- Design Plan

The team considered many factors in designing the aerobody in order to achieve maximum lift, minimum drag, and the most stable design.  These factors included aspect ratio, thickness ratio, taper ratio, Reynolds number, and dihedral.  Each of these can dramatically affect the above mentioned in-flight characteristics.

Perhaps most important to the overall lift and drag of the body is the aspect ratio of the airframe.  Aspect ratio is typically defined as the square of the wing span divided by the wing area.

Aspect Ratio Formula

Since the MAV is designed as a flying wing, the “b” term is simply the maximum tip to tail length of the body.  The “S” term represents the planform area, that is, the area of the body viewed in 2-D from the top down.  For a given lift, a long skinny wing (high Aspect Ratio) has less drag than a short, fat wing.  This is due to the wing tip vortices that occur as a result of the pressure differential around the wing.  The high-pressure air from underneath the wing moves toward the lower pressure on top of the wing.  Near the tip of the wing, the high-pressure air will slip around to reach the top of the wing.  This circulation of air around the tip creates a vortex and also pushes down on the top of the wing, spoiling lift and creating drag.  A high aspect ratio planform shape has wingtips spaced further apart.  Therefore, the formation of vortices will have less of an effect because less of the wing will be exposed to the vortices.  Aspect ratio also has a direct impact on stall angle.  Since the wingtips in a low aspect ratio wing have a lower effective angle of attack, the wing will tend to stall at a higher angle than a high aspect ratio wing.  The Inverse Zimmerman planform was selected to take the fullest advantage of all of these considerations.

Generated Tip Vortices

                           

Inverse Zimmerman Plane Form

A factor that combines with aspect ratio to affect lifting characteristics and stall angle is the thickness ratio of the selected airfoil.  The thickness ratio is the ratio of camber to chord length.  That is, the width of the airfoil at its thickest point divided by its tip to tail length.  Thickness ratio effects lift by changing the nose shape of the airfoil.  For a wing with a high aspect ratio and a moderate sweep, a large nose radius will increase the coefficient of lift.  This arrangement will also increase the wing stall angle.  For a wing with a low aspect ratio and a higher amount of sweep, the opposite is true.  In this case, a sharp nose will produce leading edge vortices, which will counteract stalling and contribute to a greater maximum lift.

Wing weight is also affected by thickness ratio.  It has is known that weight varies inversely with the square root of the thickness ratio.  Therefore, if thickness ratio were to be halved, wing weight will increase about 41%.  By maintaining a constant thickness ratio across the span, the weight of the MAV will be maintained across the body.

Another important ratio in aircraft design is the taper ratio.  Defined as the ratio of tip chord length to root chord length, the taper ratio can drastically affect how lift is distributed over the wing.  According to the Prandtl lifting theory, the ideal wing shape for the minimization of lift induced drag is elliptical.  However, elliptical wings are expensive and difficult to manufacture.  A rectangular wing is much easier to manufacture, but suffers from its constant chord length along the span.  The extra chord at the tip causes the wing to create more lift, and thus more drag, at the tip than is ideal.  In fact, a rectangular wing will generate about 7% more lift-induced drag than an elliptical wing of equivalent aspect ratio.  A taper ratio of only .45 reduces this to less than 1% from ideal.  When the weight reduction due to taper is accounted for, a taper ratio of only .4 is ideal.

An important consideration in MAV design is cruise speed, and therefore, cruise Reynolds number.  Airfoils are generally designed to be Reynolds number specific.  Since Reynolds number and velocity are directly related via Formula 2, it is important to know what velocity the craft is expected to fly at in order to correctly select the airfoil the wing is to be based on.

Reynolds Number Equation

Varying significantly from the intended Reynolds number, by half an order of magnitude or more, can have drastic effects on wing section characteristics.  This is particularly true in the case of laminar flow airfoils, or those being operated below their design Reynolds number.  This would present a problem for the MAV application because speeds are not expected to exceed 37 miles per hour; a Reynolds number of roughly 1.07e6.  However, recently airfoils have become available which are designed to operate in these lower Reynolds number ranges.  Such an airfoil has been selected for the MAV, but surface texture also presents a challenge.  In order for laminar flow airfoils to work optimally, surface roughness must be kept to a minimum.  This was an important consideration when deciding how the airframe was to be constructed. 

A final factor in wing design, which is very important in maintaining aircraft stability, is dihedral angle.  Dihedral angle is the angle the wings form with respect to the horizon when viewed from the front.  Dihedral helps to maintain aircraft roll stability.  A positive dihedral, wingtips angled up, tends to bring an aircraft back to level when it is banked.  The counter rolling moment is caused by a sideslip that results from the banking of the aircraft.  The craft will tend to “slide” toward the lowered wing, which will increase that wing’s angle of attack, thereby increasing its lift.  Since there is an unbalanced lift, the aircraft will tend to be righted.

Dihedral must be carefully calculated, because an excess of dihedral comes with a penalty.  Excessive dihedral can lead to an oscillatory disturbance in motion known as a “Dutch roll.”  Dutch roll is a repeated side to side oscillation that is a result of both yawing and rolling.  Such a phenomenon can be disastrous for a craft on the scale of the MAV, but can be countered by increasing vertical tail area.  This, in turn, will result in an increase in both the weight and drag of the aircraft.  Therefore, tail size and dihedral must be considered together to achieve the optimal design for stability, weight, and drag concerns.

The above-mentioned factors are very important in aircraft design and especially the design of aircraft on the scale of the MAV.  Because there is less wing area to generate lift than on a full size aircraft, geometric methods such as aspect ratio and thickness ratio must be used to get the most potential lift out of a limited area.  The lack of weight and area tend to make the MAV susceptible to stability issues due to relatively small wind disturbances.  Therefore, techniques such as dihedral must be used to provide stability to the aircraft.