Stellar engines, megastructures used to control the motion of a star system, may be constructible by technologically advanced civilizations and used to avoid dangerous astrophysical events or transport a star system into proximity with another for colonization. This work considers two designs for stellar engines, for both human applications in the solar system and for advanced civilizations around arbitrary stars more generally, and presents analytic calculations of the maximum acceleration and deflection of a star in its galactic orbit. The first is a large 'passive' solar sail, similar to that proposed by Shkadov, which we find produces accelerations of order 10-12m /s2 for sun-like stars. The second 'active' engine uses a thermonuclear driven jet, as in a Bussard ramjet, which collects matter from the solar wind to drive He fusion. This engine requires additional mass to be lifted from the sun, beyond what is provided by the nascent solar wind, but may achieve accelerations up to 10-9m /s2 producing deflections of 10 pc in as little as 1 Myr for a sun-like star. While passive engines may be insufficient for catastrophe avoidance on short timescales, they can produce arbitrary deflections of a star in its galactic orbit over a stellar lifetime. Active engines are sufficient for retrograde galactic orbits or galactic escape trajectories, which we argue are useful to expansionist civilizations. These populations of stars may be candidates for observationally detecting megastructures.