I don't see how the speed would go up with the field winding not
connected.

It's a counterintuitive result, but to increase speed of a
DC motor you _reduce_ the field strength.  That's why an
unloaded series-wound motor will spin itself to destruction,
there's not enough mechanical load to soak up the energy,
and the field strength goes down as the back-emf of the
spinning armature goes up (with RPM).  It's a runaway
cycle.

Series-wound motors are fairly rare.  Parallel-wound, or
series-parallel wound are more common.

-- Jim



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