Nina del Ser - Mathematics
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| octopus
v s r s Ω p s
v p r p Ω p
v p 1
v s 1
Ω s 1
r s 0.5
Ω p 1
r p 1
figure 37
At some point in time, the two velocity vectors v p and v s will inevitably be parallel to each other,
either pointing in the same direction or in opposite directions to each other. In the first of these cases, the seat
will be traveling at maximum speed, whilst in the second, it will be going at minimum speed.
In order for loops to occur, the seat must, in a sense, travel “backwards”, since it needs to return to a
position (the point of intersection) in which it was several moments prior to that. This is only achievable when
the net velocity is negative, which can occur at the minimum value only when |v s |>|v p |. If |v s | |v p | the seat
will “freeze” in space momentarily when the two vectors oppose each other, resulting in a “�
spike”. The last
case, in which |v p |>|v s | should therefore produce curves that don’t loop or spike, instead follow smooth lines.
The following tests, in which angular speeds have been kept constant but rotor lengths have been altered in
order to increase or decrease the values of the velocity vectors, appear to support this hypothesis (Note that
these pictures are not at the same scale):
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