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 :) https://store.steampowered.com/news/app/1530450/view/4168717862241492487 [h1]Scramble: Battle of Britain - Flight School, Episode #3 (part 2)[/h1] [h3]The Flight Physics of Scramble[/h3] 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. [h3]Aerodynamics Forces[/h3] Scramble considers five main forces acting on each aircraft: [i]Thrust[/i] is provided by engines and propellers, and is generally oriented axially out the nose of the aircraft. [i]Thrust[/i] is generally a function of engine throttle and airspeed. In steady, level flight [i]thrust[/i] balances [i]drag[/i]. [i]Lift [/i]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. [i]Lift[/i] is generally a function of angle of attack - the pitch of the aircraft body relative to its velocity - and airspeed. In steady, level flight [i]lift[/i] balances [i]gravity[/i]. [i]Side force[/i] is defined as the force operating perpendicular to aircraft velocity in the plane made by the aircraft velocity and the aircraft wing axis, and [i]side force[/i] generally acts laterally (to the side) of the aircraft body, roughly in the direction of the left or right wing of the aircraft. [i]Side force[/i] is generally a function of angle of sideslip - the yaw of the aircraft body relative to its velocity - and airspeed. In steady, level flight [i]side force[/i] is nullified to zero. [i]Drag[/i] 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 [i]angle of attack[/i], [i]angle of slideslip[/i], and [i]airspeed[/i]. In steady, level flight [i]drag[/i] balances [i]thrust[/i]. [i]Gravity[/i] acts in a constant direction and with a constant acceleration, pulling the aircraft toward the center of the Earth. In steady, level flight [i]gravity[/i] balances [i]lift[/i]. [h3]Equations of Motion[/h3] [i]Equations of Motion[/i] 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 [i]equations of motion[/i] are driven by Newton’s Second Law of Physics, that the [i]force[/i] acting on a body is equal to the [i]mass[/i] of the body times the resulting [i]acceleration[/i]: [i]F = mA[/i]. In Scramble I am [b]very[/b] interested in [i]Accelerations[/i]: integrating [i]Acceleration[/i] over a [i]Timestep[/i] yields the change in [i]Velocity[/i] of a body, and integrating the [i]Velocity[/i] of a body over a [i]Timestep[/i] yields the change in [i]Position[/i] of that body. If I know the [i]Accelerations[/i] 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. [h3]Scramble Aerodynamics Coefficients[/h3] 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 [i]Aerodynamics Coefficients[/i] are defined as one-dimensional curves, and multiple coefficients may contribute to the computation of each of the major [i]Accelerations[/i], for example: [i]Lift[/i] is broken into coefficients for [i]Pitch[/i] and [i]Airspeed[/i]. [i]Drag[/i] is broken into coefficients for [i]Pitch[/i], [i]Yaw[/i], and [i]Airspeed[/i]. [i]Accelerations[/i] are integrated to determine aircraft [i]Velocity[/i], and body [i]Orientation[/i] is calculated as a function of [i]Velocity[/i] and a tracked [i]Roll[/i] angle. Scramble makes the assumption that aircraft control inputs drive [i]Pitch[/i] and [i]Yaw[/i] angles relative to the aircraft velocity (angles of attack and sideslip, respectively), but [i]Roll[/i] angle is tracked independently, and [i]Roll Rate[/i] is calculated from a coefficient broken into [i]Roll Input[/i] and [i]Yaw Input[/i] terms. [h3]Aircraft Definitions & Performance[/h3] 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. [url=https://discord.gg/vt3GtGTytc][img]{STEAM_CLAN_IMAGE}/40512959/1c8255bee4c8d93ac649ada3d49296485d0ff7ae.jpg[/img][/url] [h3]Join our Discord server and don't miss any upcoming news on the game.[/h3] https://store.steampowered.com/app/1530450/Scramble_Battle_of_Britain/