專欄 球拍重量大小事(Table tennis racket weight matters)

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挑選直拍時前輩諄諄教導:「挑重拍擊球有質量,扣殺有力,推擋定直線威力好」喜愛桌球的您有細想過背後的原理是什麼嗎?而挑選刀板時也是遵從類似的挑選法則嗎?如果您也有想過以上的問題或是您好奇為什麼的話,就請繼續讀下去吧!

Experienced player taught us that racket weight matters and it should match your play style. The heavier the racket the faster the returning ball. Why things work that way? Why some penhold players concern the racket weight more than shakehand players? If you want to know more about the subject, keep reading the article.

  接下來將以牛頓力學解釋為什麼球拍愈重則回球球速愈快。假設球拍與球之間的碰撞沒有損失能量,即球拍與球之間的碰撞是彈性碰撞。則他們會遵守動量守衡(conservation of momentum)與動能守衡(conservation of kinetic energy),其中m1代表桌球拍質量(重量),m2代表桌球質量(重量),v1i代表桌球拍碰撞前的速度,v2i代表桌球碰撞前的速度,v1f代表桌球拍碰撞後的速度,v2f代表桌球碰撞後的速度(即球速)。

  The articles rationalize the phenomena, the heavier the racket the faster the returning ball, based on Newtonian mechanics. Assume the collision between table tennis racket and table tennis ball obeys elastic collision. In turn, it obeys conservation of total momentum, and is expressed by the equation conservation of momentum. Also it obeys conservation of total kinetic energy, which is expressed by the equation conservation of kinetic energy. Where m1 denotes the mass, equivalently as weight, of table tennis racket, m2 denotes the mass, equivalently as weight, of table tennis ball, v1i denotes the velocity of table tennis racket before collision, v2i denotes the velocity of table tennis ball before collision, v1f denotes the velocity of table tennis racket after collision, and v2f denotes the velocity of table tennis ball after collision.

  方程組有兩組解。第一組解是,代表碰撞還沒發生所以速度沒有改變。第二組解是,代表碰撞發生後的速度。

  These equations have trivial and non-trivial solutions. The trivial solution is  and , corresponding to the case that no collision has taken place yet. The nontrivial solution is  and , corresponding to the case that collision has taken place.

  現在我們來看看球拍重量對於回球球速(v2f)有什麼具體的影響。假設桌球碰撞前速度(v2i)為零(或說我們將系統座標平移至桌球初速為零),則桌球碰撞後速度(v2f)為。如果球拍碰撞前速度(v1i)一樣,隨著球拍重量(m1)增加,桌球碰撞後速度(v2f)將趨近上限值。

  Now all is ready for discussion on how racket weight affects the returning ball speed, v2f. Assume the velocity of table tennis ball before collision, v2i, is zero, or the coordinate is shifted such that v2i is zero. In turn, , , where the higher value of the weight of table tennis racket, m1, the more the velocity of table tennis ball after collision, v2f, approaches its upper limit value if the velocity of table tennis racket before collision, v1i, is the same.

  接下來我們來看看實際數字。桌球重量(m2)是2.7克,膠皮裁貼前重量一般是85克左右,膠皮裁貼後重量一般是40克左右。另外,職業桌球選手扣殺球速可達時速120公里,而一般業餘好手扣殺球速可達每小時100公里。球桌總長274公分,所以球桌總長除以回球球速可得反應時間。一般人最快可在0.2秒內做出反應。如果反應時間愈接近0.2秒,選手愈容易處理來球。換句話說,打亂對手擊球節奏的最好辦法就是減少對手的反應時間。


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PingPong.Bang

大學時因學姐邀請而加入系上桌球隊, 從此愛上桌球、與桌球結下不解之緣。 希望讓更多人享受到桌球的樂趣!

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