SPG:Running

Sonic Physics Guide
Basics Positions And Speeds Angles Variables Calculations (Technical) Pixel and Subpixel Hex Angles Characters Sonic Tails Knuckles
Collision
Solid Tiles (Terrain Part 1) Sensors Solid Terrain (Terrain Part 2) Layers Loops Slope Collision (Slopes Part 1) The Player's Sensors While Grounded 360 Degree Collision While Airborne Hitboxes The Player's Hitbox Trigger Areas Solid Objects Solid Objects Sloped Objects Jump Through Platforms Pushable Blocks Item Monitor
Physics
Slope Physics (Slopes Part 2) Moving Along Slopes 360 Degree Movement Falling and Slipping Down Slopes Landing On The Ground Air State Running Jumping Rolling Getting Hit Rebound Underwater Air Physics Super Speeds
Gameplay
Main Game Loop Game Objects Game Enemies Badniks Bosses Ring Loss Special Abilities Spindash Super Peel Out Drop Dash Insta-Shield Flying Gliding Climbing Elemental Shields Flame Shield Bubble Shield Lightning Shield Player 2 Player 2 CPU Respawning Special Stages Rotating Maze
Presentation
Camera Animations Animation System Variable Speed Animation Timings Normal Animation Timings Animation Rules
Special
Overlay Scripts Sonic 1 Overlay Sonic 2 Overlay

Notes:

• The research applies to all four of the Sega Mega Drive games and Sonic CD.
• The following describes physics that only apply when the Player has no special power-up and is not Underwater.

Constants

Constant	Value
acceleration_speed	0.046875 (12 subpixels)
deceleration_speed	0.5 (128 subpixels)
friction_speed	0.046875 (12 subpixels)
top_speed	6

Movement

All the characters - Sonic, Tails, and Knuckles - have the same acceleration_speed, deceleration_speed, top_speed, running and braking values. They handle identically, with no difference at all besides their special moves and their sprites (and the fact that Knuckles jumps lower than the other two).

Acceleration

If you're holding , Sonic's Ground Speed decreases by acceleration_speed every step. If you're holding (Also applies if you're holding , which you may not want in your engine), his Ground Speed increases by acceleration_speed every step.

Deceleration

If Sonic is already moving when you press or , rather than at a standstill, it's checked whether you are holding the direction he's already moving. If so, acceleration_speed is added to his Ground Speed as normal. However if you are pressing in the opposite direction than he's already moving, deceleration_speed is added instead, thus Sonic can turn around quickly.

At any time an addition or subtraction of deceleration_speed results in Ground Speed changing sign, Ground Speed is set to 0.5 (128 subpixels) in the opposite direction. For example, in the instance above, Ground Speed would become -0.5 (-128 subpixels). The bizarre result of this is that you can press for one step, and then press (or vice versa), and start running faster than if you had just pressed alone! Now, the resulting speed is still lower than 1 pixel per step, so it isn't very noticeable, but nonetheless it is true.

Friction

If you are not pressing or , friction kicks in. In any step in which the game receives no horizontal input, friction_speed is subtracted from (or added to, depending on the sign of Ground Speed) Ground Speed, where if it then passes over 0, it's set back to 0.

Top Speed

Sonic can only accelerate up to a certain point. At some point, he reaches top speed and can no longer move any faster under his own power. So, after acceleration_speed is added to Ground Speed, if Ground Speed exceeds top_speed it's set to top_speed.

In Sonic 1, while Sonic is already running at a higher speed than he can possibly achieve on his own (such as having been bounced by a Spring on a wall), if you press in the direction he's moving, acceleration_speed will be added to Ground Speed as usual. However, notice that Ground Speed now exceeds top_speed, which means Ground Speed will be set to top_speed. Thus it is possible to curtail your forward momentum by pressing in the very direction of your motion. This can be solved in your engine (and was fixed in Sonic 2 and beyond) by checking to see if Ground Speed is less than top_speed before adding acceleration_speed. Only if Ground Speed is already less than top will it check if Ground Speed exceeds top_speed.

Sonic CD and Sonic 2 actually has a fix like this, where the top_speed check won't happen if Ground Speed is already above top_speed, because in Sonic CD can perform the "Super Peel Out", which launches him above his typical top_speed, and in Sonic 2 because it's supposed to be a much faster game. The issue is, in both games, it doesn't fix this error when Sonic is in mid-air, causing him to usually lose his speed when running off of a ledge.

Here's some code logic that can accurately emulate movement and friction:

if (the player is pressing left)
{
    if (Ground Speed > 0) //if moving to the right
    {
        Ground Speed -= deceleration_speed;  //decelerate
        if (Ground Speed <= 0)
            Ground Speed = -0.5;  //emulate deceleration quirk
    }
    else if (Ground Speed > -top_speed) //if moving to the left
    {
        Ground Speed -= acceleration_speed;  //accelerate
        if (Ground Speed <= -top_speed)
            Ground Speed = -top_speed; //impose top speed limit
    }
}

if (the player is pressing right)
{
    if (Ground Speed < 0) //if moving to the left
    {
        Ground Speed += deceleration_speed; //decelerate
        if (Ground Speed >= 0)
            Ground Speed = 0.5; //emulate deceleration quirk
    }
    else if (Ground Speed < top_speed) //if moving to the right
    {
        Ground Speed += acceleration_speed; //accelerate
        if (Ground Speed >= top_speed)
            Ground Speed = top_speed; //impose top speed limit
    }
}

if (the player is not pressing left or right)
    Ground Speed -= minimum(absolute(Ground Speed), friction_speed) * sign(Ground Speed); //decelerate

Control Lock

The control lock timer is used to prevent left and right input from affecting the Player while they are on the ground. It is used (set to specific durations) when the Player slips or falls down a slope, and also when they bounce on a horizontal spring.

While this timer is non-zero and the Player is on the ground, it prevents directional input from adjusting the Player's speed with the or buttons.

When set, the control lock ticks down only when it is currently non-zero and while Sonic is on the ground, otherwise the timer remains paused. It does not affect air movement.

Notes

Note: In the original games, holding and at the same time will run both direction's code in one step, if you want in your engine, you can disable + input (Emulators like Fusion will just cancel the right input if left is also held).