You may want to take a sharper look on a known working solenoid actuator. It's not just a coil with
ferromagnetic core. It's a magnetic circuit, that's usually closed, or at least reducing a gap when
actuated. The magnetic circuit is the secret of an effective solenoid actuator.
Of course you can also have a plain coil and a iron rod. But it's much weaker, because the flux isn't
concentrated in a magnetic circuit. In a graphic view, shortening the magnetic field lines (respectively
their path in the lower permeable material) causes the magnetic force.
To learn about achievable solenoid actuator properties, you can review some professional products, e.g.
**broken link removed**
You can also use magnetostatic field simulators to evaluate the behaviour of a particular actuator geometry,
e.g. Quickfield:
www.quickfield.com
They have tutorials dealing with actuators, if I remember right.