Download and open rc1-hw1.flightlab.json, which is the configuration from hw 1. Keep span 1.200 m, area 0.192 m², airfoil, tail geometry, bodies, mass, and flight cases fixed. Only the chord and twist of the two main-wing stations will change. In flightlab a positive twist is nose up, so a negative tip twist is washout.
Wing design criteria for this problem:
(a) Three candidates. Analyze all three designs (the first is the original in hw1)
| Candidate | Root chord | Tip chord | Root twist | Tip twist |
|---|---|---|---|---|
| A: rectangular | 0.1600 m | 0.1600 m | 0° | 0° |
| B: tapered | 0.2560 m | 0.0640 m | 0° | 0° |
| C: washout | 0.1600 m | 0.1600 m | 0° | −3° |
First verify that the area of every candidate is unchanged. Run Analysis for the 12.0 m/s Cruise case and the 9.1 m/s Launch case. Check all four criteria for each candidate.
(b) Your design. None of the three candidates satisfy all of the criteria. Choose your own root chord, tip chord, and tip twist (still two stations, root twist 0°) that meets every criterion. For a linearly tapered wing with taper ratio \(\lambda = c_{tip}/c_{root}\), keeping the span and area fixed requires
\[c_{root} = \frac{2 S}{b (1 + \lambda)}, \qquad c_{tip} = \lambda c_{root}.\]You may need to iterate a few times. Report your final geometry, the values for all four criteria, and include the loading and section-lift plots for your design. Finally, run your design at the 16.0 m/s Fast case, verify that it still trims, and report its span efficiency and L/D.
Let’s again consider a large commercial airliner. In the last homework we estimated parasitic drag using some simplified methods. In flightlab the same method is used for fuselage-like objects, but for lifting surfaces we take a better route by integrating the drag across the surface using the airfoil analyses. We won’t go through those details here, but will just take the parasitic drag coefficient to be \({C_D}_p = 0.012\). This now includes the tails, nacelles, pylons, and markups, yet is only a little above the wing + fuselage estimate from the last homework because the fully turbulent assumption there was overly conservative. The rest of the specs are the same 787-like transport from HW 1, with a couple of additions:
| Quantity | Value |
|---|---|
| Mass | 230,000 kg |
| Altitude | 10,000 m |
| Mach number | 0.85 |
| Wing area | 377.0 m² |
| Span | 60.1 m |
| Quarter-chord sweep | 30° |
| Airfoil thickness-to-chord ratio | 0.12 |
| Parasitic drag coefficient | 0.012 |
Compute the (inviscid) induced drag coefficient, taking \(e_{inv} = 0.98\) (which, as you saw in the previous problem, is representative of a well-designed wing). Compute also the compressibility drag coefficient using the drag divergence and wave drag equations in the text. Compare the drag divergence Mach number to the cruise Mach number. Report the relative fraction of parasitic drag, induced drag, and compressibility drag.