EXTENDED TIP CHORD AERODYNAMIC LEADING EDGE CENTER (25% MAC) A ROOT CHORD NOMINAL CG ROOT CHORD TIP CHORD 25 CHORD .50 CHORD TRAILING EDGE TIP CHORD MEAN AERODYNAMIC EXTENDED CHORD (MAC) ROOT CHORD Figure 2: Wing Planform, Image: ERAU Span (b, in or ft): The span of a wing is the distance from wingtip to wingtip. We treat a portion of the wing area inside of the fuselage to simplify analysis. This area of the planform would not generate lift, but we include it in our calculations to provide an approximation of lift generated by the fuselage. In the image provided, you are only viewing 1/2 of the wing's span. If the aspect ratio (AR) of the wing and surface area of the wing are known, we can derive the span using the following equation. b = VAR * S Where, AR - aspect ratio of the wing . S-surface area of wing (in or ft?) Aspect Ratio (AR, unitless): The aspect ratio (AR) is a unitless measure of the ratio of span over the average chord length for the planform. In aircraft design, this parameter is a design parameter, i.e., a value is specified by the designer, and not typically calculated. However, it is good to know how to calculate the AR to analyze existing platforms in order to better understand design tradeoffs. Typical values for subsonic aircraft are between 6 to 9. A UAS built for long endurance typically have a larger aspect ratio (i.e., a high aspect ratio wing). span AR = = avg.chord SWhere, I b span of wing (in orft) - S surface area of wing (in2 or ftz ) 0 Note: ensure consistent units Surface Area (S, in2 orftz): The surface area (5) ofa planform is the surface area ofthe total wing. For rectangular wings, this can be easily calculated by deriving the area of a rectangle. For a trapezoidal configuration such as shown in the figure, the surfaced area can be calculated as follows based upon the root and chord. Given an aspect ratio and desired wing span, the design could calculate S and use its value to derive the chord lengths. cRoot + CTip) (CRoot + llCRoat) 2 s = b ( 2 Where, I b span ofwing (in or ft) - CRUD: length ofthe root chord of the wing (in or ft) - Cm, length of the chord tip of the wing (in or ft) 0 ll taper of the wing (unitless) Chord lengths (in or ft): Three chords should be considered and are shown in Figure 2 for wing design and analysis. First, the root chord is the distance between the leading and trailing edges ofthe wing at the wing's center. Second, the tip chord is the distance between the leading and training edges at the wings tip. Finally, the mean aerodynamic chord (MAC) can be calculated or derived graphically as shown, which represents the mean chord distance over the entire wing. Additionally, some calculation and analysis require chord lengths that are some percentage ofthe total chord length for a given point on the wing. In Figure 2, the 0.25 chord and the 0.50 chord are shown, which are respectively 25% and 50% ofthe chord length away from the leading edge. Taper (unitless): Taper is the ratio of the tip chord length over the root chord length. Given a root chord and taper, the tip chord length can be calculated. Sweep (A, degrees) Sweep is the angle of the 0.25 chord line as illustrated. Empennage planform surfaces: The empennage of the aircraft typically has planform surfaces providing stability to the aircraft. For a more traditional fixedwing aircraft, there are a vertical stabilizer (VT) and a horizontal stabilizer (HT), which share similar planform analysis. Detailed analysis of the tail stabilizers is outside of the scope of the course, but the following equations can help you approximate these values for preliminary analysis. Vertical Tail Stabilizer (VT): 5,\". = (0. 15).? and ARVT = 1. 5, and AW = 0.667 Where, 0 .S' surface area of wing (in2 orftz) Horizontal Tail Stabilizer (VT): SHT = (0. 25)S and ARVT = 3, and AW = 0.5 Where, 0 5 surface area of wing (in2 orft'z) The minimum distance between the center of the wing and the center ofthe tail surfaces can be derived using the following equation: LT,mm = 3 MAC Where, 0 MAC length of mean aerodynamic chord (MAC) (in or ft) Exercises: Given the following UA's design configuration, derive the remaining parameters. Given for wing planform: AR = 17.20 S = 4.20 ft2 1 = 0.85 Calculate: Span (b) CRoot Crip SVT SHT Show your work. 7