Needs:
Optional:
DCM vs CCM
Want lower losses, thus CCM > DCM
CCM more complicated but should fit needs
Misc flyback math articles
Choose $D=0.5$ duty cycle of 50%
$V_{out}=12V$
$V_{in}=[400V,600V]$
$I_{out}=1A$
Operation mode desired: CCM
Relation between windings and voltage for a transformer
In this case, $V_p=V_{in}$ but $V_s \ne V_{out}$, instead $V_s=V_f+V_{out}$ where $V_f$ is the forward voltage across the diode
$$ \frac{N_p}{N_s}=\frac{V_p}{V_s} $$
$$ \frac{N_p}{N_s}=\frac{V_p}{V_s}=\frac{V_{in}}{V_f+V_{out}} $$