From Sonic Retro
|Sonic Physics Guide
|0.0234375 (6 subpixels)
|0.125 (32 subpixels)
When the Player rolls into a ball by pressing on the directional pad, they can no longer accelerate. No matter how hard or how long you press in the direction of their motion, they'll behave as if you weren't doing a thing. The only thing that happens in this case is friction, which is roll_friction_speed, half the Player's regular friction (in Sonic 3K, Super Sonic's roll friction is hard-coded to always be half of the regular friction).
However, the Player can decelerate while rolling. If you hold in the opposite direction of their motion, Ground Speed will be slowed by roll_deceleration_speed each frame. Additionally, unlike normal walking, friction is still in effect while decelerating. So in effect, while decelerating, Ground Speed slows by roll_deceleration_speed + roll_friction_speed (0.1484375 (38 subpixels)) every frame.
Similar to the anomaly explained in Running, if absolute Ground Speed is less than that value (0.1484375 (38 subpixels)), when this value is subtracted, instead of just setting Ground Speed to 0, Ground Speed is set to 0.5 (128 subpixels) in the opposite direction. This means the Player can turn around while rolling, even though they can't accelerate.
Just because the Player cannot roll faster on their own, doesn't mean that a nice hill wouldn't give them some momentum (gaining speed on slopes is covered in Slope Physics). These hills and slopes can be used to roll at a very high speed. Just as with running though, the Player has a top speed cap when rolling as well, though this one is much higher than the former, reaching a top speed of 16. Unlike running however, the Player cannot surpass this speed cap by any means. If their X Speed reaches a point where it reaches 16, and tries to go higher, it will automatically be set to 16 instead. Notice how I said X Speed instead of Ground Speed, that's right, it caps the Player's global horizontal velocity, rather than their Ground Speed. This can cause the angle they are moving at to be incorrect compared to the angle they are supposed to be moving (though, floor collision will correct this for the Y axis, so the Player is never misaligned).
The result of all this is that the Player will be able to outrun the camera while in wall modes, but otherwise won't.
For a more fair limit, you can just cap the Ground Speed instead (before X Speed and Y Speed are set. You can also cap X Speed and Y Speed after to ensure it is enforced). That is, if you want the cap at all.
In Sonic 1, 2, and 3, the Player can't begin to roll unless absolute Ground Speed is greater than or equal to 0.5 (128 subpixels).
In Sonic and Knuckles (and Sonic 3 and Knuckles), this value is increased to 1. This is because the Player is allowed to crouch while their absolute Ground Speed is below 1, so they can perform moves such as the Spindash without needing to come to a full stop.
Also in Sonic and Knuckles, probably as a way to combat the anomaly associated with turning around while rolling in the previous games, the Player unrolls if absolute Ground Speed falls below 0.5 (128 subpixels).
If the Player's Ground Speed happens to be 0 when they try to initiate a roll (usually impossible, but happens in some cases, for example slowing to a stop in an S Tunnel, and being forced to keep rolling), their Ground Speed will be set to 2.
In Sonic 1, 2, 3, and Knuckles, you can't control the Player's trajectory through the air with the buttons if you jump while rolling. Though, in Sonic 3 and in Sonic & Knuckles, you can regain control of the directional keys if you perform a Insta-Shield, or any other jump ability.
However, in Sonic CD and Mania, you can control a jump made while rolling, as if it were a totally normal jump.