Proportional navigation

In 2D, such as a planar engagement, pure proportional navigation can be represented as: and is given by: : \vec a = -N|\vec V_r|\frac{\vec R} \times \vec \Omega If energy conserving control is required (as is the case when only using control surfaces), the following acceleration, which is normal to the missile velocity, may be used: : \vec a = -N|\vec V_r|\frac{\vec V_m} \times \vec \Omega == Variants ==

No guidance law is optimal in all situations. Optimal missile guidance requires accurately predicting the target's behavior. Since this is generally not possible, proportional navigation has been adapted into a variety of guidance laws to improve its flexibility. Other guidance laws, especially ones designed using optimal control theory, may outperform proportional navigation under specific assumptions. == In biology ==

Holcocephala fusca and Coenosia attenuata are two species of predatory flies that use proportional navigation to reach their prey. The former uses N ≈ 3 with a time delay of ≈ 28 ms, which is suitable for its long-range intercepts and minimizes the control effort required. The latter uses N ≈ 1.5 with a time delay of ≈ 18 ms, which is adapted to its short-range hunts and helps reduce overcompensation. A guidance law resulting in motion camouflage is used by a number of predator species. By setting up the chase so that the predator either appears stationary relative to the background while growing larger (real-point motion camouflage), or always appears at a fixed bearing (infinite-point motion camouflage), the predator reduces its chance of being detected. Such a guidance law is also mathematically related to proportional navigation and similarly provides an efficiency benefit over pure pursuit guidance. The infinite-point case (or "parallel navigation") can be viewed as pure proportional navigation with a distance-dependent N. ==See also==