For many virtual reality applications, a pre-calculated fly-through path is the de facto standard navigation method. Such a path is convenient for users and ensures coverage of critical areas throughout the scene. Traditional applications use constant camera speed, allow for fully user-controlled manual speed adjustment, or use automatic speed adjustment based on heuristics from the scene. We introduce two novel methods for constrained path navigation and exploration in virtual environments which rely on the natural orientation of the user's head during scene exploration. Utilizing head tracking to obtain the user's area of focus, we perform automatic camera speed adjustment to allow for natural off-axis scene examination. We expand this to include automatic camera navigation along the pre-computed path, abrogating the need for any navigational inputs from the user. Our techniques are applicable for any scene with a pre-computed navigation path, including medical applications such as virtual colonoscopy, coronary fly-through, or virtual angioscopy, and graph navigation. We compare the traditional methods (constant speed and manual speed adjustment) and our two methods (automatic speed adjustment and automatic speed/direction control) to determine the effect of speed adjustment on system usability, mental load, performance, and user accuracy. Through this evaluation we observe the effect of automatic speed adjustment compared to traditional methods. We observed no negative impact from automatic navigation, and the users performed as well as with the manual navigation.