NCAR-TN/EDD-74 the Measurement of Air Velocity and Temperature
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NCAR-TN/EDD-74 /-o /2 The Measurement of Air Velocity and Temperature Using the NCAR Buffalo Aircraft Measuring Systemi , -L/ D. H. LENSCHOW , /' June 1972 NATIONAL CENTER FOR ATMOSPHERIC RESEARCH /4ol /AJ Boulder, Colorado iii PREFACE Several years ago it was recognized that the development of iner- tial navigation systems for aircraft would make possible more accurate measurements of air velocity than were previously possible. Combining this improvement in measurement capability with the mobility of air- craft results in a very powerful tool for investigating a variety of atmospheric problems--from measurements of eddy fluxes of heat, mois- ture, and momentum within a few tens of meters of the earth's surface to measurements of lee wave structure several kilometers above the surface. The development of the measuring system on NCAR's Buffalo aircraft is a joint effort of NCAR and the Desert Research Institute (DRI), Reno, Nevada. At NCAR, both the Research Aviation Facility and the Laboratory of Atmospheric Science have contributed to its development. DRI's par- ticipation is under the direction of J. Telford. This report does not discuss measurements from all the sensors on the aircraft. Other sensors include a microwave refractometer (from which humidity fluctuations can be obtained), a dew-point hygrometer, an electrochemical ozone sensor, and a variometer (rate-of-climb sensor). Furthermore, the measurements and methods of measurements discussed here are not to be considered complete or absolute. Not only do the sensors change as new and better ways of measuring become available, but in- flight comparisons with other aircraft and with ground-based sensors and wind tunnel and laboratory tests will continue to shed new light on pres- ent methods for making airborne measurements. v CONTENTS Preface ................... ........... iii List of Figures .......................... vii 1. INTRODUCTION .................... 1 2. BASIC VELOCITY EQUATIONS ................... 4 3. USE OF THE INERTIAL PLATFORM ................. 9 4. AIR SENSING ................. 22 5. CONCLUSION ............. ........ 32 Appendix ............................ 35 References ................ 38 vii FIGURES 1. Flow measurement sensors mounted on the nose boom of the NCAR de Havilland Buffalo aircraft ............ 2 2. Spectra of vertical and lateral acceleration of the air sensing probe mounted on the end of the Buffalo nose boom . .................. ...... 3 3. Coordinate systems used in deriving the equations for calculating the air velocity components ........... 6 4. Airplane attitude angles and axes used in equations for calculating the air velocity components ......... 8 5. Block diagram of an inertial navigation system ..... 9 6. Velocity errors in an inertial navigation system ....... 14 7. Position errors in an inertial navigation system ... .... 15 8. Position and velocity errors after four flights, each of about 6-hr duration ............. .... 17 9. Block diagram of an inertial barometric vertical velocity and altitude measuring system ............ 18 10. Spectra of pressure altitude and inertial altitude and the coherence of these variables with 34 degrees of freedom . .. 20 11. Response of the Rosemount thermometer to a step-function change in temperature .................... 31 12. Comparison of the output of an unprotected resistance-wire thermometer with the Rosemount thermometer .......... 31 1 1. INTRODUCTION This report describes methods used to measure air velocity and temperature from an aircraft and their application to the measuring system on the NCAR Buffalo aircraft. The main components of this system are: * An inertial navigation system (Litton Industries, Inc., Model LN-15D) that provides measurements of airplane acceleration, velocity, position, and angles of attitude. The stabilized platform of the iner- tial navigation system is located inside the Buffalo's laminated fiber glass nose boom. * An air sensing probe (shown in Fig. 1) that provides measure- ments of angles of attack and sideslip, pitot-static pressure, and tem- perature. The probe is mounted 5 m forward of the airplane nose on a hollow steel tube. The steel tube is supported by the fiber glass nose boom, and the tube's after end is rigidly attached to the outer case of the inertial navigation system platform. Shock and vibration isolators, mounted between the steel tube and the outer fiber glass boom, insulate the platform and probe from aircraft vibrations. The spectra of verti- cal and lateral probe acceleration during a flight (Fig. 2) indicate that the natural vibration frequency of the probe is about 8 Hz, with harmonics at 16 and 24 Hz. Recently, the outer boom has been stiffened, but the effect of this modification on the probe's vibration spectra has not yet been determined. * A second pitot-static tube that provides measurements of both static pressure and pitot-static pressure. This pitot tube, which is free to align itself parallel to the airstream, is mounted 2 m forward of one of the wing tips. In the following sections the equations used to calculate the air velocity components from the inertial system and air sensing probe mea- surements are derived, use and limitations of the inertial navigation platform are discussed, methods used to calculate true airspeed and static temperature are presented, and errors in measurement and their effect on the calculated atmospheric variables are discussed. Fig. 1 Flow measurement sensors mounted on the nose boom of the NCAR de Havilland Buffalo aircraft. 3 10-' -)N II I 0I(1) '4. '~ II 5 I II I10 - - II LJ 4 Fig. 210------ Spectra0.1 of vertical and Ilateral accelerationI-I10 of the air sensing100 probeO.I moun Late endI of the Buffalo nose10 boom. 100 FREQUENCY (Hz) Fig. 2 Spectra of vertical and lateral acceleration of the air sensing probe mounted on the end of the Buffalo nose boom. 4 2. BASIC VELOCITY EQUATIONS The derivation of the air velocity equations closely follows Axford (1968). However, several changes were made in terminology and coordi- nate systems to conform to standard aeronautical engineering usage (Etkin, 1959) for the aircraft coordinate system and to standard iner- tial navigation (Kayton and Fried, 1969) and meteorological usage for the air velocity in the local earth coordinate system. The velocity of the air with respect to the earth, v = iu + jv + kw, is obtained by adding the velocity of the aircraft with respect to the earth, vp, and the velocity of the air with respect to the aircraft, v If all the measurements are made at the same point, we have v = v + v (2-1) p a The components of v are measured with sensors mounted on the aircraft, a usually on a boom forward of the aircraft to reduce as much as possible the measurable effects of the distortion of the airflow by the aircraft. The components of v are obtained from integrated accelerometer outputs p on an inertial navigation system or from a radiation transmitting and sensing device such as a doppler radar or radar altimeter. If the aircraft velocity is obtained from integrated accelerometer measurements, the velocity is measured in an inertial frame of reference. If we convert to an earth-based coordinate system, we obtain dv - a - (- + W ) x v + g (2-2) dt p e p -e -a- - - where a is the measured acceleration, t and t are the angular veloci- e p ties of the earth and platform, respectively, and g is the gravitational acceleration (which includes the centripetal acceleration). Since the accelerometers may not be located near the air velocity sensors, the 5 * + -0 term Q x R, where Q is the angular acceleration of the aircraft, and + P + + P R = iX + jY + kZ is the distance from the accelerometers to the air ve- locity sensors, must be added to Eq. (2-2). Thus, Eq. (2-1) can be com- bined with the integral of Eq. (2-2) and rewritten as v = v +[a - (u+ + x v + dt + x R = v + v + x R (2-3) a ep p p a p p In the general case, the measured components of v and v may not be in the local earth coordinate system. The air sensors, for example, are usually rigidly connected to the aircraft fuselage, or in the case of the Buffalo, rigidly connected to the inertial navigation system. Therefore, it is necessary to know the angles between the coordinates of the measuring systems and the local earth coordinates. The measured ve- locity components can then be rotated by means of the appropriate angu- lar transformation to the local earth coordinate system. The inertial system on the Buffalo is stabilized along the local earth axes so the rotation angles of the platform gimbals are equivalent to the aircraft attitude angles. From the inside platform gimbal outward, i.e., from the stabilized accelerometer and gyro cluster outward to the aircraft frame, the order of the rotations is as follows: first, a rotation l about the z-axis of the earth coordinate system; second, a rotation 6 about the y"-axis, which is the y-axis rotated in the horizontal plane by the angle i; and third, a rotation ( about the x'-axis, which is the x-axis in the aircraft coordinate system. The aircraft axes are shown in Fig. 3; a right-handed angular rotation is positive. The symbols and axes have been defined to correspond to standard aerodynamic conventions (Etkin, 1959). 6 / x / -/' Xi "' (a) x\( East (a) Aircraft Axes (b) Intermediate Local Earth Axes V.^y^^^/>~~~~/\^~ ~(c) Inertial Platform (Meteorological) Axes Fig. 3 Coordinate systems used in deriving the equations for calculat- ing the air velocity components. In matrix notation, the transformation of the air velocity from aircraft (x',y',z') to platform (x,y,z) coordinates [same as (b) coordi- nates in Fig. 3] is given by [uil [T i [u ] (2-4) where cosi -sin 0 cos9 0 sine 1 0 0 T . = sini cosi 0 -(2-5)0 1 0 0cos -sin) 0 0 1 -sine 0 cos9 0 sin) cos) cosicose -sinicos4 + cosJsinesin4 sinisin) + cosisinOcos4 sinpcose cosicos) + sinsinessinj sinisinecosI - cosisinJ (2-6) -sine cosesin4 coseco s The terms of Q x R must also be transformed to the local earth P coordinate system.