Proportional navigation has been proved to be a useful guidance technique in several surface-to-air and air-to-air homing systems for interception of airborne targets. Besides the familiar pure, true, and generalized proportional navigation guidance laws, a new guidance scheme, called ideal proportional navigation, with commanded acceleration applied in the direction normal to the relative velocity between interceptor and target, is presented. In this study the closed-form solutions of ideal proportional navigation are completely derived for maneuvering and nonmaneuvering targets, and some important characteristics related to the system performance are introduced. Under this scheme the capture criterion is related to the effective proportional navigation constant only, no matter where the initial condition and target maneuver are. With some more energy consumption, this new guidance scheme has a larger capture area and is much more effective than the other schemes. Nomenclature a = acceleration r = distance between interceptor and target T = total time of flight t = time of flight V = velocity v = relative velocity between interceptor and target F = gamma function 6 = angle between line of sight and inertial reference line X = effective proportional navigation constant (/) = angle between relative velocity and line of sight Subscripts c = commanded value / = final value M = missile, interceptor r = parallel to line of sight T = target z = normal to the intercept plane 0 = normal to line of sight 0 = initial value 1 = state at maximum r Superscript ' = time derivative

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