Maintaining certain conditions on a trail's surface is essential for a trail to function properly and serve its purpose of transporting hikers and other trail users. Understanding how trail design influences erosion and changes to the soil condition of a trail is critical to building and maintaining trails with sustainable surface conditions. Published practices for controlling water erosion on trails are based on hypotheses about length of slope and drainage area that are understudied or not studied at all. To test these hypotheses, this study applies the stream power equation to erosion on trails. This novel approach to multivariate modeling of trail design variables reveals that drainage area and length of slope have positive logarithmic effects on erosion. Trail slope was observed to have an exponential relationship with erosion when modeled independently of other variables, but a linear relationship with erosion when mediated by drainage area. Three on-trail soil conditions -- organic content, compaction, and particle size -- were measured along with design variables and erosion. Organic content showed the strongest correlation with these variables.