Link to spreadsheet: https://docs.google.com/spreadsheets/d/1kn22d-hnXbN9RuNuCiraiVNUGw5E6ZtTgUoTMSd4JNk/edit?usp=sharing

Methodology Outline

The wing structure primarily consists of the main spar, the rear spar, the joiners for both spars, the balsa skeleton, and the monokote skin. These components make up the bulk of the weight. The final assembled product will of course have additional weight from glue, bolts, and other stuff, but those shall be ignored for now in order to obtain a rough weight estimate. The objective within this rough weight estimate is to obtain an equation that describes the spanwise linear mass/weight density of the wing, which we can then use for total mass and inertia calculations.

The spars and their joiners are untapered beams, so their linear mass density is easy to find. On the other hand, the balsa and monokote portions of the wing are much harder to estimate the weight of due to both how their volume consists of a series of oddly shaped bodies and the tapered nature of the wing. Ultimately, the amount of balsa and monokote used depends on the wing chord, span, and thickness, variables that all change with tapering. So how do we go about doing this? Well, thickness is related to chord length, and, with a tapered wing, chord length is related to span. Through this, we can (fingers-crossed) hopefully first relate the total volume of balsa and surface area of monokote to first the planform area, which we can then multiply by their respective material densities to achieve area-based densities. With these area-based densities, we can multiply them by the tapered chord length to get a spanwise linear density (because lb/in^2 times in equals lb/in).

List of Wing Components

• Main Spar: 0.75x0.75x0.125 in. 6061 aluminum trim channel; assuming covers entire 60 in. semi-span for now https://www.metalsupermarkets.com/product/aluminum-channel-6061/
  • Density: 0.0975 lb/in^3
  • Cross-Sectional Area: [3(0.75)(0.125)-2(0.125)^2] = 0.25 in^2
  • Weight Per Inch: 0.0244 lb/in
• Main Spar Joiner: 1x1x0.125 in. 6061 aluminum square tube; assuming covers fuselage semi-span of 10.5 in. https://www.metalsupermarkets.com/product/aluminum-square-tube-6061/
  • Density: 0.0975 lb/in^3
  • Cross-Sectional Area: 1^2-(1-2(0.125))^2 = 0.4375 in^2
  • Weight per Inch: 0.0427 lb/in
• Rear Spar: 0.375x0.375x0.0625 in. 6061 aluminum square tube; assuming covers from 5.5 in. outboard of fuselage root to 20 in. outboard of fuselage root https://www.mcmaster.com/products/aluminum-square-tubing/multipurpose-6061-aluminum-rectangular-tubes/
  • Density: 0.0975 lb/in^3
  • Cross-Sectional Area: 0.375^2-(0.375-2(0.0625))^2 = 0.0781 in^2
  • Weight per Inch: 0.00762 lb/in
• Rear Spar Joiner: 0.5x0.5x0.0625 in. 6063 aluminum square tube with two 10-degree bends to accommodate swept flap/aileron hinge line, but we’ll approximate it as a straight beam rn; assuming covers entire 10.5 in. fuselage semi-span
  • Density: 0.0975 lb/in^3
  • Cross-Sectional Area: 0.5^2-(0.5-2(0.0625))^2 = 0.1094 in^2
  • Weight per Inch: 0.0107 lb/in
• Balsa Skeleton: assuming covers entire wing from fuselage root to tip to somewhat account for the center wing box
  • Density: 0.00579 lb/in^3
  • From conceptual CAD: 54.841 in^3 balsa / 594 in^2 planform area = 0.09232 in^3 balsa/in^2 planform area
  • Planform area density: 5.54 E-4 lb/in^2 planform
  • Chord-length equation: c(y) = 33.103 - 0.3036y (y=0 is root, y=60 is tip, units in in.)
  • Weight per Inch: (5.54E-4)(33.103-0.3036y) = 0.0183 - 1.682E-4 lb/in
• MonoKote Skin: assuming covers from wing-fuselage root (y=10.5) to tip
  • Density: 8.679E-5 lb/in^2
  • From conceptual CAD: 1203 in^2 monokote / 594 in^2 planform = 2.025 in^2 monokote / in^2 planform
  • Planform area density: 1.76E-4 lb/in^2
  • Weight per Inch: (1.76E-4)(33.103-0.3036y) = 0.00583 - 5.34E-5 lb/in

Piecewise Density Function

These numbers are a bit off from the ones above because I rounded differently, but the gist of it is that based on this, the total wing weight will be somewhere around 6.22-6.26 lb