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In this paper we study the morphological properties of spiral galaxies,including measurements of spiral arm number and pitch angle. Using Galaxy Zoo2, a stellar mass-complete sample of 6,222 SDSS spiral galaxies is selected. Weuse the machine vision algorithm SpArcFiRe to identify spiral arm features andmeasure their associated geometries. A support vector machine classifier isemployed to identify reliable spiral features, with which we are able toestimate pitch angles for half of our sample. We use these machine measurementsto calibrate visual estimates of arm tightness, and hence estimate pitch anglesfor our entire sample. The properties of spiral arms are compared with respectto various galaxy properties. The star formation properties of galaxies varysignificantly with arm number, but not pitch angle. We find that galaxieshosting strong bars have spiral arms substantially ($4-6^\mathrm{o}$) looserthan unbarred galaxies. Accounting for this, spiral arms associated withmany-arm structures are looser (by 2$^\mathrm{o}$) than those in two-armgalaxies. In contrast to this average trend, galaxies with greaterbulge-to-total stellar mass ratios display both fewer and looser spiral arms.This effect is primarily driven by the galaxy disc, such that galaxies withmore massive discs contain more spiral arms with tighter pitch angles. Thisimplies that galaxy central mass concentration is not the dominant cause ofpitch angle and arm number variations between galaxies, which in turn suggeststhat not all spiral arms are governed by classical density waves or modaltheories.

Galaxy Zoo and SpArcFiRe: Constraints on spiral arm formation mechanisms from spiral arm number and pitch angles