# Advanced Scale-Propeller Design Using a MATLAB Optimization Code
### Historical Perspective
Formulae are then developed for calculating the torque, thrust, energy loss and efficiency, in terms of the mass coefficient, for any propeller with ideal circulation distribution, from the downstream wake conditions. In 1979, [PERSON] and [PERSON] working for Boeing, published a report entitled Low-Speed Single-Element Airfoil Synthesis [13] which outlines the design criteria and the practical restraints for an airfoil operating at low Reynolds numbers. The report also describes a'synthesis' based approach to airfoil design, in contrast to the typical 'analytical' approach. First, the boundary layer characteristics are defined, as they define the pressure distribution and therefore the airfoil performance. From this, powerful computational tools were used to generate an airfoil shape which yields the pre-defined boundary layer. A Master's thesis by [PERSON] (2009) entitled Automatic Dynamic Propeller Testing at Low Reynolds Numbers [14] focuses on the testing of propellers and reducing propeller test times, by designing a system in which propeller data can be acquired systematically. The effect of the Reynolds number on efficiency and propeller pitch were also examined. Another Master's thesis by [PERSON] (1998) called the Design and Performance Calculations of a Propeller for Very High-Altitude Flight [15] examined propellers for use in low Reynolds number flow regimes (60,000-100,000). A design process utilizing BET and ADPAC (a numerical Navier-Stokes code) was used to optimise a propeller for high altitude flight. The operating conditions for this study were 25.9 km (85,000 ft) at Mach 0.4, and each propeller was required to absorb 63.4 kW (85 bhp). Propeller Performance Measurement for Low Reynolds Number Unmanned Aerial Vehicle Applications [16] focused on the testing of small propellers, particularly those used on UAV systems. An Integrated Propulsion Test System (IPTS) was used to evaluate the performance of many propellers, and a database of performance data was created. This IPTS setup is similar to the one in use at the University of Illinois at Urbana-Champaign's (UIUC) Department of Aerospace Engineering, where a vast propeller database has been created [2]. Using a load cell to measure thrust and a torque cell to measure torque, efficiency curves have been plotted, and in modern propeller research this database is often used for comparative reasons. Similarly, in Low Reynolds Propellers for Increased Quadcopters Endurance [17], the design process for creating a propeller for use in low Reynolds number flow is detailed by [PERSON] (2013). A validation exercise of the UIUC Propeller database [2] was also completed, by comparing the UIUC experimental results of the APC Slow Flyer 10\({}^{\prime\prime}\)\(\times\) 7\({}^{\prime\prime}\) to simulated results on JBLADE software v.17. The highest efficiency value was found to be 61% from JBLADE simulations, compared to the experimental value of 59%. Note: The UIUC database was updated in March 2015, to account for a new wind tunnel correction method for the drag due to the propeller mounting fixture. This had the result of increasing the peak efficiency of props by approximately 10%. A journal paper entitled Propeller Performance Measurements at Low Reynolds Numbers [18] by [PERSON], et al. (2015) discussed the design of propellers for use on high-altitude airships. Two APC propellers were tested between 4 m/s and 28 m/s in 1 m/s intervals, and the data was compared to the UIUC database in order to validate the test-rig. It was shown that as the Reynolds number increases with increasing RPM values, the efficiency and thrust coefficient of the propeller was increased significantly. It is also stated that the test-rig would be used to create experimental data that could improve the JBLADE software v.17 in the future. In a 2016 paper by [PERSON], et al. entitled Quadcopter Propeller Design and Performance Analysis [19] used SolidWorks to analyse the efficiency of a two-bladed 16\({}^{\prime\prime}\)\(\times\) 5\({}^{\prime\prime}\) propeller.