Trans. Japan Soc. Aero. Space Sci. Vol. 53, No. 182, pp. 250–257, 2011

Comparison Study and Sensitivity Analysis of Flight Test Techniques for Air Data Position Error Correction in Small Aircraft

By Sang-Jong LEE,1Þ Jae Won CHANG,1Þ Jeong Ho PARK,2Þ Byoung Soo KIM3Þ and Kie Jeong SEONG1Þ

1ÞFlight Control Team, Korea Aerospace Research Institute, Daejeon, Republic of Korea 2ÞPGM R&D Lab, LIG Nex1 Co. Ltd., Yongin, Republic of Korea 3ÞSchool of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Republic of Korea

(Received May 18th, 2009)

The flight test is important in the development and certification phases of an aircraft. It is composed of various tests, but the position error correction test should be performed first to determine error of the pitot-static measurement system that is the basis for evaluating flight characteristics. This paper investigates and compares recent test methods using real flight test results. The ground course and arbitrary heading method are both considered using GPS and DGPS to measure ground speed. The arbitrary heading method was most efficient and precise. In addition, new method is proposed and successfully used to determine accurate position error by comparison with DGPS results. Finally, sensitivity analysis was performed to analyze the effect of error sources. It shows that the most important error is the measured indicated airspeed following by measured true airspeed, outside air temperature, and pressure altitude.

Key Words: Flight Testing, Aircraft, Airworthiness, Position Error Correction, Analysis

Nomenclature CAM: measured by camcorder DGPS: measured by DGPS aSL: speed of sound at sea level GPS: measured by GPS HI: indicated pressure altitude s: standard day condition HIC: indicated pressure altitude corrected for instrument W: wind error x: vector component of x-axis HPC: altimeter position error y: vector component of y-axis Pa: ambient pressure PSL: pressure at sea level 1. Introduction qc: dynamic pressure t: time The flight test plays a key role in evaluating the per- t: time taken flying between waypoints of ground course formance of an aircraft and its subsystems. The ICAO VC: calibrated airspeed (International Civil Aviation Organization) certifies new VC: compressibility error commercial aircraft using its own certification system. Con- VE: equivalent airspeed sequently, every country has its own certification regula- VG: ground airspeed tions and government certifying agency, such as the FAA VI: indicated airspeed (Federal Aviation Administration) in the USA, JCAB (Japan VIC: indicated airspeed corrected for instrument error Civil Aviation Bureau) in Japan, and EASA (European VIC: instrument error Aviation Safety Agency) in the EU. At certification, the VPC: airspeed position error flight test is the final compliance test for evaluating flight VT: true airspeed characteristics and certifying that design, flight safety, and 1) VW: wind speed structural safety meet all requirements. The flight test : pressure ratio includes various tests, including performance, handling, : temperature ratio aero-elastic/flutter stability, structural loads, and avionics/ a: ambient air density equipment performance. The position error correction SL: ambient air density at sea level (PEC) flight test is the starting point to process the other : air density ratio of test day tests because aircraft performance is based on airspeed s: air density ratio of standard day and altitude from the pitot-static measurement system. : heading angle Errors are generated by the pressure field and flow angular- Subscripts ity as a result of the position of the pitot and static port. This A: one waypoint of ground course creates a difference between the readings and true airspeed B: one waypoint at ground course and altitude. Therefore, this error must be defined at the PEC flight test and corrected. Ó 2011 The Japan Society for Aeronautical and Space Sciences Feb. 2011 S.-J. LEE et al.: Comparison Study of Flight Test for Air Data Position Error Correction 251

The classic PEC flight tests use a test boom, trailing cone, 2–4) ðVGA þ VGB Þ tower-fly-by, pacer aircraft, ground course method, etc. VT ¼ ð1Þ GPS (Global Positioning System) is used with the ground 2 course method to measure ground speed during reciprocal This method has several limitations: (1) timing error, (2) test flying along a track. This implementation reduces error from altitude, (3) crosswind. Use of GPS or DGPS removes lim- measuring time to fly a known distance. Lewis5) of the itations (1) and (2), but (3) cannot be removed because exact NTPS (National Test Pilot School) proposed a flight track true airspeed can be calculated from components parallel to along the wind direction and Bailey6) of the AFFTC (Air the flying track as defined in Eq. (2). The magnitude as well Force Flight Test Center) suggested a 90 track to the wind as the source of the error is described by Rogers,7) and we in both directions. However, both methods require knowl- describe the derivation of Eq. (2) in Appendix A. edge of the wind direction before the test flight. Rogers7) V GA V GB VGAx þ VGBx calculated the error due to variation in wind speed and angle VT ¼jV Tj¼ ¼ ð2Þ 2 2 for the ground course method using GPS. New test methods using GPS have been proposed by several researchers and 2.2. Arbitrary heading method institutes. All are based on multi-track flying of least This paper uses Gray’s method11) for the PEC flight test, three legs. In addition, no information on wind direction is and it is the recommended FAA certification method.14) needed. Fox8) first proposed an accurate method for deter- Both GPS and DGPS were used to measure ground speed mining true airspeed using GPS. The test aircraft is flown and the results are compared. It is necessary to fly three along three ground tracks 90 to each other. It is more con- legs to determine three unknown parameters such as the venient for pilots to adjust the heading instead of the ground true airspeed and two components of wind speed. Since track on the fly, so a three-orthogonal heading technique ground speed is a vector sum of true airspeed and wind was suggested.9,10) This is known as the horseshoe heading speed, they can be solved from the simultaneous equations method and extends from Fox’s method. However, these defined in Eqs. (3), (4), and (5). Gray provided a spread- techniques are limited to successive 90 headings. Although sheet to calculate the unknown parameters and this paper the true airspeed calculation is more complex, the arbitrary shows the mathematical procedure to reach the solution in heading method proposed by Gray11) can be applied easily Appendix B. to the PEC flight test. Finally, some of these methods are ðV V Þ2 þðV V Þ2 ¼ V 2 ð3Þ compared with classical methods.12,13) G1x Wx G1y Wy T 2 2 2 This paper investigates the flight test results for various ðVG2x VWx Þ þðVG2y VWy Þ ¼ VT ð4Þ PEC test methods using GPS or DGPS (Differential GPS) ðV V Þ2 þðV V Þ2 ¼ V 2 ð5Þ and compares their effectiveness and usefulness. Further- G3x Wx G3y Wy T more, sensitivity analysis is used to analyze error due to 2.3. Single camcorder method indicated airspeed (IAS), true airspeed (TAS), outside air This method is similar to the ground course method for temperature, and indicated altitude. DGPS is common today, eliminating the timing error. With the progress of digital so it deserves investigating. Five PEC methods were com- technologies, a small camcorder is easily installed on an pared: (1) arbitrary heading using DGPS, (2) arbitrary head- aircraft to record video with time synchronization. In this ing using handheld GPS, (3) ground course using DGPS, (4) paper, one camcorder was installed under the left wing. ground course using GPS, and (5) single camcorder method. By using this technique, ground observers and other equip- The last method records a video using an under-wing ment are not required and the exact time required to fly camera. Analysis of time frames gives accurate ground between known waypoints can be determined. speed without the timing error of classic ground course methods. 3. Flight Data Reduction

2. Flight Test Methods and Mathematics The same data reduction procedure can be applied to three methods explained in the previous section. Several To find position error, all PEC methods using GPS calcu- kinds of airspeed are used for calibration of the pitot-static late true airspeed from ground speed measured by GPS and system as shown in Fig. 1. Using ground speed, the true then compare it with indicated airspeed. Hence, the key role airspeed can be determined by a flight test and equivalent of GPS is how it can be used to obtain the accurate true airspeed (EAS) can be obtained by correcting the density airspeed under the existing wind conditions. altitude. This EAS is the calibrated airspeed (CAS) corrected 2.1. Ground course method for compressibility. Assuming that instrument error is cor- To find true airspeed, the test aircraft is flown back and rected (VIC ¼ 0), the indicated airspeed (IAS) can be used forth between two fixed waypoints (A and B) to eliminate directly to obtain CAS. Therefore, the reduction procedure wind effects. Usually, observers on the ground use a chro- provides CAS and airspeed position error can be defined nometer to measure time and true airspeed is calculated in Eq. (6). simply using Eq. (1). 252 Trans. Japan Soc. Aero. Space Sci. Vol. 53, No. 182

Never Exceed VI (IAS) : Indicated Airspeed from instrument in aircraft MTOW 2,850 lbs Speed 180 kts ∆ VVVIC=+I V IC Max. Cruise Max. Fuel 68 gal Speed 160 kts VIC (IAS) : Indicated Airspeed corrected for instrument error ∆ Length 22 ft Stall Speed 61 kts VVVCICPC=+ V 1,100 Width 34 ft Max. Climb Rate VC (CAS) : Calibrated Airspeed fpm VVV =+∆ V Cabin EC C 50 in Take-off Length 1,250 ft Width VE (EAS) : Equivalent Airspeed V V = E T σ Fig. 2. Test-bed aircraft (Firefly) and specification.

VT (TAS) : True Airspeed + VV=VGTVW

VG (GS) : Ground Airspeed 9 CAS converted from ft/s to knots V Fig. 1. Data reduction procedure. C ð15Þ 1:6878

10 Airspeed position error calculated from CAS of pffiffiffi Eq. (13) and measured IAS VI þ VIC þ VPC þ VC ¼ VT VPC ¼ VC VIC ð16Þ ) VPC ¼ VC VIC ð6Þ 11 Altimeter position error determined as This paper summarizes and combines several data reduc- H tion procedures and uses as follows:3,5,15,16) H ¼ V PC ð17Þ PC PC V 1 TAS obtained from GS measured by GPS, DGPS or PC camcorder where, aSL ¼ 661:48 kts and 2 Temperature ratio calculated as "# 2 2:5 HPC 58:566 VIC VIC Ta Ta ¼ 1 þ 0:2 ð18Þ ¼ ¼ ð7Þ VPC s aSL aSL TSL 288:15 K 3 Ambient pressure ratio calculated using measured In general, in aerospace flight tests knot (nautical mile per pressure altitude as hour) and feet are commonly used as units referring to air- 6 5:2559 speed and altitude but they are not standard SI units. ¼½1 6:87559 10 HIC ð8Þ

4 Ambient air density ratio of test day obtained from 4. Flight Test Facilities and System Eqs. (7) and (8) 4.1. Test-bed aircraft and test site ¼ ð9Þ The test-bed aircraft was canard-type Firefly #3 designed and developed as a normal single-engine aircraft by KARI 5 Air density ratio of standard day calculated as (Korea Aerospace Research Institute) (Fig. 2). It is a 6 4:2559 pusher-type four-seat aircraft built mainly of composite s ¼½1 6:87559 10 HIC ð10Þ materials. Cruising speed is 120 kts and stall speed is 6 Ambient pressure and density calculated using 61 kts. It can take off and land in strong crosswinds (more Eqs. (8) and (9) than 25 kts) due to outstanding lateral stability. 2 Flight tests were conducted at Hanseo Flight Education Pa ¼ PSL ¼ 2116:22 lb/ft ð11Þ Center in Taean-Gun, Chungcheongnam-do on the west ¼ ¼ 0:002377 slug/ft3 a SL coast of South Korea. There are facilities, such as an air- 7 EAS calculated from TAS using Eq. (9) traffic control tower, and hangars to support flight tests ffiffiffi p and IFR and VFR services can be provided. The runway is VE ¼ VT ð12Þ 1.2 km long and 25 m wide. The direction of the runway is 8 CAS determined as 33–15 (330 to north and 150 to south). vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u "#4.2. Flight data acquisition system u 1 t PSL qc 3:5 The data acquisition system (DAS) consisted of onboard VC ¼ 7 þ 1 1 ð13Þ instrumentation, ground telemetry and a data processing SL PSL room (Fig. 3). The onboard instrumentation measured where, every flight characteristic. All measured flight test were "#transferred to the ground in real time via an S-band 2 3:5 ð1:6878 VEÞ a 2.2 GHz telemetry system. During the flight test, hand- qc ¼ Pa þ 1 1 ð14Þ 7 Pa recorded data were taken by the flight test engineer as a backup. Feb. 2011 S.-J. LEE et al.: Comparison Study of Flight Test for Air Data Position Error Correction 253

120 kts 110 kts 1 100 kts 90 kts finishing 0.5 80 kts line of runway

H (km) 0 at 15-mark finishing 5 line of runway 4 at 33-mark 3 2 1 0 -1 -2 3 -3 2 1 North (km) -4 0 -1 -5 -2 East (km)

Fig. 3. Data acquisition system with telemetry. Fig. 4. 3D Flight trajectory of ground course method.

4.3. DGPS and camcorder system Table 1. Measured data for ground course method (GPS, DGPS).

In this test, the most accurate position data were acquired Case Event VIC HIC ðVGÞGPS ðVGÞDGPS using the RTK (Real Time Kinematic) system of Novatel (kts) No. (kts) (ft) (deg) (kts) (kts) Flexpak with 20 Hz sampling frequency. To apply the 1 80 250 327.2336 91.3 90.4571 80 GPS method, the flight test engineer records position data 2 80 320 149.1075 84.0 83.9168 from a Garmin GNS430 on the flight deck. The DGPS 3 91 400 330.5537 99.8 99.0826 90 accuracy is better than 20 cm for position and 0.03 m/s for 4 91 440 149.8926 93.8 92.6189 velocity. Single GPS provides a position accuracy of 15 m 5 100 400 329.6370 109.0 108.7858 100 and a velocity accuracy of 0.05 m/s. 6 103 320 149.9967 101.0 99.9870 The single camcorder system beneath the left wing 7 112 320 329.8794 118.0 115.8344 recorded video of the runway with time. Its frame rate 110 8 110 320 149.0399 113.0 111.1891 was 30 fps, so the time resolution was determined as 9 122 400 328.7493 128.0 128.3859 0.033 s using captured images during flight. 120 10 123 410 149.8578 123.0 121.8873 5. Flight Test Results and Sensitivity Analysis skill is good enough to produce stabilized flight data to 5.1. Flight test results of ground course method obtain position errors. Each test flight data and event range The flight trajectory for the ground course method using are shown in Fig. 5. GPS and DGPS are shown in Fig. 4. Five test airspeeds The single camcorder method was used on same test (80, 90, 100, 110, and 120 kts) were used. At each airspeed, flights. The distance between the two finishing lines on the two reciprocal flights were made and corresponding events runway is 980.4 m, so ground speed can be calculate precisely. are numbered in order. The starting point of each event is One captured image at both finishing line is shown in Fig. 6 the finishing line of the runway position at the 33-mark and the measured flight data are summarized in Table 2. and the ending point is the runway position at the 15-mark The data reduction process described in section 3 was (vice versa in opposite flying). It took about 27 minutes applied to the test data for the three methods. The average 12 seconds (1,632.5 s) to perform all tests. During the test ground speed from Tables 1 and 2 are calculated using flights, DGPS data, altitude, and other flight information Eq. (1) and resulting position errors are summarized in were recorded automatically and the indicated airspeed Table 3. and single GPS data were recorded on a test card by the test 5.2. Flight test results of arbitrary heading method engineer (Table 1). The arbitrary heading methods used the GPS and DGPS To determine the actual test event ranges for data reduc- at the same airspeed as the ground course method. Continu- tion, the recorded counter data button pressed by the test ous three constant headings of 340,60, and 205 were engineer and LOS (Line-Of-Sight) data were used to detect selected, so the total number of events was 15 (three at each the runway finishing lines as shown in Fig. 5. LOS was airspeed). The test pilot tried to hold these headings at each calculated by subtracting the position of the runway entry event and the resultant mean and standard deviation are location from the accurate position data of the flying aircraft [342.4598, 62.7188, 200.2864] (deg) and [4.2516, 2.0072, using DGPS; a zero value means the aircraft directly entered 5.5623] (deg), respectively. Although these results are the runway position at the 33-mark or 15-mark. This pro- slightly larger than the ground course method, there is no vides very useful information to find each event range. problem because the arbitrary heading method does not The ideal heading is 330 and 150 because the test pilot depend exactly on the constant heading output at each event. flew the aircraft parallel to the runway. The resultant mean The resultant flight trajectory is a triangular track (Fig. 7). and standard deviation are [329.2106, 149.5789] (deg) and It took about 31 minutes (1,860 s) to perform all tests. [1.2801, 0.4646] (deg), respectively. Hence, the test pilot Compared to the ground course method, this might be more 254 Trans. Japan Soc. Aero. Space Sci. Vol. 53, No. 182

4 Event 1 Event 2 4 Event 3 Event 4 x 10 x 10 Table 2. Measured data for single camcorder method. 5 4.1

4 4 Counter Counter Case Event VIC t1–t2 t ðVGÞCAM ðVGÞCAM 3 3.9 1550 1600 1650 1700 1750 1800 1850 1200 1250 1300 1350 1400 1450 1500 100 120 (kts) No. (kts) (h:m:s)–(h:m:s) (s) (m/s) (kts) )

s 100

80 (kt

(kts) G G 80 V V V 1 80 3:39:19.033–3:39:40.099 21.066 46.5394 90.4659 60 60 1550 1600 1650 1700 1750 1800 1850 1200 1250 1300 1350 1400 1450 1500 80 200 2 80 3:42:52.231–3:43:15.099 22.868 42.8721 83.3372 200 100 H (m) H (m) 100 3 91 3:33:14.396–3:33:33.561 19.165 51.1558 99.4395 0 1550 1600 1650 1700 1750 1800 1850 1200 1250 1300 1350 1400 1450 1500 90 400 400 4 91 3:36:15.594–3:36:36.462 20.868 46.9810 91.3243

200 200 (deg) (deg) ψ ψ 0 0 5 100 3:27:11.825–3:27:29.297 17.472 56.1126 109.0748 1550 1600 1650 1700 1750 1800 1850 1200 1250 1300 1350 1400 1450 1500 100 4 4 6 103 3:30:07.561–3:30:26.693 19.132 51.2440 99.6110 2 2 LOS (km) LOS (km) 0 0 7 112 3:21:16.726–3:21:33.198 16.472 59.5192 115.6968 1550 1600 1650 1700 1750 1800 1850 1200 1250 1300 1350 1400 1450 1500 time (sec) time (sec) 110 8 110 3:24:12.561–3:24:29.759 17.198 57.0066 110.8126 (a) 80 kts (Event 1 and 2) (b) 90 kts (Event 3 and 4)

Event 5 Event 6 9 122 3:15:58.297–3:16:13.132 14.835 66.0870 128.4636 x 104 x 104 Event 7 Event 8 3.9 3.8 120 10 123 3:18:29.462–3:18:45.066 15.604 62.8300 122.1325 3.8 3.7 Counter Counter 3.7 3.6 850 900 950 1000 1050 1100 450 500 550 600 650 700 750 140 140 120 120 100 (kts) (kts) G G 100 V V 80 80 60 850 900 950 1000 1050 1100 450 500 550 600 650 700 750 200 200

100 100 H (m) H (m) Table 3. Data reduction results for ground course method. 0 0 850 900 950 1000 1050 1100 450 500 550 600 650 700 750 400 400 Average 200 200 Methods 80 kts 90 kts 100 kts 110 kts 120 kts (deg) (deg) ψ ψ Value 0 0 850 900 950 1000 1050 1100 450 500 550 600 650 700 750 4 5 ðV Þ T DGPS 87.1870 95.8507 104.3864 113.5117 125.1366 2 (kts) LOS (km) LOS (km) 0 0 850 900 950 1000 1050 1100 450 500 550 600 650 700 750 time (seec) time (sec) GC VC (kts) 84.0149 92.1393 100.4537 109.3146 120.3268 (c) 100 kts (Event 5 and 6) (d) 110 kts (Event 7 and 8) V (DGPS) PC 4.0149 1.1393 1:0463 1:6854 2:1732 Event 9 Event 10 (kts) x 104 3.6 HPC 3.4 17.0336 5.5243 5:6535 9:9553 14:2172 Counter 3.2 (ft) 150 200 250 300 350 400 450

150 ðVTÞGPS

(kts) 87.65 96.80 105.0 115.5 125.50 G V 100 (kts) 150 200 250 300 350 400 450 200 GC VC (kts) 84.461 93.052 101.04 111.23 120.68 100 H (m) VPC 0 (GPS) 150 200 250 300 350 400 450 4.461 2.0519 0:4558 0.2295 1:8238 400 (kts)

200 (deg) H ψ PC 0 18.927 9.9492 2:4628 1.3555 11:931 150 200 250 300 350 400 450 (ft) 4

2 ðVTÞCAM LOS (km) 86.9016 95.3819 104.3429 113.2547 125.2981 0 150 200 250 300 350 400 450 (kts) time (sec) (e) 120 kts (Event 9 and 10) GC VC (kts) 83.7398 91.6886 100.4118 109.0670 120.4820 V (Cam.) PC 3.7398 0.6886 1:0882 1:9330 2:0180 Fig. 5. Time history of flight data of ground course method. (kts) H PC 15.8666 3.3389 5:8797 11:4175 13:2017 (ft)

120 kts 110 kts 100 kts 2 90 kts 80 kts Fig. 6. Captured image of finishing line on runway. 1 H (km) 0 10 efficient from the timing view point. Less than 3 minutes is 8 required to complete 5 event flights. Same measured data 6 are summarized in Table 4. 4 2 To determine the actual test range for data reduction, 0 6 4 recorded counter data button pressed by the test engineer -2 2 North (km) 0 is useful and the stabilized range was selected by a flight -4 -2 East (km) analyst. Test flight data and corresponding event ranges are shown in Fig. 8. The same data reduction process was Fig. 7. 3D Flight trajectory of arbitrary heading method. Feb. 2011 S.-J. LEE et al.: Comparison Study of Flight Test for Air Data Position Error Correction 255

Table 4. Measured data for arbitrary heading method (GPS, DGPS). Table 5. Data reduction results of arbitrary heading method.

Case Event V H ðV Þ ðV Þ Average IC IC G GPS G DGPS Methods 80 kts 90 kts 100 kts 110 kts 120 kts (kts) No. (kts) (ft) (deg) (kts) (kts) Value 1 80 1,020 340.5108 96.0 95.9879 ðV Þ T DGPS 87.7254 97.0979 104.1894 115.4859 124.5092 80 2 80 920 61.7676 101.0 101.2358 (kts) 3 80 920 209.9846 72.0 72.2183 VC (kts) 83.6536 92.0477 98.9153 109.8213 118.5043 V 4 91 1,280 341.3938 102.0 102.8527 AH PC 3.6536 1.0477 1:0847 1:8787 2:1624 (kts) 90 5 91 1,250 64.6761 110.0 110.2484 (DGPS) H PC 15.8087 5.2055 5:9024 11:3998 14:1668 6 91 1,220 197.2613 84.2 84.1784 (ft)

7 100 1,150 347.9883 110.0 111.4157 VW (kts) 15.5447 14.2124 14.4204 13.7289 15.1156

100 8 100 1,100 65.0966 117.0 117.5794 W (deg) 34.3799 43.8835 44.6500 34.1798 34.8229 9 100 1,080 196.4837 91.7 91.2540 ðV Þ T GPS 87.5566 96.7833 103.7859 115.3576 125.4453 10 111 1,000 345.3046 125.0 124.0514 (kts)

110 11 111 1,020 61.0341 128.0 127.5676 VC (kts) 83.4926 91.7494 98.5322 109.6993 119.3954 V 12 110 1,040 197.8588 101.0 102.2457 AH PC 3.4926 0.7494 1:4678 2:0007 1:2713 (kts) 13 121 980 337.1013 132.0 131.9238 (GPS) H 120 14 120 960 61.0197 138.0 137.8932 PC 15.1120 3.7235 7:9870 12:1403 8:3286 (ft) 15 121 980 199.8434 112.0 109.8460 VW (kts) 15.5835 14.0706 13.8973 14.7392 13.9602

W (deg) 33.7013 45.9107 48.1416 31.8383 36.3870

4 Event 1 Event 2 Event 3 4 Event 4Event 5 Event 6 x 10 x 10 6 4 3.6 FAR Part 23 Boundary 3.8 3.4 5 3.6 Counter Counter Arbitrary Heading Method (DGPS) 3.4 3.2 4 4050 4100 4150 4200 4250 4300 4350 4400 4450 3600 3650 3700 3750 3800 3850 3900 3950 4000 4050 4100 Arbitrary Heading Method (GPS) Ground Course Method (DGPS) 140 140 3 120 120 Ground Course Method (GPS) 100 (kts) (kts) 100 Single Camcorder Method G G 2 V 80 V 80 Curve Fitting 60 60 4050 4100 4150 4200 4250 4300 4350 4400 4450 3600 3650 3700 3750 3800 3850 3900 3950 4000 4050 4100 1 500 500 400 400 0 H (m) 300 H (m) 300 -1 200 200 4050 4100 4150 4200 4250 4300 4350 4400 4450 3600 3650 3700 3750 3800 3850 3900 3950 4000 4050 4100 400 400 -2 (airspeed position error) (kts)

200 200 PC (deg) (deg) -3 ψ ψ V ∆ 0 0 4050 4100 4150 4200 4250 4300 4350 4400 4450 3600 3650 3700 3750 3800 3850 3900 3950 4000 4050 4100 -4 time (sec) time (sec) -5 FAR Part 23 Boundary (a) 80 kts (Event 1, 2, and 3) (b) 90 kts (Event 4, 5, and 6) -6 70 80 90 100 110 120 130 V (indicated airspeed) (kts) IC 4 Event 7Event 8 Event 9 4 Event 10 Event 11 Event 12 x 10 x 10 4.5 3.8 (a) airspeed position error 4 3.7

3.5 3.6 Counter Counter 40 3 3.5 3200 3250 3300 3350 3400 3450 3500 3550 3600 3650 2800 2850 2900 2950 3000 3050 3100 3150 3200 3250 140 160 FAR Part 23 Boundary 120 140 30 120 100 (kts) (kts) Arbitrary Heading Method (DGPS) G G V V 80 100 Arbitrary Heading Method (GPS) 60 80 20 3200 3250 3300 3350 3400 3450 3500 3550 3600 3650 2800 2850 2900 2950 3000 3050 3100 3150 3200 3250 Ground Course Method (DGPS) 500 500 Ground Course Method (GPS) 400 400 10 Single Camcorder Method Curve Fitting H (m) H (m) 300 300

200 200 3200 3250 3300 3350 3400 3450 3500 3550 3600 3650 2800 2850 2900 2950 3000 3050 3100 3150 3200 3250 0 400 400

200 200 (deg) (deg) -10 ψ ψ

0 0 (altitude position error) (ft) 3200 3250 3300 3350 3400 3450 3500 3550 3600 3650 2800 2850 2900 2950 3000 3050 3100 3150 3200 3250 time (sec) time (sec) PC

H -20 ∆ (c) 100 kts (Event 7, 8, and 9) (d) 110 kts (Event 10,11, and 12) -30 FAR Part 23 Boundary

4 Event 13 Event 14 Event 15 x 10 -40 3.6 70 80 90 100 110 120 130 V (indicated airspeed) (kts) 3.4 IC Counter 3.2 2400 2450 2500 2550 2600 2650 2700 2750 2800 2850 (b) altitude position error 160 140 120 (kts) G

V 100 Fig. 9. Comparison of position errors. 80 2400 2450 2500 2550 2600 2650 2700 2750 2800 2850 400

300

H (m) applied to the test data for the data sets. The average ground 200 2400 2450 2500 2550 2600 2650 2700 2750 2800 2850 400 speed from Table 4 was calculated using Eqs. (3)–(5) and

200

(deg) the resulting position errors were summarized in Table 5. ψ

0 2400 2450 2500 2550 2600 2650 2700 2750 2800 2850 5.3. Summary results and sensitivity analysis time (sec) The acquired position errors in Tables 3 and 5 are com- (e) 120 kts (Event 13, 14, and 15) pared in Fig. 9. In accordance with FAR 23.1325 and Fig. 8. Time history of flight data for arbitrary heading method. 23.1323,17) the airspeed position error should not exceed 256 Trans. Japan Soc. Aero. Space Sci. Vol. 53, No. 182

0 1.2 does not require ground observers on external equipment. -0.2 1 Sensitivity analysis proved that variation of indicated air- t ic -0.4 0.8 V V ∂ ∂ speed should be measured as accurately as possible because ) / ) / -0.6 0.6 pc pc V V

∆ position error is proportional to this error. Finally, from the ∆ (

( -0.8 0.4 ∂ ∂ cost-effective view point, single GPS could be utilized if -1 0.2

-1.2 0 data could be recorded automatically like DGPS. 80 90 100 110 120 80 90 100 110 120 V (kts) V (kts) ic ic

x 10-3 Acknowledgments 0 0

-0.5 -0.05

ic ic The authors would like to thank Professor Soo-Bog PARK who T H ∂ ∂ -1 served as a test pilot and Professor Gyo-Young HONG at Hanseo ) / -0.1 ) / pc pc V V -1.5 ∆

∆ University for helpful supports. ( ( ∂ -0.15 ∂ -2

-0.2 -2.5 References 80 90 100 110 120 80 90 100 110 120 V (kts) V (kts) ic ic 1) FAR Part 21, Certification Procedures for Products and Parts, FAA, Fig. 10. Result for sensitivity analysis of airspeed. 2009. 2) Haering, E. A.: Airdata Measurement and Calibration, NASA TM-104316, 1995. 3% of CAS or 5 kts, whichever is greater, and the altitude 3) Olson, W. M.: Aircraft Performance Flight Testing, AFFTC-TIH- position error should not exceed 30 feet per 100 kts speed. 99-01, Air Force Flight Test Center, Edwards Air Force Base, 2003 (unpublished paper available at www.camasrelay.com/ Apparently, the obtained position error of all five PEC aircraftperformance.htm). methods obeys these rules. The position error decreases as 4) Gallagher, G. L., Higgins, L. B., Khinoo, L. A. and Pierce, P. W.: airspeed increases. In addition, all methods except the U.S NAVAL Test Pilot School Flight Test Manual-Fixed Wing ground course method using GPS provided similar results Performance, USNTPS-FTM-No. 108, 1992. 5) NTPS (National Test Pilot School): Professional Course Flight Test with small deviation (Fig. 9). For the ground course method Technique Demonstrations, NTPS, 1997. using GPS (Table 1), measured ground speeds show some 6) Bailey, W. D.: Investigation of Using Global Positioning System for deviation compared to other methods, causing the error. Air Data System Calibration of General Aviation Aircraft (Have Pacer Since GPS data were not recorded automatically but were II), AFFTC-TR-95-76, 1996. 7) Rogers, D. F.: ASI Calibration, Newsletter of the World Beechcraft read by the test engineer, there is some variation, especially Society, 12 (2000), pp. 10, 11, 37. for a maximum of 2.1 kts at 110 kts. However, it is worth- 8) Fox, D.: Is Your Speed True (Determine Using GPS and Pocket while noting that high accuracy and fast sampling is availa- Calculator), Kitplanes Magazine, 108 (1995), pp. 49–50. ble for single GPS now. Using GPS is simple and cost effec- 9) Lewis, G. V.: A Flight Test Technique Using GPS for Position Error Correction Testing, Cockpit, Proceedings of the Society of Experi- tive compared to DGPS. The single camcorder method can mental Test Pilots Conference, 1997, pp. 20–24. be used as a new method to estimate position error precisely. 10) Rogers, D. F.: Horseshoe Heading Technique, 2001 (unpublished Its airspeed position error compared to DGPS is less than paper available at www.nar-associates.com/technical-flying/ 0.4507 kts. This good result is due to elimination of timing horseshoe heading/horseshoehead screen.pdf). 11) Gray, D.: Using GPS to Accurately Establish True Airspeed (TAS), error based on its resolution of 0.0333 s. 5 Larkspur Place, Heathcote, New South Wales, Australia., 1998 Sensitivity analysis was used to analyze the effect of (unpublished paper available at www.ntps.edu/downloads.htm). some measured error sources. As shown in Fig. 10, the most 12) Lewis, G. V.: Using GPS to Determine Pitot-Static Errors, NTPS, important factor is measured indicated airspeed. This mea- 2003 (unpublished paper available at www.ntps.edu/Files/ GPS%20PEC%20Method.doc). suring error directly affects inaccurate estimation of position 13) Olson, W. M.: Pitot-Static Calibrations Using a GPS Multi-Track error. In other words, the magnitude of the position error is Method, 29th Annual Symposium Proceedings of SFTE, Reno, NV, proportional to the amount of error. The second most impor- 1998 (available at www.camasrelay.com/aircraftperformance.htm). tant error is true airspeed and outside air temperature. Posi- 14) FAA AC 23-8B, Flight Test Guide for Certification of Part 23 Airplanes, FAA, 2003, pp. A9-12–A9-14. tion error may be less affected by variation in measured 15) Ward, D. T.: Introduction to Flight Test Engineering, Elsevier Science pressure altitude relative to other factors. Therefore, it is Publishers B.V., Amsterdam, 1993. important to measure indicated airspeed more accurately. 16) Kish, B. A., Graham, G. L., Larson, D. N., Faber, J. J. and Halasi-Kun, This has been disregarded previously. D. L.: Pitot Static Testing of the RU-38A, Proceedings of Aerospace Conference, 1999, pp. 73–80. 17) FAR Part 23, Airworthiness Standards—Normal, Utility, Acrobatic, 6. Conclusions and Commuter Category Airplanes, FAA, 2009, pp. 293–294.

This paper investigated five PEC flight test methods to Appendix A. TAS in Ground Course Method determine the position error of the pitot-static system of an aircraft. Measuring ground speed by GPS or DGPS is Assuming that wind speed vector is constant, the graphi- useful to calculate true airspeed. In particular, the proposed cal speed vector schematic is in the inertial coordinates as single camcorder method was successful and provided an shown in Fig. A1. The true airspeed is the average of the accurate position error compared to DGPS. This method ground speed in both directions. Thus, Feb. 2011 S.-J. LEE et al.: Comparison Study of Flight Test for Air Data Position Error Correction 257

Fig. A1. Vector schematic of ground course method.

V TA V TB VT ¼jV Tj¼ ðA:1Þ 2

The ground speed vector is the vector sum of the true Fig. B1. Vector schematic of arbitrary heading method. speed and wind speed and can be expressed as Eq. (A.2).

V TA ¼ V GA þ V W ¼ðVGAx VWx Þi þðVGAy þ VWy Þj V þ V V þ V V T ¼ V G þ V W ¼ðVG VW Þi þðVG þ VW Þj G1y G2y G1x G2x B B Bx x By y B1 ¼ M1 ðB:3Þ ðA:2Þ 2 2 Substituting Eq. (A.2) into Eq. (A.1), then where,

ðV GA þ V WÞðV GB þ V WÞ V GA V GB VG2x VG1x V T ¼ ¼ M1 ¼ ðÞ ðB:4Þ 2 2 VG2y VG1y ðV þ V Þi þðV V Þj ðV þ V Þi ¼ GAx GBx GAy GBy ¼ GAx GBx 2 2 ðA:3Þ Applying the same mathematical procedures to Eqs. (4) and (5), Therefore, the final representation of exact true airspeed is VG1y þ VG3y VG1x þ VG3x B2 ¼ M2 ðB:5Þ V þ V 2 2 V ¼jV j¼ GAx GBx ðA:4Þ T T 2 where,

VG3x VG1x Appendix B. TAS in Arbitrary Heading Method B2 ¼ VWx þ VWy ðB:6Þ VG3y VG1y Assuming that the wind and true airspeed vector are and constant, the graphical speed vector diagram of the three VG3x VG1x legs is shown in Fig. B1. In each leg, the vector sum of M2 ¼ ðÞ ðB:7Þ VG VG the true speed and wind speed is the ground speed expressed 3y 1y as Eq. (3)–(5) in section 2. Subtracting Eq. (4) from Eq. (3), Subtracting Eq. (B.6) from (B.3) and combining Eq. (B.4) then and (B.7), the wind component can be obtained as 2 2 2 B1 B2 B1 B2 VG1x 2VG1x VWx þ 2VG2x VWx VG2x þ VG1y ! VWx ¼ ¼ ðB:8Þ M2 M1 2 VG2x VG1x VG3x VG1x 2VG1y VWy þ 2VG2y VWy VG2y ¼ 0 VG2y VG1y VG3y VG1y ) 2½VWx ðVG2x VG1x ÞþVWy ðVG2y VG1y Þ 2 2 2 2 From Eq. (A.9), ¼ðVG2x VG1x ÞþðVG2y VG2y Þ VG2x VG1x VWy ¼ ðÞVWx þ B1 ¼ VWx M1 þ B1 ðB:9Þ ) 2ðVG2y VG1y ÞB1 VG2y VG1y ¼ðV 2 V 2ÞþðV 2 V 2ÞðB:1Þ G2x G1x G2y G2y Finally, the wind speed and true airspeed are where, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 VW ¼jV Wj¼ VWx þ VWy ðB:10Þ VG2x VG1x B1 ¼ VWx þ VWy ðB:2Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi VG2y VG1y 2 2 VT ¼jV Tj¼ ðVG1x VWx Þ þðVG2y VWy Þ ðB:11Þ

If M1 is defined as below, Eq. (B.1) can be rearranged as