Proportional navigation is a method of homing navigation used by most homing air target missiles. It depends on the fact that two vehicles are on a collision path when their missile turn rate is directly proportional to the turn rate in space of the line of sight.

a_{n} - Missile velocity vector
N - is the PN constant
λ - is the line of sight rate
V - is the velocity.
R - Rotate vector
Ω - Line of sight
a^{->} - Relative velocity

An antenna provides the line of sight rate at 28 meters with the Proportionality constant value (N) 20, velocity 20 and rotate vector 40.Calculate the missile velocity vector of the antenna, rotation vector and the relative velocity.

Proportionality constant value N = 20
Line of sight rate λ = 28 meters
Velocity V_{m} = 20
Rotate vector R = 40

Missile velocity vector a_{n}
Rotation vector of the line of sight Ω
Relative velocity a^{->}

Calculate the value of Missile velocity vector (a_{n})
a_{n} = N x λ x V
= 20 x 28 x 20
= 11200

Calculate the value of Rotation vector of the line of sight Ω
Ω= V x R / R^{2}
= 20 x 40 / 402
= 800 / 402
= 0.5

Calculate the value of Relative velocity a^{->}
a^{->} = N x V x Ω
= 20 x 20 x 0.5
= 200

Learn how to calculate the Missile velocity vector and Acceleration in this tutorial, given with the definition, formula and example.