Rotation

Rotation is used to describe the vehicle's orientation in 3D space.

Overview

Internally, the game uses quaternions and Euler angles to compute rotation. However, it is much more convenient to use the aircraft principal axes to describe the rotations and movement of the vehicle.

Yaw rotation describes the rotation around the Y (vertical) axis, along the XZ (horizontal) plane. A positive change in yaw represents rotation to the right, and vice-versa. Yaw 0 represents the cardinal direction south. Turning and drifting are common ways to affect yaw rotation on every vehicle.
It is important to make a distinction between facing and moving yaw. The first represents the direction that the vehicle is facing towards visually, while the latter is the actual direction of motion. These two values can diverge significantly, for example when the vehicle has a lot of EV, and during a drift for any outside-drifting vehicles. Notably, facing yaw determines the direction of motion after a wallclip.

Pitch rotation describes the rotation around the X axis, along the YZ plane. A positive change in pitch represents rotation to face upwards, and vice-versa. Pitch 0 represents the vehicle facing directly forwards. In the air, vehicles can affect pitch rotation by holding up or down, to nosedive and taildive respectively. Bikes can also affect their pitch rotation by performing a wheelie. Driving on any slope also affects pitch rotation.

Roll rotation describes the rotation around the Z axis, along the XY plane. A positive change in roll represents the vehicle tilting to the right, and vice-versa. Roll 0 represents the vehicle not tilting in either direction. Bikes can gain roll rotation by drifting in either direction, with inside-drift bikes gaining much more rotation than outside-drift.

Rotation conversion

In Mario Kart Wii, the axes of rotation are not static; rather, they change to match the vehicle's orientation. Mathematically, this leads to interesting consequences; if the vehicle is rotated around its X axis, then around its Y axis, and finally around its X axis in the opposite direction, the final result is equivalent to a single rotation around the Z axis. This can be applied in many subtle ways to turn tighter than usual, by using a combination of pitch and roll rotations to affect pitch rotation.

A common application of rotation conversion is drifting tighter when landing from a trick, particularly on inside-drift bikes. For stunt tricks, tricking in the same direction as the drift allows the bike to turn tighter on landing. Down flip tricks cause tighter drifting in many situations, as pitch corrects by increasing upon landing. For the same reason, nosediving in the air allows for both reduced airtime and tighter turning in all cases.

Another common application for bikes is driving in a wheelie on a steep slope transition; the large change in roll rotation combined with pitch rotation has a noticeable effect on yaw rotation. This is most evident on DS Yoshi Falls, at the bridge stick, and on GCN Mario Circuit, using the slanted curbs before the tunnel to realign in a wheelie. This is also used on the sloped curbs on Mario Circuit and Luigi Circuit, in combination with a spindrift, to drift much tighter than normal.

On automatic drift, rotation conversion can be used in subtle ways to drift tighter than normal with bikes. When starting a drift to the right, turning left for one frame after 11 frames (vice-versa for a left drift) allows the bike to turn tighter than normal. When dropping the wheelie, leaning left for a few frames before drifting to the right (or vice-versa) allows for significantly increased rotation at the start of a drift.

A-tech is a subtle application of rotation conversion. Releasing A affects the bike's pitch rotation, keeping it more pointed up. While IV is decreasing due to a deceleration in max speed (e.g. a boost has just ended), the usual IV reduction from releasing A is not very impactful. Therefore, releasing A at this point while the vehicle has roll rotation allows it to turn tighter in the direction of the roll rotation, without losing any speed in most circumstances. For certain vehicles on manual drift with high wheelie turn speed loss, such as the Spear, A-tech does cause a small IV loss even while decelerating from the boost, so it is generally not worth doing. A-tech is most useful for automatic drift, where decelerating from a boost with very high roll rotation is common due to the lack of miniturbos.