External velocity: Difference between revisions

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'''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 [[ultra| 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.

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=== Leaning ===

'''Leaning''' is a major mechanic for both [[IDB | inside-drift]] and [[ODB | outside-drift]] bikes. Karts lack the ability to lean ~~whatsoever~~.

'''Leaning''' is a major mechanic for both [[IDB | inside-drift]] and [[ODB | 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. [[Barrel roll | Soft walls]] also disable leaning while the HWG timer is non-zero.

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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.

The following table lists all possible values for the lean rate and lean cap values, depending on the bike's drift type and state.

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.

{| class="wikitable" style="text-align:center;"

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|-

!

! IV < 5 u/f

!| |IV| < 5 u/f

! IV > 5 u/f

!| |IV| > 5 u/f

! SSMT

! Drifting

! IV < 5 u/f

!| |IV| < 5 u/f

! IV > 5 u/f

!| |IV| > 5 u/f

! SSMT

! Drifting

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|-

! Drift type

! IV < 5 u/f

! | |IV| < 5 u/f

! IV > 5 u/f

! | |IV| > 5 u/f

! SSMT

! Drifting

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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 ==

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=== 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.

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.

=== Supergrinding ===

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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.

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.

~~=== 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. The EV to IV conversion makes superhopping impossible for IDBs.

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.

=== Supersliding ===

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'''[[Supersliding#Autosliding | 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. Example inputs: +6 for 11 frames, -7 for 1 frame, +5 for 1 frame.

=== 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:

~~===~~ It ~~was called hydro pump or something idr ===~~

*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.

:''~~Main article~~: [[It ~~was called hydro pump or something idr~~]]''

*'''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. [[Vehicles#Wario Bike | Wario Bike]] seems to be by far the best vehicle at RRVS, being able to exceed 2000 EV.

~~== History ==~~

@@ Line 1: / Line 1: @@
 '''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 [[ultra| 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.
@@ Line 10: / Line 11: @@
 === Leaning ===
-'''Leaning''' is a major mechanic for both [[IDB | inside-drift]] and [[ODB | outside-drift]] bikes. Karts lack the ability to lean whatsoever.
+'''Leaning''' is a major mechanic for both [[IDB | inside-drift]] and [[ODB | 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. [[Barrel roll | Soft walls]] also disable leaning while the HWG timer is non-zero.
@@ Line 16: / Line 17: @@
 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.
-The following table lists all possible values for the lean rate and lean cap values, depending on the bike's drift type and state.
+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.
 {| class="wikitable"  style="text-align:center;"
@@ Line 24: / Line 25: @@
 |-
 !
-! IV < 5 u/f
+!| |IV| < 5 u/f
-! IV > 5 u/f
+!| |IV| > 5 u/f
 ! SSMT
 ! Drifting
-! IV < 5 u/f
+!| |IV| < 5 u/f
-! IV > 5 u/f
+!| |IV| > 5 u/f
 ! SSMT
 ! Drifting
@@ Line 49: / Line 50: @@
 |-
 ! Drift type
-! IV < 5 u/f
+! | |IV| < 5 u/f
-! IV > 5 u/f
+! | |IV| > 5 u/f
 ! SSMT
 ! Drifting
@@ Line 70: / Line 71: @@
 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 ==
@@ Line 85: / Line 89: @@
 === 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.
+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.
 === Supergrinding ===
@@ Line 91: / Line 95: @@
 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.
+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.
-=== 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. The EV to IV conversion makes superhopping impossible for IDBs.
-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.
 === Supersliding ===
@@ Line 104: / Line 102: @@
 '''[[Supersliding#Autosliding | 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. Example inputs: +6 for 11 frames, -7 for 1 frame, +5 for 1 frame.
+=== 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:
-=== It was called hydro pump or something idr ===
+*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.
-:''Main article: [[It was called hydro pump or something idr]]''
+*'''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. [[Vehicles#Wario Bike | Wario Bike]] seems to be by far the best vehicle at RRVS, being able to exceed 2000 EV.
-== History ==