Tool 6 · Advanced Control Systems

Guidance Law Simulator

Explore two important guidance ideas: proportional navigation for intercept problems and gravity-turn guidance for launch/ascent intuition. This tool connects control laws to trajectory shaping, closing speed, commanded acceleration, pitch program, and flight-path evolution.

What this tool computes

Guidance laws convert mission objectives into steering commands. This page provides two educational modes: an intercept problem using proportional navigation and a simplified launch gravity-turn simulation.

Proportional navigation intercept trajectory
Line-of-sight rate and commanded lateral acceleration
Miss distance and intercept time
Gravity-turn trajectory and altitude history
Pitch angle, velocity, and downrange evolution

Proportional navigation

Proportional navigation commands acceleration proportional to closing speed and line-of-sight rate:

\[ a_c = N V_c \dot{\lambda} \]

The navigation constant \(N\) usually controls how aggressively the chaser turns toward the intercept geometry.

Gravity-turn intuition

A gravity turn begins with a vertical climb, then a small pitch-over allows gravity and velocity direction to bend the trajectory naturally.

\[ \dot{v} \approx \frac{T-D}{m}-g\sin\gamma \] \[ \dot{\gamma} \approx -\frac{g\cos\gamma}{v} \]

The simulator is simplified, but it shows why pitch-over timing strongly affects downrange distance, altitude, and flight-path angle.

Engineering interpretation

Guidance laws shape trajectory; controllers execute the commands.
PN is useful for intercept and pursuit-style guidance concepts.
Gravity-turn planning links launch trajectory, pitch program, and energy management.
Both examples show why timing matters in GNC.

Educational simplification

This page is for learning. It does not include full 6DOF aerodynamics, actuator limits, sensor noise, Earth rotation, staging, orbital insertion constraints, or certified flight software logic.

Interactive guidance simulator

Guidance mode

Select PN for intercept guidance or gravity turn for launch/ascent guidance intuition.

Chaser and target initial states

Chaser x (m)

Chaser y (m)

Target x (m)

Target y (m)

Chaser speed (m/s)

Target vx (m/s)

Target vy (m/s)

Navigation constant N

Max lateral accel (m/s²)

Initial heading (deg)

Thrust (kN)

Initial mass (kg)

Mass flow (kg/s)

Pitch kick (deg)

Pitch kick time (s)

Drag strength

Launch duration (s)

Gravity (m/s²)

Scenario preset

Presets switch the mode and fill relevant inputs automatically.

PN simulation duration (s)

Time step (s)

Results

Primary outcome

—

Final / closest range

—

Peak command

—

Final speed

—

Final altitude

—

Final flight path / heading

—

Interpretation

Run a guidance simulation to see trajectory shaping and command history.

Trajectory

Guidance command / pitch history

Range or altitude history

Assumptions and limitations

This simulator assumes:

2D planar guidance examples
Simplified point-mass dynamics
Ideal command response
No sensor delay, actuator dynamics, or closed-loop autopilot lag
Gravity-turn model is conceptual, not launch-vehicle design software

← Back to Tools