Proportional navigation

Two missiles on a collision course

Proportional navigation (also abbreviated to PN or Pro-Nav ) is a guidance method that is used in most modern guided missiles . It takes advantage of the fact that two objects moving linearly at constant speed are on a collision course if and only if the bearing does not change.

The course must therefore be corrected in such a way that the target can always be seen in the same direction in relation to your own missile (α and β constant in the image on the right). For this, the speed vector must change proportionally to the speed of rotation of the connecting line between the missile and the target.

${\displaystyle a_{n}=n{\dot {\lambda }}v_{m}}$

Here, the acceleration perpendicular to the velocity vector of the missile, is a dimensionless proportionality constant, the rotational speed of the connection line and the speed of the missile. ${\displaystyle a_{n}}$ ${\displaystyle n}$ ${\displaystyle {\dot {\lambda }}}$ ${\displaystyle v_{t}}$

In vector notation, the acceleration can be calculated as follows:

${\displaystyle {\vec {a}}=n{\vec {V}}_{m}\times {\vec {\Omega }}}$

with the speed of rotation of the connecting line : ${\displaystyle \Omega }$

${\displaystyle {\vec {\Omega }}={\frac {{\vec {V}}_{t}\times {\vec {R}}}{R^{2}}}}$

This simple principle was used in first generation guided missiles, e.g. B. in the AIM-9 Sidewinder , still implemented in analog technology . Modern missiles extend this process with algorithms for predicting the flight path of the target.

Individual evidence

1. ^ Neil F. Palumbo et al .: Basic Principles of Homing Guidance. (PDF; 3.4 MB) Accessed December 6, 2012 . 
2. ↑ George M. Siouris: Missile Guidance and Control Systems . ISBN 0-387-00726-1 .