. .—- NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS , TECHNICAL NOTE No. 1120 , STANDARD NOMENCLATURE FOR AIRSPEEDS WITH TABLES AND CHARTS FOR USE IN CALCULATION OF AIRSPEED . By William S. Aiken, Jr. Langley hCemoriaI Aeronautical Laboratory Langley Field, Va. Washington September 1946 ,. * -.. * NA!215EAL ADVW3RY COMMITTEE FOR AERONAUTICS . .● ✌. TECHNICAL NOTE No, 1120 . .- . AND CEM?TS FOR USE IN CALCULATION W AIRSPEED -. By William S . Mbn, Jr. Symbols and definitions of various airspeed terms that have been adopted as st~dard by the NACA SubcGEP mittee on Aircraft structural Design are presented. The ● equations, charts, and tablgs required In the evaluation of true sirspeed, calibrated airspeeds equivalent air~ s-peed,im-p.actand dynamic nressures, and }:achand Reynolds nlmnbers have been cor,piled~ Tables of the standard . akmosghera to an alt?tude of 65,.200feet and a tentative extension to an altitude of 1009000 feet are given along .“ with tha basic equations and ccfistants on whi~h both the standard atmosphere and the tentative extension are based~ INTI?ODUCTION In s.nalyses of aerodynamic data very often wind- tunnel or fligb.t measurements must bs converted into air- speed and related quar.ttties that are used in engineering calculatt ons, Attsmpts to accomplish such confers!.on by use of available m.etkods have been corc~licated by the diversity of s~mbols and definitions and by the necessity of referring to equations, charts, and tables from a nwn”oer of different sources. A standard set of symbols and definitions of v.micms atrsgaad terms that were adopted by the KACA Subcommittee on Aircraft Structural Design and a cow~ilation of th~ necessary equations, charts, ‘ and tables f~r converting measured pressures and temper- atures into airs~eeds, determining Mach numbars sand Re~~~ds zi’~ber~, snd determtnir.g otker quantities such as dynamic and iwqp.ct pressures that are of interest are therefore presented Mrein. -.-— In the preparation of tha pres~nt paper results that have been included in ~reti.ous papers have been ext,?nded to includ~ higher qltitudas and quantities not . .,, ~i.ven h the ~i~~vious pa~a.=:? since recsnt raquests have indicated the need for such an extension of stani!ard- atuosphere tables. ● ● The tables and figuz-es have been arranged for ease in determination of the ~irSP6f3ds ‘Hb.fichts usually bcsed on the interpretation of measurements of’differential Fressures obtained with “some pttct-static &rranSe?nent. The Interrelation of the various airspeed quantitie= is independent Of the method used in the measurement. Instrument and installation errors have been ass-wed to have been taken into account. ST.AKDARD SYH13GZSA.liDXFIN121CNS At the ??ovem’oar191f4meeting of tileNACA Subcommittee on .Aircrai’tStructural .Wsign, reprcsent=tivsti frozUtins A??M7’ Yavy, CAA, ??AC-A,and several aircraft manufacturers ado~;ed as standard the folloring symbols and def:nttions for air,sneecls..- : -i true ai.rspoecl vq indicated airspeed (the reading of’a differer.tial- nressure airs~eed indicator, calib~-ated in ~ccordance wi>bi the accepte~ standtirdadiabattc . formula to ii~d.icatetrue &irspeed for stmdard sea-level conditions only, unccrr~cted for . instrument and installatim tirrors) . Ve equivalent airspeed (,,.1/2) . uce of’equivalent ai~s~eed in combination with various subscripts is custor.ary, particularly in stvuc- tursl desi~n, to d~si~gate various design conditions. Zt is sug~ested that the i’oregolng 8P301s tieretained Intact when furtb-er subscripts are necessary. NA.CA TN Na, 1120 3 . D ~~ostof tjhefollowing symbols, which ar”eused herein, . have already been accepted as standard and are used throughout aeronautical literature. The units given apply < to the development Of the equationsin the present report. .- v, true airspeed, feet per second . Vc calibrated airspeed, feet per second Ve equivalent airspeed, feet per second a speed of sound in ambient air, feet per second M Mach number (V/a) . P mass density of ambient air, slugs per cubic foot Po standard mass density of dry ambient air at sea ; level, 0.002578 slug per cubic foot CY density ratio (p/PO) .- q dynamic pressure, pounds per SW=’Q foot ()~pv1 2 qc impact pressure, pounds per square foot (total . pressure minus static pressure p) P static pressure ,of free stream, pounds per squsre foot static pressure of free stuesm under standard sea- ‘o Mvel conditions, pounds per s“quare foot ,. t temperature, oF or oC . At difference between free-air temperature and tem- . perature of standard atmosphere, ‘F . T absolute temperature, ‘F absolute or ‘C absolute .,9 . T star.dard-atmospb.erefree-air temperature, % absolute . S td TO standard sea-level absolute temperature, 518.4 ‘F absolute . hnrmonic mean absolute temperature, ‘F absolut~ (defined in equation (E5)) . ? .’.. compressibility factor defined in equation (11) compressibility factor d6fined in equation (1~) ratio of’specific beat at constant pressure to . specific heat at constant volume (assumed equal to l.1+for air) I , absolute altitude, feet pressure altitude, feet acceleration of gravity, 32.174.0feet per second per second modulus for common “logarithms, lo~lOe (O .k3&Th ) coefficient of viscosity, SIUGS pm foot-second kinematic viscosity, square fe6t per second (P/P) . “- ReWolds number p~ ()w Reynolds number f’orstandard s.tmospheric conditions characteristic lerigth, feet . CALCULATIOiJ OF AIRSPEED AND PLELATED QUANTITIES . ~ecause pit”ot-static arrangements are used as the basis for the determlnati.on of atrspeed, aeronautical engineering practice has develop6d to include the use of a number of’airspeed terms and quantities, each of which has a particular field of usefulness. True airspeed is :Irincipally of use to aerodynamicists, and indicated and c&librated airspeeds are principally of use to pil.ota. Equivalent airspeed is used by structural engineers, since all load specifications have long b6en based on this quantity. , s Ik5finite r61ationshi~s exist between true airspGecl, . Mach number, Reynolds number, calibrated airspeed, and Equivalent airspeed, and all these quantities may be . NJLCATN ~0, 1120 5 . , related either to the dynamic Qressure . q or to the .,. impact pre3sure qc . Some of the relations presented \ hsreln apply to the calculation of true airspeed and . Mach number from airspeed measurements obtained with an .- airspeed indicator of standard calibration, C?therrela- tions apply to the calculation of true airspeed when the impact pressure is measured directly. If it is assumed that tb.6total-head tl~beand the static-head tube measure their respective p~essures cor- rectly and that these ,tubes are connected to an a~pro- priate instrument, the impact pressure measured is given bT tb.eadiabatic equation wb.en V <, a: (1) Standard airspeed indicators usefl in Aruy and Navy airplanes since 1~25 have been calibrated according to equation (1) for standard sea-level conditions; that is, according to the equation when V < a, w-here t~ie subscript O denotes standard sea-level con- &itiorIs and VC 1s the calibrated airspeed. The c8.1i- b~ated airspeed is, therefore, equal to true airspeed only for standard sea-level cor.ditions. Determination of True Airspeed - from Calibrated Airspeed The formula that relates the true airspeed to the . calibrated airspead may be found “Qy equating the rigb.t- “ .- hand terms of equations (1) and (2) as follows: 6 NACA TN No. 1120 ● Because the exact numerical solution of equation (j) for . true airspeed is involved and requires a great deal of . .:. time, a number of charts for the determination of the \ t~ue airspeed from the cal~brated airspeed for vartous ,’ atmospheric conditions have been derived. (See refer- .- ences 1 to 3.) A typical chart (taken from reference 1) Wiiatshows the relationship between Mach number, cali- ‘orated airspeed, pressure altitude, temperature, and true airspeed is given in figure 1. ~iS chart iS Widely used.because of’its convenience. Airspeed may be obtained froii~this chart with an accuracy within 2 miles per hour wl~c:nstandard conditions hold and when values of airspeed” and pressure altitude explicitly given by the chart are ehcsen; the possible errors increaoe to within ~ miles peimhour, however, when the temperature conditions are not standard and when interpolation is required for both altitude and airspeed. For some prposes, charts such as figure 1 are not sufficiently accurate . A series of logarithmic tables that may be used to determine the true airspeed in knots from observed values of calibrated airspeed, pressure altituile, and free-air temperature is given in reference 4. LoCarithwdc tables of the type given in reference )Aare of limited usefulness since they cannot bb used conveniently to evaluato the intermediate quantities (impact pressure and ?.:achnumber) that are involved. in the computation of true airspeed. A series of tables (tables T to V) is given in the prc.sentreport to permit determination of impact pres- sure !lC in pournds per square foot, Uach number 1;, and true airspeed V in mil(ss per hour or knots for okscrved values of Vc in miles par hour or knots, press-are alti- tude h~ In f~et, and t~mperature in dcErees Fahrenheit or Centlgratie. The accuracy of the tables is far greater than that with which experimental data can normally be obtained. ~~~th ordinar;~ care in interpolation, errors should be less than 0.25 mile per hour throughout the greater part of tlieairspeed and altitude ranEes. !’able I, which gives values of impact pressure qc . in pounds per square foot for values of Vc in miles per . hour, was computed directly from equation (2]; standard . values were used for all the constants occurring in this “ equation. Table II gives values of impact pressure qc . in pounds per square foot for values of Vc in knots. * . In computing the values of’ in table II, the conve~.= .. sion from feet to nautical ni‘fes used was as follows: .