DELPHIER

2004年02月08日

考え事 - スケボーのチックタックでレースをするゲーム

なんか新しいゲームが作りたいので考えていたら、
スケボーのチックタックでレースをするものを作ろう！と思いました。
というわけで、チックタックでなぜスケボーが進むのかをまず考えてみました。

チックタックは、スケボーに体重をのせて
軸足を固定し、左右に振るという、
なんとも不思議な運動によって前に進みます。
まず、どうやって力が発生していくかを追ってみます。

1.軸足を固定し、ボードを少し浮かせて回転させる
　ここでトルクが発生している？
2.適当に回転させたボードを地面に着ける
3.1の動作を反対方向に行う
4.2を行う
5.これを繰り返す

1と3でトルクを発生された覚えはあるのですが、
それが前に進む力にどうやってなるかがわからない・・・。
でも、回転の力が前に進む力に変換されているのは確かです。
ということは、トルクと力の関係を思い出せば、わかりそうです。
トルクと力の関係に確かこんな関係があります。

トルクをτ、位置ベクトルをｒ、力をFとすると、

τ ＝ｒ × Ｆ

なんとか、トルクから力を求めることができそうです。
力がもとまれば、物理の偉大な公式「F=ma」で加速度が求まり、
加速度から速度が求まり、位置が決定できます。

じゃぁトルクは何かっていうと、角運動量と関係があります。
ちなみに角運動量Ｌは、角速度ωと関係があります。
慣性モーメントをＩとすると、

Ｌ＝Ｉ・dω/dt

角運動量とトルクの関係は次式で表されます。

τ ＝ dL/dt

ここまでをまとめると、

Ｉ・d/dt・（dω/dt）=ｒ ×Ｆ

になるのかな？
目的は、回転の力がどうやって前に進む力になるかでした。
なので、ゴールは力を求めるということです。
上式を展開すると、三つの連立方程式に未知数が三つなので、
方程式を解くことができます。
そして、力Ｆが求まります。

あとは、F=maに従い、スケボーの質量を代入してやればＯＫですね。
わかりきっていたことですが、
体重ができるだけ軽い人で、強い回転力を生める人が
高速チックタックレースを制することになりそうです。

今日はこんなところで。

なぜ、スケボーの醍醐味であるオーリーをゲームに
しないかというと、僕ができないからです。

okumura - 2004年02月08日00時45分59秒 - TrackBacks(0)

こんばんは、onikumaです。

--- スケボーゲームについて ----

これはエキサイトバイクのような2Dゲームになるのでしょうか？

FLASHで実装したら, ちょっと楽しそうですね。
ランキングでタイムを競ってみたりして。

「くにおくんの運動会」ような,
他人の邪魔をする要素があると楽しいと思います。

-----------------------
TEAM SAMURAI
http://homepage.broba.ws/onikuma/

2004年02月09日 00時31分17秒 onikuma

F-ZERO的視点のものを考えていますが、
2Dか3Dかはまだわかりません。
ただ、Flashでは難しそうですが・・・。

できれば、3D＆ネット対戦をやりたいですね。
（といいつつ最近時間がないので全然進んでない・・・）

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