  We define a one-dimensional family of "Euler" stability conditions on
$\mathbb{P}^n$ which are conjectured to converge to Gieseker stability for
coherent sheaves. Here, we focus on ${\mathbb P}^3$, first identifying Euler
stability conditions with double-tilt stability conditions, and then we
consider moduli of one-dimensional sheaves, proving some asymptotic results,
boundedness for walls, and then explicitly computing walls and wall-crossings
for sheaves supported on rational curves of degrees $3$ and $4$.
