Geração da geometria RAO é dividido em 2 partes:

1) Encontra thetan e thetas, que é o ângulo inicial 
e o ângulo final da parabola com base: no comprimento 60, 70, 80, 90 e 100% da tubeira de 15°
e na razão de expansão desejada.

2) Com base no raio da garganta, razão de expansão, percentual do divergente de 15°, nos ângulos 
encontrados (thetan e thetas) para a parabola e um passo espacial é construido o divergente



Tabela de DADOS da parte 1:

 s_rao rao[] = {
{'n',60,{{5,28.2895},{6.31579,29.7368},{7.63158,30.7895},{8.94737,31.7105},{10.2632,32.3684},{11.5789,33.0263},{12.8947,33.5526},{14.2105,33.9474},{15.5263,34.3421},{16.8421,34.7368},{18.1579,35},{19.4737,35.2632},{20.7895,35.5263},{22.1053,35.7895},{23.4211,36.0526},{24.7368,36.3158},{26.0526,36.4474},{27.3684,36.5789},{28.6842,36.8421},{30,36.9737},{31.3158,37.1053},{32.6316,37.2368},{33.9474,37.2368},{35.2632,37.3684},{36.5789,37.5},{37.8947,37.6316},{39.2105,37.7632},{40.5263,37.7632},{41.8421,37.8947},{43.1579,38.0263},{44.4737,38.0263},{45.7895,38.1579},{47.1053,38.1579},{48.4211,38.2895},{50,38.2895}}},
{'n',70,{{5,25.3947},{6.31579,26.1842},{7.63158,26.9737},{8.94737,27.6316},{10.2632,28.1579},{11.5789,28.8158},{12.8947,29.4737},{14.2105,30},{15.5263,30.3947},{16.8421,30.9211},{18.1579,31.3158},{19.4737,31.7105},{20.7895,31.9737},{22.1053,32.3684},{23.4211,32.6316},{24.7368,32.8947},{26.0526,33.0263},{27.3684,33.2895},{28.6842,33.4211},{30,33.5526},{31.3158,33.6842},{32.6316,33.8158},{33.9474,33.9474},{35.2632,33.9474},{36.5789,34.0789},{37.8947,34.2105},{39.2105,34.2105},{40.5263,34.3421},{41.8421,34.4737},{43.1579,34.4737},{44.4737,34.6053},{45.7895,34.6053},{47.1053,34.7368},{48.4211,34.7368},{50,34.7368}}},
{'n',80,{{5,22.6316},{6.31579,23.4211},{7.63158,24.2105},{8.94737,24.8684},{10.2632,25.5263},{11.5789,26.1842},{12.8947,26.7105},{14.2105,27.2368},{15.5263,27.7632},{16.8421,28.2895},{18.1579,28.6842},{19.4737,29.0789},{20.7895,29.3421},{22.1053,29.6053},{23.4211,29.8684},{24.7368,30.1316},{26.0526,30.2632},{27.3684,30.5263},{28.6842,30.6579},{30,30.7895},{31.3158,30.9211},{32.6316,31.0526},{33.9474,31.1842},{35.2632,31.3158},{36.5789,31.4474},{37.8947,31.4474},{39.2105,31.5789},{40.5263,31.7105},{41.8421,31.7105},{43.1579,31.8421},{44.4737,31.8421},{45.7895,31.9737},{47.1053,31.9737},{48.4211,32.1053},{50,32.1053}}},
{'n',90,{{5,21.0526},{6.31579,21.8421},{7.63158,22.6316},{8.94737,23.2895},{10.2632,23.8158},{11.5789,24.4737},{12.8947,25},{14.2105,25.5263},{15.5263,26.0526},{16.8421,26.4474},{18.1579,26.8421},{19.4737,27.2368},{20.7895,27.6316},{22.1053,27.8947},{23.4211,28.1579},{24.7368,28.4211},{26.0526,28.6842},{27.3684,28.9474},{28.6842,29.0789},{30,29.2105},{31.3158,29.3421},{32.6316,29.4737},{33.9474,29.6053},{35.2632,29.7368},{36.5789,29.7368},{37.8947,29.8684},{39.2105,30},{40.5263,30},{41.8421,30.1316},{43.1579,30.1316},{44.4737,30.2632},{45.7895,30.2632},{47.1053,30.3947},{48.4211,30.5263},{50,30.5263}}},
{'n',100,{{5,19.8684},{6.31579,20.6579},{7.63158,21.3158},{8.94737,21.9737},{10.2632,22.5},{11.5789,23.0263},{12.8947,23.5526},{14.2105,23.9474},{15.5263,24.3421},{16.8421,24.7368},{18.1579,25.1316},{19.4737,25.5263},{20.7895,25.7895},{22.1053,26.1842},{23.4211,26.4474},{24.7368,26.7105},{26.0526,26.9737},{27.3684,27.2368},{28.6842,27.5},{30,27.6316},{31.3158,27.8947},{32.6316,28.0263},{33.9474,28.1579},{35.2632,28.2895},{36.5789,28.5526},{37.8947,28.6842},{39.2105,28.8158},{40.5263,28.8158},{41.8421,28.9474},{43.1579,29.0789},{44.4737,29.0789},{45.7895,29.2105},{47.1053,29.2105},{48.4211,29.3421},{50,29.3421}}},
{'s',60,{{5,19.8684},{6.31579,18.9474},{7.63158,18.1579},{8.94737,17.5},{10.2632,16.9737},{11.5789,16.5789},{12.8947,16.0526},{14.2105,15.7895},{15.5263,15.5263},{16.8421,15.2632},{18.1579,15},{19.4737,14.7368},{20.7895,14.4737},{22.1053,14.3421},{23.4211,14.0789},{24.7368,13.9474},{26.0526,13.8158},{27.3684,13.6842},{28.6842,13.5526},{30,13.4211},{31.3158,13.4211},{32.6316,13.2895},{33.9474,13.1579},{35.2632,13.1579},{36.5789,13.0263},{37.8947,13.0263},{39.2105,13.0263},{40.5263,12.8947},{41.8421,12.8947},{43.1579,12.8947},{44.4737,12.8947},{45.7895,12.8947},{47.1053,12.8947},{48.4211,12.8947},{50,12.8947}}},
{'s',70,{{5,16.4474},{6.31579,15.5263},{7.63158,14.8684},{8.94737,14.3421},{10.2632,13.9474},{11.5789,13.4211},{12.8947,13.1579},{14.2105,12.7632},{15.5263,12.5},{16.8421,12.2368},{18.1579,12.1053},{19.4737,11.8421},{20.7895,11.7105},{22.1053,11.4474},{23.4211,11.3158},{24.7368,11.1842},{26.0526,11.0526},{27.3684,10.9211},{28.6842,10.7895},{30,10.6579},{31.3158,10.5263},{32.6316,10.5263},{33.9474,10.3947},{35.2632,10.2632},{36.5789,10.2632},{37.8947,10.2632},{39.2105,10.1316},{40.5263,10.1316},{41.8421,10.1316},{43.1579,10.1316},{44.4737,10},{45.7895,10},{47.1053,10},{48.4211,10},{50,10}}},
{'s',80,{{5,13.4211},{6.31579,12.5},{7.63158,11.8421},{8.94737,11.1842},{10.2632,10.7895},{11.5789,10.3947},{12.8947,10},{14.2105,9.73684},{15.5263,9.60526},{16.8421,9.47368},{18.1579,9.21053},{19.4737,9.21053},{20.7895,9.07895},{22.1053,8.94737},{23.4211,8.94737},{24.7368,8.81579},{26.0526,8.68421},{27.3684,8.68421},{28.6842,8.55263},{30,8.55263},{31.3158,8.42105},{32.6316,8.42105},{33.9474,8.28947},{35.2632,8.28947},{36.5789,8.15789},{37.8947,8.15789},{39.2105,8.02631},{40.5263,8.02631},{41.8421,7.89474},{43.1579,7.89474},{44.4737,7.89474},{45.7895,7.76316},{47.1053,7.76316},{48.4211,7.63158},{50,7.63158}}},
{'s',90,{{5,11.1842},{6.31579,10.3947},{7.63158,9.60526},{8.94737,8.94737},{10.2632,8.55263},{11.5789,8.15789},{12.8947,7.89474},{14.2105,7.76316},{15.5263,7.63158},{16.8421,7.5},{18.1579,7.5},{19.4737,7.36842},{20.7895,7.36842},{22.1053,7.36842},{23.4211,7.23684},{24.7368,7.23684},{26.0526,7.23684},{27.3684,7.10526},{28.6842,7.10526},{30,7.10526},{31.3158,6.97368},{32.6316,6.97368},{33.9474,6.8421},{35.2632,6.8421},{36.5789,6.8421},{37.8947,6.71053},{39.2105,6.71053},{40.5263,6.71053},{41.8421,6.57895},{43.1579,6.57895},{44.4737,6.44737},{45.7895,6.44737},{47.1053,6.44737},{48.4211,6.31579},{50,6.31579}}},
{'s',100,{{5,8.68421},{6.31579,7.89474},{7.63158,7.23684},{8.94737,6.8421},{10.2632,6.31579},{11.5789,6.05263},{12.8947,5.92105},{14.2105,5.78947},{15.5263,5.65789},{16.8421,5.65789},{18.1579,5.52631},{19.4737,5.52631},{20.7895,5.52631},{22.1053,5.39474},{23.4211,5.39474},{24.7368,5.39474},{26.0526,5.26316},{27.3684,5.26316},{28.6842,5.26316},{30,5.26316},{31.3158,5.13158},{32.6316,5.13158},{33.9474,5.13158},{35.2632,5},{36.5789,5},{37.8947,4.86842},{39.2105,4.86842},{40.5263,4.86842},{41.8421,4.73684},{43.1579,4.73684},{44.4737,4.73684},{45.7895,4.60526},{47.1053,4.60526},{48.4211,4.60526},{50,4.60526}}} };


O índice 'n' é o ângulo de início da parábola e 's' é do ângulo de saída.
O primeiro valor é o da razão de expansão e o segundo é o do ângulo em graus


Cálculo da parte 2:

A tubeira é dividia em 3 partes, um raio de arredondamento no convergente, outro no divergente e uma 
parábola

  R1 = 1.5*Rt;
  R2 = 0.382*Rt;
  Re = sqrt(epsilon)*Rt;
  x0 = -sqrt(2.0)*R1/2.0;
  tn = thetan * M_PI / 180.0;
  ts = thetas * M_PI / 180.0;
  ttn = tan(tn);
  tts = tan(ts);
  alpha15 = 15.0 * M_PI / 180.0;
  leng = Rt * (sqrt(epsilon)-1.0);
  leng = leng + R1*((1.0/cos(alpha15))-1.0);
  leng = leng / tan(alpha15);
  lengf = (leng * Lf / 100.0);
  xn = R2*cos(M_PI_2 - tn);
  yn = Rt+R2-R2*sin(M_PI_2 - tn);
  xe = lengf - xn;
  ye = Re - yn;
  P = (ye*ttn + ye*tts - 2*xe*tts*ttn) / (2*ye - xe*ttn - xe*tts);
  S = (sqr(ye-P*xe)*(ttn-P)) / (xe*ttn-ye);
  Q = -S / (2*(ttn-P));
  T = Q*Q;


  // primeiro arco de circulo
-- de x = x0 até x = 0
  função:
  y = Rt + R1 - sqrt(R1**2-x**2);

  // segundo arco de circulo
-- de x = 0 até xn
  função:
    y = Rt + R2 - sqrt(R2**2-x**2);

  // parábola
-- de x = xn até lengtf-xn
  funções:
  ppasso = (lengf-xn) / ipasso;
    x = xp + xn;
    y = P*xp + Q + sqrt(S*xp+T) + yn;