it was derived. Some consider this a testament to the robustness of Fitts's law. In its general form, the steering law can be expressed as where T is the average time to navigate through the path, C is the path parameterized by s, W(s) is the width of the path at s, and a and b are experimentally fitted constants. In general, the path may have a complicated curvilinear shape (such as a spiral) with variable thickness W(s). Simpler paths allow for mathematical simplifications of the general form of the law. For example, if the path is a straight tunnel of constant width W, the equation reduces to where A is the length of the path. We see, especially in this simplified form, a speed–accuracy tradeoff, somewhat similar to that in Fitts's law. We can also differentiate both sides of the integral equation with respect to s to obtain the local, or instantaneous, form of the law: which says that the instantaneous speed of the user is proportional to the width of the tunnel. This makes intuitive sense if we consider the analogous task of driving a car down a road: the wider the road, the faster we can drive and still stay on the road, even if there are curves in the road. Derivation of the model from Fitts's law This derivation is only meant as a high level sketch. It lacks the illustrations of, and may differ in detail from, the derivation given by Accot and Zhai (1997). Assume that the time required for goal passing (i.e. passing a pointer through a goal at distance A and of width W, oriented perpendicular to the axis of motion) can be modeled with this form of Fitts's law: Then, a straight tunnel of length A and constant width W can be approximated as a sequence of N evenly spaced goals, each separated from its neighbours by a distance of A/N. We can let N grow arbitrarily large, making the distance between successive goals become infinitesimal. The total time to navigative through all the goals, and thus through the tunnel, is Note that b is an experimentally fitted constant and let . Therefore, Tstraight tunnel = . Next, consider a curved tunnel of total length A, parameterized by s varying from 0 to A. Let W(s) be the variable width of the tunnel. The tunnel can be approximated as a sequence