Below is a simple charging circuit using LM317 and BC547 and it is mostly classified as a float charger in many forums. This seems to reduce the current flow when the battery is fully charged, however does not turn off the charger completely. Hence can this be connected to SLA batteries indefinitely without affecting the battery life? or is this a trickle charger, which should be disconnected after charging.
By definition float charger will only turn on and charge your battery when it has self-discharged below a certain level, whereas a trickle charger continuously emits a small current of electricity regardless of the charge level or even if it's full. It is also mentioned that for SLA batteries, a float charger could be connected indefinitely where as the trickle chargers needs to be disconnected after charging.
simulate this circuit – Schematic created using CircuitLab
Updated components as per recommendation
Best Answer
When no battery is connected the circuit operates as a constant-voltage source having an output voltage of \$\mathrm{V_o=11\cdot 1.25V = 13.75VDC}\$ with zero current flow.
When a battery is connected, if the battery voltage is less than, say, 12V then the circuit will work as a constant-current source having a constant output current of \$\mathrm{I_o[A]=V_{BE-BC547}[mV]/470\approx1.5[A]}\$.
During the battery is charging the battery voltage will rise up to a point that the D1 gets reverse biased (Note: Charge current may drop as the battery voltage increases, but I'm not sure about that). So the circuit will switch its operating mode from constant current to constant voltage with zero current flow even if the battery is not removed.
So, this circuit fits in your "float charger" definition:
PS: The circuit may not work with 15V source since the LM317 requires a minimum difference of 3V between the input and output. For a source voltage of 18VDC and an output current of 1.5A, the LM317 will dissipate at least 7.5W. I'm sure you know what that means.