{"id":175,"date":"2005-07-07T18:09:17","date_gmt":"2005-07-08T01:09:17","guid":{"rendered":"http:\/\/www.jpbadminton.com\/?p=175"},"modified":"2010-08-02T19:12:03","modified_gmt":"2010-08-03T02:12:03","slug":"the-connection-between-math-and-badminton-1-the-trajectory-of-the-shots","status":"publish","type":"post","link":"https:\/\/www.jpbadminton.com\/?p=175","title":{"rendered":"The Connection between Math and Badminton #1: The Trajectory of the Shots"},"content":{"rendered":"

Subtitle: Improve your understanding of badminton and enable you to play smarter.<\/p>\n

A famous person once said that “an uneducated army is a stupid army.” We know that a stupid army can’t win any battles. This also applies to badminton as well, as a person can’t win a game by brute force alone.<\/p>\n

If you think about it, badminton is a sport with four dimensions. The height, width and length of the playing space, plus time, make it so that players must have a lot of skill, speed, fitness and accuracy. That’s why it takes a long time for a novice to become a skilled veteran, but there is a shortcut where a player can greatly increase his\/her “combat” power with the same fundamental skills, and it involves understanding the connections between math and badminton.<\/p>\n

Other than fundamental skills, accuracy, angle, power, and speed are the most important factors in a game of badminton. If you pay attention to the trajectories of the birds, you’ll notice that the trajectories are all different curves. Because of the way the shuttlecock is designed, it is easily affected by wind and air resistance. At the same time, the bird is also affected by gravity, which means the bird will eventually enter a state of free fall. From a mathematical point of view, the trajectories of a shuttlecock are a bunch of mathematical functions. Here are some common examples:<\/p>\n

1) A powerful smash from mid court will have an almost straight trajectory represented by a function such as:
\nAX + BY +C = 0<\/p>\n

Picture 1:
\n\"\"<\/p>\n

2) A long serve can be represented by the following function:
\nY = 5SinX<\/p>\n

Picture 2:
\n\"\"<\/p>\n

3) The trajectory of a backhand short serve has a function of:
\nY = COS X<\/p>\n

Picture 3:
\n\"\"<\/p>\n

4) A back court drop shot looks like:
\nY = arc tan x<\/p>\n

Picture 4:
\n\"\"<\/p>\n

5) A hairpin drop looks like:
\nY =5 Sin 2x<\/p>\n

Picture 5:
\n\"\"<\/p>\n

6) A cross court drop near the top of the net looks like half an ellipse:
\nYY\/AA + XX\/BB = 1<\/p>\n

Picture 6:
\n\"\"<\/p>\n

7) An underhand drop shot from back court can be represented by this complicated function:
\n(XX+YY)(XX+YY) – 2AA(XX-YY) = 0<\/p>\n

Picture 7:
\n\"\"<\/p>\n

8) A crosscourt drop shot near the net using an underhand grip looks like a semi-circle:
\nYY + XX = RR<\/p>\n

Picture 8:
\n\"\"<\/p>\n

9) A defensive clear looks like part of this function:
\n(XX +YY)(XX+YY)-2AX(XX+YY)=AAYY
\nor X =A COSt (1 + COS t)<\/p>\n

Picture 9:
\n\"\"<\/p>\n

10) An attacking clear also looks like half an ellipse:
\nXX\/AA + YY\/BB = 1<\/p>\n

Picture 10:
\n\"\"<\/p>\n

11) An underhand clear looks like part of this complicated function:
\n(XX+YY)(XX+YY) – 2AA(XX-YY) = 0
\nor pp = 2 aa cos 2?<\/p>\n

Picture 11:
\n\"\"<\/p>\n

12) A mid court interception drop shot looks like this:
\nXX\/AA \u2013 YY\/BB = 1<\/p>\n

Picture 12:
\n\"\"<\/p>\n

13) The trajectory of the bird after blocking a smash:
\nX = a (cos t + t sint), Y = a (sin t – t cos t )<\/p>\n

Picture 13:
\n\"\"<\/p>\n

The point of the above examples is to illustrate the connection between mathematical formulas and badminton. People don’t need to actually remember that actual function of each curve, but they should remember the basic characteristics of each so they can try and create these trajectories in practices and competitions.<\/p>\n

Badminton is a fluid and ever changing game. Using appropriate shots to counter your opponents shot can make your opponents deplete their strength, move out of their best position, commit errors and create opportunities for you to attack. You can compare this to chess where every move you make is important. If you can control what shots are being made, then you can control the pace of the game. If you can’t control the shots, then all you can do is defend yourself while your opponents attack you continuously. You need to be able to think, react, and adapt quickly to a situation. If you are able to think of three counters for every shot your opponent makes, then you have a really high badminton “IQ.” Just remembering one response to every shot doesn’t work, since your opponent will catch on eventually, and counter your only counter, which will put you in a precarious situation.<\/p>\n

It’s not difficult to improve your badminton “IQ.” Just take some time to think about the appropriate returns to shots people normally would make in certain situations, and also watch some high level competition and see how world class players react. Throw in some practice, and you can easily ascend to a higher level of playing badminton.<\/p>\n

\u6587\u7ae0\u4e2d\u6587\u7248<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Subtitle: Improve your understanding of badminton and e […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[9],"tags":[20],"class_list":["post-175","post","type-post","status-publish","format-standard","hentry","category-skills","tag-dual-language"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p10Mdy-2P","jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/www.jpbadminton.com\/index.php?rest_route=\/wp\/v2\/posts\/175","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.jpbadminton.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.jpbadminton.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.jpbadminton.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.jpbadminton.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=175"}],"version-history":[{"count":0,"href":"https:\/\/www.jpbadminton.com\/index.php?rest_route=\/wp\/v2\/posts\/175\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.jpbadminton.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.jpbadminton.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.jpbadminton.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}