One day, a small jet was flying over the concretist poem "Velocidade" (Speed), by the Brazilian poet Ronaldo Azeredo.
In order to cover every vowel present in this poem, it goes in straight line from one letter to another either orthogonally or diagonally adjacent, never making a turn sharper than 45 degrees*.
Assuming the letters are like points in a square lattice, and the jet travels at constant speed, what is the fastest way this can be achieved by the pilot?
Notice that no restrictions were placed in where the jet should start, except that its position goes from one letter to another. Also, the jet is not allowed to leave the matrix of letters.
* Measured by the external angle, i.e. deviation from the original path, so that a 0 degree turn leads to the same direction, while a 180 degree turn makes the jet go in the reverse.