Physics in flight simulators

Why fly in a simulator first

Testing new software or a new mission on a real drone is risky. A mistake can crash the drone, damage it or endanger people. A flight simulator lets you try things any number of times with no risk: training pilots, testing autonomous missions and tuning control systems.

But a simulator is only as accurate as the physics inside it. This module opens it up to see what it computes, using Modules 1–4 and the calculus from DRT 111.

What a simulator computes

A simulator runs a loop hundreds to thousands of times per second.

1. State holds the current position, velocity, attitude and rotation rates.
2. The force model computes all forces and moments from the current state: thrust, weight, drag and wind.
3. Integration in time uses Newton’s second law to find acceleration, then computes the new state after $\Delta t$.
4. Simulated sensors and autopilot produce what the IMU, GNSS and barometer should read, with noise. The autopilot computes new motor commands and the loop returns to step 1.

Stepping forward with the Euler method

The simplest method is the Euler method, which assumes acceleration and velocity stay constant over a short interval $\Delta t$:

Drag and terminal velocity

Air drag on a whole drone can be approximated by

where $C_{D}A$ is the effective drag area. As an object falls, drag rises with speed until it equals weight and speed stops increasing. This is the terminal velocity:

SITL and HITL

Both ArduPilot and PX4 include SITL and connect to 3D simulators such as Gazebo. You will keep using SITL in DRT 226, DRT 334 and DRT 335.

When simulation and reality disagree

The gap between simulation and reality has several causes:

• Thrust and efficiency curves in the model do not match the real motors and propellers.
• Battery voltage sag, covered in Module 4, is often not modelled.
• Gusts and turbulence are more complex in reality.
• Ground effect: within about one rotor diameter of the ground, thrust increases.
• Sensor noise and delay differ from the settings.

To validate a model, compare flight logs from simulation and real flight on the same mission: hover power, climb rate and response to commands. Then adjust the model parameters to bring them closer.

Module lab

Common mistakes

Summary

• A simulator loops through state, forces, integration, and sensors with a controller.
• The Euler method computes $v_{k+1}=v_k+a\Delta t$ and $h_{k+1}=h_k+v_k\Delta t$; smaller steps are more accurate.
• Drag $D=\frac{1}{2}\rho C_{D}A{v}^2$ and terminal velocity $v_t=\sqrt{2mg/(\rho C_{D}A)}$.
• SITL runs the software on a computer; HITL uses real hardware with simulated sensors.
• Always validate simulation results against real flight logs.

Check your understanding

1. A 1 kg drone has 12 N of thrust, ignoring drag. What is its vertical acceleration?
2. Using Euler with $\Delta t=0.5$ s and the acceleration from question 1, find the velocity at $t=1$ s.
3. If $C_{D}A$ doubles, by what factor does terminal velocity change?
4. To test firmware on a real flight-controller board without flying, would you use SITL or HITL?
5. Give two reasons why simulated flight time might be longer than real flight time.