Incorporate R: how to decide what R to use for manufacturing

[avikde]

Related to #88

Other than the aero correction, inertia works out as

• Izz = mw ycp^2 0
• Ixx = cbar^2 gamma^2 mwing -- should this not have R in it??

UPDATE: see #106 (comment)

Scaling for minal was assuming constant R

• but lift \propto R as well
• (see notes) - in 2D, R increase by factor α + T_2D decrease by α <-> dynamically equivalent in act coords

Conclusions

Aero correction: Notes on this are in the "Incorporate R" page in OneNote

• 4/3 for rect wing
• 1.265 for robobee wing

Included R in the param opt

• turns out long wing is favored
• use [Chen (2016)] to limit AR; inner polytope approx

[avikde]

Result with correction:

Having trouble getting good results from IPOPT after 1.9

[avikde]

After adding R as a param

Found R = 17.5 Opt minal=1.7, τ2/1 lim=2.0 => 0, [5.111 15.98 0.818 25.14 17.935 31.959 17.5 0.084], fHz=264.8, al[mg]=177.5, u∞=61.2, J=68.3

-> quite reasonable

• paramAffine not done yet

N, trajt, traj0, opt, avgLift0 = initTraj(KINTYPE; uampl=uampl, fix=true)
cu.affineTest(m, opt, traj0, param0, POPTS)

Master

2×45 Array{Float64,2}:
  6.66134e-16  3.9968e-15   -4.44089e-16  -8.88178e-16  …  -7.99361e-15  -3.9968e-15   4.21885e-15  -2.60902e-15
 -9.76996e-15  2.04281e-14   0.0           7.10543e-15     -2.4869e-14   -1.06581e-14  3.19744e-14  -3.9968e-14

New

2×45 Array{Float64,2}:
 -0.0308604  0.038468  0.0871819  0.123191  0.147851  0.157574  …  -0.0240836  -0.133683  -0.204164  -0.193012  -0.11419 
  0.17003    0.210992  0.385727   0.718308  0.955837  1.03008      -1.14466    -1.29701   -0.670145   0.28307    0.417038   

With R included in paramAffine it seems to pick the smallest R Opt minal=1.7, τ2/1 lim=2.0 => 0, [5.111 15.98 0.818 22.251 15.91 31.959 15.0 0.095], fHz=235.2, al[mg]=152.1, u∞=58.2, J=61.7

With Aw in paramAffine Opt minal=1.7, τ2/1 lim=2.0 => 0, [0.985 15.98 0.345 1.644 2.194 31.959 86.89 0.056], fHz=400.0, al[mg]=172.4, u∞=25.5, J=11.8

• was able to set much lower mw due to smaller cbar (and higher R)
• need to redo wing density constraint

[avikde]

Changing wing density constraint to between mw,Aw

Opt minal=1.7, τ2/1 lim=2.0 => 0, [0.1 15.98 0.869 0.308 0.388 31.959 86.89 0.085], fHz=260.4, al[mg]=172.4, u∞=43.6, J=34.6

[avikde]

RegionPlot[{Aw/cb^2 <= 4, -cb + 0.025 Aw <= -2.5}, {cb, 0.1, 10}, {Aw, 50, 150}]

Use this for now as an inner approx but need to do this analytically.

Opt minal=1.7, τ2/1 lim=2.0 => 0, [4.672 15.98 0.869 21.809 16.89 31.959 86.89 0.087], fHz=255.7, al[mg]=172.4, u∞=63.1, J=72.5 AR=4.0

[avikde]

scaling params

8×11 Adjoint{Float64,Array{Float64,2}}:
 4.6      15.9795  0.84      20.7856  16.7325  31.9591    84.0     0.0839263  59.7406  0.925322  6.10267
 4.6      15.9795  0.84      20.6473  16.7503  31.9591    84.0     0.0839263  59.7406  0.945053  6.10267
 4.67226  15.9795  0.868904  21.8085  16.8896  31.9591    86.8904  0.0869232  63.0525  0.834388  6.46755
 4.80004  15.9795  0.920016  24.9653  19.3748  31.9591    92.0016  0.0823686  69.0008  0.88494   7.07518
 4.92782  15.9795  0.971128  26.6531  19.7925  31.9591    97.1128  0.0873821  75.159   0.98834   7.74165
 5.0556   16.1096  1.02224   31.7771  24.0085  27.6225   102.224   0.0772203  81.4264  0.999956  8.35244
 5.18338  16.5636  1.07335   37.6247  28.9021  12.4899   107.335   0.0692057  87.5641  0.999991  8.91841
 5.31116  16.8172  1.12446   48.4617  38.7857   4.03822  112.446   0.0555556  93.5242  1.00001   9.65341