Drag Polar Analysis
This page will include the drag polar plot and associated L/Dmax, along with a comparison to the previously defined L/Dmax.
Calculating Drag Polar
The drag polar was calculated using the following formula:
In this equation, the total drag CD consists of two different types of drag. the first, CD0 represents the parasitic drag produced by the aircraft geometry. This drag slows the aircraft down while producing no lift. some sources of this drag include the fuselage and some other equipment that the aircraft may need such as a pitot tube. The second kind of drag is the induced drag produced by the aircraft's airfoil. This drag varies as the aircraft travels or manoeuvers at various different angles of attack.
The parasitic drag for the aircraft is very difficult to calculate. It would require complex calculations or CFD analysis of the aircraft. For this reason, Raymer has tabulated various constants to calculate the approximate parasitic drag gathered from historical data [1]. The equation to approximate the parasitic drag can be seen below:
Where Cfe can be found in Table 12.3 of Raymer [1]. In this case, a CFE of 0.0045 was chosen as it represents a light twin-engine aircraft. The parasitic drag was calculated to be 0.01916 assuming Swet and Sref of 1219.22 ft2 and 286.3482 respectively. Note that the Swet value differs from the previous analysis as it was calculated using the almost final 3D model of the aircraft.
Lastly, the equation requires the Oswald efficiency value which can be calculated as follows:
The Oswald efficiency determines how efficient the wing is compared to the ideal elliptical wing shape.
Drag Polar Plot
This plot shows the more accurate L/D compared to the initial sizing L/D. The slope was obtained by creating the best fit line between the origin of the axis and a tangent point to the drag polar curve. This line was denoted as the orange "Tangent" line on the curve with a slope of 14.666. This graph also shows the lift coefficient and drag along the various different angles of attacks. It is important to note that the angle of attack will not likely reach anywhere above 15 degrees as it will most likely stall above that.
Further Discussion
The value of L/D produced from the drag polar was considerably larger than the initial rough L/D estimation. From the drag polar, L/D was found to be 14.6657 which is 21% higher than the initial estimation of 11.5685. The new L/D is higher which indicates a better performing aircraft. The increased L/D ratio is largely caused by the changes in the wing geometry. The wing has increased in the area which increased the lift of the aircraft. Secondly, the wetted area calculation has also changed as this analysis utilized the new updated model of the aircraft. The updated model has a much more refined geometry with a more refined aerodynamic property. Since the new L/D indicates an improvement to the aircraft, no further changes were done in the wing geometry or flaps. It is important to note however that the higher L/D would yield lower MTOW had the iterative analysis of the aircraft been performed. In this design, the original MTOW was still used since it would mean that the aircraft would be capable of performing better than the expected original performance.
References
[1] Raymer, Aircraft Design: A Conceptual Approach, Sixth Edition. Washington, DC: American Institute of Aeronautics and Astronautics, Inc., 2018.