Airspeed Calibration Using GPS Three-Vector Method ( Cloverleaf Method)

Transcription

1 Airspeed Calibration Usin GPS Three-ector Method ( Cloverleaf Method) An Informal Memo by Wayne Olson Updated: 1/10/2005 An Informal Memo by Wayne Olson...1 Déjà vu I ve seen this before:...1 Introduction...2 Ground Speed Course Errors Due to Crossind...3 The Three-ector Method Is Simply a Better Way...5 History of the Concept...5 Cloverleaf Computations ith 1927 Airship Data...8 Airspeed Measurements by Germany In True Airspeed Calibration Usin Three Radar Passes...11 AFFTC F-15 Data...12 AFFTC F-16B Pacer Data...13 Cessna Airspeed Calibration Usin GPS...14 Embraer EMB 140 Cloverleaf Data...16 The Dou Gray Alorithm...22 Gray Alorithm Comparison Usin Cessna 180 Data...22 Gray Alorithm versus F16 Data...23 Finally...23 References...24 List of Fiures and Tables...25 Abbreviations...25 Symbols...26 Déjà vu I ve seen this before: Since this is an informal memo, I feel free to ive a short personal note about a discovery I made recently. While in the process of donloadin a number of old NACA documents hich are available for free donload at.larc.nasa.ov, I found somethin that I had seen before (as in déjà vu). Let me take you back to early in my career at Edards. It as early 1970s. My 1

2 supervisor at the time as Willie Allen. The airspeed calibration uy for the center as Al DeAnda. [Al retired in 2002 after 50 years in federal service and 46 years of that at Edards]. Anyho, I noticed Willie and Al in Willie s office ith this hue sheet of paper and various lare drain tools. Hue as in 4 to 6 feet square. On that as dran a circle. Inside that circle ere three vectors. The vectors ere dran to scale ith appropriated anles. The lenths corresponded to round speed and the anles ere course over the round. There ere three of these vectors. This as actual data from three radar tracked runs ith the AFFTC pacer aircraft. From this, they fiured out true airspeed and ind speed and direction. It just looked afully hard there just had to be a better ay. After all e had computers no. Some time later in a math class at the Test Pilot School, e ere learnin about vectors and matrices. It struck me - 3 equations in 3 unknons! It as then just a matter of formulatin those 3 equations. So, they ere nonlinear. Nonlinear in the sense that the unknons (2 components of ind and an unknon error in true airspeed) ere on both sides of the equations. Iterate! I learned that in collee. The déjà vu part came hen I came across a circle ith speed vectors that looked identical to Willie and Al s circle dran almost 50 years later. In History of the Concept, pae 5, you ill see the NACA drain. Introduction This memo ill recommend that the FAA accept a GPS Three-ector Method as a viable airspeed calibration method for aircraft certification. In a 1998 Society of Fliht Test Enineers symposium paper 1, the mathematics for one such three-vector method is detailed. In that paper, the references list a fe other variations on the method. To our knolede, all of the other methods make assumptions about the anles in order to solve the equations. Dou Gray 2 makes no such anle assumption, hoever he does assume that all three true airspeed vectors fall ithin a perfect circle. No such assumptions are made here; the equations are solved in a nonlinear iteration. The details are contained in the paper here I ill present a summary. The paper also contains three sets of data collected to illustrate the method. We initially developed the technique to calibrate the Air Force Fliht Test Center pacer aircraft, here e used Radar to measure round speed and direction. Al DeAnda and Willie Allen of AFFTC developed the fliht test technique and I created the computer softare. The technique as first described in an unpublished Edards AFB office memo 8, hich I ill discuss later in this document. Our method as also described in a 1983 AGARD document 3 ; hoever, the AGARD document did not include our mathematical alorithm. 2

3 The method is a true airspeed method. GPS, even ithout usin differential GPS, provides very accurate velocity information in the horizontal plane. The accuracy is on the order of ± 0.1 knot or better. [I should add that the resultant true airspeed accuracy is not necessarily accurate to the same ±0.1 knot.] It is not necessary to acquire lon time histories of data a fe seconds averae ill be sufficient. The GPS velocity, hoever, is inertial or a round speed. What e ould like is true airspeed. The basic relationship in the horizontal plane is that true airspeed ( t ) is round speed ( ) plus ind ( ). These three speeds are all vectors ith both manitude and direction. We ill ork ith these in the north and east direction. GPS provides (or e can compute) north and east components of round speed. The aircraft air data system ives us an indicated true airspeed (e may have to compute that from other parameters). The indicated true airspeed ( t i ), ill have some unknon error ( t ). The ind speed components in the north direction ( N ) and in the east direction ( E ) are unknons. The equation e ill be solvin is (1.1). ( t t ) ( N N ) ( E E ) i = (1.1) By flyin in three distinctively different directions (ideally about 120 derees), e can expand (1.1) to three equations in three unknons. These are three nonlinear equations in three unknons. They are nonlinear in the sense that no matter ho hard I tried; I could not come up ith equations here the three unknons appear only on one side of the equations. An iterative solution is easy to do no ith a PC. I recently discovered that David Gray came up ith a solution (See: The Dou Gray Alorithm, pae 22). Others have been able to derive exact formulas for special cases. One of these 4,5 is here to passes are exactly 180 derees apart and the third is perpendicular to the first to. This has been called the horseshoe headin method. These also require that the airspeeds are identical for each pass. These are both viable and quite acceptable techniques. One just needs to be aare of these limitations. Ground Speed Course Errors Due to Crossind I ould suest usin this Three-ector method to replace the venerable round speed course. Unless you have an INS and are able to estimate the manitude of the crossind and correct for it, there ill alays be some error in the round speed course method. An example ill illustrate the effect. The example ill use hat some ould say is an extreme case. Hoever, this ind example is very near a common ind speed at the AFFTC. Let us assume e 3

4 are flyin a track of due North at 100 knots indicated true airspeed. We shall assume e have computed the true airspeed from our Pitot-static parameters. Then, presume a ind speed of 20 knots at 90 derees. Wind direction is from hich the ind is bloin, so the ind is bloin from due east. We no have a speed trianle as shon in Fiure 1. Then, e turn and o don our round speed due South. For simplicity, e are assumin our round speed course is laid out due North-South. Fiure 2 shos the reverse run. Fiure 1 Run 1 of Ground Speed Course Fiure 2 Run 2 of Ground Speed Course Then, from our trianles, e can compute the to roundspeeds. = + = = = (1.2) t t knots 4

5 = + = = = (1.3) t t knots By the round speed course method, the true airspeed is the averae of the round speeds or 98.0 knots. In this case, e incurred an error of 2.0 knots due to the method. That is ith a measurement of round speed usin GPS here the GPS accuracy is of order of 0.1 knots. We do not incur any error due to the method ith the Three-ector method. The Three-ector Method Is Simply a Better Way The crossind problem completely disappears. In fact, you end up ith both speed and direction for the ind as ell as the error in true airspeed. The accuracy of GPS (even a handheld one) is at least ± 0.1 knot. This is an accuracy I have demonstrated on several projects that are discussed in this memo. History of the Concept In 1927, the NACA used a method they referred to as a trianle method to calibrate airspeed systems on an airship 6. Fiure 3 is a speed diaram of their data extracted from the NACA report. Fiure 3 Graphical Solution for Airspeed and Wind speed. 5

6 The technique described by NACA is precisely the technique for the GPS Three-ector Method. In lieu of GPS, they timed the vehicle over a knon distance to et roundspeed. The knon distances also had a knon compass headin. From compass headin and manetic declination, one can compute the true round track. The local declination in 1927 as (-11) derees. GPS provides the same information, namely roundspeed and true round track. Fiure 4 is a portion of the NACA description. Fiure 4 NACA Test Technique Description The key part to note here is that they determined the ind as nearly constant at 10.2 knots from the southest, and ship s airspeed as 58.4 knots. Next is the data they collected in Fiure 5. 6

7 Fiure 5 NACA Speed Data The oriinal softare prorammed in FORTRAN as created to reduce Three-ector airspeed calibration data. In early 1970s, method as used to calibrate the AFFTC pacer aircraft usin Radar. In the late 1990s, the same alorithm as used to calibrate AFFTC pacers, hoever this time the round speed and track anles ere provided by GPS. In addition, the ne softare has been reprorammed in Excel. Since the pacers fly hat ould appear in 7

8 the sky as a cloverleaf maneuver, e dubbed this the cloverleaf maneuver and the softare is denoted as Cloverleaf. The airship did not fly a cloverleaf and loer speed aircraft ould not more like the trianle maneuver as described by NACA. Cloverleaf Computations ith 1927 Airship Data I ran the airship data throuh the cloverleaf Excel proram. I did run one and run to as to separate runs. Table 1 contains the test data. The point of this exercise is to sho that had they had GPS in 1927, they already had the maneuver and just needed the softare that solves a set of nonlinear equations. I ill use the electric meter as airspeed since it is the only airspeed of the four that is a true airspeed. The electric meter is a indmill device and labeled it propeller in Table 1. NACA, of course, preferred their Pitot-static instrument. The others are all Pitot-static instruments. Table 1 NACA Data Processed With Cloverleaf Proram Run Course NACA Propeller No. Le (True) Lenth Time Speed Speed Airspeed Airspeed De Feet Sec Ft/Sec Knots Knots Knots 1 AC , CB 89 60, BA , AB , BC , CA , I did the calculations of the speeds in feet/sec and knots from the lenth and time. They aree to ithin 0.1 ft/sec and 0.1 knot for the most part; hoever, a couple of points are farther apart orst case of 0.4 knots. The rather small differences ere more than hat ould be explained by the old nautical mile of 6,080 feet versus today of 1,852 meters (exactly), hich comes to feet, for the units conversion of meters per foot. In addition, I anted to avoid chanin units in the softare. From Table 1, one interestin note is that each le as takin about 10 minutes and coverin about 10 nautical miles. An arument used today aainst this method is that it is too time consumin. It is not if it is planned and flon ell you do not need a lot of data points to et a ood averae speed and headin. You ill see ho little time they can take in the Cessna 180 data later in this memo. 8

9 The NACA report did not specify the altitude or the ambient temperature for these speed runs. They ere flyin above a trianular course beteen Sandy Hook, Staten Island, and Rockaay. With that, and map softare by Microsoft, I have dran an approximate course in Fiure 6. Fiure 6 Course for Airship Trials As can be seen it is over ocean, so e can at least hope for some reasonably stable conditions. To make thins easy, I ill assume standard day sea level conditions. Since e ill be enterin true airspeed, the atmospheric conditions should not influence the ind computations. Hoever, the inputs to the softare are total pressure, static pressure and total temperature. Each run, ith three les each, is one data point. The SFTE paper ill o throuh the math in detail, but hat e are doin is solvin three equations in three unknons. Each le provides constants for one of the three equations. The three unknons are to components of ind (north and east) and an error in true airspeed. Then, from the assumption that all of the Pitot-static system error is contained in static pressure, e can compute true values of Mach number, calibrated airspeed, and ambient temperature. We already kno total pressure and total temperature since e assumed they had zero error. 9

10 So, hat is the best estimate for true airspeed and ind for these six passes? They assumed a constant true airspeed for all six runs (the same constant) that produces a perfect circle. From their raphical method (Fiure 3), they came up ith the folloin. t = 58.4 knots = 10.2 knots ( ) ψ = "from the southest" = 225 I obtained almost exactly hat they ot. Our results: 58.6 knots, 10.0 knots at 225 derees rounded to the number of diits they expressed. I computed this as to sets of data - run 1 and run 2. Then, I averaed those to results. Airspeed Measurements by Germany In 1918 An even earlier determination of true speed usin the same method as conducted by Germany 7. They used to phototheodolities to track aircraft travelin at altitudes of 9,000 to 14,000 feet and speeds in the 80 to 90 knot rane. Our Excel softare reproduced their results almost exactly. They solved the speed trianles usin the same raphical methods used by NACA. Fiure 7 as extracted from the NACA translation of the German tests. Fiure 7 elocity Diaram from 1918 (Germany) 10

11 I used their symboloy for the speeds and inds and converted to knots. Table 2 compares their results to ours. The first number is ours and the second is theirs. Table 2 Airspeed Trianle Data from Germany in 1918 Fi.13 t= 86.8 Fi.16 t= 87.0 e= e= = 21.4 = 13.5 = = Fi.14 t= 86.2 Fi.17 t= 84.1 e= e= = 32.3 = 8.6 = = Fi.15 t= 84.2 Fi.18 t= 83.4 e= e= = 40.9 = 21.7 = = For instance, for run Fi.13, I computed an airspeed of 86.8 knots, hile they came up ith 45.0 m/sec, hich converts to 87.5 knots. I ot a ind speed of 21.4 knots and their ind speed converts to 20.8 knots. That as excellent areement iven some room for error on our part, as I needed to measure the round track anle raphically from their diarams (as in Fiure 7). For the most part, our airspeeds ere ithin one knot at just over 80 knots. True Airspeed Calibration Usin Three Radar Passes In the early 1970s at the AFFTC, e essentially reinvented the heel developed first by the Germans in At the time, this author as not aare of the German tests. We used Radar to calibrate the AFFTC pacers 8. To do the computation, instead of a rather laborious raphical solution, an iterative computer alorithm as developed. That alorithm alon ith diarams and actual test data are included in the 1976 office memo. Nearly the identical alorithm as converted to an Excel version to process GPS data 1 some 20 years later. The oriinal memo presented nine data points all collected on the same fliht at same altitude and the same airspeed. The oal as to sho repeatability 11

12 and accuracy of the method. Table 3 presents the data in a different form than in the early memo. The nine runs ill be rouped in blocks of three. Table 3 Run Summary of Radar track data ti σ t No. Knots Knots De Knots Knots De ψ Each set of three runs ill produce a set of the three unknons ( t, N and E ). The ind speed manitude ( ) and direction ( ψ ) are then computed from the components. There as a substantial difference in the speed error term beteen these three sets. Without access to the oriinal data, it is impossible to determine the source of the problem. The positive ay to look at the results is that the errors ere ell less than 1% of the true airspeed. AFFTC F-15 Data One of the three data sets I presented in the SFTE paper 1 as on the AFFTC F-15B pacer aircraft. The data ere flon in Auust 1997 at nominal conditions of 0.6, 0.7 and 0.8 Mach number at 30,000 feet pressure altitude. Because e anted to compare GPS to Radar, test coordination time added sinificantly to the total test time. These three cloverleaf points consumed about 40 minutes of fliht time. In addition, each pass as a full minute lon. Without these to factors, e ould be able to collect this data in much less time. These tests ere on the previously calibrated F-15B pacer. We had a hih deree of confidence in the calibration curves. One lesson e learned on this data set is that e need an accurate total temperature. Initially, the data shoed rather lare errors versus the pacer curves on order of 3 knots. After the temperature probe as recalibrated, the errors ere dramatically reduced. We did not lose the data as e did the temperature calibration post fliht. 12

13 Table 4 Run Summary of F-15B Pacer Cloverleaf Data σ ti ψ t t PACER t Ref 1 No. Knots De Knots Knots De Knots Knots Knots 1a b c a b c a b c Notes: The output parameter for airspeed error is t The next column ( t PACER ) is the airspeed error from the pacer curves Last column is the airspeed error presented in Reference 1. That last note deserves some explanation. In processin this 1997 data, I could not precisely reproduce the results in the SFTE paper 1. I did do some additional processin of the data after the submittal deadline of the paper. Anyho, the results in the paper ere slihtly different (larer errors) hoever the orst case difference as less than one knot in true airspeed. One miht onder ho e ere able to achieve airspeed accuracies of better than one knot at speeds beteen 360 knots and 500 knots. First, e had precision pressure transducers that ere calibrated to better than ± in H. At 300 knots calibrated airspeed at 30,000 feet, an error of in H in static pressure comes to 0.02 knots. Then GPS, even ithout differential GPS is a ± 0.1 knot error system. Hoever, that is on any iven data point. By averain over even as little as 10 seconds, one should have a fraction of 0.1 knot accuracy. AFFTC F-16B Pacer Data A second set of data in the SFTE report 1 as ith the AFFTC F-16B pacer. On this data at the same conditions as the F-15, hoever, e had very hih inds (over 100 knots) and had to use Radar instead of GPS. Despite those problems, e still had results here the true airspeed errors ere less than 1% of the pacer data. I felt that ere the GPS orkin and e did the maneuvers quicker, e ould have otten better results. The data, all at 30,000 feet, ere flon in April The true airspeed from the pacer already has corrections 13

14 applied. Then, e are essentially seein ho close e can et ith this cloverleaf data. The parameter e ould like to be near zero is the true airspeed correction to be added ( ). The results are shon in Table 5. t Table 5 Run F-16B Pacer Cloverleaf Data Summary σ t t ψ No. Knots De Knots Knots Knots De 1a b c a b c a b c Cessna Airspeed Calibration Usin GPS On June 20, 2001, e had a fliht in a Cessna 180 to collect airspeed calibration data. We fle out of Grove Field in Camas, WA. The test area as enerally over Kelso, WA. This as not a formal test fliht just a fliht that pilot Bob Elliot had raciously areed to fly Paul Cannon and myself. My personal oal as to check out usin a handheld GPS in fliht test. By 2001, usin GPS in fliht test as old hat. Hoever, this author had not done it as of yet. I had, hoever collected considerable data in a career at Edards, AFB. We had planned to obtain cloverleaf data at three airspeeds (90, 100 and 110 MPH) and at three altitudes (3,000, 5,000, 7,000 and 9,000 feet). Since the aircraft climb speed is 90 MPH, the plan as to collect airspeed calibration data at the climb speed and 10 MPH on either side. Hoever, due to a failure ith my laptop computer e only obtained four out of the 12 planned points. Fiure 8 shos the latitude versus lonitude trace for the first run. This as a continuous maneuver only the data points used in the cloverleaf proram are shon. From the first data symbol on the plot to the last as under four minutes and the total time from first data point to last as less than one hour. 14

15 Of sinificance here is these three passes ere not flon in a cloverleaf pattern, but rather in a turn. Our pilot ould stabilize on speed for about 15 seconds, then turn 120 derees and stabilize aain at same speed, then repeat a third time. Run MPH at 9,000 feet Latitude (de North) a 1.1 b 1.1 c Lonitude (de West) Fiure 8 Latitude versus Lonitude First Run Even thouh I did not compare the data collected from this cloverleaf method to another method, I did sho that the Pitot-static errors ere quite small. I did not have airspeed, altitude or total temperature recorded. We relied on pilot Bob to fly on condition. From a combination of his pilotin skill and the fact on his old Cessna 180, he had some modern Avionics includin an autopilot e obtained rather smooth data. The tests ere all flon on the MPH needle of the airspeed indicator. Hoever, the softare is all in Knots, so beare of some mixed units. Then, keepin this memo short the summary of the numbers are in Table 6 and Table 8. The airspeeds and altitudes are pilot aim conditions. 15

16 Table 6 GPS Inputs for Cessna 180 Run () 1 σ () 1 ( 2) σ ( 2) ( 3) σ ( 3) # Knots De Knots De Knots De Table 7 Cloverleaf Outputs for Cessna 180 Run H ic ic C t i t # Feet MPH MPH MPH MPH Knots Derees 1.1 9, , , , , Note: parameters are correction to be added This represents only a fe runs; hoever, there are some confidence builders in the correctness of the data. The first ould be that iven that the readability of the airspeed indicator is at best to the nearest 1 MPH, the variation in the correction to be added is very small and a correction to be added of -1 knot ould be quite reasonable. Then, notice that runs 1.1 and 2.1, hich are at the same altitude produce computed ind speed, and direction that is only 0.5 knot apart and essentially identical ind direction. I should note also that from the beinnin of the first run at 9,000 feet to the end of the last run, also at 9,000 feet the total elapsed time as 55 minutes. This as the total clock time, not just the test time. Each run identified in the tables consisted of three sements, such as shon in Fiure 8 for run 1.1, has sements 1.1a, 1.1b and 1.1c. These are all about 120 apart in headin. It is NOT critical that the runs be 120. In fact, I have used this softare to reduce data from horseshoe headin method. ψ Embraer EMB 140 Cloverleaf Data The to cloverleaf maneuvers presented in this memo ere performed as ind calibration maneuvers for sideslip calibration. The airspeed altitude system had been previously calibrated durin certification usin other accepted 16

17 techniques. The sideslip data ill not be presented here. In order to compute a sideslip anle from inertial data (velocities N, E, D and anles headin, pitch and roll), e ould need true airspeed and the components of ind (N and E). The cloverleaf maneuver ives you that data. When used as an airspeed calibration maneuver, the ind components serve as a maneuver quality parameter. That is, if one ere to conduct a series of runs at the same pressure altitude on the same day you ould expect to see a minimal variation of ind as a function of time. This is especially true at hiher altitudes. At loer altitudes, you ould experience much larer variations in ind versus time. The to runs (e ill label them GPS-1 and GPS-2) ere on the same fliht, both at an airspeed of 200 knots and pressure altitude of 15,000 feet. Fiure 9 and Fiure 10. are plots of the course over the round. The differential GPS (DGPS) data as from an AshTech (subsidiary of Thales ) system. [This is not meant to be an endorsement of that particular brand as the accuracies are primarily a result of the GPS constellation]. The oriin (0,0) of the plots is the location of the GPS round station. In a DGPS system, the round station is a transmitter essentially identical to the GPS satellites. This is also called a pseudolite [a ord combinin pseudo and satellite]. While the satellites are some 20,000 kilometers above the earth, the round station is less than 100 kilometers from the aircraft. This factor is hat ives the DGPS, typically, accuracies don to the centimeter level versus current quoted GPS accuracies of about 3 meters. The cloverleaf method is a true airspeed method. I ill compute true airspeed from the Pitot-static system data (total pressure, static pressure and total temperature). That true airspeed is denoted ( ti ), or indicated true airspeed. The alorithm ill also compute true airspeed from GPS round speed components plus ind components. The essence is that e ill have three equations (one for each of three les of our cloverleaf maneuver) and three unknons. The three unknons are to components of ind (north and east) and an unknon error in true airspeed. 17

18 GPS North Distance from Ground Station (meters) Run 1.1 Run 1.2 START Run East Distance from Ground Station (meters) Fiure 9 Course over the round for GPS-1 One minute or more of data as averaed from each of the three straiht sements. The total time of this maneuver as just over 13 minutes. A suestion is that equal quality data could be obtained in much less time. One ould perform a trianle maneuver, instead of a cloverleaf. Instead of one full minute of data, ith hih quality DGPS data at to sps, about 10 seconds of data averaed should be sufficient. The cloverleaf maneuver as used on the hihly maneuverable hih speed pacer aircraft at the AFFTC. For slo speed aircraft, e have found the trianle maneuver to be preferable. The trianle maneuver requires a 120 turn beteen data points, hile the cloverleaf maneuver requires a 240 turn beteen data points. 18

19 GPS North Distance from Ground Station (meters) Run 2.2 Run 2.1 Run East Distance From Ground Station (meters) Fiure 10 Course over round for GPS-2 Fiure 11 is a time history plot of the three les of GPS-1. Each of the three starts at a different time, so to et them conveniently on the same plot they are all plotted versus their correspondin elapsed time. The data are the round speeds ( ), hoever on the plot are shon the averae values for track anle ( σ ), and indicated true airspeed ( ti ). We ill compute the error (correction to be added) in true airspeed ( (, ). N E t ) as ell as the components of ind speed 19

20 GPS-1 Ground Speeds [DGPS] t1 = knots σ = = knots 270 Ground Speed (knots) t 2 = knots σ = = knots 3 3 = knots σ = = knots t Elapsed time (seconds) Fiure 11 Input data for GPS-1 The output of the Excel proram contains a number of parameters. This includes all of the input parameters for each of the three les, several airspeed calibration parameters and ind speed and ind direction. The anser of primary interest is the correction to be added to true airspeed. Once that number is computed, the Excel proram also calculates corrections to calibrated airspeed, Mach number, pressure altitude and static pressure. These are all based upon the assumption that all of the error is due to errors in static pressure. The assumption of all the error in the Pitot-static system is due to the static pressure is the usual assumption in most air data calibrations. Results: t = 0.22 knots Where the averae of the three indicated true airspeeds is: ti = knots The ind components ere computed at the folloin. 20

21 = knots N = knots E The key here is that e must satisfy the basic airspeed formula: = + t (1.4) Expandin in north and east direction: tn = N + N and te = E + E (1.5) Then, = + (1.6) 2 2 t tn te True airspeed is also the indicated true airspeed plus an error in airspeed. Settin those equal to each other yields the folloin. We ill do the check for each of the three les in Table 8. ( ) ( ) 2 2 ti t N N E E + = (1.7) Table 8 Summary of inputs and outputs for GPS-1 and GPS-2 The last column is the square root term, hile the fourth column on the left is indicated true airspeed plus correction term. These to runs ere about 20 minutes apart. You should observe the very small corrections to true airspeed and that the computed ind speed components ere nearly the same from one cloverleaf run to the next. 21

22 The Dou Gray Alorithm Dou Gray 2 presents an Excel spreadsheet that computes true airspeed and ind speed. The primary assumption is that three airspeed vectors all lie on a circle, hich is equivalent to all three airspeeds bein equal. I have coded up his Excel file and reproduced the numbers in his paper. In addition, the numbers from Cessna 180 areed exactly due to the airspeeds bein identical on all three passes. When the true airspeeds are not identical, e ould obtain somehat different results. Within the assumption that each of the three passes has the same ind and error in true airspeed, our alorithm ives an exact solution. Gray Alorithm Comparison Usin Cessna 180 Data As a check case of the Cloverleaf Excel proram versus Dou Gray s Excel spreadsheet, I ill use run 1.4 of the Cessna 180 as presented in Table 6 and Table 7. The one chane is I ill convert units to knots. I should note that the airspeed indicator can be read to at best 2 knots and here e are presentin data to nearest 0.01 knot. I am doin that to compare the alorithms this is not to suest that the Cessna 180 airspeed correction is ood to 0.01 knots. Table 9 Run Comparison of Gray Alorithm ith Cloverleaf σ ti t ( t t) + No. Knots De Knots Knots Knots Knots De 4.1a b c a-Gray b-Gray c-Gray As you can see, e ot identical results for the true airspeed, ind speed and ind direction. In my case, I as not solvin for true airspeed but rather an error in true airspeed. The assumption is that the three unknons are all remain constant for the three passes. ψ 22

23 Gray Alorithm versus F16 Data The F16B data (Table 5) had airspeeds that ere not identical on each of the three passes. We ill add an additional column of corrected true airspeed ( t + t ). Then, for the exact same input parameters I ill compute true airspeed, ind speed and ind direction usin Gray s Excel file. We chose the second run due to it havin the larest variation in true airspeed. The first three ros of Table 10 are computed usin the Cloverleaf method and the last three from the Gray Excel file. Notice there is no input for true airspeed for the Gray method. Table 10 Run Comparison of Cloverleaf and Gray Alorithm σ t t ( t t) + No. Knots De Knots Knots Knots Knots De 2a b c Averae= a-Gray b-Gray c-Gray As can be seen, the averae true airspeeds are identical. It is only in the ind computations that e see a difference. To the nearest 0.1 knot, all of the runs evaluated in this memo had identical averae true airspeed results. As in Table 10, there ere small differences in inds for any run here the true airspeeds ere not identical for all three passes. To compute the averae true airspeed, the Gray method orks reat. ψ Finally So, I onder hy this basic concept of three speed runs to calibrate airspeed has not cauht on? The round speed course, ith its basic fla of the crossinds, just seems to liner on. For one thin, NACA 9, in their 1937 The Measurement of Air Speed of Airplanes donplays the method. They state that the analytic solution is too laborious for convenience. Granted they did not have modern computers, hoever, the Dou Gray alorithm should not have been too laborious ith slide rules. That simple statement in a idely distributed NACA report, may have contributed to the end of usin speed course methods or at 23

24 least the three le methods. As the Germans 7 demonstrated usin phototheodolite cameras, one need not have a laid out course to perform a speed run method. The speed runs could be to 180 deree apart runs ( round speed course ) or any of the 3-vector patterns. A 1995 NASA Report 10 Airdata Measurement and Calibration, makes no mention of any speed course or speed run method. In addition, the AFFTC Standard Airspeed Calibration Procedures 11 thouh it has a 1981 date is simply a reprint of the oriinal April 1968 document and it, also, does not mention any Three-ector methods. References 1. Olson, W.M., Pitot-Static Calibrations Usin a GPS Multi-Track Method, Presented at SFTE Symposium, Reno, N, [Can be donloaded at.camasrelay.com/aircraftperformance.htm ] 2. Gray, Dou, Usin GPS to Accurately Establish True Airspeed, June [Can be donloaded at.ntps.edu ] 3. Laford, J.A. and Nipress, K.R., Calibration of Air Data Systems and Flo Direction Sensors, paes 16-20, AGARD AG-300-1, September Fox, David, Is Your Speed True, KITPLANES Maazine, February [Can be donloaded at.camasrelay.com/aircraftperformance.htm ] 5. Leis, G.., A Fliht Test Technique Usin GPS for Position Error Correction Testin, Cockpit, Quarterly of the Society of Experimental Test Pilots, Jan-Mar, 1997, paes De France, S.J., and Buress, C.P., Speed and Deceleration Trials of U.S.S. Los Aneles, NACA Report No. 318, [Report may be donloaded at.larc.naca.ov ] 7. Heidelber,. and Holzel, A. Speed Measurements Made By Division A of the Airplane Directorate, Subdivision for Fliht Experiments, NACA TN No. 147, July [Report may be donloaded at.larc.naca.ov ] 8. Olson, W.M., True Airspeed Calibration Usin Three Radar Passes, Performance and Flyin Qualities Office Memo, AFFTC, Auust [Donloadable at.camasrelay.com/aircraftperformance.htm ] 9. Thompson, F.L., The Measurement of Air Speed of Airplanes, NACA No. 616, [Report may be donloaded at.larc.naca.ov ] 10. Haerin, E.A., Jr., Airdata Measurement and Calibration, NASA TM , December [Report may be donloaded at.dfrc.nasa.ov ] 11. DeAnda, A.G., AFFTC Standard Airspeed Calibration Procedures, AFFTC-TIH [A reprint of April 1968 document] 24

25 List of Fiures and Tables Fiure 1 Run 1 of Ground Speed Course...4 Fiure 2 Run 2 of Ground Speed Course...4 Fiure 3 Graphical Solution for Airspeed and Wind speed...5 Fiure 4 NACA Test Technique Description...6 Fiure 5 NACA Speed Data...7 Fiure 6 Course for Airship Trials...9 Fiure 7 elocity Diaram from 1918 (Germany)...10 Fiure 8 Latitude versus Lonitude First Run...15 Fiure 9 Course over the round for GPS Fiure 10 Course over round for GPS Fiure 11 Input data for GPS Table 1 NACA Data Processed With Cloverleaf Proram...8 Table 2 Airspeed Trianle Data from Germany in Table 3 Summary of Radar track data...12 Table 4 Summary of F-15B Pacer Cloverleaf Data...13 Table 5 F-16B Pacer Cloverleaf Data Summary...14 Table 6 GPS Inputs for Cessna Table 7 Cloverleaf Outputs for Cessna Table 8 Summary of inputs and outputs for GPS-1 and GPS Table 9 Comparison of Gray Alorithm ith Cloverleaf...22 Table 10 Comparison of Cloverleaf and Gray Alorithm...23 Abbreviations AFB Air Force Base AFFTC Air Force Fliht Test Center AGARD Advisory Group for Aerospace Research & Development DGPS Differential GPS FAA -- Federal Aviation Administration FORTRAN FORmula TRANslation GPS -- Global Positionin System INS Inertial Naviation System NACA National Advisory Committee for Aeronautics NASA National Aeronautics and Space Administration SFTE - Society of Fliht Test Enineers 25

26 Symbols Note: Symbols are sorted alphabetically by description since Word does not reconize the symbols. t - Correction to be added to true airspeed E - East component of round speed E - East component of ind speed - Ground speed ti - Indicated true airspeed N - North component of round speed N - North component of ind speed σ - Track anle t - True airspeed ψ - Wind direction - Wind speed 26