Aerodynamic design I

As it has been seen before, during the description of the propulsion system, is absolutely necessary to know some aerodynamic characteristics in order to determine the performance of the airplane and therefore to check if the aircraft meets the design requirements. To facilitate the task, the plane has been divided into the following parts: wing, fuselage, tail and control surfaces. The first two are discussed in this article, the others will be discussed along with the stability of the plane.

In this design phase, besides the necessary theoretical analysis, two computer tools have been used: Javafoil for 2D airflow study and the airfoil selection and Ansys CFX, for the visualization of 3D airflow over every element as well as to determine the global forces and moments over the airplane.

Most of the aerodynamic design is optimized for cruise flight due to airplane spends most of the time in this situation. 

Wing:

The wing design begins with the selection of the airfoil or airfoils that will be used on its construction. The airfoils chosen must be fitted to flight conditions (Mach and Reynolds numbers), must assure the correct behavior of the boundary layer and must achieve enough lift force at the same time that tries to minimize the associated drag.

From the propulsion system study the cruise speed was stablished between 80 and 120 meters per second at an altitude of around 40000 feet so the Mach number will be under 0.4 in nominal flight conditions. At that altitude and speed with a MAC of 1.35 meters the Reynolds number will be around 5x10⁶. The first study with thin laminar airfoils showed a good performance for low speeds. At that speeds and Reynolds intervals, the boundary layer remains laminar and attached even at 50 percent of the chord.

Some of the airfoils tested:

Its dependence of lift coefficient with attack angle and polar for ideal cases (infinite wing and clean surface conditions) where shown below:

  

The NACA 6 series showed the best results in drag, with and efficiency factor over 50 with NACA standard surface conditions. Besides the good results that shows these thin airfoils, was necessary to increase the thick of the wing to allow enough fuel volume inside the wings and to prevent structural problems. I decided to keep trying with NACA 6 family and after several tests the final airfoil selected was NACA 64-517 (a=0.9).

 Flow field

 Polar

 cl vs attack angle

 Numerical results for Re=5x10⁶

With the airfoil data and an estimation of the maximum weight at cruise (steady level) conditions, the wing surface can be easily calculated. Must be remembered that the airplane will spend most of the flight time in this conditions.

Considering as cruise conditions h=40000ft, V_T=90m/s and MTOW=3800kg, the wing surface needed to maintain a steady level flight can be expressed as a function of the lift coefficient as follows:

A few values to illustrate this relationship:

Cl	0.3	0.45	0.6	0.75	0.9	1.05
Sw (m2)	84.2	56.1	42.1	33.7	28.1	26.5

An early design of the wing attending to the selected airfoil with a slight modification in taper ratio (almost 0.45) and sweep angle is presented below. With this modification is intended to obtain a surface of around 30 square meters, a smoother transition for the installation of the winglet at tip airfoil and a lift force with almost elliptical distribution.

With a surface of 30m² (as shows the above design) the initial lift coefficient that must be achieved at cruise conditions is 0.84 By interpolation in the airfoil data, it means that the angle of attack needed to maintain a steady level flight would be approximately 2.4^o. According the consulted bibliography, this angle is on the normal range for commercial aircrafts at initial cruise conditions. In the same way at the end of the cruise phase the aircraft weight will be of only 2000kg, the lift coefficient needed will fall to 0.46 and the associated angle of attack will be of -0.6^o. This variation of 3 degrees during the cruise has to be accounted in order set an appropriate offset angle between the body and the wing of the aircraft.