Proportional navigation (also known as PN or Pro-Nav) is a guidance law (analogous to proportional control) used in some form or another by most homing air target missiles. It is based on the fact that two vehicles are on a collision course when their direct line-of-sight does not change direction as the range closes. PN dictates that the missile velocity vector should rotate at a rate proportional to the rotation rate of the line of sight (Line-Of-Sight rate or LOS-rate), and in the same direction. Where is the acceleration perpendicular to the missile's instantaneous velocity vector, is the proportionality constant generally having an integer value 3-5 (dimensionless), is the line of sight rate, and V is the closing velocity. Since the line of sight is not in general co-linear with the missile velocity vector, the applied acceleration does not necessarily preserve the missile kinetic energy. In practice, in the absence of engine throttling capability, this type of control may not be possible. Proportional navigation can also be achieved using an acceleration normal to the instantaneous velocity difference: where is the rotation vector of the line of sight: and is the target velocity relative to the missile and is the range from missile to target. This acceleration depends explicitly on the velocity difference vector, which may be difficult to obtain in practice. By contrast, in the expressions that follow, dependence is only on the change of the line of sight and the magnitude of the closing velocity. If acceleration normal to the instantaneous line of sight is desired (as in the initial description), then the following expression is valid: If energy conserving control is required (as is the case when only using control surfaces), the following acceleration, which is orthogonal to the missile velocity, may be used: A rather simple hardware implementation of this guidance law can be found in early AIM-9 Sidewinder missiles. These missiles use a rapidly rotating parabolic mirror as a seeker. Simple electronics detect the directional error the seeker has with its target (an IR source), and apply a moment to this gimballed mirror to keep it pointed at the target. Since the mirror is in fact a gyroscope it will keep pointing at the same direction if no external force or moment is applied, regardless of the movements of the missile. The voltage applied to the mirror while keeping it locked on the target is then