  The prospects of superradiant lasing on the 7.5 kHz wide $^1$S$_0$-$^3$P$_1$
transition in $^{88}$Sr is explored by using numerical simulations of two
systems based on realistic experimental numbers. One system uses the idea of
demonstrating continuous superradiance in a simple, hot atom beam with high
flux, and the other system is based on using ultra-cold atoms in a dipole
guide. We find that the hot beam system achieves lasing above a flux of $2.5
\times 10^{12}$ atoms/s. It is capable of outputting hundreds of nW and
suppressing cavity noise by a factor of 20-30. The second order Doppler shift
causes a shift in the lasing frequency on the order of 500 Hz. For the cold
atom beam we account for decoherence and thermal effects when using a repumping
scheme for atoms confined in a dipole guide. We find that the output power is
on the order of hundreds of pW, however the second order Doppler shift can be
neglected, and cavity noise can be suppressed on the order of a factor 50-100.
Additionally we show that both systems exhibit local insensitivity to
fluctuations in atomic flux.
