reconstructing the features and performances of historic airplanes

American Institute of Aeronautics and Astronautics1

Reconstructing the features and performances ofhistoric airplanes

Rodrigo Martinez-Val1, Emilio Perez.2 and Jose F. Palacin3

Universidad Politecnica de MadridMadrid, Spain, 28040

The process of modelling the aerodynamics and performances of historic airplanes issomehow similar to the conceptual and preliminary design phases of a new project with twomajor advantages: 1) the configuration is known beforehand and 2) the airplaneairworthiness has already been proved. Unlike a new project it is unnecessary to outline andassess many different alternatives. But the drag polar, most key performances, stabilityfeatures, etc, are frequently unknown or incomplete. In the present research work, two casesare addressed: the Grand Raid of the Spanish “Cuatro Vientos”, and the rivalry between theSupermarine Spitfire and the Messerschmitt Me-109. The legendary Spanish airplane, aBréguet XIX Super TR, flew non-stop from Seville to Cuba (about 7500 km or 4100 nauticalmiles, mostly over the seas) in around 40 hours, one of the last Grand Raids, beforedisappearing in a relatively short stage between Havana and Mexico a few days later. On itsturn, the legendary English and German aircraft were for many years the protagonists of airfight in the Western European front of Second World War. The modelling considered in thispaper takes well known expressions of Aerodynamics and Flight Mechanics to obtainestimations of the drag polar and some relevant performances such as cruise conditions andrange for the Grand Raid, and time to climb, radius of gyration, etc for the fighters. Thisapproach, mixed up of historic considerations and quantitative analysis, is very wellappreciated by students for its pedagogic and motivating character.

I. IntroductionNLY a few decades after the first successful flight of the Wright’s brothers, the 1920s and 1930s were years ofenormous 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 countries and aeronautics was establishing thedefinitive scientific and technical ground required for the astonishing development it has had up to present.1

This golden period corresponds to the epoch of the Grand Raids and various trophies and prices, like theSchneider’s Cup. The ambiance stimulated the search for fame, national glory, political impulse or the establishmentof new commercial routes. On the side of long routes, the North Atlantic track received the greatest attention, forlying between the two areas of the world with higher economic and technical development. The geography andmeteorology produce some bias in favour of West-to-East flights between the East Coast of USA and Canada on oneside and Ireland or Great Britain on the other. A few can be named among many relevant achievements:2

• Vicecmdr. Read with Curtiss NC4 from Newfoundland to Azores, Lisbon and Plymouth, on May 1919;• Alcock and Brown, aboard a Vickers Vimy, flew for the first time non-stop between America and Europe inJune 1919;• Lindbergh, on the “Spirit of St. Louis” boosted aviation to the largest journal headlines with his solo fromNew York to Paris in May 1927;• Von Hünefeld, Koehl, Spinder and Fitzmaurice carried out the first East-West flight from Berlin to Irelandand to Labrador in April 1928 with Junkers W33L;• Costes and Bellonte, linked Paris and New York, in September 1930, in a Bréguet XIX Super TR; and

1 Professor of Airplane Design, Dep. Vehiculos Aeroespaciales, ETSIA, AIAA Associate Fellow2 Assoc. Prof. Airplane Design, Dep. Vehiculos Aeroespaciales, ETSIA, AIAA Member3 Assist. Prof. Applied Physics, Dep. Appl. Phys. & Chem. Aeronautics, EUITA

O

45th AIAA Aerospace Sciences Meeting and Exhibit8 - 11 January 2007, Reno, Nevada

AIAA 2007-154

Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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• Amelia Earhart, flew the second solo (first for a woman) from America to Europe, in May 1932 on aLockheed Vega.On the side of combat airplanes, fighters in particular, the evolution was rather slow; and it was not uncommon

to see biplanes being used for this purpose well into the thirties. However, some competitions, like the Schneider’sCup, boosted the development of new aerodynamic shapes which were the basis of the new combat aviation.Specifically, the Supermarine Spitfire came in the wake of the great achievements in the aforementioned Cup. Onthe German side, the limitations imposed to the Luftwaffe in the Versailles’ Treaty stopped any meaningfuldevelopment for about 15 years, but after Hitler’s advent into power, the designers started a quick run to fill the gap.For example, Prof. Messerschmitt took a good sport four seater named Bf 108 Taifun, to design the later well knownBf 109.

Many features and performances of historic airplanes are unknown or lost because of war damage to archives,incomplete files, etc. The present paper aims at reconstructing some relevant characteristics of three selectedaircraft. The approach used here is a fruitful mixture of History and Flight Mechanics which has proved to beunderstandable, pedagogic and motivating for undergrads and grad students.3

In the present research work two cases are considered: the Grand Raid of the Spanish “Cuatro Vientos” fromSeville to Havana and the rivalry between the Spitfire and the Me-109 at the Battle of Britain and subsequentoperations.

II. Planning the Cuatro Vientos Grand RaidThe airplane selected for the Spain-Cuba flight was, logically, a Bréguet XIX sesquiplane specially prepared and

modified by CASA for the purpose.4 As its precedent, the Bréguet XIV, the XIX had been designed by LouisVuillierme. It was exhibited for the first time on November 1921 in the Aeronautics Salon of Paris, although its firstflight took place in March 1922.5 The original version had an empty weight of 1387 kg, a maximum take-off weightof 2500 kg, powered by various engines from 400 to 500 CV, which allowed it to reach about 215 km/h ofmaximum speed, a ceiling above 7000 m and a range of some 800 km.6 Many countries like France, Spain, Belgium,Yugoslavia, China and Argentina, had this aircraft as basis for their air forces in the 20s and 30s.

A suitable route was selected among the eleven studied as the most favourable: Seville, Madeira Islands (ofPortugal), Puerto Rico, Santo Domingo and Cuba. A certain advantage of this route, which extended more than 6000km over the waters, was the possibility of using Madeira and Puerto Rico as landing areas along the path (but theseareas were 3000 NM apart from each other) as well as the suitability of several Cuban airfields for landing, oncearrived there.7 Interestingly, this route is the one almost exactly followed by current jets in their way from WesternEurope to the Caribbean region.

Due to the extremely long distance to be flown, the airplane required some modifications with respect toordinary Breguet XIX to increase the specific range, essentially by means of aerodynamic improvements.7,8 CASA’sengineers worked side by side with aerodynamicists of the Cuatro Vientos wind tunnel, which resulted in anenlargement of the wingspan, an increase in the wing gross area, fairing of the main landing gear and, finally, fairingand closing the cockpit for both pilot and navigator (see Figure 1). Also various modifications were carried out inthe Hispano Suiza engine. Table 1 summarises the main data of the modified aircraft.3,8

Table 1. Main data of Bréguet XIX Cuatro VientosEngine Hispano Suiza

12NbMaximum power (HP) 720

Wingspan (m) 18.30Length (m) 10.70

Wing area (m2) 59.97MTOW (kg) 6375

Empty weight (kg) 1900Wing loading (kg/m2) 106.4

Fuel capacity (l) 5325Oil capacity (l) 250

Maximum speed (km/h) 230Cruise speed (km/h) 190

Range (km) Estim. 8500

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The enormous fuel tank (bidón, as it was named) between the engine and the cockpit also posed importantproblems, for it had to be part of the structure and had to transmit the stresses and forces from the engine to the restof the airframe. A quick discharge pump was installed; so the plane could float in the sea in case of ditching.

All controls and most flying instruments were duplicated, which was very important not only to share thepiloting workload in an extremely long flight, but also in the case of sudden sickness as it happened in the middle ofthe raid. The plane incorporated engine indicators (RPM, oil and fuel manometers, oil and water thermometers, andfuel quantity), flying indicators (anemometer, variometer, altimeter, artificial horizon, turn-and-bank, pitching angle,and clock) and navigation instruments (compass, chronometers, sextants, etc). The cockpit could be open in flight toallow the the use of astronomical instruments and the firing of smoke and luminous torches, thus providinginformation on the winds and bearing shifting.

A two blade, fixed pitch propeller of 3.1 m diameter and a Hispano Suiza 12Nb engine, derived from the HS12Lb, provided power and thrust to pull the aircraft in the mission. It is important to notice that, like in other longdistance flights, the fuel was a mixture of gasoline (80%) and benzol (20%), which provided the minimum specificfuel consumption and a detonation free operation; crucial to avoid engine failures.

The total cost of the flight, including all previous studies, the airplane itself, spares sent to Cuba, etc, wasfinanced by the Spanish Ministry of War (official name on 1933). The airplane, numbered 195 in the Spanishproduction line, had a cost of some 80.000 pesetas, engine apart, about double than a common Bréguet XIX.Finished on 15 April 1933, it flew more than 50 hours in May to check the flying qualities and for the adaptation ofthe pilots to night flights.

III. Aerodynamics and performances of the “Cuatro Vientos”As indicated earlier, modelling the aerodynamics and performances of historic airplanes is similar to the

preliminary design phases of a new project, with the main advantage of knowing beforehand the configuration andthat the airplane is airworthy. However, the drag polar and other relevant features are unknown or incomplete andcan only be estimated. For various reasons, not being the least important two World Wars and a dramatic Civil Warin the Spanish case, many plans and details have been lost; even of those airplanes proudly shown in nationalmuseums. This happens for example with the Bréguet XIX type: the Paris and Madrid Air Museums, among others,exhibit well preserved and beautiful models, but the technical data available are very scarce indeed.

The first step is to identify the airfoil. This was carried out with the help of a few constructive plans andphotographs that depicted the airfoil shape with high precision. Later, by comparison with the geometric data ofmany airfoils included in technical reports of the 1920s a perfect matching was found to the Halbronn 3, a relativelythin airfoil (8%) developed in France and tested in the Eiffel wind tunnel on 1916. This airfoil had a rathersymmetric drag polar, negligible lift at zero angle of attack and a maximum lift over drag ratio near 20 at an angle ofattack of about 5 degrees.9

The next step has been to estimate the drag polar of the complete airplane. A common drag polar with a parasiticcomponent and a parabolic term depending on the lift coefficient is used.10,11

20D D LC C k C= + (1)

The first term in the right hand side is the sum of all contributions from the braced, wired wing, thefuselage, empennage, landing gear and engine cowling. To obtain it, the friction coefficients have been computed atthe Reynolds number corresponding to 190 km/h and 1000 m, with transition from laminar to turbulent boundarylayer at 15% chord. All geometric data have been measured on production plans and three view drawings. The resultis CD0=0.0148, which gives an equivalent parasitic area (CD0 times S) of 0.89 m2, just on the lower end of the 0.9 to1.7 m2 range typical of most biplanes of this period,12 as it should be for a distance record breaking aircraft.Interestingly, the increase in drag produced by the voluminous tank in the front fuselage is more than compensatedby the increase in wing area.

The lift dependent component was estimated according to the classical biplane theory plus a correction fortrim drag and viscous induced drag; this last known from the airfoil data. Numerically the estimated drag polar is7

20.0148 0.101D LC C= + (2)

With this parabolic polar the estimated maximum lift over drag ratio is 12.93 (at CL=0.383), exactlymatching the reported figure of 13 found in the wind tunnel tests.13 As another checking of the correctness of the

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guessed drag polar, the estimated maximum speed at 0.9 MTOW and 1000 m, with a propeller efficiency of 0.70 isabout 225 km/h, accurate enough for the present purpose.

Using again the biplane theory the lift curve slope is computed to be approximately 4.5 rad-1. According toproduction plans and documents, the wing was fitted to the fuselage at an angle of incidence of about 4.5 º, veryclose to the one corresponding to maximum L/D, providing a lift coefficient of 0.35 at zero angle of attack of theaircraft.

The main performance of a long distance flight is, precisely, the specific range. And also, in parallel, thespeed, altitude and attitude to obtain in each moment the maximum distance per unit mass of fuel burnt. Thedistance travelled is obtained according the so-named Breguet range equation (Eq. 3):

i

f

W

h m

PW

L dWR

gc D W

η η= ∫ (3)

Assuming that ηh, ηm, (propeller and mechanical efficiencies) and cP (specific fuel consumption) areconstant, the best range is obtained when, for any given weight W, L/D is maximum. This is equivalent to fly atconstant angle of attack: in this case at CL=0.383, or αfus=0.4º all along the flight. Available engine data show that,although cP varied both with power and regime, the variation was moderate, even negligible, except during the lastpart of the flight, when the power demanded was only about 1/3 that of the beginning.

IV. Flying conditions during the Grand Raid to CubaThe flying conditions on June 9-10 1933 were defined by aerodynamicists and engineers.7,8,13 The altitude

was limited by engine operation and cockpit temperature between 500 and 2000 m. Since after take-off the wingloading was relatively high (106 kg/m2), the setting was established at around 200 km/h and 500 m, correspondingto CL=0.58; far from optimum conditions but still at L/D=11.9. The prescribed subsequent evolution of speed,altitude and engine regime was defined to reach the maximum specific range within the limitations of the engineoperating envelope, meteorological conditions, etc.

Figure 2 shows the route followed by the “Cuatro Vientos”. When the pilots, Barberán and Collar, flewover Madeira they knew that they were ahead of schedule (5-10%) but also that they had burnt between 15 and 20%too much fuel. They reacted by decreasing the power setting, adjusting regime and speed, but continued a little bittoo fast and a little bit too high. The flight was almost always faster than planned, arriving at Camagüey in 40.4hours, some 3 hours earlier than scheduled (i.e. 7%). The reason for that is not known. The error in the angle ofattack between the optimum and the one guessed in this reproduction is only about 1.5º, and between the oneguessed and that prescribed by the Aerodynamics Laboratory only 0.5º, very difficult to assess with the instrumentsof that time.

The effect of this small speed off-set was worsened by the exigency of flying almost permanently at 1500m for meteorological reasons, since for the drag polar and engine performance the best range would had required afour step cruise, at 500, 1000, 1500 and 2000 m, each one for some 10 hours. To keep the appropriate dynamicpressure, flying higher equalled to fly faster, thus mismatching the prescribed optimum cruise conditions at anygiven time, with the corresponding effect in fuel consumption and the aircraft weight. The flatness of the L/D versusCL curve allowed the pilots to reach Cuba, but not Havana, the desirable landing point. From Camagüey to Havanathe distance is 500 km, requiring about 150 kg of fuel at the end of the journey, but the airplane had only some 80 kgleft on landing at Camagüey.8

Wind effects have been considered as a plausible cause for the aforementioned mismatching in the presentinvestigation but have to be discarded for they can not produce at the same time a faster flight (which is equivalentto have a tailwind) and a less efficient flight (burning more fuel). The already cited explanation based on a smallmismatch in speed and altitude seems to be the most appropriate from the technical point of view. On the otherhand, a crack was found in the enormous fuel tank after landing at Havana. Could this be the cause for theapparently extra fuel burnt? Very likely not, for a crack leaking fuel over so many hours, partly in turbulent weather,would have produced a larger spill. The crack was probably produced in one of the two landings in Cuba: Camagüeyor Havana; for the important stresses concentrated around the engine-tank-wings-fuselage joint.7

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V. Air fighting in the Battle of BritainThe Second World War started with two “blitzkriegs” (lightning wars) carried out by the German Army: the

invasion of Poland in September 1939; and the conquest of France and the Benelux in May-June 1940. By mid June1940 the military operations had ended in Western Europe.14 The Nazi Government wanted a Peace Treaty with theUnited Kingdom and, for some weeks, Britain was free of severe attacks. Only some of the important harbours inthe English Channel or the North Sea were bombed. It was the time for discrete diplomacy. But the British, underthe leadership of their Prime Minister, Sir Winston Churchill, were resolved to restore borders and “status quo” inContinental Europe. The naval raid to Marsa-al-Kabir (Algeria) to destroy the core of the French Navy and avoid itbeing taken by the Germans and other less spectacular operations were clear signs of the British determination.Hitler and his General Staff prepared operation “Seelöwe”, the invasion of Britain. However, due to the absolutenaval supremacy of the United Kingdom, the invasion could only take place after selective bombing of harbours andinland facilities and the destruction of the Royal Air Force.

At the end of July 1940 near 3000 aircraft (including about 900 Me-109), scattered from Norway to Bretagne,were ready for “Seelöwe”. But because of adverse meteorological conditions the air offensive was delayed up toAugust 12 when several squadrons bombed radar facilities in the South of England. On August 13 hundreds ofaircraft attacked military objectives in the Southeast, but the results were poor. On the contrary, the Luftwaffe lostnear 50 aircraft for only 13 airplanes on the British side. The German tactics consisted on arranging squadrons ofbombers escorted by Me-109. But, because of its short range, the Me-109 could only fly a few miles into Britain,leaving the bombers vulnerable to Hurricanes, RAF’s second rank fighters. The Spitfires concentrated in avoidingMe-109 penetration. Both airplanes exhibited similar performances as will be shown later, albeit with someadvantage for the British airplane. The ferrous determination and unbelievable skills of British pilots, authenticheroes of the Battle of Britain, more than counterbalanced the numerical superiority of the Luftwaffe.

On the other hand, the character and energy of Lord Beaverbrook, Minister of the newly created Ministry ofAeronautical Construction, and of Sir Hugh Dowding, Air Chief Marshal, were essential to have the RAF perfectlyprepared for the Battle of Britain. The Ministry succeeded in assigning top priority to fighter production, thusdelivering to the RAF many more aircraft than expected, mainly Spitfires; whereas the Air Chief Marshal organisedthe squadrons in the most efficient way and attracted large numbers of young, well motivated pilots.

Till the end of October 1940 the Luftwaffe attempted either the destruction of the RAF’s and the airplanemanufacturing facilities, or the weakening of the British moral strength. The Luftwaffe failed in both aims. In spiteof severe bombing and dramatic damages, Britain resisted mainly thanks to the air superiority.14,15 The close rivalrybetween Me-109 and Spitfire forced the respective design teams to continuously improve both aircraft. Thisevolution will be described in the next chapter. Most data reported here refer to the initial protagonists of the Battleof Britain; i.e. Spitfire Mk I and Me Bf 109E; but later versions will also be described.

VI. Comparative evolution of Me-109 and SpitfireThe Me-109 was designed by Prof. Wilhelm Messerschmitt, as a development of the successful Bf 108 Taifun. It

entered into service in 1937 as Me Bf 109B, equipped with a Jumo engine of 670 HP. Because of its cleardisadvantage with respect to the British counterparts, subsequent versions were gradually improved. The mostpopular of them, the Me Bf 109E, appeared in 1939 equipped with a 1100 HP direct injection Daimler-Benz engine.Although the total number of Me-109 produced is not known, it is estimated to pass 30000.16

On the other side, the Supermarine Spitfire was developed by R.J. Mitchell from the Supermarine S6 that hadwon the Schneider Trophy for hydroplanes over three successive years at mid 30s. The first Spitfire Mk I enteredinto service in 1938 equipped with a Rolls Royce Merlin engine which delivered 900 HP. The airframe wascompact, light and with elliptic planform wings. The liquid-cooled engine, although adequate for high speed andtight turns, had an ordinary carburettor; that obliged the airplane to dive before making vertical loops to havepositive “g”. This problem was later solved. Many versions were developed during the war, until denomination MkIX, with different engines, weapons and propellers, totaling near 25000 aircraft produced.17

In the present investigation, the main objective is to obtain accurate estimates of the drag polar and somerelevant performances of the different versions of Spitfire and Me-109. To this end, the first step as in the formerstudy of the “Cuatro Vientos” airplane, a parabolic drag polar is assumed.10,11

22

0 0L

D D L D

CC C k C C

Aπ ϕ= + = + (4)

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The induced drag efficiency factor, φ, depends mainly upon the circulation distribution and, secondarily, on theairfoil drag polar and the trimming of the aircraft. The literature reports values between 0.75 and 0.9.10,11,18,19 Sincethe wing planform of the Spitfire was designed to minimise the induced drag, suitable values of φ for Spitfire andMe-109 were assumed to be 0.87 and 0.85, respectively. Then CD0 is computed from data of maximum speed andavailable power. With published performances16,17 the estimated parabolic drag polars are CD=0.0172+0.0652 CL

2

for the Spitfire Mk I and CD=0.0214+0.0623 CL2 for the Me Bf 109E. The maximum lift-over-drag ratio is 14.9 for

the British airplane and 13.7 for the German aircraft. This supremacy in aerodynamic efficiency was kept during thewar in subsequent versions.

The Spitfire Mk I was fitted with NACA 2213 airfoil at the root and NACA 2209.4 at the tip, providing amaximum lift coefficient of 1.35. In the Me Bf 109E the airfoils were NACA 2R1 14.2 and NACA 2R1 11.35 at theroot and tip, respectively, which yielded CLmax=1.4. Taking into account the wing loading of both airplanes, theirstall speeds were 37.8 m/s (73.5 kts) for the Spitfire and 39.9 m/s (77.6 kts) for the Me-109.

Figures 3 to 6 present the maximum level speed and maximum rate of climb in terms of the altitude for theSpitfire and Me-109 respectively. The curves show the progress achieved along the war. The maximum speedincreased from 153 to 200 m/s in the case of the Spitfire, and from 150 to 195 m/s in the Me-109, almost 50 m/s inboth aircraft. Analogously, the maximum rate of climb was permanently improved. For example, the Spitfireincreased 10 m/s at sea level in a period of four years. Interestingly the British improvements were always a stepfurther than that of their German rivals, which favoured its air superiority in all European and North Africanoperation theaters.

Manoeuvrability is a key point for air superiority. In the present work it is represented by the features ofsustained turns in the horizontal plane. The tightest sustained turns are performed at VA, close to stall. That means20

1/3

2max

0

2A

LD

PV

CS C

A

η

ρπ ϕ

=

+

(5)

where P is available power, η stands for propeller-transmission combined efficiency (assumed to be 0.8 in all cases),ρ is air density and S is gross wing area. The corresponding load factor is computed from Equation 6:20

2max

2A LV S C

nW

ρ= (6)

Within the limited accuracy of the methods used here, the sustained turn load factor found is 2.9 for the SiptfireMk I and 3.0 for the Me Bf 109E. The load factor of later versions of the Spitfire increased up to 3.2, whereas thoseof the German aircraft were kept around 3.0.

In an analogous way, the minimum radius of gyration is obtained from Eq. 7:20

2

min 2 1AV

rg n

=−

(7)

As indicated earlier, the Spitfire exhibited a smaller radius of gyration, 155 m against 172 m for the Me-109.Interestingly, the results obtained with the present model show that no further improvements were achieved in thisvariable during the later years of war in any of both airplanes.

Figure 7 shows the evolution in weight and power of the Spitfire and the Me-109. Heavier but most powerful,the British aircraft was always ahead of its German rival.

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VII. ConclusionsHistory is a permanent source of inspiration for technical work. The approach used here, mixing up case studies

of historical relevance and equations derived from Aerodynamics and Flight Mechanics, is very well appreciated bystudents for its pedagogic and motivating character.

On the other hand, this approach may throw some light on features and performances of historic airplanes thatare lost or inaccessible. This is the case of the Spanish “Cuatro Vientos” whose journey from Seville to Camagüey,Cuba, has been reproduced in technical details that were not known. Regarding the rivalry between the Spitfire andthe Me-109, the present research shows that although it is generally argued that the superiority of the British airplanecame from its Rolls Royce Merlin engine, its advanced aerodynamics played a similar role in achieving suchsuperiority.

AcknowledgmentsThe authors express their gratitude to Antonio Gonzalez-Betes for his important contributions to the study of the

“Cuatro Vientos”, including the search of technical details completely hidden in various places. The authors dedicatethis paper to their graduate students of the optional course on “Quantification of the evolution of airplanes”;particularly to Messrs. Iñaki Ascacibar, Iñaki Armendariz, Francisco Herrada and Jose Miguel Encinas, whoprovided much of the material used to analyse the rivalry between the Spitfire and the Me-109.

References1Anderson, J. D., A History of Aerodynamics and Its Impact on Flying Machines, Cambridge University Press, Cambridge

(UK), 1997.2Beaty, D., The Water Jump, Secker & Warburg, London (UK), 1976.3Martinez-Val, R., Palacin, F.J., Alonso, J.J. and Lopez, O., “Debating Aeronautics from History. A Doctorate Experience”,

43rd Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA, AIAA Paper 2006-0331.4Sánchez Méndez, J., and Delgado Rubí, J., Dornier Wal and Bréguet XIX, Flying Together, EADS CASA, Madrid (E),

2000.5 “Les avions de 1923”, Revue General de L'Aéronautique, Vol. 3, Nº 21, 1923, p. 1–20.6Warleta, J., “La serie Bréguet XIX en España”, Aeroplano. Revista de Historia Aeronáutica, Nº 1, 1983.7Martínez-Val, R. and Gonzalez-Betes, A., “Modelling the aerodynamics and performances of a historic airplane: the Spanish

Cuatro Vientos", 3rd International Conference on Advanced Engineering Design, Prague, Czech Republic, June 2003.8González-Betes, A., “Gloria y tragedia del vuelo Sevilla-Cuba-Méjico”, Aeroplano. Revista de Historia Aeronáutica, nº 1,

1983.9“Aerodynamic Characteristics of Aerofoils”, NACA Report 93, 1921.10Torenbeek, E., Synthesis of Subsonic Airplane Design, Kluwer, Dordrecht (NL), 1982.11Roskam, J., Airplane design. Volume 6: Preliminary Calculation of Aerodynamic, Thrust and Power Characteristics,

Roskam Aviation, Ottawa (KA, USA), 1987.12Warner, E. P., Airplane Design: Performance, 2nd Edition, McGraw-Hill, New York (USA), 1936.13Herrera, E., “Barberán y Collar”, Madrid Científico, 1934, p.197-199.14Cartier, R., La Segunda Guerra Mundial, Larousse-Paris Match-Planeta, Barcelona (E), 1966.15Legrand, J., Crónica de la aviación, Plaza y Janés, Esplugues (E), 1992.16www.bf109.com17www.spitfiresociety.demon.co.uk/index.htm18Stinton, D., The anatomy of the aeroplane, 2nd Edition, Blackwell, Oxford (UK), 1998.19Whitford, R., Fundamentals of fighter design, Airlife, Shrewsbury (UK), 2000.20Miele, A., Theory of flight paths, Addison-Wesley, Reading (Mass., USA), 1962.

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Figure 1. The Spanish Breguet XIX Super TR “Cuatro Vientos”.

Figure 2. The route of “Cuatro Vientos” grand raid from Seville to Camaguey, Cuba, and then to Havannaand Mexico.

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http://arc.aiaa.org/action/showImage?doi=10.2514/6.2007-154&iName=master.img-000.jpg&w=324&h=230



Figure 3. Evolution of maximum level speed of Supermarine Spitfire.

Figure 4. Evolution of maximum rate of climb of Supermarine Spitfire.

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Figure 5. Evolution of maximum level speed of Messerschmitt Me109.

Figure 6. Evolution of maximum rate of climb of Messerschmitt Me109.

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Figure 7. Evolution of weight (solid lines) and power (dashed lines) of Spitfire and Me-109.

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reconstructing the features and performances of historic airplanes

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