External velocity

External velocity, or EV, is one of four main types of velocity in Mario Kart Wii. It collectively refers to the effect of many forces other than the vehicle's engine, such as gravity, momentum from kart bumps and wall collisions, and leaning. Using physics exploits, EV can be used to maintain high speeds for prolonged periods of time, and its widespread recognition in 2022 has since led to the discovery of numerous ultras.

Overview

EV is represented as a vector, with a direction and magnitude. The direction of EV is always (nearly) perpendicular to the vehicle's facing direction at any given moment; if there is a EV vector component parallel to the facing direction, the games tends to convert it to IV. Gravity EV is an exception; it is always purely directed in the (negative) Y direction, no matter the vehicle's pitch rotation, but it can still be converted to IV on the ground.

The magnitude of the EV vector is, notably, uncapped. While internal velocity is capped at 120 u/f, and the sum of IV, EV, and moving road speed is also capped at 120 u/f, it is possible to accumulate EV in the thousands. It is worth noting that a vehicle with 1000 EV still moves at 120 u/f; however, the high amount of EV allows it to maintain its speed for a very long time.

EV naturally decays exponentially at a rate of 0.2% per frame at all times. This EV decay is universal and can't be disabled. Additionally, if one or more of the vehicle's wheel hitboxes are making contact with the ground, a constant rate of ~6-10 EV per frame is applied. This rate is independent for each wheel and each bike, and this behavior isn't well understood at the moment. The wheel decay does not apply if the wheels do not properly make contact with the ground, such as when the bike is airborne, or in a low traction state such as supersliding.

EV sources

Leaning

Leaning is a major mechanic for both inside-drift and outside-drift bikes. Karts lack the ability to lean entirely.

Leaning is tracked through a lean rotation value (not to be confused with roll rotation). Inputs from +2 to +7 increment this counter by an amount known as the lean rate, which is a function of the bike's drift type and state. Inputs from -2 to -7 decrement the counter by the lean rate. This can be thought of more simply as leaning to the right or left, respectively. Inputs of 0 and ±1 are known as neutral inputs, and decrease the lean rotation exponentially by a rate of 10% per frame. For airborne bikes, leaning is disabled after 20 frames. Soft walls also disable leaning while the HWG timer is non-zero.

The lean rotation is bounded both left and right by the lean cap value, which varies with the lean rate. On each frame, if the lean rotation increases and does not become (strictly) greater than the lean cap, the bike gains EV directed to the right. Vice versa, if lean decreases and does not become (strictly) less than the lean cap, the bike gains EV to the left. The EV gained per frame by leaning is 1.0 u/f^2 for IDBs, and 0.8 u/f^2 for ODBs. Considering the universal EV decay, this gives an upper limit to leaning EV of 500 for IDBs and 400 for ODBs; in practice, wheel decay and lean rotation make true limits much lower.

The following table lists all possible values for the lean rate and lean cap values, depending on the bike's drift type and state. Note that |IV| means the absolute value, or magnitude of the IV vector.

	Inside-drift bikes				Outside-drift bikes
	|IV| < 5 u/f	|IV| > 5 u/f	SSMT	Drifting	|IV| < 5 u/f	|IV| > 5 u/f	SSMT	Drifting
Lean rate	0.08	0.1	0.15	0.05	0.08	0.08	0.15	0.1
Lean cap	0.6	1.0	1.3	0.7 - 1.5	0.6	1.0	1.6	0.8 - 1.2

Optimal efficiency for leaning involves approaching the lean cap quickly, then alternating between neutral and leaning inputs in a pattern, staying just below the lean cap. This is because lean rotation decays more quickly at higher values.

Drifting directly sets the lean rotation value, so drifting for one frame to set lean rotation to a high magnitude in the opposite sign is an effective way to gain more leaning frames. This is occasionally referred to as drift resetting. This trick is commonly used to optimize superhopping and autosliding.

The theoretical optimal leaning patterns for each combination of lean rate and lean cap are contained in the table below. Note that 0 represents any neutral input, and 7 represents any leaning input. Inputs in brackets should be looped as many times as indicated before continuing with the pattern.

Drift type	|IV| < 5 u/f	|IV| > 5 u/f	SSMT	Drifting
IDB	(0 0 7 0 7) * 3 0 7	0 7	0 (0 7) * 4 0 (0 7) * 5	0 7 7 7
ODB		(0 7) * 5 7	0 7	(0 7) * 7 7

Gravity

Gravity applies a constant acceleration of 1.3 u/f^2, directed in the negative Y direction, as long as the vehicle is airborne. As mentioned previously, EV from gravity is never converted to IV as long as the bike remains airborne, no matter its pitch rotation.

After 50 frames of airtime, the pitch rotation of the vehicle affects gravity. The rate of acceleration is constant from 0° to -20° (facing down), increases linearly from -20° to -40°, and reaches its maximum modifier of 20% at -40° and beyond. (Vice versa if facing up.) Therefore, gravity is bounded between [1.04, 1.56] u/f^2.

Wall hits

Wall collisions apply a force to the vehicle, acting on both EV and IV. The amount of EV gained generally depends on the angle of the bike relative to the wall; facing head-on to the wall affects only IV, while facing increasingly sideways grants more and more EV. In general, a good wall hit can gain about 40 EV, starting at low EV.

Applications

Start slides

Bikes are able to move during the countdown due to leaning EV. Any bike can do a wheelie to rotate sideways, then use the |IV| < 5 u/f pattern to slide sideways. For longer bikes, double wheelies can cause them to go airborne too, which significantly decreases EV dissipation and allows them to slide much further. In this case, the optimal inputs change for each bike, and are not well understood.

TF physics

Main article: TF physics

TF physics are caused directly by a combination of leaning EV and roll rotation. When a bike gains a large amount of roll rotation, for example by drifting with IDBs, the leaning EV vectors follow the orientation of the bike, and therefore point partially upwards or downwards. For example, in a IDB drift to the right, leaning to the right causes EV to point down, e.g. reducing airtime, while leaning to the left causes EV to point up, e.g. increasing airtime.

Side trick abuse

Main article: Trick#Side trick abuse

During a left/right stunt trick, bikes rotate clockwise/counterclockwise, respectively. This causes one side of the vehicle to temporarily face forwards. Leaning to the left/right during this animation causes the leaning EV to be converted to IV, as the two vectors are parallel, for an IV increase of about 7 u/f. The bike also gains a small amount of roll rotation during the animation, so the EV also causes a small airtime increase due to TF physics.

Leaning to the right/left during the trick causes reverse side trick abuse, with leaning EV decreasing both IV and airtime.

Spindrifts

Main article: Drift#Spindrift

Spindrifts are a technique exclusive to bikes, caused by leaning EV. By committing to a drift in any direction, then holding the opposite direction in the air, bikes can generate EV which, upon landing, causes them to drift more sharply in the initial part of the drift compared to holding toward the drift the whole time.

Neutral gliding

During any (large) hop or wallclip, alternating between neutral and leaning inputs can be a small optimization, giving a bit more lateral distance. This is caused by the lean rotation value reaching the cap during the airtime, so input alternations (before the 20 frame limit) may generate more EV. This is often useful for superhopping as well.

Supergrinding

Main article: Supergrinding

Through the use of rapid fire hopping, the vehicle can get stuck in the ground. In this state, its wheels are not counted as making contact with the ground, and bikes can accumulate EV by leaning. However, much of the EV from supergrinding also comes from gravity and collisions with the terrain, in ways that are not properly understood yet. Karts are also able to gain EV from rapid fire hopping in certain situations, such as on a downhill.

Optimal inputs for supergrinding involve the |IV| > 5 u/f pattern. However, for ODBs, the optimal pattern is not always useful, because two consecutive turning inputs result in a much tighter turning arc, so alternating every frame (like the IDB pattern) is usually preferable.

Supersliding

Main article: Supersliding

Some IDBs and Wario Bike are able to drive on the ground on their body hitboxes, instead of their wheels. The EV decay effect only applies to wheels and not body hitboxes, therefore they can simply lean to gain EV after entering this state. Supersliding is not stable for most vehicles, with the exception of Wario Bike. The optimal inputs for supersliding depend on the bike's state, according to the table above. If it's possible to initiate a slipdrift, it can be a very efficient way to gain EV in a superslide.

Autosliding is a technique exclusive to automatic drift. It involves holding ±6/±7 inputs to lean and begin an automatic drift (which requires 12 consecutive frames of ±6 or greater), switching to the opposite direction on the last frame to drift in the opposite direction and reset lean rotation, then immediately ending the drift to lean again. The inputs for the widest possible rotation to the right are as follows: +6 for 11 frames, -7 for 1 frame, +5 for 1 frame.

Taking into account the lean patterns, the theoretical limit of superslide EV is calculated by multiplying the average EV gain by 499. For manual, this results in ~217.75 for ODB, and 249.5 for IDB. With autosliding, the limits are about 380 for ODB and 470 for IDB, depending on how many frames each drift lasts.

Supergliding

Main article: Supergliding

Performing slow ramp abuse allows the bike to preserve the slow ramp properties while being on the ground. In this state, the IV vector is mostly locked (only affected by wheelies and wall collisions), and wheel decay is disabled. Therefore, bikes are able to gain EV by leaning and redirect themselves using walls. The optimal leaning inputs follow the |IV| > 5 u/f pattern.

Superhopping

Main article: Superhopping

Outside-drift bikes can gain EV anywhere by drifting and rotating the IV vector away from the facing direction, then repeatedly spindrifting in the same direction. This causes a positive feedback loop, gaining more EV by leaning than is dissipated from wheel decay and EV to IV conversion. For IDBs, IV cannot be rotated away from the facing direction, so EV to IV conversion makes superhopping impossible.

Superhopping is tough to optimize, as the inputs must be adapted depending on the situation. In general, to gain the most speed when superhopping to the right; start with a ~45° angle between facing direction and IV, -2 angle hop, +1 drift commit, hold -7 to lean, release drift before landing (wheelie optional); hop again with -2 angle hop, +1 drift commit, hold -7 to lean and neutral glide as needed, drift for 1 frame upon landing to drift reset, and repeat.

Outside drift momentum

Main article: Outside drift momentum

Outside-drift bikes can also gain EV by drifting off any surface, then ending the drift and leaning in the opposite direction in the air. Like superhopping, this tech relies on the IV vector being rotated away from the bike's facing direction.

ODM is notably useful for tracks with many slow ramps in a row, like Mushroom Gorge and GBA Bowser Castle 3. Slow ramps provide airtime, which helps setting up ODM, and greatly reduce IV in the air, making the speed from EV more desirable.

Hydroplaning(?)

Main article: Hydroplaning

Karts and outside-drift bikes can gain very high EV by simply drifting on moving road, either with a boost or on very fast moving road. Hydroplaning appears to happen because the wheel decay function erroneously increases EV instead of reducing it, but it is not very understood at the moment. In optimal conditions (a circle of fast moving road), the EV gain seems to differ greatly between vehicles; lightweight karts have reached above 2000 EV.

Slope boosting

Main article: Slope boosting

As mentioned previous, the EV from gravity is always directed in the negative Y velocity while in the air. When landing on a downhill slope, this EV is redirected horizontally. Hopping immediately after landing on a steep downhill slope converts most of the vertical gravity EV into horizontal EV.

This is easier to perform with karts and outside-drift bikes, by drifting before gaining gravity EV and landing with the IV vector pointing away from the facing direction; however, IDBs are also able to take advantage of slope boosting on tracks like GCN DK Mountain. Karts are best at slope boosting, because landing with only one wheel results in less wheel EV decay, and their inability to lean allows them to turn in the direction opposite the EV vector without reducing EV.

Velocity stacking

Main article: Velocity stacking

Velocity stacking is a catch-all term encompassing methods of gaining very high EV without moving. Currently, the following velocity stacking methods are known:

• On GCN DK Mountain, falling onto the wooden ramps with high Y velocity may cause the bike to enter a superslide state, and the bike very rapidly gains EV in the negative Y direction. This is presumably because of the walls in the ramp pushing the bike while it is stuck inside. It is possible to reach over 8000 EV with this method.
• Reject road velocity stacking: Certain full pipes on tracks like Koopa Cape and N64 Mario Raceway have reject road collision on the ceiling of the pipe. It is possible to fully stop and start and SSMT while hanging upside down; the game tries to push the bike away and generates very high EV, while the SSMT keeps it stopped. Wario Bike seems to be by far the best vehicle at RRVS, being able to exceed 2000 EV.