Modeling the Aerodynamics and Performances of a Historic Airplane : the Spanish " Cuatro Vientos '

The process of rnodcling the.aerodynanics and perfonnanc3s of a historic airplane is aery similar to the conceptual and preliminary d2sign phases of a new plane, with the adaantage of knowing tlu confguration ind that the aitplane uas air-orthy; thus it i" ,nnrrirrory to outline and, assess rnany dffirent altematfues. Howeaer, the drag polar, the real pefonnanies, stabilirl features, etc, are still unknown.'For aarious rea.sons (in particular because of tuo l/ttorld Wars, or the Civil War in the Spanish case) moit d,etaik of many historical airplanes haue been losl. In,thepres-entresearchworh,.thesituationtsylolLgtls InJunelg)ithe"Cucttt'oVientos",aspanish-buittBrdguetXIXSuperTR,fleu non-stop frotn Seuille to Cyla; a dislance of 7500 hn (about 4 100 na'utical nriles) itt oround 40 hours. A qti aoy later, in a yai tess nmpLtcated stage between Hauana and Mexico, the airplane was lost with its occupants to a stonn in the Yuiatan peninsula. The rnodeling considered in tltis ltape.r starts by ad.dressing the aerodynarnic modificatiotts introd,uced, in the ahplani for th,e extremely long Jlight. 'fhgn, with the help of old,and present day aerodlnarnic datu and nrctltods the d,rag polar is estimated. ihe aiailabte engine 'd,ara u cornpleted and extrapctlated t0 obtain t@nlati?! on pou,er and fuel consunlttion. ninally, all this data is integrated, ro proaiie a reliable and technically sound reprorluction of the Seaille-Cuba Jlight.


Introduction
Only a couple of decades after the first successful flight of the Wright brothers, the 1920s and lg30s were years of enormous advances in aviation.The Great War had ended and many enthusiasts could use the large surplus of airplanes left behind.Aviation was becoming popular in many coun- tries and aeronautics was establishing the sound scientific and technical basis required for the astonishing development aviation has had up to the presenr day [1].
This period corresponds to the time of the Grand Raids that were stimulated by the search for fame, rewards, national glory political impulse or the establishment of new commer- cial routes.As nowadays, the North Atlantic track received the greatest attention, since it lay between the two areas of the world with the highest economic and technical development [2].The geography and meteorology produce some bias in favour ofwest-to-east flights betrveen the east coast ofthe USA and Canada on the one hand, and Ireland or Great Britain on the other [2].A few flights can be noted among rhe Captain BarberdLn was a very well prepared and highly rained airman of this period.At the age of only 30, in 1g25, he had participated in the preparation of the "Plus Ultra" flight from Seville to Buenos Aires [3][4][5][6]  Thus, the objectives of the flight were: to establish a new route between Spain (i.e., Europe) and America; to consoli- date the cultural and economic ties with Cuba and Mexico: and to show the capability and comperence of Spanish aviation in the record-breaking race of those years.storms, etc.) at latitudes between 10 and 50 degrees North, etc.
Finally, a route was selected from among the eleven stud- ied: Seville, the Portugese Madeira Islands, Puerto Rico, Santo Domingo, Cuba and Mexico.A certain advantage of this route, which extended more than 6000 km over wate4 was the possibility of using Madeira and Puerto Rico as landing areas along the path (but these areas were 3000 NM apart), as well as the suitability of several Cuban airfields for landing, once arrived there.Interestingly, this route is almost exactly followed by present-dayjets in their flight frorn Western Europe to the Caribbean region [5,6].
Captain Barberdn found a very good and experienced first pilot for this raid: LieutenantJoaquin Collar.The prepa- ration included a series of night flights onboard an unmodified Brdguet XIX within the Iberian Peninsula, and some flights to the Canary Islands and the West Afiican coast [5,6].
3 The Br6guet XtX Super TR o'Cuatro Vientos" The airplane selected for the Spain-Cuba flight was, logically, a Br€guet XIX sesquiplane specially prepared and modified by CASA for the purpose [8,9].Like its predecessor, the Br6guet Xry the XIX had been designed by Louis Vuillierme.It was exhibited for the first time in November l92l at the Aeronautics Salon in Paris, although its first flight took place in March 1922 [4].The original version had an empty weight of 1387 kg, a maximum take-off weight of 2500 kg, powered by various engines from 400 to 500 CV which allowed it to reach about 215 km/h of maximum speed, a ceiling above 7000 m and a range of some 800 km [8, l0].Many countries, e.g., France, Spain, Belgium, Yugoslavia, China and Argentina, had this aircraft the basis for their air forces in the 1930s [4,8,9].l8 From the very beginning, because ofits excellent capabili- ties and flight qualities, this airpiane was used in some long distance attempts; for example the Madrid-Manila 18 stage flight in 1926 [3,4].The incorporation of rwo exrra fuel tanks and a more powerful engine in 1924 increased the range and led to the GR (Grand Raid) version.An extra fuel tank between the engine and the cockpit resulted in 1926 in the TR fliansatlantique) followed in 1927 by the Super TR or Superbid6n version, which carried more than 5000 lirres of fuel [4][5][6].Due to the extremely long distance to be flown, the airplane required some modifications to increase the specific range, essentially by improving the aerodynamics, in the wings, fuselage and everywhere else.CASA engineers worked side by side with aerodynamicists of the Cuatro Vientos wind tunnel [5, 6], which resulted in an enlargement of the wing- span, an increase in the wing gross area, fairing of the main landing gear and, finally, fairing and closing the cockpit for both pilot and navigator.Various modifications were also carried out in the Hispano Suiza engine.
The enormous fuel tank (bid6n, at itwas named) between the engine and the cockpit also posed major problems, since it had to be part of the structure and had to transmit the stresses and forces from the engine to the rest of the airframe.
A quick discharge pump was installed, so that the plane could float in the sea in case of ditching.
Thble I shows the main diflerences benveen the ordinary Br€guet XIX and the Superbid6n airplane.To be specially In the present investigation the first step was to identifr the airfoil.This was carried out with the help of a few con- struction plans (and photographs) that depicted the airfoil shape with high precision.Latet by comparison with the geometric data of many airfoils included in technical reports of the I 920s, a perfect matching was found to the Halbronn 3, a relatively thin airfoil (8 7o) developed in France and tested in the Eiffel wind tunnel in I 9 I 6 [ I 2].This airfoil had a rather symmetric drag pola4 negligible lift at zero angle of attack and a maximum lift over drag ratio near 20 at an angle of attack ofabout 5o.
The next step was to estimate the drag polar of the complete airplane.A common drag polar with a parasitic component and a parabolic term depending on the lift coeffi- cient is used [l3, l4].
Co =Coo + K Cl (l) The first term on the right hand side is the sum of all contributions from the braced, wired wing, the fuselage, empenage, Ianding gear and engine cowling.In the present work this has been estimared as [14]: Cao = (Cn"Fn"S*"nu/S +Crs&s S*etB/S)If * (Z) +Ct FLSru.t./S + Cp6rS-;r/S, where Cg are friction coefficients, Fp form factors and S*., exposed area ofwing, body and empenage, S the wing area, and the last term accounrs for the drag produced by the cowling, rvindshield, landing gear and srrurs.
The friction coefficients were computed at the Reynolds number corresponding to lg0 km/h and 1000 m, with the transition from the laminar to the turbulent boundary layer at 15 7o chord.All geometric data were measured on production plans and three-view drawings.The result is Cp6 =9.99143, which gives an equivalent parasitic area (C29S) of 0.89 m2,just on the lower end of the 0.9 to 1.7 m2 range typical of most biplanes of this period [5], as it should be for a distance record breaking aircraft.Interestingly, the increase in drag produced by the voluminous tank in rhe front fuselage is more than compensated by the increase in wing area.
The lift dependent componenr was estimated according to classical biplane theory [6, l7], plus a correcrion for trim drag and viscous induced drag; this last is known from the airfoil data.The parabolic parameter is /< = s (1 + s/[',.(l,b,)t], (3) rvhere S is the rving area, e is the Oswald factor for the spanwise lift distribution, l, a parameter depending on rhe relative sizes and vertical separation benveen planes, b1 the span of the upper wing, and 6 an efficiency parameter related to both the viscous induced drag and the trim drag [3, l4].

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With this parabolic polar the estimated maximum lift over drag ratio is 12.93 (at Cr = 0383), exactly matching the reported figure of 13 found in the wind tunnel [8].As another check on ofthe correctness ofthe guessed drag pola6 the estimated maximum speed at 0.9 MTOW and 1000 m, with a propeller effrciency of 0.70 lgl is about 225 kmlh, accurate enough for the present purpose.
Using biplane theory again [16, l7], the lift cur-ve slope is computed to be approximately 4.5 rad-r.According to production plans and documents, the wing was fitted to the fuselage at an angle of incidence of about 4.5", very close to that corresponding to maximum Z/D, providing a lift coeffi- cient of0.35 atzero angle ofattack ofthe aircraft.
The main performance of a long distance flight is, pre- cisely, the specific range.And also, in parallel, the speed, altitude and attitude to obtain in each moment the maximum distance per unit mass of fuel burnt.The vertical and hori- where W is weight, T thrust, L lift, D drag and llTpV2 the dynamic pressure.The fuel consumption is dmldt = -cp P, (7) where cp is the specific fuel consumption and P the power delivered by the engine.The thrust of the propeller and the engine power are linked through [19] TV =\n\*p, (g) wherer17, andl* are the propeller and mechanical efliciency, respectively.
The distance travelled is Eqs. 5 and 6, can be rewrrtten as LdW D W (lo) The effect of this small speed off-set was worsened by the exigency of llying almost permanently at 1500 m for meteorological reasons, since for the drag polar and engine performance the best range would have required a four--step cruise, at 500, 1000, 1500 and 2000 m, each one for some l0 hours.To keep the appropriate dynamic pressure, flying higher equalled {lying faste4 thus mismatching the prescribed optimum cruise conditions at any given time, with the corresponding effect in fuel consumption and aircraft weight, as shown in Thble 3. The flatness of the t/D versus C.
cuwe (given by the parameter values of Eq. 4) allowed the pilots to reach Cuba, but not Havana, the desirable landing point.From Camagiiey to Havana the distance is 500 km, requiring about 150 kg of fuel at the end of the journey, but the airplane had only some 80 kg left on landing ar Camagiiey.
Obviously wind effects have been considered in the pres- ent investigation but have to be discarded, since they cannor produce at the same time a faster flight (which is equivalenr to having a tailwind) and a less e{Iicient flight (burning  Assuming that\n,\m and c, are constant, the best range is obtained when, for any given weight W UD is maximum.This is equivalent to flying at a constant angle of attack [8]: in the present case at Cz = 0383, or cL 6r= Q.{o all along the flight.
Available engine data I I l] shows that, although c" varied both with power and regime, the variation was moderate, even negligible, except during the last part of the flight, when the power required was only about 1/3 that of the beginning.The consumption data for the flight reproduction has been scaled Ilom HS l2Lb values I l].

The mission profile
The flying conditions on June 9-l 0 I 933 were defined by aerodynamicists and engineers [8] as should be done at the present time.The altitude was limited by engine operation and cockpit temperature between 500 and 2000 m.Since after take-offthewing loadingwas relatively high ( 106 kd-t), the setting was established at around 200 km/h and 500 m, correspondin g to C7 = 058; far from optimum conditions but still at LID =11.9.The prescribed subsequent evolution of speed, altitude and engine regime was defined to reach the maximum specihc range within the limitations of the engine operating envelope, meteorological conditions, etc I I 8].
Thble 2 shows some key points obtained in the present investigation during the reproduction of this flight.When Barber6n and Collar overflew Madeira they knew that they were ahead ofschedule (5-10 Vo) but also that they had burnt between 15 and 207otoo much fuel.They reacted by decreasing the power setting, adjusting the regime and speed, but continued a little too fast and a little too high.As shown in Table 3, the flight was almost always faster than planned, arriving at Camagiiey in 40.4 hours, some 3 hours earlier than scheduled (i.e., 7 Vo).The reason for this is not known.more fuel).The already cited explanation based on a small mismatch in speed and altitude seems to be the most appro- priate from the technical point of view.On the other hand, a crack was found in the enormous fuel tank after landing at Havana.Could this have been the cause ofthe apparent extra fuel burnt?Very likely not, for a crack leaking fuel over so many hours, partly in turbulent weathet would have implied a greater loss.The crackwas probably produced in one of the nvo landings in Cuba: Camag0ey or Havana, since the major stresses were concentrated around the engine-tank-wings--fuselage joint [5,6].

Final considerations
The aerodynamic and performance methods developed over decades for airplane design are very accurate indeed.Accurate enough to allow an in-depth study of all circumstances of the main flights of the golden years, and to fully understand the technical reasons behind the preparation and execution of these flights.Part of our current knowledge is thus due to the airmen whose flights made possible the advancement of aviation.And so we are indebted to all of them and the study of their endeavours deserves our enthusiasm.
The "Cuatro Vientos" flight was one of the greatest raids of all time: more than 7500 km non-stop, .mainlyover water.The precise and exhaustive preparation, including the selection of aircraft, engine and route, represented an extraordinary achievement, never repeated and extremely difficult even with latest technology.T[e grear effort made by Barberin and Collar was warmly recognised on their arrival in Havana and around the world, during the forrnight of the raid.However, their glory was sadly obscured by the accident that occurred a few days late6 onJune 20 1933, on rheirway to Mexico City.The remains of the aircraft and the pilots have never been found.
Fig. I depicts a two-view drawing of rhe aircraft.All these versions werc employed in some important raids in the late 1920s and early 1930s, like the already cited flights by Costes and Bellonte in 1930, piloting the "Point d'Inter- rogation" from Paris to New York [2, I 0, I I ], and the flights of Iglesias and Jim€nez on board 'Jesirs del Gran Poder" from Madrid to Baghdad in 1928 and from Seville to Bahia and other South American cities in 1929 [3, 4].
's equation for propeller-driven aircraft.

Fig. l :
Fig. l: Plan and side view of the Brdguet XIX Super TR "Cuatro Vientos", drawn by Miranda many remarkable achievements: o Vicecmdr.Read with Curtiss NC4 fi'om Newfoundland to the Azores, Lisbon and Plymouth, in May 1919; o Alcock and Brown, aboard a Vickers Vimy, flew for the first time non-stop betweenAmerica and Europe inJune 1919; o Lindbergh, on a Ryan Special, boosted aviation to the newspaper headlines with his solo flight from New York to Paris in May 1927; o Von Hiinefeld, Koehl, Spinder and Fitzmaurice crossed for the first time east-west from Berlin to Ireland and to Labrador in April 1928 with aJunkers W33L; o Costes and Bellonte crossed from Paris to New York in September 1930, now from the European mainland in a Br6guet XIX Super TR; o Amelia Earhart, flew the second solo flight (first for a woman) from America to Europe, in May 1932, in a Lock- Mid and South Atlantic routes were less important from the economic point ofview, but much more challenging in terms of distance to be covered, adverse meteorology and the absence or scarcify of suitable airfields along the track.Howeve4 for Spanish and Portuguese pilots these links re- presented fame and glory [3].So, as early as in 1922, Cabral and Coutinho tried a flight from Portugal, just arriving and crashing on the Brazilian coast.In January 1926, Ram6n Franco, Dur6n and Rada flew in a Dornier Wal hydroplane fiom Seville to Buenos Aires with a few stops in West Africa The section above describes the ambience and the level of the technology and achievements before 1932.In this euphoric environment the Spanish aviator Captain Mariano Barber6n conceived an incredible flight from Spain to Cuba: almost 8000 km, to be continued until Mexico in a second stage: a mere 1900 km extra.
2he4]nd Brazil.Iglesias andJim6nez flew more than 3000 nautical miles (almost a world record) to reach Brazil non-stop from Spain in March 1929[3,4].2Preparingthe grand raid support he approached the Defence Minisrer of the newly esrablished Spanish Republic [3].Politically the time was very good, since the new Governmenr wanted to strengthen the relationship with Central and South America.
alt4]ugh, for various reasons, he did not finally fly on board[3,4].In the early 1930s he was appointed the Head of the Aviation Observers School at Cuatro Vientos airfield, in the outskirts of Madrid.And, then, the idea of a world record flight to the Caribbean region fuzzily appeared.Captain Barber6n first convinced t7 some key aviation generals, and with their

Table I :
Main data of Brdzuet XIX airplanes are the increased wing span, wing loading, and useful load.All conrrols and most flying instruments were duplicated, which was very imporranr nor only to share the piloring workload on an extremely long flight, but also in the case of sudden sickness as happened in the middle of the raid.The plane incorporated engine indicators (RPM, oil and fuel manometers, oil and water thermometers, and fuel quantity), flying indicators (anemomete6 variometer; altimete4 artificial horizon, turn-and-bank, pitching angle, and clock) and navi- gation instruments(compass, chronometers, sextants, etc).The cockpit could be open in flighr to allow the the use of astronomical instruments and the firing of smoke and lumi- nous torches, thus providing inlbrmation on the winds and bearing shifting[5, 6].A two blade, fixed pitch propeller of 3.1 m diamerer and a Hispano Suiza l2Nb engine, derived from the HS l2Lb, provided power and thrust to pull the aircraft in the mission Il I ].It is important to note that, as in other long distance flights, the fuel was a mixture of gasoline (80 %) and benzol (20 Vo), which provided the minimum specific fuel consumption and detonation free operation, which was crucial to avoid engine failures [5, 6].The total cost of the flight, including all previous srudies, the airplane itself, spares sent to Cuba, etc., was financed by the Spanish Ministry of lVar (official name in 1933).The airplane, numbered 195 in the Spanish production line, had a cost of some 80.000 pesetas, apart from the engine, about double the cost of an ordinary Br6guet XIX [3].Complered on l5 April 1933, it flew more rhan 50 hours in May to check the flying qualities and in order to familiarize the pilots with Modeling the aerodynamics and the performance of his- torical airplanes is similar to the preliminary design phases of the project for a new aircraft, with the main advantage of knowing beforehand the configrration and thar rhe airplane is airworthy, but the drag polar and other relevanr features are uncertain and can only be estirnated.Forvarious reasons, not the least important being nvo World Wars and a dramatic Civil War in the Spanish case, most plans and details have been lost; even of those airplanes proudly shown in national museums.And this is tone of the Brdguet XIX rype: rhe Paris and Madrid Air Museums, among others, exhibit well preserved and beautiful models, but the available technical data is very scarce indeed.
noted 4 Aerodynamics and performance of the "Cuatro Vientos"

Table 2 :
Evolution ofselected variables in the reproduction ofthe "Cuatro Vientos" flight guessed Cr. (in this reproduction) is only about 1.5", and between guessed and prescribed by the Aerodynamics Laboratory only 0.5', very difficult to assess with the instrumenrs of that time.

Table 3 :
Weight and speed evolution prescribed in 1933 and