# Theory of projecting

**The Approach for synthesis of Low-Reynolds High-Performance Wing Shape**

**Wing design technique contains two main stages:**

*1. Step of core and tip airfoils synthesis for trapezoidal wing synthesis.*

*2. Checking of the laminar-turbulent transition boundary and estimation of zero lift wing drag Cd(Cl=0) using numerical simulations based on solution of Navier-Stokes equations on a high density grid.*

**Wing airfoils generation technique**

*For the specified aspect ratio, narrowing and geometric twist of trapezoidal wing root and tip profiles are generated with requirements of elliptic distribution of the circulation along the span. Main optimization criteria are:*

*• minimizing zero lift wing drag Cd(Cl=0);*

*• maximizing of the maximum lift coefficient (Clmax);*

*• maximizing the Cl/Cd at Cl = 0.8.*

*An additional requirement to the tip profile is achievement of a smooth boundary layer separation at the aileron trailing edge, which provides effectively aileron operation near maximum lift and guarantee model roll control and the absence of instability in the yaw channel.*

*Wing airfoils optimization is performed using a fast genetic algorithm based on the solution of the full potential equation with the empirical laminar-turbulent boundary layer. The dimension of the optimization vector for a single profile is 50. The plane shape of the wing tip is formed by the conic curves which provides:*

*• minimum induced drag of the wing;*

*• normally condition for the aileron operation at high angles of attack;*

*• movement of the pressure center line to the optimum position in relative to the axis of the wing stiffness.*

**Checking**** of the laminar-turbulent transition boundary and estimation of wing Cd(Cl=0)**

* *

*For the verification of the wing laminarization rate at specified lift range the semi-direct numerical solutions Navier-Stokes equations is conducted. Usually the dimension of an unstructured mesh is more than 20 million control volumes. For example, the figure below shows the distribution of pressure on the upper surface of the F-3-D model wing. The area of the big scale pressure fluctuation appears near the trailing edge, which indicating the loss of stability of the laminar boundary layer. The area should be considered as the zone of the turbulent boundary layer.*

The pressure coefficient distribution on upper wing surface of pylon race model.