altitude , calibrated airspeed, or Mach number using the other two parameters. Understanding and using these RELATIONSHIPS properly is important to every flight tester who provides flight test conditions in their reports. This document will promote a proper understanding and use of these RELATIONSHIPS . iv This page was intentionally left blank. v TABLE OF CONTENTS Page No. EXECUTIVE SUMMARY .. iii BACKGROUND .. 1 USE OF THIS HANDBOOK .. 1 RESOLUTION AND SIGNIFICANT FIGURES.

9 1 LIMITATIONS OF VALIDITY .. 2 DERIVATION OF AN ATMOSPHERIC MODEL .. 4 relationship FOR AIR DENSITY .. 5 Non-dimensional Equation of State .. 5 Specific Gas Constant for Dry Air .. 6 relationship FOR THE LOCAL ACCELERATION DUE TO GRAVITY .. 6 Introducing Geopotential Height .. 6 Introducing PRESSURE altitude .. 9 MODIFYING THE INTEGRAL .. 9 Solving for a Linearly Varying Ambient Air Temperature .. 12 Solving for a Constant Ambient Air Temperature .. 18 PRESSURE altitude AND AMBIENT AIR PRESSURE .. 21 DENSITY altitude .. 22 STANDARD DAY.

10 22 PRESSURE altitude and Ambient Air PRESSURE .. 22 PRESSURE altitude and Ambient Air Temperature .. 22 Density altitude .. 23 NON-STANDARD DAY .. 24 ([TOTAL AIR PRESSURE ]/[AMBIENT AIR PRESSURE ]) RATIO AND MACH NUMBER .. 25 LOCAL SPEED OF SOUND .. 28 TRUE AIRSPEED (HISTORICALLY) .. 30 TRUE AIRSPEED USING PT, Pa, AND 33 CALCULATING AMBIENT AIR TEMPERATURE .. 33 CALCULATING TRUE AIRSPEED .. 34 EQUIVALENT AIRSPEED .. 38 INCOMPRESSIBLE DYNAMIC PRESSURE .. 39 ANOTHER EQUATION FOR EQUIVALENT AIRSPEED .. 41 calibrated AIRSPEED .. 42 vi SAMPLE PROBLEMS.