Velocity

In Mario Kart Wii, velocity is defined as the difference in the vehicle's position between two consecutive frames. It is measured in u/f (units per frame).

Overview

Velocity can be represented as a vector, with direction and magnitude. The magnitude is the value shown on speedometers, indicating how much the vehicle has moved from the previous frame. The direction simply represents the direction of motion.

It can be useful to split velocity into multiple components. The most common choice is to separate the horizontal (XZ plane) and vertical (Y axis) components. The horizontal component is sometimes also divided into forward and sideways (where forward is the vehicle's facing yaw), or the X and Z axes.

Sources of velocity

The velocity vector is the sum of three other vectors:

• Internal velocity / IV, representing the speed from the vehicle's engine by pressing A or B, limited by maximum velocity;
• External velocity / EV, the total effect of external forces acting on the vehicle, such as gravity, wall hits, or leaning;
• Moving road speed, the speed boost from moving road collision if the vehicle is driving on it.

Speed cap

Velocity from the three main sources is capped at 120 u/f; if the result of the sum is a vector with magnitude above 120, it is simply resized to fit the cap. However, direct position updates and cannons can cause velocity to exceed the cap of 120 u/f. The speed cap isn't actually a constant, but strangely, it is proportional to the scale factor of the vehicle.

The most notable case is using a Mega Mushroom, which multiplies the speed cap by the vehicle's Mega scale stat while it is active. Among bikes, this stat ranges from 1.60x for the Phantom, up to 2.60x for the Bit Bike and Quacker, resulting in speed caps between 192 and 312 u/f. Because EV is not capped, performing any EV expoit and activating a Mega Mushroom lets vehicles move significantly faster than normal.

Another known case of the speed cap being affected by size scaling is the growing animation after being shocked, either by the Koopa Cape zappers or items such as the Thunder Cloud or Lightning. This animation is, however, very brief, thus the increased speed cap is not as abusable as the Mega Mushroom case.

Direct position update

A direct position update is any source of velocity that doesn't affect IV, EV, or moving road speed. As such, direct position updates can be used to briefly exceed the speed cap.

All of the following interactions are direct position updates:

• During a supergrind, the ground is constantly pushing the vehicle out while it remains stuck. It is common to sustain speeds slightly above 120 u/f, especially on downhills.
• Being pushed out by wall collision may force the vehicle to move faster than 120 u/f for 1 frame. For example, during the ramp lowtrick on Luigi Circuit NG flap, the bike collides with the back of the ramp, pushing it forwards with good QM, up to ~164 u/f. Another example is the horizontal wall glitch shroom on SNES Ghost Valley 2 NU, where driving into a block as HWG ends forces the bike to be pushed upwards out of the block, reaching about 170 u/f.
• Driving on barrel roll collision at high speed causes the HWG timer to be set to 10; while the timer is non-zero, a direct position update of up to ±10 u/f is applied to the vehicle. With the right orientation relative to the barrel roll collision, it is possible to move up to 130 u/f briefly after touching it.
• Reject road always tries to move the vehicle away from it. Moving up the reject wall at an angle allows the vehicle to move at very quick speed while the road tries to turn it away. Notably, on Koopa Cape NG 3lap, it is possible to sustain speeds of over 200 u/f through the underwater pipe.
• Sticky road attempts to keep the vehicle driving on it using direct position updates.

Two other sources of direct position updates are cannons and upwarps. Cannons on tracks like DK Summit or Maple Treeway allow vehicles to move at almost 500 u/f during the animation. Upwarps do not have a speed cap, so it theoretically possible to move in the thousands of u/f (vertically) for 1 frame.