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An inference on the actual time needed to reach maximum speed from a standstill

Discussion in 'Articles' started by Mister Wu, Jan 23, 2015.

  1. Mister Wu

    Mister Wu

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    AN INFERENCE ON THE ACTUAL TIME NEEDED TO REACH MAXIMUM SPEED FROM A STANDSTILL
    Mister Wu[1]

    [1]Passons, Italy

    INTRODUCTION

    It is very difficult to evaluate when a vehicle has reached its maximum speed in Mario Kart 8. Previous attempt used the smoke coming out from the vehicle[1] or the sound of the engine, the latter of which proved to be unreliable. Here a new method is presented that allow to estimate the time needed to reach maximum speed and an application that allowed to measure it for combinations having an acceleration tier greater or equal than 3 and to infer the remaining times.

    MATERIALS AND METHODS

    MARIO KART 8 VERSION
    Mario Kart 8 version 3.0 was used.

    CONTROLLERS USED
    The first player used a classic controller.
    The second player used the Wii U GamePad in normal (non-gyroscopic) mode.
    To evaluate the time needed for the smoke to disappear, the Wii U GamePad in normal mode was used.

    TRACK USED
    Toad Harbor was used as track.

    COMBINATIONS USED
    The folowing combinations were used for the measurement of the time needed to reach full speed:
    tier 3 acceleration: Roy + Pipe Frame+ Sponge Tires + Bowser Kite
    tier 4 acceleration: Ludwig + Pipe Frame + Button Tires + Bowser Kite
    tier 5 acceleration: Iggy + Mr. Scooty + Roller Tires + Bowser Kite

    The following combinations were used to infer the time needed for the smoke to disappear:
    tier 1a acceleration: Morton + Standard ATV + Monster Tires + Super Glider
    tier 1b acceleration: Morton + Standard ATV + Monster Tires + Bowser Kite
    tier 1c acceleration: Roy + Standard ATV + Monster Tires + Bowser Kite
    tier 2a acceleration: Ludwig + Mach 8 + Slim Tires + Super Glider
    tier 2b acceleration. Iggy + Circuit Special + Slick Tires + Bowser Kite
    tier 3 acceleration: Wendy + Standard Kart + Standard Tires + Super Glider
    tier 4 acceleration: Larry + Sports Bike + Standard Tires + Bowser Kite
    tier 5 acceleration: Lemmy + Landship + Sponge Tires + Bowser Kite

    STOPWATCH USED
    The iOS 7 clock app was used as stopwatch.

    METHODS

    TIME NEEDED TO REACH FULL SPEED
    A 2 players match race was started. Both players used the same combination. 150cc was chosen as engine class and no CPU opponents were added. After starting, both players positioned themselves using the "b" or "B" button so that there was a small distance between them, while having most of the straight part at the beginning of Toad Harbor ahead.
    starting_point.jpg
    The first player pressed and kept pressed the "a" button, immediately after the second player pressed and kept pressed the "A" button and the stopwatch started its measurements. When the distance between the two racers didn't change over time, this was the moment when both of them reached full speed and therefore the stopwatch was stopped and the time was measured. Four iterations of this procedure per combination were performed.

    TIME NEEDED FOR THE SMOKE FROM EXHAUST PIPES TO DISAPPEAR
    A time trial without ghost was started. All measurements started from a standstill. Each measurement started as the "A" button was pressed and kept pressed and ended as the smoke disappeared from the exhaust pipes of the vehicle. After a mesurement the "A" button was released and, if needed, the "B" and "A" button were used to reach a more suitable starting point. Nine measurements per combination were performed.

    RESULTS

    TIME NEEDED TO REACH FULL SPEED


    RAW DATA
    tier 3: 8.78 s, 8.51 s, 8.92 s, 8.69 s
    tier 4: 7.21 s, 7.72 s, 7.82 s, 7.61 s
    tier 5: 5.81 s, 6.08 s, 5.95 s, 6.04 s

    MEAN ± STANDARD DEVIATION
    tier 3: 8.73 s ± 0.15 s
    tier 4: 7.59 s ± 0.23 s
    tier 5: 5.97 s ± 0.10 s

    TIMES RELATIVE TO FASTEST TIME ± STANDARD DEVIATION
    tier 3: 1.46 ± 0.05
    tier 4: 1.27 ± 0.02
    tier 5: 1

    TIME NEEDED FOR THE SMOKE TO DISAPPEAR

    RAW DATA
    tier 1a: 2.76 s, 2.73 s, 2.72 s, 2.69 s, 2.07 s, 2.76 s, 2.75 s, 2.8 s, 2.83 s
    tier 1b: 2.64 s, 2.62 s, 2.69 a, 2.68 s, 2.74 s, 2.70 s, 2.66 s, 2.70 s, 2.70 s
    tier 1c: 2.66 s, 2.68 s, 2.56 s, 2.64 s, 2.59 s, 2.62 s, 2.64 s, 2.60 s, 2.61 s
    tier 2a: 2.03 s, 2.08 s, 2.06 s, 2.03 s, 2.08 s, 2.12 s, 2.14 s, 2.03 s, 2.06 s
    tier 2b: 2.04 s, 2.03 s, 2.06 s, 1.98 s, 2.17 s, 1.96 s, 1.97 s, 1.98 s, 2.05 s
    tier 3: 1.85 s, 1.79 s, 1.76 s, 1.77 s, 1.69 s, 1.67 s, 1.77 s, 1.79 s, 1.68 s
    tier 4: 1.49 s, 1.44 s, 1.50 s, 1.52 s, 1.45 s, 1.44 s, 1.45 s, 1.54 s, 1.50 s
    tier 5: 1.15 s, 1.13 s, 1.20 s, 1.13 s, 1.17 s, 1.22 s, 1.17 s, 1.22 s, 1.15 s

    MEAN ± STANDARD DEVIATION
    tier 1a: 2.75 s ± 0.05
    tier 1b: 2.68 s ± 0.04
    tier 1c: 2.62 s ± 0.04
    tier 2a: 2.07 s ± 0.04
    tier 2b: 2.03 s ± 0.07
    tier 3: 1.75 s ± 0.06
    tier 4: 1.48 s ± 0.04
    tier 5: 1.17 s ± 0.04

    TIMES RELATIVE TO FASTEST TIME ± STANDARD DEVIATION
    tier 1a: 2.35 ± 0.07
    tier 1b: 2.29 ± 0.06
    tier 1c: 2.24 ± 0.09
    tier 2a: 1.77 ± 0.06
    tier 2b: 1.73 ± 0.08
    tier 3: 1.50 ± 0.08
    tier 4: 1.26 ± 0.05
    tier 5: 1

    DISCUSSION

    This method, as can be seen especially in the case of tier 4, is not very precise. Also, it is expected that a little lag, due to the need of percieving that the distance no longer changes over time, is introduced in the measurement. Unfortunately, the time needed to reach full speed for combinations with an acceleration tier less than 3 was over 9.5 seconds and therefore was not reliably measurable on this track as the straight part was not long enough.
    It is anyway apparent that the time needed to reach full speed is greater than the time needed for the smoke to disappear[1]. However, since the relative times are similar, this time was again measured. Although the raw data are not fully in agreement with the previously acquired data[1], the relative times are in good agreement.
    The time needed for the smoke to disappear and the time needed to reach full speed appear to be correlated, since the Pearson correlation coefficient between the relative times is 0.998036693, therefore a reconstruction of the missing times and the times measured based on the fastest time measured was performed. These are:

    tier 1a: 14.0 s ± 0.4
    tier 1b: 13.7 s ± 0.4
    tier 1c: 13.4 s ± 0.5
    tier 2a: 10.6 s ± 0.3
    tier 2b: 10.3 s ± 0.5
    tier 3: 8.93 s ± 0.46
    tier 4: 7.55 s ± 0.28
    tier 5: 5.97 s

    The reconstructed and mesured data are summarized in the following plot:
    Acceleration_plot.png

    CONCLUSIONS

    A method was devised to measure the time needed to reach full speed, the data was then used along with the time needed for the smoke from the exhaust pipes to disappear to reconstruct the values for the acceleration tiers which could not be measured. The data confirmed previous relative times based on the time needed for the smoke to disappear.

    COMPETING INTERESTS

    The author declares no competing interests.

    REFERENCES
    [1]post #1883 by MKBoards' user DTC of the "General MK8 Discussion" thread in the "Mario Kart 8 - General Discussion" section of MKBoards' forum (http://mkboards.com/forums/threads/general-mk8-discussion.8/page-76#post-130954)


    ACKNOWLEDGEMENTS

    The direct help of user Ade in suggesting a proper formatting for articles as well as the indirect help of MKBoards' user DTC in developing the method to measure the time needed for the smoke to disappear is acknowledged.

    CONTACTS

    If more information is needed, or complaints and suggestions have to be made, the MKBoards' user Mister Wu may be contacted.
     
    Last edited: Jan 23, 2015
  2. Mister Wu

    Mister Wu

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    Corrected the title.
     
  3. Dragmirejr

    Dragmirejr Always keep an open mind! World Cup Staff

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    This pretty much proves 2 acceleration is the way to go. Thanks for the find Wu :D
     
  4. Don D

    Don D

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    Great article! Thx for this :thumbsup:

    I realy like the paper-style formatting.
     
  5. ★Kεlmαηατοr★

    ★Kεlmαηατοr★

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    I admire your inquisitive mind and curiosity of the game... if only I could understand the significance of what you are discovering!
     

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