Wing

\label{sec:trade_wing} This chapter includes the trade-off for the wing planform and the trade-off for the wing tips. First the wing planform is chosen after which a suited wing tip is traded off.

Trade-Off Criteria and Weights

The different criteria will be further explained here and their weights are prevented in Table \ref{tab:wing_weights}.

• Maneuverability: The wing has a major influence on the maneuverability of the entire wing, that is why this is one of the main criteria.

• Complexity: A more complex wing will result in higher development costs and design risks, which should be avoided.

• L/D: The wing is the main part that contributes to the lift, therefore it also has a major influence on the aerodynamic efficiency of the overall aircraft. In order to decrease drag of the total design the lift-to-drag ratio of the wing should be maximized.

• Weight: In order to achieve the desired overall efficiency and maneuverability the weight of the wing should be minimized.

• Stall Characteristics: The aircraft performs many maneuvers, for those it is required that the aircraft does not stall. Also in case the aircraft is deliberately stalled, it should still be controllable. It is better that the stall starts near the root in order to maintain control over the aircraft.

\label{tab:wing_weights}

Trade-off Wing and Wingtips

Wing

Before the trade-off is conducted an ‘analysis of all the weaknesses’ has been conducted. This means that all the options that are not applicable for the current mission profile are removed. During this process the wing subsystem design option tree has been used as a guide line. The first aspect that was analyzed were the three positions of the wing: high, mid or low. Since it is desired to have the wing centered to decrease the Moment of Inertia the mid configuration is selected. The next step was determining which parameters are applicable for an aerobatic racing aircraft, here a closer look was taken at the dihedral angle. The effect of a positive dihedral angle with a mid located wing is that it tends to decrease the roll angle, which means it has a stabilizing effect. As an aerobatic aircraft should also be able to fly upside-down, which reverses the dihedral effect. Therefore no dihedral will be added to the wing. The same reasoning is used for the twist. Twist is used to prevent tip stall at high angle of attacks. It is not desired to have wing tip stall while the aircraft is reversed.

Another parameter to consider is sweep. Swept wings are only desirable at transonic and supersonic speeds, since it reduces the drag \cite{zerodragcoefficient} at high Mach-numbers. At subsonic speeds the drag for a wing with and without sweep are comparable, however a swept wing is heavier since it needs to account for a torque. For these reasons a swept wing should preferably be avoided for E-SPARC.

The following step was trading of each step of the design option tree. The first trade-off was determining whether a rectangular or an elliptical wing is more beneficial. The main advantage of an elliptical wing is that the lift distribution is optimal along the wing span. However the complexity is slightly larger compared with a rectangular wing. Also the stall characteristics are not as favorable in respect to a rectangular wing, because that stall propagation starts over the entire wing whereas the rectangular wing starts at the root. Therefore E-SPARC will have a rectangular wing.

The following parameter that was traded-off after was the aspect ratio. The main advantages of a wing with an aspect ratio is that L/D increases, however when keeping the same surface area the span becomes larger which means that the moment of inertia also increases and reduces the maneuverability for roll. Also a high aspect ratio will result in a higher structural wing weight. During the trade-off a low aspect ratio was the result.

Lastly a trade-off with respect to taper was performed. The three options were high taper ratio, low taper ratio and no taper ratio. The goal of introducing taper is to come closer to the lift distribution of an elliptical wing. A wing with a taper ratio of \(0.5\) comes closer to the lift distribution of an elliptical wing compared to a taper ratio of \(0\). That is when the tip chord is very small. The most suitable taper ratio is \(0.45\) \cite{zerodragcoefficient} which results in an almost elliptical lift distribution, the difference is that the drag is \(1\,\%\) higher. However when a wing is heavily tapered the stall propagation starts at the wing tip, this effect is reduced when the wing is less tapered. Another downside is that a tapered wing is slightly more complicated to manufacture. During the trade-off a low tapered wing was the outcome, which means that the taper ratio should be between \(0.45\) and \(1\).

All results for the trade-offs discussed above are tabulated in Table \ref{tab:trade_wing}.

\label{tab:trade_wing}

Wing Tips

The wing tip shape has an influence on the creation of tip vortices and thus if properly designed can reduce the drag and increase the effective wing span. That is why the selection of the wing tip is very important during the design and a proper trade-off has to be conducted. There are several kinds of wing tips shown in Figure \ref{fig:tips}, they are listed below with a short explanation of their influence:

• Rounded Here the wing tip is rounded, this allows the air easily flow around the tip.

• Sharp A sharp edge makes it more difficult for the air to flow around the tip, decreasing the induced drag.

• Cut-Off: Here the induced drag is also lower than a rounded tip, because the sharp edges make it more difficult for the air to flow to the top. The flow over a cut-off wing tip and a rounded wing tip in shown in Figure \ref{fig:rounded}.

• Hoerner: The Hoerner wing tip has a sharp edge, the upper surface continues with the upper surface of the wing, whereas the lower surface is canted with respect to the horizontal and may have a concave shape. Here the effective wing span is increased, improving the aerodynamic efficiency. The flow over the wing tip is shown in Figure \ref{fig:hoerner}.

• Drooped & Upswept: A drooped or upswept wing tip is curved upwards or downwards respectively. These wing tips increase the effective wing span. It also changes the vertical position of the starting point of the wing tip vortex. The flow over these two wing tips are shown in Figure \ref{fig:raised}.

• Aft-Swept: An aft-swept wing tip has a lower drag because the wing tip vortex starts near the trailing edge. However this increases the torsional loads on the wing, slightly increasing the total weight of the wing.

• Cut-Off Forward Swept: This wing tip is specially designed for supersonic speeds. This shape manages that the shock cone formed at the wing tip contributes to the lift. It also reduces the torsional load.

• End-plate: End-plates are used to prevent that the high pressured air beneath the wing reaches the top of the wing. The use of an endplate has an effective span increase of 80% of the height when added to the wing span. The wetted area of the end-plated creates drag itself.

• Winglet: It is a special designed endplate designed by NASA, decreasing the total wing drag and increasing the effective wing span. Ideally a winglet can have a 200% increase of the effective span in terms of the winglet height \cite{zerodragcoefficient}. The use of these winglets are beneficial when there are strong vortices. However it adds weight and can induce flutter, which results that a stronger wing structure is needed. Also a winglet is optimized for one velocity, for other velocities it is less efficient.

Overview of all possible the wing tips

\label{fig:tips}

\label{fig:hoerner}

\label{fig:raised}

\label{fig:rounded}

During the process of the trade-off the Hoerner wing tip was considered the best option as presented in Table\ref{tab:trade_wingtips}.

\label{tab:trade_wingtips}