In 1800's...

Initially, a serious work on development of airfoils is done from late 1800's. People at that time know that the flat plates would produce lift when some angle of incidence is given. Later this work is improved by inducing some shapes with curvatures as an experiment for obtaining more lifts. JOUKOWSKI TRANSFORMATION explained the procedure and the working methods for construction of Airfoils. Various airfoils with different shapes are produced based on this transformations. Based on the equation of flows about a circular cylinder's with circulation, solutions which produces a lift force are shown. A circle which is in a quadrant is considered and based on the centre of circle and its location in the quadrant, shape of the airfoils is developed by doing a huge mathematical calculations.

The above figure shows us the Joukowski Transformation in which a airfoil is constructed  from a circle by  applying various mathematical operations. The location of the centre of the circle is a prime factor in obtaining the airfoil. Many airfoil shapes are based on this. If the centre of the circle is located at the origin, then a straight-line or flat plate airfoil is obtained. Then, this experiments are re-conducted for studying the results  for various angles of attack for assumed circulation. Based on these experimental results, various parameters like Lift and Moment coefficients are found. These parameters are now applied to a number of Joukowshi airfoils which are obtained  for various centre of the circle positions  so that the theoretical characteristics of the particular Airfoils are obtained.

When the centre of the cirlce is located on the y-axis, a thin circular-arc airfoil is obtained from Joukowski transformation. In the same way, when the centre of the circle is located to the right of and above the origin, then a Cambered airfoil is obtained.  These Joukowski transformations are simple and direct ways for finding  flate-plate and circular-arc airfoils. But these transformations are found to be complicated in the case of cambered airfoils. So to make the construction of cambered airfoils easier, a researcher called TREFFTZ developed a method called Trefftz Graphical Construction. This method is the extension of Joukowski transformation. In this method, each point on the circle is transformed twice and both the transformations yields circles. Now again many mathematical operations are done on the trefftz method for obtaining the cambered airfoils. 

The above figure shows the construction of Joukowski airfoil with 4-ft chord, 4 per cent camber, 10 percent thick by the Trefftz method. The same methods are used for Construction of Thin-Airfoils and Thick Airfoils. 

  

Early 1920's...

Till now, the development of Airfoils has been mostly entirely empirical. The development of airfoils gradually increased and led to a more systematic experimental approach. Many modern wing sections have been developed at GOTTINGEN during our first world war. Most of the wing sections which are developed at Gottingen are used even in the period of Second world war. During this period, National Advisory Committee for Aeronautics (NACA)  tested many families of wing sections in laboratories of various countries. This work by NACA was found to be very interesting and impressive. These investigations are systematized by  separation of the effects of camber and thickness distribution an experimental word very higher Reynolds numbers, experimental work was performed. These NACA wing sections are in common use till date. We can say that the work done by NACA was simply outstanding. First laminar flow airfoil sections are developed in 1939 by NACA. 

These airfoils produce a very low drag and the above shown airfoil has a lift to drag ratio of 300. Based on various parameters like thickness of the airfoil, maximum camber, maximum value of mean-line, NACA derived four-digit wing sections, five-digit wing wing sections, 1-series wing sections, 6-series wing sections, 7-series wing sections. These types of wing sections are found to be in interest even for today's aircraft manufactures.    

Computational World...

After the late 1800's and 1900's, A huge development in the technologies has been observed and all the models, designs and analysis are performed by various computational approaches using various pre-processing and post-processing software's. Computational Fluid Dynamics is one of the most rich and diverse subject and also as emerged as a major component for determining various parameters and flow over the airfoils. In the same, the development of advanced computers and numerical algorithms has been increased gradually. These type of technologies made people to work on various airfoils computationally without many empirical forms or experimental forms. These type of computational approaches reduces the stress of an individual,  Cost and time of work can be reduced, changes can be done easily for obtaining accuracy and many more advantages have been observed in computational approaches.

. As the physical and Chemical models of the flow physics are mainly responsible in CFD for solving basic and applied scientific/engineering problems, Once these Physical and Chemical models are known, the analysis and determination of various parameters is a very simple task.

After these Computational Approaches came into existence, Optimization of airfoils have been observed for obtaining high-lift airfoils. Various approaches have been investigated for increasing the efficiency of the airfoils.So we can say that, the main idea of airfoils and its construction has been derived from many empirical operations and experimental methods. Then, people started to increase the efficiency of the work which has been derived in the late 1800's and 1920's.

References...

1) W. F. Durand, " Aerodynamic Theory", Vol. I, pp. 89-104, Verlag Julius Springer, Berlin, 1934
2) Leonard Bairstow, " Applied Aerodynamics,", p.325, Longmans, Green & Co., inc, New York.
3) E. trefftz, GraphixL Construction of joukowski Wings, T M 336, 1925
4) H. Glauert, A Generalized Type of Joukowski Aerofoil, R & M 911. 1924
5) Alan Pope, Wing and Airfoil Lecture notes, Georgia Institute of Technology, Atlanta, Ga
6) Ira H. Abbott and Albert E. Von Doenhoff, " Theory of Wing Sections," McGraw- Hill Book Company,
    Inc., new York, 1949

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      Sampath Emani

      M.Tech Computational Fluid Dynamics ( 2011-2013)

      University of Petroleum and Energy Studies, Dehradun, India

      Contact no : +91 7411435835

      Sampath.evs@gmail.com