Matrix Games

 Hi, everyone, this is Jon, the nerdy guy from the whiteboard drawings in the Scramble Flight School videos. I sat down to compose this dev log several times over the past couple weeks and have struggled to find a level of detail that both satisfies my engineering sensibilities but is also digestible for anyone without an aerospace background. I settled on a post that I hope explains and excites the bulk of you, but one I certainly wouldn’t share with my old professors; I’ll let the aerodynamicists in our audience take it up with me on the Scramble Discord server; I hope you enjoy :) 

Tap here to read the news about Episode #3 part 1
 

Scramble: Battle of Britain - Flight School, Episode #3 (part 2)

The Flight Physics of Scramble

The Scramble engine simulates aerial combat in six degrees of freedom with analog flight physics, projectile dynamics, and subsystem damage modeling. Though Scramble gameplay is turn-based, its physics integrate in real-time, broken into two-second chunks, and its axis-based control inputs allow players to pilot aircraft with a precision and fidelity not previously offered in turn-based dogfighting games. 

Aerodynamics Forces

Scramble considers five main forces acting on each aircraft: 

Thrust is provided by engines and propellers, and is generally oriented axially out the nose of the aircraft. Thrust is generally a function of engine throttle and airspeed. In steady, level flight thrust balances drag.

Lift is defined as the force operating perpendicular to aircraft velocity in the plane made by the aircraft velocity and canopy, and it generally acts in a direction upward, through the canopy, relative to the aircraft wings. Lift is generally a function of angle of attack - the pitch of the aircraft body relative to its velocity - and airspeed. In steady, level flight lift balances gravity.

Side force is defined as the force operating perpendicular to aircraft velocity in the plane made by the aircraft velocity and the aircraft wing axis, and side force generally acts laterally (to the side) of the aircraft body, roughly in the direction of the left or right wing of the aircraft. Side force is generally a function of angle of sideslip - the yaw of the aircraft body relative to its velocity - and airspeed. In steady, level flight side force is nullified to zero.

Drag is defined as the force opposing an aircraft’s travel through the air, and is applied in opposition to the aircraft velocity. Drag is a complex force, a catch-all definition for any forces slowing the aircraft down, but is generally a dominated by angle of attack, angle of slideslip, and airspeed. In steady, level flight drag balances thrust.

Gravity acts in a constant direction and with a constant acceleration, pulling the aircraft toward the center of the Earth. In steady, level flight gravity balances lift. 

Equations of Motion

Equations of Motion are the physics equations that define the movement and rotation of a body through space - in the case of Scramble, through three-dimensional space. 

The standard Newtonian equations of motion are driven by Newton’s Second Law of Physics, that the force acting on a body is equal to the mass of the body times the resulting acceleration: F = mA. In Scramble I am very interested in Accelerations: integrating Acceleration over a Timestep yields the change in Velocity of a body, and integrating the Velocity of a body over a Timestep yields the change in Position of that body. 

If I know the Accelerations on an aircraft I can move it through space, and I made a decision early in Scramble development to make the simplifying assumption that I could define Scramble physics in terms of accelerations rather than in terms of forces. This decision allowed me to ignore aircraft mass, which for any individual aircraft remains essentially constant throughout a dogfight, and it allowed me to directly compare the performance of two aircraft without performing any math: an aircraft capable of 7Gs of acceleration (7 times the force of gravity) can turn more tightly than an aircraft capable of 5Gs of acceleration. 

Scramble Aerodynamics Coefficients

Aircrafts in Scramble have elevators, rudders, ailerons and throttles, all of which actuate through a full axis of control and which drive the aircraft angles of attack and sideslip, roll rate, and thrust acceleration. Aircraft aerodynamics in Scramble are built from coefficients that vary with airspeed and the control inputs previously mentioned. 

The Aerodynamics Coefficients are defined as one-dimensional curves, and multiple coefficients may contribute to the computation of each of the major Accelerations, for example: 

Lift is broken into coefficients for Pitch and Airspeed. 

Drag is broken into coefficients for Pitch, Yaw, and Airspeed. 

Accelerations are integrated to determine aircraft Velocity, and body Orientation is calculated as a function of Velocity and a tracked Roll angle. Scramble makes the assumption that aircraft control inputs drive Pitch and Yaw angles relative to the aircraft velocity (angles of attack and sideslip, respectively), but Roll angle is tracked independently, and Roll Rate is calculated from a coefficient broken into Roll Input and Yaw Input terms. 

Aircraft Definitions & Performance

Every Scramble aircraft is defined as a table of aerodynamics coefficients curves. This table determines the nominal performance envelope of an aircraft and it allows me to compare rough accelerations, level airspeed, and roll rates between different aircraft. 

Scramble is a game that prioritizes the essence of performance differences between airplanes rather than raw numerical differences, so the assumptions I have made in our physics modeling simplify the gameplay balance process in a way that keeps me focused on applied performance of aircraft: turn rates, roll rates, turn radii, dive accelerations, climb performance, etc. 

Another benefit is that when I want to model new flight phenomena, like stalling, I am inherently defining the impact those phenomena have on the acceleration and rotation rates directly; this point might get lost in the weeds of this pretty dense physics article, but hopefully it garners some sympathy from those of you who have worked yourselves with forces and moments and mass properties and the delicate balance required to move objects of that fidelity through space.

The final benefit to the Scramble aerodynamics coefficients system is that it has allowed me to create simple coefficient-based definitions for the aerodynamics impacts of subcomponent damage like lost control surfaces, leaking fuel systems, or broken wings. I’m excited to elaborate on Scramble damage modeling in a future dev log. 

Godspeed.

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