Abstract
The main objectives of this study are to investigate parametrically the possible use of alternative airfoils (Joukowski and Göttingen) for propellers and to assess the effects of varying the chord and pitch angle distributions as well as the use of multiple airfoils along the blade on the performance parameters of the propeller. In this study, a validated homebuilt FORTRAN code based on the BEM method with incorporated tip and compressibility losses is used. The detailed investigation of the blade geometry is done to help in selecting a configuration that is efficient and easy to manufacture. The linear pitch distribution is found to reduce the coefficients of thrust and power as well as higher blade loading at the intermediate region and lower loading at the tip region in comparison with the Göttingen 796based propeller. The results show that the power coefficient and efficiency of the generalized Joukowskibased propeller are greater than the respective coefficients of Göttingen 796based propeller for advanced ratio J = 0.85 and higher. The predicted results indicate that the use of the elliptical chord distribution provokes reduction in the blade loading at the tip region and increases at the intermediate region of the blade. It is found also that it reduces the coefficient of thrust, torque and power in comparison with the blade having the reference chord distribution.
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Abbreviations
 \(a\) :

Inflow factor
 a _{0} :

Lift curve slope at zero Mach number (i.e., in incompressible flow) (radians^{−1})
 a _{M} :

Lift curve slope at zero Mach number (radians^{−1})
 \(b\) :

Swirl factor
 \(B\) :

Number of blades of the propeller
 \(c\) :

Local blade chord (m)
 \(C_{\text{d}}\) :

Twodimensional drag coefficient of the local blade chord
 \(C_{\text{l}}\) :

Twodimensional lift coefficient of the local blade chord
 \(D\) :

Diameter of the propeller (m)
 \(f_{\text{tip}}\) :

Tip loss correction used to calculate Prandtl loss factor F
 \(f_{\text{hub}}\) :

Hub loss correction used to calculate Prandtl loss factor F
 \(F\) :

Prandtl loss factor for combined tip and hub losses which arise due to the finite number of the propeller blades
 \(J\) :

Advance ratio of the propeller \(J = {V \mathord{\left/ {\vphantom {V {(n{\kern 1pt} D)}}} \right. \kern0pt} {(n{\kern 1pt} D)}}\)
 \(k_{\text{P}}\) :

Power coefficient of the propeller \(k_{\text{P}} = {P \mathord{\left/ {\vphantom {P {(\rho {\kern 1pt} n^{3} D^{5} )}}} \right. \kern0pt} {(\rho {\kern 1pt} n^{3} D^{5} )}}\)
 \(k_{\text{Q}}\) :

Torque coefficient of the propeller \(k_{\text{Q}} = {Q \mathord{\left/ {\vphantom {Q {(\rho {\kern 1pt} n^{2} D^{5} )}}} \right. \kern0pt} {(\rho {\kern 1pt} n^{2} D^{5} )}}\)
 \(k_{\text{T}}\) :

Thrust coefficient of the propeller \(k_{\text{T}} = {T \mathord{\left/ {\vphantom {T {(\rho {\kern 1pt} n^{2} D^{4} )}}} \right. \kern0pt} {(\rho {\kern 1pt} n^{2} D^{4} )}}\)
 M :

Local Mach number of the relative flow
 \(n\) :

Rotational speed of the propeller (rps)
 \(N\) :

Rotational speed of the propeller (rpm)
 \(p\) :

Geometric pitch of the blade section (m)
 \(P\) :

Power supplied at the propeller axis (Nm/s)
 \(Q\) :

Torque applied on the propeller (Nm)
 \(r\) :

Radius of the transversal section of the blade of the propeller (m)
 \(R\) :

Radius of the blade tip of the propeller (m)
 \(Re_{75}\) :

Reynolds number of the propeller based on the local chord and resultant velocity at a radial distance of 0.75 of the tip radius
 \(T\) :

Thrust force of the propeller (N)
 \(V\) :

Advance velocity of the propeller (m/s)
 \(V_{0}\) :

Axial component of the flow velocity relative to the blade (m/s)
 \(V_{\text{R}}\) :

Resultant flow velocity relative to the blade (m/s)
 \(V_{\text{S}}\) :

Axial component of the flow velocity relative to the propeller at exit of the slipstream (m/s)
 \(V_{\text{w}}\) :

Rotational component of the flow velocity relative to blade (m/s)
 \(\alpha\) :

Angle of attack is the angle between the resultant velocity vector \(V_{\text{R}}\) and the zero lift line of the blade airfoil (radians)
 \(\alpha_{\text{c}}\) :

Angle between the resultant velocity vector \(V_{\text{R}}\) and the chord line of the blade airfoil (radians)
 \(\delta {\kern 1pt} k_{\text{Q}}\) :

Torque loading coefficient of the blade element
 \(\delta {\kern 1pt} k_{\text{T}}\) :

Thrust loading coefficient of the blade element
 \(\eta\) :

Efficiency of the propeller
 \(\theta_{\text{c}}\) :

Pitch angle of the blade section (radians)
 \(\lambda\) :

Taper ratio of the propeller blade
 \(\rho\) :

Specific mass of the fluid (air) (kg/m^{3})
 \(\sigma\) :

Solidity of the rotor
 \(\phi\) :

Angle of the resultant velocity \(V_{\text{R}}\) with the plane of rotation of the propeller (radians)
References
Theodorsen T (1948) Theory of propellers. McGrawHill, New York, pp 6–15
Dumitrescu H, Cardos V (1998) Wind turbine aerodynamic performance by lifting line method. Int J Rot Mach 4(3):141–149. https://doi.org/10.1155/S1023621X98000128
Palmiter SM, Katz J (2010) Evaluation of a potential flow model for propeller and wind turbine design. J Aircr 47(5):1739–1746
Slavík S (2004) Preliminary determination of propeller aerodynamic characteristics for small aeroplanes. Acta Polytech 44(2):103–108
Gur O, Rosen A (2008) Comparison between bladeelement models of propellers. Aeronaut J 112(1138):689–704
Uhlig DV, Selig MS (2008) Post stall propeller behavior at low Reynolds numbers. In: 46th AIAA Aerospace Sciences Meeting and Exhibit. 20080407
Bohorquez F, Pines D, Samuel PD (2010) Small rotor design optimization using blade element momentum theory and hover tests. J Aircr 47(1):268–283. https://doi.org/10.2514/1.45301
Khan W, Nahon M (2015) Development and validation of a propeller slipstream model for unmanned aerial vehicles. J Aircr. https://doi.org/10.2514/1.C033118 (AIAA Early Edition)
Drela M (2013) XFOIL Subsonic airfoil development system, XFOIL 6.99. Massachusetts Institute of Technology, Cambridge, MA, USA. http://web.mit.edu/drela/Public/web/xfoil/. Accessed 12 April 2016
Morgado J (2016) Development of an open source software tool for propeller design in the MAATProject. University of Beira Interior, PhD Thesis, March
Silvestre MAR, Morgado J, Páscoa JC (2013) JBLADE: a propeller design and analysis code. In: 2013 International powered lift conference. American Institute of Aeronautics and Astronautics, Los Angeles, CA, USA. https://doi.org/10.2514/6.20134220
Morgado J, Abdollahzadeh M, Silvestre MAR, Páscoa JC (2015) High altitude propeller design and analysis. Aerosp Sci Technol 45:398–407. https://doi.org/10.1016/j.ast.2015.06.011
MacNeill R, Verstraete D (2017) Blade element momentum theory extended to model low Reynolds number propeller performance. Aeronaut J 121(1240):835–857. https://doi.org/10.1017/aer.2017.32
Wald QR (2006) The aerodynamics of propeller. Prog Aerosp Sci 42(2):85–128
Glauert H (1926) The elements of aerofoil and airscrew theory. Cambridge University Press, Cambridge, pp 199–221
Houghton EL, Carpenter PW, Collicott SH, Valentine DT (2013) Aerodynamics for engineering students, 6th edn. Elsevier, Amsterdam, pp 643–687
Wald QR (1964) The distribution of circulation on propellers with finite hubs. ASME Paper 64WA/UNT4, Winter Annual Meeting, New York
Glauert H (1935) Airplane propellers, Vol IV, Div L, Chap VII. In: Durand WF (ed) Aerodynamic theory. Julius Springer, Berlin [Reprinted 1963 by Dover Publications, Inc., New York], pp 251–269
Hartman EP, Biermann D (1938) The aerodynamic characteristics fullscale propellers having 2, 3 and 4 blades of Clark Y and RAF 6 airfoil sections. NACA Report No. 640. Langley Memorial Aeronautical Laboratory, National Advisory Committee for Aeronautics, Langley Field, VA, USA
Lyon CA, Broeren AP, Giguère P, Gopalarathnam A, Selig MS (1998) Summary of lowspeed airfoil data, vol 3. Department of Aeronautical and Astronautical Engineering, University of Illinois at UrbanaChampaign, SoarTech Publications, Virginia Beach, VA, USA
Glauert H (1924) A generalised type of Joukowski aerofoil. ARC RM No. 911
Acknowledgements
The first author wishes to thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for the PQ Research Grant.
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Ismail, K.A.R., Rosolen, C.V.A.G. Effects of the airfoil section, the chord and pitch distributions on the aerodynamic performance of the propeller. J Braz. Soc. Mech. Sci. Eng. 41, 131 (2019). https://doi.org/10.1007/s404300191618x
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DOI: https://doi.org/10.1007/s404300191618x
Keywords
 Small propeller
 Momentum theory
 Blade element theory
 Panel method
 Blade aerodynamics
 Airfoil section