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Halaman ini menggunakan Javascript. Browser Anda tidak mendukung Javascript atau Anda memilikinya dimatikan. Untuk melihat halaman ini seperti yang dimaksudkan untuk muncul silahkan gunakan browser Javascript enabled. Fisika Baseball Bola yang melaju sejauh 400 kaki dalam kondisi quotestquot: lebih jauh 6 kaki lebih jauh jika ketinggiannya 1.000 kaki lebih tinggi 4 kaki lebih jauh jika udara 10 derajat lebih hangat 4 kaki lebih jauh jika bola 10 derajat lebih hangat 4 kaki lebih jauh jika Barometer turun 1 inci merkuri 3 12 kaki lebih jauh jika teko 5 mph lebih cepat 30 kaki lebih jauh jika dipukul dengan tangkai aluminium Untuk mencapai bola jarak maksimum yang dimungkinkan, lintasan dari kelelawar harus memiliki sudut 35 derajat. Sebuah jalur drive menempuh jarak 100 yard dalam 4 detik. Seekor lalat ke luar berjalan 98 yard dalam 4,3 detik. Angin kepala rata-rata (10 mph) bisa mengubah home run 400 kaki menjadi rutin 370 kaki. Sebuah curveball yang tampaknya menembus 14 inci tidak pernah benar-benar menyimpang dari garis lurus lebih dari 3 12 inci. Sebagian penyimpangan bola dari garis lurus diatur oleh persamaan: yang menggambarkan besarnya perbedaan tekanan antara sisi kiri dan kanan bola basket yang berputar dan dilempar. Berikut adalah cara yang tidak mungkin (tidak termasuk softball) untuk melempar bola cepat yang naik yang benar-benar naik. Tidak termasuk kondisi yang aneh secara meteorologis, bola yang dipukul tidak dapat berjalan lebih lama dari jarak 545 kaki. Tabrakan kelelawar dan bola bisbol hanya berlangsung sekitar 11000 detik. Kabar gembira untuk batters: Kecepatan quotmuzzle velocityquot dari bola basket bernada melambat turun sekitar 1 mph setiap 7 kaki setelah meninggalkan pegangan tangan, sehingga kehilangan kira-kira 8 mph pada saat melintasi pelat. Berita buruk untuk batters: Jika Anda mengayunkan 1100 detik terlalu cepat bola akan jatuh ke sisi kiri lapangan (adonan tangan kanan). 1100 detik terlambat dan pelanggarannya di kursi lapangan yang tepat, dan keputusan untuk berayun harus terjadi dalam waktu 4100 detik. Aerodynamics amp Curve Balls Selama lebih dari satu abad penggemar bisbol telah memperdebatkan pertanyaan apakah bola quotcurve sebenarnya adalah kurvaquot. Hanya jarang ada pengujian ilmiah yang obyektif untuk memverifikasi apa yang tampak jelas dari sebuah kurva. Kepentingan Igor Sikorskys berasal dari telepon yang ia terima dari United Aircrafts Lauren (Deac) Lyman yang saat makan siang dengan Walter Neff dari United Airlines, telah mendiskusikan pertanyaan tentang lintasan bola basket. Sikorsky, yang memiliki terowongan angin, memanggil para insinyurnya untuk mempresentasikan masalahnya sebagai berikut: quotHere kita memiliki bola yang solid, bergerak cepat di ruang angkasa dan berputar pada sumbu vertikal. Kamu melihat. Tujuannya adalah untuk menghindari pria dengan stickquot tersebut. Perlu dicatat bahwa enggak adalah usaha yang agak asing bagi Mr. Sikorsky. Sebagai seorang sains, dia menyadari bahwa sebuah bola bernada, yang berjalan dengan jalan melengkung, adalah contoh tindakan aerodinamis dalam kehidupan sehari-hari. Kekuatan yang menyebabkan bola berputar ke kurva dalam penerbangan adalah quot Magnus effect quot. Sikorskys masalah pertama adalah untuk menentukan berapa banyak putaran pitcher bisa memakai bola bisbol dalam peraturan enam puluh kaki, enam inci jarak dari gundukan ke piring. Insinyur yang penggemar baseball dengan senang hati menyumbangkan sebagian waktu off-tugas mereka. Studi yang cermat dibuat dari foto gerak cepat yang menunjukkan proses satu nada. Mempelajari perubahan posisi jahitan baseballs dari gambar ke gambar membuktikan bahwa laju rotasi sekitar lima putaran untuk pitch, atau sekitar 600 putaran per menit. Masalah selanjutnya adalah menentukan apakah putaran ini bisa menyebabkan bola bisbol melengkung dalam penerbangan. Pengujian dimulai di Terowongan Angin Sikorsky Vertikal selama kuerset berikutnya - dengan timequot antara uji kinerja model pesawat terbang. Karena bola cepat Big Leaguers secara resmi berada pada kecepatan 98,6 mil per jam, kecepatan maju udara yang bergerak melalui terowongan angin bervariasi antara 80 dan 110 mil per jam. Menggunakan bola mata bola National American League yang resmi - identik kecuali tanda mereka - Sikorsky menusuk mereka pada lonjakan ramping yang terhubung ke poros motor kecil dan memutarnya di antara nol dan 1.200 putaran per menit. Motor dipasang pada skala seimbang yang mengukur arah dan kekuatan semua tekanan yang dibawa pada bola lampu. Untuk mengamati efek maksimal dan minimum, bola baseball dimuntahkan dan diputar pada dua sudut yang berbeda. Dalam satu posisi empat jahitan bertemu angin selama setiap revolusi. Ini mereka temukan menghasilkan kekuatan sisi terbesar. Hanya dua lapisan yang memenuhi angin di posisi uji lainnya yang menyebabkan friksi kurang dan sedikit kekuatan samping. Kesimpulan Sikorskys adalah bahwa bola bisbol pada kenyataannya akan melengkung dalam arti bahwa bola basket berputar tidak mengikuti busur mantap, daripada berjalan dalam garis lurus dan kemudian mengutip Breaking quot. Sebuah teko yang bisa melepaskan enggak sehingga empat jahitan memenuhi angin bisa mengeluarkan pecahan quot sebanyak 19 inci. Dengan kecepatan dan putaran yang sama, dua pitch jahitan akan pecah 7,5 inci. Untuk adonan, yang memandang bola terbang terbang di suatu sudut, nampak bahwa bola bisbol berjalan cukup lurus hampir sepanjang jalan dan kemudian mengutip Breaks mendadak mendadak dan tajam di dekat piring, ini adalah ilusi optik. Catatan: Persepsi memainkan peran besar dalam bola melengkung: Kurveball yang khas hanya melewati 3,4 inci penyimpangan dari garis lurus yang ditarik antara tangan pitcher dan sarung tangan penangkap. Namun, dari sudut pandang teko dan adonan, bola bergerak 14,4 inci. Ini membuktikan bahwa bola melengkung benar-benar melengkung. Angin juga merupakan faktor utama dalam persepsi total break. Fisik Bola Curve Rahasia untuk memahami curveball adalah kecepatan udara yang bergerak melewati permukaan bola. Sebuah kurva memiliki topspin, yang berarti bahwa bagian atas bola bergerak ke arah yang sama dengan membuang dan arah OPPOSITE dari aliran udara relatif terhadap arah lemparan. Begitu juga sebaliknya untuk bagian bawah bola. Ini bergerak dalam arah yang sama seperti aliran udara relatif terhadap lemparan. Lihat prinsip Bernoullis, yang mengatakan bahwa kecepatan rendah udara di atas bola menciptakan lebih banyak tekanan pada bola, itulah yang membuat lengkungan mereda ke bawah. (Berkat Lizbeth untuk memperbaiki info ini)) Perbedaan apa yang membuat perbedaan kecepatan lebih tinggi memberi tekanan lebih pada arus yang mengalir di sekitar bagian bawah bola. Tegangan itu membuat udara mengalir di sekitar bola lepas landas dari permukaan bola lebih cepat. Sebaliknya, udara di bagian atas bola pemintal, yang mengalami sedikit tekanan karena perbedaan kecepatan yang rendah, dapat quothang kequot permukaan bola lebih lama sebelum melepaskan diri. Akibatnya, udara yang mengalir di atas bola meninggalkannya ke arah yang menunjuk sedikit ke bawah daripada lurus ke belakang. Seperti yang ditemukan Newton hampir tiga ratus tahun yang lalu, karena setiap tindakan ada reaksi yang sama dan berlawanan. Jadi, saat bola berputar melempar udara ke bawah, udara mendorong bola ke atas untuk meresponsnya. Bola yang dilempar dengan backspin oleh karena itu akan sedikit terangkat. Curveball liga utama bisa membelokkan sebanyak 1712 inci dari garis lurus pada saat ia melintasi lempeng. Selama pitch, defleksi dari garis lurus meningkat dengan jarak dari teko. Jadi curvalls melakukan sebagian besar melengkung mereka pada kuartal terakhir perjalanan mereka. Mengingat bahwa dibutuhkan sedikit waktu bagi bola untuk melakukan perjalanan sejauh 15 kaki terakhir (sekitar 16 detik) daripada yang dibutuhkan adonan untuk mengayunkan kelelawar (sekitar 15 detik), hitter harus memulai ayunan mereka sebelum bola dimulai. Untuk menunjukkan banyak kurva. Tidak heran bila curvalls sangat sulit dipukul. Satu perbedaan penting antara fastball, curveball, slider, dan screwball adalah arah bola berputar. (Faktor penting lainnya adalah kecepatan pitch dan kecepatan putaran.) Secara umum, bola yang dilemparkan dengan putaran akan melengkung ke arah yang sama dengan bagian depan bola (sisi pelat rumah, saat bernada) berubah. Jika bola berputar dari atas ke bawah (topspin), maka bola akan cenderung menetes ke kotoran. Jika pemintalannya dari kiri ke kanan, lapangan akan menembus base ketiga. Semakin cepat laju putaran, semakin banyak lintasan jalur bola. Fisika Kelelawar The quotSweet Spotquot Seekor pemukul bisbol memiliki tiga titik petik entah yang salah satunya disebut kuotent perkusi kuototnya (COP). Thats fisikawan berbicara untuk titik di mana dampak bola menyebabkan kejutan terkecil ke tangan Anda. Jika Anda memukul bola bisbol lebih dekat ke pegangan kelelawar daripada ke tengah perkusi, Anda akan merasakan sedikit kekuatan mendorong pegangan ke telapak tangan atas Anda. Jika Anda menekan bola lebih jauh dari pada COP, Anda akan merasakan sedikit dorongan pada jari Anda ke arah yang berlawanan, mencoba membuka pegangan Anda. Tapi jika Anda memukul bola tepat di COP, Anda tidak akan merasa ada kekuatan pada pegangannya. Untuk menemukan COP di kelelawar, cobalah aktivitas sederhana ini. Kelelawar Bola Seorang teman Apa yang Harus Dilakukan dan Dicari: Bila Anda memegang kelelawar dengan tangan di bagian bawah pegangan (pegangan normal), COP terletak sekitar enam sampai delapan inci dari ujung lemak kelelawar. Jika Anda tersedak pada kelelawar, COP bergerak mendekati akhir lemak. Itu karena letak bagian atas tangan Anda adalah tempat yang Anda inginkan agar kelelawar pivot. Mengubah posisi tangan Anda pada perubahan kelelawar dimana titik pivotnya berada, yang karenanya mengubah posisi COP menjadi satu yang sesuai dengan titik pivot baru. Untuk menemukan COP pada kelelawar, pegang sejajar dengan tanah di tangan Anda. Pastikan Anda memegangnya di tempat yang sama seperti biasanya saat bermain game. Yang lebih mudah untuk merasakan dorongan jika Anda memegang kelelawar dengan hanya satu tangan pegangan dua tangan membantu menangkal dorongan ke kedua arah. Tapi pastikan untuk memegangnya dengan posisi top di posisi quotestotnya, tidak mendekati gagang pegangan daripada yang biasa Anda gunakan. Tutup mata Anda, sehingga Anda bisa berkonsentrasi pada sensasi yang Anda rasakan dengan tangan Anda. Mintalah seorang teman melempar bola ke kelelawar dari jarak beberapa inci, mulai dari ujung terjauh dari tangan Anda dan bergerak ke bawah kelelawar. Semakin keras dia bisa membuangnya, semakin baik (asalkan mereka bisa mengendalikan di mana kelelawar melempar bola). Perhatikan bagaimana kelelawar merasa di tangan Anda saat bola menyentuhnya. Ketika kami mencoba ini di Exploratorium, kami bisa merasakan getaran dan kekuatan yang mendorong kami. Jumlah getaran dan quotpushquot bervariasi, tergantung dari mana kelelawar memukul bola. Beberapa dari kita merasa agak sulit membedakan dua perasaan itu, tapi jika bisa, COP adalah tempat Anda merasakan dorongan terkecil di tangan Anda. Kelelawar pada dasarnya adalah tongkat panjang. Ketika Anda menekan tongkat di tengah, dua hal terjadi: Seluruh tongkat ingin bergerak lurus ke belakang, dan juga ingin berputar di sekitar pusatnya. Kecenderungan ini untuk memutar yang membuat kelelawar menangani mendorong kembali atau menarik keluar dari tangan Anda. Saat bola menyentuh kelelawar COP, Anda tidak merasakan dorongan atau tarikan saat pemukul mencoba berputar. Itu karena ketika kelelawar berputar, ia berputar-putar di sekitar satu titik stasioner. Saat Anda memukul bola di COP, titik stasioner bertepatan dengan posisi tangan teratas Anda. Jadi tangan Anda tidak merasakan dorongan satu arah atau yang lain. Hal ini penting jika Anda ingin memukul bola jauh-jauh. Setiap kali Anda memukul bola pada titik yang bukan COP kelelawar Anda, sebagian energi ayunan Anda bergerak untuk memindahkan kelelawar di tangan Anda, bukan untuk mendorong bola agar bergerak menjauh dari Anda lebih jauh dan lebih cepat. Jika kurang dari energi kelelawar masuk ke tangan Anda, lebih banyak yang bisa diberikan pada bola. Fisika Kelelawar Tertawa Frekuensi alami kelelawar kayu sekitar 250 siklus per detik, atau 250 Hertz. Karena bola meninggalkan kelelawar begitu cepat (1 milidetik), perpindahan energi ke bola tidak terlalu efisien. Jika kelelawar telah dilubangi dan disumbat, tidak lagi kaku dan akan mendapatkan frekuensi alami yang lebih rendah dan transfer energi yang bahkan kurang efisien ke kelelawar. Bola baseball memantul dari kelelawar lebih cepat dari gabus yang bisa menyimpan energi yang bisa diletakkan kembali di bola. Gabus itu bisa mematikan suara kelelawar yang dilubangi, tapi tidak mendorong bola. Itu tidak bisa Jadi, bola memukul dengan kelelawar berkaki jangan sampai sejauh ini. Beberapa Keterangan tentang Kelelawar yang Dikepang Alan M. Nathan Berapakah kelelawar yang berkepala? Kelelawar yang disumbat adalah satu di mana rongga dibor secara aksial ke dalam tong pemukul kayu. Biasanya, diameter rongga kira-kira 1 inci dan dibor sampai kedalaman sekitar 10 inci. Rongga mungkin atau mungkin tidak diisi dengan beberapa zat, seperti gabus terkompres, superballs kecil, dan lain-lain. Efek positif apa yang dimiliki kinerja ini Karena kayu telah dikeluarkan dari kelelawar dan (mungkin) diganti oleh beberapa zat dengan kerapatan yang lebih kecil. Dari kayu, kelelawar lebih ringan 1-2 oz. Tergantung pada dimensi rongga dan densitas zat pengisi. Tidak hanya kelelawar pemantik api, tapi pusat gravitasi, atau titik keseimbangan, kelelawar bergerak lebih dekat ke tangan. Ini berarti bahwa bobot ayunan kelelawar juga berkurang. Dalam bahasa fisika teknik, momen inersia (MOI) kelelawar tentang kenop berkurang karena kelelawar yang berkerut. Anda bisa menganggap MOI sebagai inersiaquot quotrotational kelelawar. Sama seperti tanda kutip atau kuota benda mengukur daya tahan benda terhadap perubahan gerak translasinya, inersia rotasi mengukur ketahanan terhadap perubahan gerak rotasinya. Efeknya mudah dimengerti: Jauh lebih mudah mengayunkan sesuatu saat beban terkonsentrasi lebih dekat ke tangan Anda (MOI lebih kecil) daripada saat terkonsentrasi jauh dari tangan Anda (MOI yang lebih besar). Anda bisa mencoba percobaan seperti itu sendiri. Cukup dengan mengambil kelelawar dengan pegangan dan ayunan cobalah putar dengan cepat. Lalu putar kelelawar di sekitar, memegang larasnya, dan coba lakukan hal yang sama. Anda harus menemukan bahwa lebih mudah untuk memutar itu dalam kasus kedua. Oleh karena itu, adonan seringkali bisa mendapatkan kecepatan kelelawar yang lebih tinggi dengan kelelawar yang disumbat daripada kelelawar yang sebanding yang belum disumbat. Semua hal lainnya sama, kecepatan ayunan yang lebih tinggi memunculkan kecepatan bola yang lebih tinggi dan jarak yang lebih jauh pada bola terbang panjang. Tentu saja, semua hal lainnya tidak sama, dan massa yang berkurang di laras menghasilkan tabrakan yang kurang efektif, seperti yang akan kita lihat di bagian selanjutnya. Efek tambahan adalah bahwa bobot yang lebih ringan dan bobot ayunan yang lebih kecil juga menyebabkan kontrol kelelawar yang lebih baik, yang memiliki efek menguntungkan bagi pemukul tipe kontak, yang hanya mencoba untuk memenuhi bola dengan tepat daripada mendapatkan kecepatan bola dengan kecepatan tertinggi. Adonan tersebut bisa mempercepat kelelawar dengan kecepatan tinggi lebih cepat dengan kelelawar berkerut, membiarkan adonan bereaksi terhadap nada lebih cepat, menunggu lebih lama sebelum melakukan ayunan, dan lebih mudah berubah pada ayunan tengah. Seperti yang telah ditunjukkan oleh Bob Adair dalam bukunya, adonan dapat mencapai efek yang sama secara legal dengan tersedak pada kelelawar atau dengan menggunakan pemukul yang lebih ringan (dan karena itu mungkin lebih pendek). Tentu saja, ada beberapa alasan mengapa seseorang mungkin tidak ingin tersedak atau menggunakan kelelawar yang lebih pendek, terutama dalam situasi di mana Anda perlu melindungi bagian luar piring. Dalam situasi seperti ini, kelelawar yang bisa disembuhkan bisa memberi keuntungan yang pasti. Banyak pemain softball pitch cepat mengambil isu kontrol kelelawar hingga ekstrem. Inilah sebabnya mengapa peraturan softball kelelawar sangat penting. Permainan cepat-pitch sangat membantu pitcher, jadi adonan sering kali lebih tertarik untuk melakukan kontak yang baik daripada mengayunkan pagar. Batters ini menggunakan kelelawar yang sangat ringan25 oz. Atau kurang - untuk memperbaiki kontrol kelelawar dan waktu reaksi. Karena mereka menggunakan butiran aluminium terutama, mereka dapat mencapai berat badan rendah tanpa biaya panjang. Efek negatif apa yang dimiliki kinerja ini Efisiensi kelelawar dalam mentransfer energi ke bola sebagian bergantung pada berat bagian kelelawar di dekat titik impak bola. Untuk kecepatan kelelawar yang diberikan, kelelawar yang lebih berat akan menghasilkan kecepatan bola yang lebih tinggi daripada kelelawar yang lebih ringan. Itulah sebabnya kepala supir golf lebih berat dari pada setrika: Anda ingin mengarahkan bola lebih jauh. Dengan mengurangi berat pada ujung laras kelelawar, efisiensi kelelawar berkurang, sehingga meningkatkan kecepatan bola dan mengurangi jarak pada bola terbang panjang. Ini adalah sisi negatifnya menggunakan kelelawar yang sudah disumbat. Jadi, apa efek bersihnya? Kita melihat bahwa menyumbat kelelawar mengarah pada kecepatan ayunan yang lebih tinggi namun pada tabrakan ball-bat yang kurang efisien. Kedua efek ini kira-kira saling membatalkan, membiarkan efek sedikit atau tidak ada sama sekali pada kecepatan bola yang memukul atau pada jarak bola terbang yang panjang. Contoh spesifik yang menunjukkan bagaimana hal ini terjadi akan diberikan di bawah ini. Tapi adakah efek trampolin Efek trampolin cukup dikenal di kelelawar logam berongga. Cangkang logam tipis benar-benar menekan saat tabrakan dengan bola dan mata air kembali, seperti trampolin, yang mengakibatkan hilangnya energi lebih sedikit (dan karena itu kecepatan bola yang lebih tinggi) daripada jika bola menyentuh permukaan yang benar-benar kaku. . Hilangnya energi yang saya rujuk sebagian besar berasal dari bola. Selama tabrakan, bola memampatkan seperti pegas. Energi gerak awal (energi kinetik) diubah menjadi energi kompresi (energi potensial) yang tersimpan di musim semi. Musim semi kemudian mengembang kembali lagi, mendorong kelelawar, dan mengubah energi kompresif kembali menjadi energi kinetik. Ini adalah proses yang sangat tidak efisien karena hanya sekitar 25 energi kompresi yang tersimpan yang dikembalikan ke bola dalam bentuk energi kinetik. Sisanya hilang akibat gaya gesek, deformasi bola, dll. Anda bisa melihat efek kehilangan energi ini untuk diri sendiri. Turunkan bola bisbol ke permukaan yang keras dan keras, seperti lantai kayu yang solid. Bola memantul kembali hingga hanya sebagian kecil dari ketinggian awalnya karena energi hilang dalam tumbukan bola dengan lantai. Kerugiannya terutama berasal dari mengompres dan kemudian melebarkan bola. Ketika sebuah bola bertabrakan dengan permukaan yang fleksibel, seperti dinding tipis batangan aluminium, bola memampatkan kurang dari pada saat bertabrakan dengan permukaan yang kaku, karena dinding tipis memang sedikit mengompres. Kurang energi disimpan dan akhirnya hilang dalam bola, sedangkan permukaan fleksibel sangat efisien saat mengembalikan energi kompresinya kembali ke bola dalam bentuk energi kinetik. Efek bersihnya adalah bola memantul dari permukaan fleksibel dengan kecepatan lebih tinggi daripada yang lepas dari permukaan yang kaku. Inilah intisari efek trampolin. Ngomong-ngomong, efek trampolin sangat dikenal para pemain tenis, dimana efeknya berasal dari senar raket. Semua pemain tenis tahu bahwa untuk memukul bola lebih keras, Anda harus menurun daripada meningkatkan ketegangan pada senar. Banyak orang yang tidak bermain tenis menganggap ini berlawanan dengan intuisi, tapi memang benar. Ketegangan yang lebih rendah membuat senar lebih fleksibel, sama seperti trampolin. Anda bahkan bisa mencoba percobaan berikut. Turunkan bola baseball dari lantai dan ukur rasio tinggi akhir dengan ketinggian awal. Sekarang turunkan enggak dari senar raket tenis, pastikan kerangka raket dijepit sehingga tidak bergetar. Anda harus menemukan bahwa rasio akhir terhadap tinggi awal lebih tinggi daripada saat bola jatuh ke lantai. Itu adalah efek trampolin dalam tindakan. Dengan pengantar yang panjang itu, kita kembali ke pertanyaan kita: Adakah efek trampolin dari kelelawar kayu yang dilubangi atau pengisi gabus Pemahaman saya sendiri tentang fisika tabrakan bola menunjukkan bahwa jawabannya adalah tidak. Mengapa tidak lubang 1-diameter pada batangan kayu berdiameter 2-12 berarti ketebalan dinding, yang setidaknya 7 kali lebih tebal dari pada kelelawar aluminium biasa. Ini membutuhkan kekuatan yang jauh lebih besar untuk memampatkan kelelawar seperti itu daripada memampatkan kelelawar aluminium. Dalam bahasa teknik fisika, konstanta pegas dari pemukul kayu berongga jauh lebih besar daripada kelelawar aluminium biasa. Oleh karena itu, energi kompresinya sangat sedikit disimpan di dalam balok kayu berongga saat tabrakan, sehingga efek trampolin sedikit pun maksimal. Untuk menguji gagasan ini, saya melakukan eksperimen beberapa tahun yang lalu dengan Profesor Jim Sherwood di Pusat Riset Baseball (yang dididik oleh Jim) di University of MassachusettsLowell. Kami mengambil dua kelelawar Louisville Slugger R161 identik, masing-masing dengan panjang 34 dan berat 32,5 oz. Ke dalam satu kelelawar saya mengebor lubang diameter 78, 9-14 jauh ke dalam laras, mengeluarkan total 2,0 oz. dari kayu. Kami kemudian mengukur kecepatan keluar bola saat bola 70 mph memengaruhi kelelawar pada titik 6 dari ujung kelelawar. Kecepatan kelelawar pada titik itu ditetapkan pada kecepatan 66 mph. Dengan menggunakan kecepatan keluar terukur, sifat inersia yang diketahui dari kelelawar, dan formula kinematik yang sesuai, kami mengekstrak koefisien restitusi ball-bat (COR), yang merupakan ukuran keaktifan kombinasi bola-kelelawar. Kami menemukan COR identik untuk dua kelelawar, setidaknya dalam keseluruhan percobaan. Seandainya ada efek trampolin, orang akan menemukan COR yang lebih besar untuk kelelawar yang dilubangi. Berbekal informasi ini, saya kemudian melakukan perhitungan kecepatan bola yang diharapkan di lapangan, dengan asumsi kecepatan pitch 90 mph dan kecepatan kelelawar yang sedikit lebih tinggi untuk kelelawar cekung, berdasarkan model untuk hubungan antara Kecepatan ayunan kelelawar dan bobot ayunan kelelawar. Model ini didasarkan pada studi eksperimental (tidak dipublikasikan) tentang Crisco dan Greenwald, yang memberikan hubungan pasti antara MOI kelelawar dan kecepatan ayunan. Perhitungan menunjukkan bahwa pemukul yang tidak dimodifikasi benar-benar melakukan sedikit lebih baik daripada kelelawar cekung (lihat gambar di bawah). Selain itu, mengisi rongga dengan gabus, yang jauh lebih mudah dikompres daripada kayu itu sendiri, tidak mungkin bisa membantu. Waktu respon gabus terlalu lamban untuk memberi efek trampolin. Waktu tabrakan ball-bat yang khas kurang dari 11000 detik, yang jauh lebih cepat daripada periode getaran alami gabus. Selama waktu tabrakan pendek, gabus hampir tidak punya waktu untuk kompres. Akibatnya, energi ditransfer ke gabus dalam bentuk impuls, yang sebenarnya menghasilkan lebih banyak disipasi energi daripada jika rongga itu kosong. Selain itu, menambahkan gabus mengembalikan beberapa berat yang telah dilepas, sehingga setidaknya sebagian meniadakan peningkatan kecepatan ayunan yang dihasilkannya. Tampaknya meninggalkan lubang berongga akan lebih baik daripada mengisinya dengan gabus. Gambar 1. Perhitungan kecepatan bola hit dari dua kelelawar kayu identik. Sehubungan dengan kelelawar normal, kelelawar berkerak memiliki rongga pada laras berdiameter 0,875 dan kedalaman 9,25, sehingga menghilangkan massa total 2 oz. Dari laras kelelawar. Perhitungannya mengasumsikan bahwa ball-bat COR sama untuk setiap kelelawar, seperti yang ditunjukkan dari percobaan, dan mengasumsikan hubungan tertentu antara kecepatan ayunan kelelawar dan momen inersia kelelawar. Perhitungan menunjukkan bahwa kelelawar normal sedikit mengungguli kelelawar yang disumbat. Bagaimana Mengisi Cavity dengan Superballs Ini adalah pertanyaan yang menarik. Pertanyaan yang lebih umum adalah apakah ada beberapa zat yang bisa dikompres (sehingga menghemat energi) tapi tidak terlalu kompresibel sehingga tidak mengembalikan energi ke bola. Ini adalah pertanyaan yang patut dipikirkan dan layak dilakukan beberapa pengukuran eksperimental untuk mempelajari pengaruhnya. Percobaan semacam itu saat ini dalam tahap perencanaan. Dan Bottom Line Hal ini sangat tidak mungkin bahwa corking kelelawar akan menghasilkan efek yang cukup berarti, baik yang menguntungkan atau merugikan, pada jarak bola terbang yang panjang. Hal ini cenderung menghasilkan rata-rata batting yang lebih tinggi untuk hitter tipe kontak. Pada bulan Juli 2003, tim retak Profesor Dan Russell dari Universitas Kettering, Profesor Lloyd Smith dari Washington State University, dan saya melakukan serangkaian pengukuran pada beberapa kelelawar kayu yang disediakan oleh Rawlings, kepada siapa kami mengucapkan terima kasih dan ucapan terima kasih. Pengukuran menggunakan fasilitas pengujian batuan di Laboratorium Ilmu Olah Raga di Negara Bagian Washington (mme.wsu.edu ssl), yang Lloyd adalah pendiri dan sutradara. Tes tersebut terdiri dari menembaki sebuah bola bisbol dari sebuah meriam kecepatan tinggi dengan kecepatan sekitar 110 mph ke sebuah kelelawar yang dijepit pada pegangan ke struktur berporos. Kecepatan bola masuk dan rebound diukur, dan persamaan kinematik digunakan untuk menentukan kor bat. Kelelawar utama yang kami gunakan adalah kelelawar 34 dengan berat yang tidak dimodifikasi 30,5 oz. Kelelawar yang tidak dimodifikasi itu terkena total 6 kali. Kemudian rongga 1 dengan diameter dan 10 dalam dibor ke laras kelelawar, mengurangi bobot menjadi 27,6 oz. Kelelawar dibor ini terkena total 6 kali. Kemudian rongga itu dipenuhi potongan gabus yang dihancurkan (dari anggur yang saya nikmati dua minggu sebelumnya), menaikkan berat badan menjadi 28,6 oz. Pemandian omong kosong ini terkena dampak 12 kali. Kemudian gabus itu dilepas dan kelelawar pengebor itu terkena dampak lagi 5 kali. Sayangnya, kelelawar itu mematahkan pegangan pada dampak terakhirnya. Kami bermaksud mengisi rongga itu dengan bahan superball, tapi bagian percobaan itu dipotong pendek dengan memecah kelelawar. Semua dampak menggunakan bisbol yang sama dan semuanya berada di lokasi yang sama, 5 dari ujung laras pemukul. Berbagai pemeriksaan dilakukan untuk memastikan bahwa sifat bola tidak berubah selama pengukuran. Ringkasan hasil kami diberikan pada Gambar 2. Data ini menunjukkan bahwa tidak ada efek trampolin yang terukur saat kelelawar kayu dibor atau disumbat. Sistem Informasi QuesTec QuesTec adalah perusahaan media digital yang sebagian besar dikenal dengan Umpire Information System (UIS) yang digunakan oleh Major League Baseball untuk memberikan umpan balik dan evaluasi wasit Major League. Perusahaan QuesTec, yang berbasis di Deer Park, New York, sebagian besar terlibat dalam tayangan ulang televisi dan grafis sepanjang sejarahnya. Pada tahun 2001, bagaimanapun, perusahaan tersebut menandatangani kontrak 5 tahun dengan Major League Baseball untuk menggunakan teknologi pelacak lapangannya sebagai alat untuk meninjau kinerja wasit pelat rumah saat pertandingan bisbol. Kontrak terus berlanjut sepanjang musim 2008 dengan perpanjangan tahunan dan berada di 11 ballparks. Pada tahun 2009 digantikan oleh Evaluasi Zona MLB. Major League Baseball telah mengontrak QuesTec untuk menginstal, mengoperasikan, dan memelihara UIS untuk mendukung MLB yang sebelumnya mengumumkan inisiatif zona pemogokan. UIS menggunakan teknologi pengukuran eksklusif QuesTec yang menganalisis video dari kamera yang dipasang di kasau setiap rata-rata untuk menemukan bola di koridor lapangan. Informasi ini kemudian digunakan untuk mengukur kecepatan, penempatan, dan kelengkungan pitch sepanjang seluruh jalurnya. Sistem pelacakan UIS adalah proses otomatis yang tidak memerlukan perubahan pada bola, bidang permainan, atau aspek permainan lainnya. Kamera tambahan dipasang di tingkat lapangan untuk mengukur zona pemogokan untuk masing-masing adonan, masing-masing pitch masing-masing, untuk masing-masing kelelawar. Informasi ini dikompilasi pada disk CD ROM dan diberikan ke wasit wasit rumah segera setelah setiap permainan. UIS menggunakan teknologi pengukuran eksklusif QuesTec. Cukup berbeda dengan teknologi insertionquot quotvideo yang hanya menambahkan grafis ke video broadcast, teknologi QuesTec benar-benar mengukur informasi tentang peristiwa menarik selama permainan yang tidak akan tersedia dengan cara lain. Teknologi ini sangat inovatif sehingga muncul dalam artikel Scientific American pada bulan September 2000. Komponen pelacak bola menggunakan kamera yang dipasang di tribun dari garis dasar pertama dan ketiga untuk mengikuti bola saat meninggalkan tangan kendi sampai melewati pelat. Sepanjang jalan, beberapa titik trek diukur untuk secara tepat menemukan bola di ruang dan waktu. Informasi ini kemudian digunakan untuk mengukur kecepatan, penempatan, dan kelengkungan pitch sepanjang seluruh jalurnya. Seluruh proses otomatis termasuk deteksi awal pitch, pelacakan bola, perhitungan lokasi, dan identifikasi objek non-bisbol seperti burung atau angin yang menyapu puing-puing yang bergerak melalui bidang pandang. Tidak ada perubahan yang dilakukan pada bola, bidang permainan, atau aspek permainan lainnya, untuk bekerja dengan teknologi QuesTec. Teknologi pelacakan pada awalnya dikembangkan untuk militer AS dan perusahaan telah menyesuaikannya dengan aplikasi olahraga. Sistem Evaluasi Zona MLBs Bola basket Liga Utama menggantikan sistem QuesTec dengan Zona Evaluasi di semua ballpark pada musim 2009, dengan tiga kali pengumpulan data. Sistem mencatat posisi bola dalam penerbangan lebih dari 20 kali sebelum mencapai pelat. Setelah masing-masing wasit memiliki tugas piring, sistem menghasilkan disk yang memberikan evaluasi akurasi dan menggambarkan adanya inkonsistensi dengan zona pemogokan. Evaluasi Zona berhasil dioperasikan di 99,8 persen dari 2.430 game yang dimainkan selama musim 2009, menurut MLB. Tapi, wasit telah menunjukkannya, keakuratan sistem tersebut terganggu begitu sebuah pitch memasuki zona pemogokan karena zona tersebut melayang di atas pelat lima sisi karena lebih dari prisma tiga dimensi, bukan persegi panjang yang dilihat oleh pemirsa televisi. Mereka mempertahankan bahwa meskipun QuesTec (seperti Zone Evaluation) mengumpulkan data dalam tiga dimensi, posisi hitter di kotak batters atau gangguan seperti gerakan kelelawar dapat menutupi informasi, sehingga tidak sesuai untuk keputusan evaluatif tentang wasit. J.D. Drews 1997 Latar Belakang Homer :: J.D. Drew menabrak rumah monster selama musim 1997, tapi menabrak pohon dengan pesawat terbang (sementara masih berada di atas tanah) sehingga panjang homer tidak dapat ditentukan. Setelah membaca sebuah artikel di koran tentang masalah ini, termasuk beberapa perkiraan oleh pelatih dan sebuah permintaan untuk bantuan (mungkin ada masalah sains untuk Anda, kata pelatih FSU Mike Martin.) Kami harus membawa salah satu profesor sains kami ke Hitung seberapa jauh yang mungkin telah berlalu.quot), saya mampir berlatih untuk mencari tahu lebih banyak dan melihat apakah saya dapat membantu. Dua surat untuk Coach Martin termasuk di bawah adalah hasilnya. Surat pertama memberikan data yang relevan yang diperoleh dari percakapan dengan pelatih dan perkiraan pertama, sedangkan huruf kedua memberikan ringkasan temuan numerik saya. Model numerik dalam program saya didasarkan pada persamaan dan koefisien hambatan tabulasi di The Physics of Baseball oleh Robert K. Adair. Pelatih Mike Martin Moore Athletic Center FSU Campus 4043 Tanggal: 5 Februari 1997 Pelatih yang terhormat Martin: Saya pikir akan berguna untuk meringkas kesimpulan saya tentang durasi home run JD Drew yang dicapai akhir pekan lalu, yang menyatakan fakta-fakta seperti yang saya ketahui di Kali ini dan perkiraan jarak bola yang akan ditempuh. Seperti yang saya katakan di lapangan kemarin, perkiraan konservatif menempatkan home run di sekitar 500. Bisa lebih lama, tapi saya perlu melakukan beberapa perhitungan seperti yang dijelaskan di bawah ini untuk memperkirakan efek angin berikut dan lintasan yang lebih rendah. The one number that I consider reliable is the distance to the fence where the ball went out. You told me 325, and this is consistent with what I would expect for a point about 23 of the way between the line (307) and the light tower (339). I paced off the distance from the wall to under the top of the tree as being about 100. It will be convenient to use 430 for the total distance to the tree. I agree with the estimate that the ball hit the tree about 80 to 90 up. Improving the accuracy of these numbers would help some, but the answer will always be uncertain. My estimate of where the ball would have landed is obtained from a graph in The Physics of Baseball by Robert Adair. His calculations have some absolute uncertainty (that is, the speed required for a particular trajectory might be wrong), but the key thing we need is the shape -- the curvature -- of the trajectory on its downward flight. This is probably quite good for our purposes, but his graph does assume the ball was hit at the optimum angle of 35 degrees. We can use Adairs graph to bracket where the ball would land based on the numbers above. An upper limit would be if the ball was 90 high at 435 from the plate it would land about 510 away. This ball would have left the bat at 130 mph. A lower limit would be if the ball was 80 high at 425 away it would land about 490 out, having left the bat at about 125 mph. Either would have been in level flight and about 130 high when going over the fence. Based on comments in the paper and from a maintenance man I talked to, it seems likely that the ball was hit on a lower trajectory and therefore much harder, which is reasonable since an aluminum bat was used. The weather forecast suggests there might have been as much as a 10 mph following breeze, which also helps the ball carry. These would, I believe, increase the distance to the final landing point, but to quantify this I will have to put together a program to repeat the calculations Adair did. I will let you know what I learn. In the meantime, I think it is safe to say that the ball would have traveled at least 500, and possibly more. By the way, descriptions of Reggie Griggs home run suggest it was close to 500 if it did hit in that old oak tree. If it was hit higher in the air than J.D.s ball, that would suggest a flatter and longer trajectory for Drews homerun than this initial estimate. Thanks for taking the time to talk to me during practice. Coach Mike Martin Moore Athletic Center FSU Campus 4043 Dated: February 7, 1997 Dear Coach Martin: As I wrote in my previous letter concerning an estimate of the actual length of J.D. Drews home run last weekend against UNC-Asheville, if the ball was hit on a lower trajectory -- that is, more of a line drive than a fly ball -- it would travel further than the minimum distance of 500 I estimated from a graph in The Physics of Baseball by Robert Adair. In order to say more, it was necessary to assemble a computer program that did the same calculation shown in Adairs book. That has now been done, and my results appear to be the same within the accuracy of the graphs included in the book. As a reminder, relative effects (like the downward trajectory of a hit ball) are the most reliable predictions of such a model. I attach a graph that shows a variety of trajectories that (except for a 400 fly ball included for comparison) all go through the same point on the tree, 85 up and 430 away from home plate. The solid curve is the 500 fly ball described in the last letter. The longest shot, landing over 550 away, is possible if the ball is hit very hard, almost 10 harder than the 500 fly ball, on a much lower trajectory. It barely gets over 100 in the air and would have been still rising as it went over the fence. The curves in-between are at an intermediate angle, one showing the effect of a following wind. In conclusion, Drews home run was probably in the 520 to 550 range and could have been longer. Comparison of these curves to what various witnesses saw should allow you to get a better estimate of how long it was. For example, if it never got much higher that a 400 batting practice shot that hits in the street out there, Drews home run would have been in the 550 territory. Give my regards to J.D. Graph Included with Second Letter click for full view Both axis are in feet. This drawing has an exaggerated vertical scale. The legend in the upper corner (from gnuplot) will be relocated when I get a chance to clean up the drawing. The solid curve is on the optimal 35 degree trajectory, launched at 125 mph. The longest ball was hit at 136 mph at 25 degrees. They were in flight for about 6 seconds, as the half-second marks show. It should be obvious that I did not include any technical remarks in my letter to Coach Martin, for obvious reasons. You may note that I did document my assumptions about the data upon which the calculational estimates are based, but not much else.This was the first web page I wrote on Wavelets. From this seed grew other web pages which discuss a variety of wavelet related topics. For a table of contents see Wavelets and Signal Processing. This web page applies the wavelet transform to a time series composed of stock market close prices. Later web pages expand on this work in a variety of areas (e.g. compression, spectral analysis and forecasting). When I started out I thought that I would implement the Haar wavelet and that some of my colleagues might find it useful. I did not expect signal processing to be such an interesting topic. Nor did I understand who many different areas of computer science, mathematics, and quantitative finance would be touched by wavelets. I kept finding that one thing lead to another, making it difficult to find a logical stopping place. This wandering path of discovery on my part also accounts for the somewhat organic growth of these web pages. I have tried to tame this growth and organize it, but I fear that it still reflects the fact that I did not know where I was going when I started. The Java code published along with this web page reflect the first work I did on wavelets. More sophisticated, lifting scheme based, algorithms, implemented in Java can be found on other web pages. The wavelet lifting scheme code, published on other web pages, is simpler and easier to understand. The wavelet lifting scheme also provides an elegant and powerful framework for implementing a range of wavelet algorithms. In implementing wavelet packet algorithms, I switched from Java to C. The wavelet packet algorithm I used is simpler and more elegant using Cs operator overloading features. C also supports generic data structures (templates), which allowed me to implement a generic class hierarchy for wavelets. This code includes several different wavelet algoriths, including Haar, linear interpolation and Daubechies D4. Like the wavelet algorithms, the financial modeling done here represents very early work. When I started working on these web pages I had no experience with modeling financial time series. The work described on this web page lead to more intensive experiments with wavelet filters in financial models, which I continue to work on. On this web page I use stock market close prices. In financial modeling one usually uses returns, since what you are trying to predict is future return. I became interested in wavelets by accident. I was working on software involved with financial time series (e.g. equity open and close price), so I suppose that it was an accident waiting to happen. I was reading the February 2001 issue of WIRED magazine when I saw the graph included below. Every month WIRED runs various graphic visualizations of financial data and this was one of them. If stock prices do indeed factor in all knowable information, a composite price graph should proceed in an orderly fashon, as new information nudges perceived value against the pull of established tendencies. Wavelet analysis, widely used in communications to separate signal (patterned motion) from noise (random activity), suggests otherwise. This image shows the results of running a Haar transform - the fundamental wavelet formula -- on the daily close of the Dow and NASDQ since 1993. The blue mountains constitute signal. The embedded red spikes represent noise, of which the yellow line follows a 50-day moving average. Noise, which can be regarded as investor ignorance, has risen along with the value of both indices. But while noise in the Dow has grown 500 percent on average, NASDAQ noise has ballooned 3,000 percent, far outstripping NASDAQs spectacular 500-percent growth during the same period. Most of this increase has occurred since 1997, with an extraordinary surge since January 2000. Perhaps there was a Y2K glich after all -- one that derailed not operating systems and CPUs, but -- -- investor psychology. - Clem Chambers (clemcadvfn). Graph and quote from WIRED Magazine, February 2001, page 176 I am a Platonist. I believe that, in the abstract, there is truth, but that we can never actually reach it. We can only reach an approximation, or a shadow of truth. Modern science expresses this as Heisenberg uncertainty. A Platonist view of a financial time series is that there is a true time series that is obscured to some extent by noise. For example, a close price or bidask time series for a stock moves on the basis of the supply and demand for shares. In the case of a bidask time series, the supplydemand curve will be surrounded by the noise created by random order arrival. If, somehow, the noise could be filtered out, we would see the true supplydemand curve. Software which uses this information might be able to do a better job because it would not be confused by false movements created by noise. The WIRED graph above suggests that wavelet analysis can be used to filter a financial time series to remove the associated noise. Of course there is a vast area that is not addressed by the WIRED quote. What, for example, constitutes noise What are wavelets and Haar wavelets Why are wavelets useful in analyzing financial time series When I saw this graph I knew answers to none of these questions. The analysis provided in the brief WIRED paragraph is shallow as well. Noise in the time series increases with trading volume. In order to claim that noise has increased, the noise should be normalized for trading volume. Reading is a dangerous thing. It can launch you off into strange directions. I moved from California to Santa Fe, New Mexico because I read a book. That one graph in WIRED magazine launched me down a path that I spent many months following. Like any adventure, Im not sure if I would have embarked on this one if I had known how long and, at times, difficult, the journey would be. Years ago, when it first came out, I bought a copy of the book The World According to Wavelets by Barbara Hubbard, on the basis of a review I read in the magazine Science . The book sat on my shelf unread until I saw the WIRED graph. Wavelets have been somewhat of a fad, a buzzword that people have thrown around. Barbara Hubbard started writing The World According to Wavelets when the wavelet fad was starting to catch fire. She provides an interesting history of how wavelets developed in the mathematical and engineering worlds. She also makes a valiant attempt to provide an explanation of what the wavelet technique is. Ms. Hubbard is a science writer, not a mathematician, but she mastered a fair amount of basic calculus and signal processing theory (which I admire her for). When she wrote The World According to Wavelets there were few books on wavelets and no introductory material. Although I admire Barbara Hubbards heroic effort, I had only a surface understanding of wavelets after reading The World According to Wavelets . There is a vast literature on wavelets and their applications. From the point of view of a software engineer (with only a year of college calculus), the problem with the wavelet literature is that it has largely been written by mathematicians, either for other mathematicians or for students in mathematics. Im not a member of either group, so perhaps my problem is that I dont have a fluent grasp of the language of mathematics. I certianly feel this when ever I read journal articles on wavelets. However, I have tried to concentrate on books and articles that are explicitly introductory and tutorial. Even these have proven to be difficult. The first chapter of the book Wavelets Made Easy by Yves Nievergelt starts out with an explaination of Haar wavelets (these are the wavelets used to generate the graph published in WIRED). This chapter has numerous examples and I was able to understand and implement Haar wavelets from this material (links to my Java code for Haar wavelets can be found below). A later chapter discusses the Daubechies wavelet transform. Unfortunately, this chapter of Wavelets Made Easy does not seem to be as good as the material on Haar wavelets. There appear to be a number of errors in this chapter and implementing the algorithm described by Nievergelt does not result in a correct wavelet transform. Among other things, the wavelet coefficients for the Daubechies wavelets seem to be wrong. My web page on the Daubechies wavelet transform can be found here. The book Ripples in Mathematics (see the references at the end of the web page) is a better reference. There is a vast literature on wavelets. This includes thousands of journal articles and many books. The books on wavelets range from relatively introductory works like Nievergelts Wavelets Made Easy (which is still not light reading) to books that are accessable only to graduate students in mathematics. There is also a great deal of wavelet material on the Web. This includes a number of tutorials (see Web based reference. below). Given the vast literature on wavelets, there is no need for yet another tutorial. But it might be worth while to summarize my view of wavelets as they are applied to 1-D signals or time series (an image is 2-D data). A time series is simply a sample of a signal or a record of something, like temperature, water level or market data (like equity close price). Wavelets allow a time series to be viewed in multiple resolutions. Each resolution reflects a different frequency. The wavelet technique takes averages and differences of a signal, breaking the signal down into spectrum. All the wavelet algorithms that Im familiar with work on time series a power of two values (e.g. 64, 128, 256. ). Each step of the wavelet transform produces two sets of values: a set of averages and a set of differences (the differences are referred to as wavelet coefficients). Each step produces a set of averages and coefficients that is half the size of the input data. For example, if the time series contains 256 elements, the first step will produce 128 averages and 128 coefficients. The averages then become the input for the next step (e.g. 128 averages resulting in a new set of 64 averages and 64 coefficients). This continues until one average and one coefficient (e.g. 2 0 ) is calculated. The average and difference of the time series is made across a window of values. Most wavelet algorithms calculate each new average and difference by shifting this window over the input data. For example, if the input time series contains 256 values, the window will be shifted by two elements, 128 times, in calculating the averages and differences. The next step of the calculation uses the previous set of averages, also shifting the window by two elements. This has the effect of averaging across a four element window. Logically, the window increases by a factor of two each time. In the wavelet literature this tree structured recursive algorithm is referred to as a pyramidal algorithm. The power of two coefficient (difference) spectrum generated by a wavelet calculation reflect change in the time series at various resolutions. The first coefficient band generated reflects the highest frequency changes. Each later band reflects changes at lower and lower frequencies. There are an infinite number of wavelet basis functions. The more complex functions (like the Daubechies wavelets) produce overlapping averages and differences that provide a better average than the Haar wavelet at lower resolutions. However, these algorithms are more complicated. Every field of specialty develops its own sub-language. This is certainly true of wavelets. Ive listed a few definitions here which, if I had understood their meaning would have helped me in my wanderings through the wavelet literature. A function that results in a set of high frequency differences, or wavelet coefficients. In lifting scheme terms the wavelet calculates the difference between a prediction and an actual value. If we have a data sample s i . s i1 . s i2 . the Haar wavelet equations is Where c i is the wavelet coefficient. The wavelet Lifting Scheme uses a slightly different expression for the Haar wavelet: The scaling function produces a smoother version of the data set, which is half the size of the input data set. Wavelet algorithms are recursive and the smoothed data becomes the input for the next step of the wavelet transform. The Haar wavelet scaling function is where a i is a smoothed value. The Haar transform preserves the average in the smoothed values. This is not true of all wavelet transforms. High pass filter In digital signal processing (DSP) terms, the wavelet function is a high pass filter. A high pass filter allows the high frequency components of a signal through while suppressing the low frequency components. For example, the differences that are captured by the Haar wavelet function represent high frequency change between an odd and an even value. Low pass filter In digital signal processing (DSP) terms, the scaling function is a low pass filter. A low pass filter suppresses the high frequency components of a signal and allows the low frequency components through. The Haar scaling function calculates the average of an even and an odd element, which results in a smoother, low pass signal. Orthogonal (or Orthonormal) Transform The definition of orthonormal (a.k.a. orthogonal) tranforms in Wavelet Methods for Time Series Analysis by Percival and Walden, Cambridge University Press, 2000, Chaper 3, section 3.1, is one of the best Ive seen. Ive quoted this below: Orthonormal transforms are of interst because they can be used to re-express a time series in such a way that we can easily reconstruct the series from its transform. In a loose sense, the information in the transform is thus equivalent to the information is the original series to put it another way, the series and its transform can be considered to be two representations of the same mathematical entity. In terms of wavelet transforms this means that the original time series can be exactly reconstructed from the time series average and coefficients generated by an orthogonal (orthonormal) wavelet transform. This is also referred to as de-noising. Signal estimation algorithms attempt to characterize portions of the time series and remove those that fall into a particular model of noise. These Web pages publish some heavily documented Java source code for the Haar wavelet transform. Books like Wavelets Made Easy explain some of the mathematics behind the wavelet transform. I have found, however, that the implemation of this code can be at least as difficult as understanding the wavelet equations. For example, the in-place Haar wavelet transform produces wavelet coefficients in a butterfly pattern in the original data array. The Java source published here includes code to reorder the butterfly into coefficient spectrums which are more useful when it comes to analyzing the data. Although this code is not large, it took me most of a Saturday to implement the code to reorder the butterfly data pattern. The wavelet Lifting Scheme, developed by Wim Sweldens and others provides a simpler way to look as many wavelet algorithms. I started to work on Lifting Scheme wavelet implementations after I had written this web page and developed the software. The Haar wavelet code is much simpler when expressed in the lifting scheme. See my web page The Wavelet Lifting Scheme. The link to the Java source download Web page is below. There are a variety of wavelet analysis algorithms. Different wavelet algorithms are appplied depending on the nature of the data analyzed. The Haar wavelet, which is used here is very fast and works well for the financial time series (e.g. the close price for a stock). Financial time series are non-stationary (to use a signal processing term). This means that even within a window, financial time series cannot be described well by a combination of sin and cos terms. Nor are financial time series cyclical in a predictable fashion (unless you believe in Elliot waves ). Financial time series lend themselves to Haar wavelet analysis since graphs of financial time series tend to jagged, without a lot of smooth detail. For example, the graph below shows the daily close price for Applied Materials over a period of about two years. Daily close price for Applied Materials (symbol: AMAT), 121897 to 123099. The Haar wavelet algorithms I have implemented work on data that consists of samples that are a power of two. In this case there are 512 samples. There are a wide variety of popular wavelet algorithms, including Daubechies wavelets, Mexican Hat wavelets and Morlet wavelets. These wavelet algorithms have the advantage of better resolution for smoothly changing time series. But they have the disadvantage of being more expensive to calculate than the Haar wavelets. The higer resolution provided by these wavlets is not worth the cost for financial time series, which are characterized by jagged transitions. The Haar wavelet algorithms published here are applied to time series where the number of samples is a power of two (e.g. 2, 4, 8, 16, 32, 64. ) The Haar wavelet uses a rectangular window to sample the time series. The first pass over the time series uses a window width of two. The window width is doubled at each step until the window encompasses the entire time series. Each pass over the time series generates a new time series and a set of coefficients. The new time series is the average of the previous time series over the sampling window. The coefficients represent the average change in the sample window. For example, if we have a time series consisting of the values v 0 . v 1 . v n . a new time series, with half as many points is calculated by averaging the points in the window. If it is the first pass over the time series, the window width will be two, so two points will be averaged: The 3-D surface below graphs nine wavelet spectrums generated from the 512 point AMAT close price time series. The x-axis shows the sample number, the y-axis shows the average value at that point and the z-axis shows log 2 of the window width. The wavelet coefficients are calcalculated along with the new average time series values. The coefficients represent the average change over the window. If the windows width is two this would be: The graph below shows the coefficient spectrums. As before the z-axis represents the log 2 of the window width. The y-axis represents the time series change over the window width. Somewhat counter intutitively, the negative values mean that the time series is moving upward Positive values mean the the time series is going down, since v i is greater than v i1 . Note that the high frequency coefficient spectrum (log 2 (windowWidth) 1) reflects the noisiest part of the time series. Here the change between values fluctuates around zero. Plot of the Haar coefficient spectrum. The surface plots the highest frequency spectrum in the front and the lowest frequency spectrum in the back. Note that the highest frequency spectrum contains most of the noise. The wavelet transform allows some or all of a given spectrum to be removed by setting the coefficients to zero. The signal can then be rebuilt using the inverse wavelet transform. Plots of the AMAT close price time series with various spectrum filtered out are shown here. Each spectrum that makes up a time series can be examined independently. A noise filter can be applied to each spectrum removing the coefficients that are classified as noise by setting the coefficients to zero. This web page shows a histogram analysis of the three highest frequency spectrum of the AMAT close price. The result of a filter that removes the points that fall within a gaussian curve in each spectrum is also shown. The gaussian curve has a mean and standard deviation of the coefficients in that spectrum. Another way to remove noise is to use thresholding. My web page outlining one thresholding algorithm can be found here. How do Haar wavelet filters compare to simple filters, like windowed mean and median filters A plot of the AMAT time series, filtered with a median filter (which in this case is virtually identical to a mean filter) is shown here here. These filters can be compared to the spectrum filters (where a given wavelet coefficient spectrum is filered out) here.. Whether a wavelet filter is better than a windowed mean filter depends on the application. The wavelet filter allows specific parts of the spectrum to be filtered. For example, the entire high frequency spectrum can be removed. Or selected parts of the spectrum can be removed, as is done with the gaussian noise filter. The power of Haar wavelet filters is that they can be efficiently calculated and they provide a lot of flexibility. They can potentially leave more detail in the time series, compared to the mean or median filter. To the extent that this detail is useful for an application, the wavelet filter is a better choice. The Haar wavelet transform has a number of advantages: It is conceptually simple. It is fast. It is memory efficient, since it can be calculated in place without a temporary array. It is exactly reversible without the edge effects that are a problem with other wavelet trasforms. The Haar transform also has limitations, which can be a problem for some applications. In generating each set of averages for the next level and each set of coefficients, the Haar transform performs an average and difference on a pair of values. Then the algorithm shifts over by two values and calculates another average and difference on the next pair. The high frequency coefficient spectrum should reflect all high frequency changes. The Haar window is only two elements wide. If a big change takes place from an even value to an odd value, the change will not be reflected in the high frequency coefficients. For example, in the 64 element time series graphed below, there is a large drop between elements 16 and 17, and elements 44 and 45. Since these are high frequency changes, we might expect to see them reflected in the high frequency coefficients. However, in the case of the Haar wavelet transform the high frequency coefficients miss these changes, since they are on even to odd elements. The surface below shows three coefficient spectrum: 32, 16 and 8 (where the 32 element coefficient spectrum is the highest frequency). The high frequency spectrum is plotted on the leading edge of the surface. the lowest frequency spectrum (8) is the far edge of the surface. Note that both large magnitude changes are missing from the high frequency spectrum (32). The first change is picked up in the next spectrum (16) and the second change is picked up in the last spectrum in the graph (8). Many other wavelet algorithms, like the Daubechies wavelet algorithm, use overlapping windows, so the high frequency spectrum reflects all changes in the time series. Like the Haar algorithm, Daubechies shifts by two elements at each step. However, the average and difference are calculated over four elements, so there are no holes. The graph below shows the high frequency coefficient spectrum calculated from the same 64 element time series, but with the Daubechies D4 wavelet algorithm. Because of the overlapping averages and differences the change is reflected in this spectrum. The 32, 16 and 8 coefficient spectrums, calculated with the Daubechies D4 wavelet algorithm, are shown below as a surface. Note that the change in the time series is reflected in all three coefficient spectrum. Wavelet algorithms are naturally parallel. For example, if enough processing elements exist, the wavelet transform for a particular spectrum can be calculated in one step by assigning a processor for every two points. The parallelism in the wavelet algorithm makes it attractive for hardware implementation. The Web page for downloading the Haar wavelet source code can be found here. This Java code is extensively documented and this web page includes a link to the Javadoc generated documentation. A simpler version of the Haar wavelet algorithm can be found via my web page The Wavelet Lifting Scheme. The plots above are generated with gnuplot for Windows NT. See my web page of Gnuplot links here. I am only marginally statisified with gnuplot. The software is easy to use and the Windows NT version comes with a nice GUI and a nice help system. However, when it comes to 3-D plots, the software leaves some things to be desired. The hidden line removal consumes vast amounts of virtual memory. When I tried to plot one of the coefficients surfaces with the x and z axes switched, it ran out of memory on a Windows NT system with 256K of virtual memory. Also, the surface would be much easier to understand if it could be colored with a spectrum. If you know of a better 3D plotting package that runs on Windows NT, please drop me a note. I have also had a hard time getting gnuplot to generate 2-D plots with multiple lines that have different colors. I have succeeded in doing this only when the data for each line was in a separate file, which can be awkward. I was sent the reference to Root by a physicist, Costas A. Root is a data analysis framework that is targeted at the massive amounts of data generated by high energy physics experiments at CERN and elsewhere. Although Root leans heavily toward physics, it looks to me like Root would be useful in other areas. Some of the statistical techniques that are used to analyze results in experimental physics is also used in quantitive finance, for example. Root has different goals than gnuPlot. It is targeted at a much more challenging data analysis enviroment (terabytes of data). But it has a large learning curve and Im skeptical if it can be easily used by those who do not have a sophisticated command of C. In contrast gnuPlot is a simple plotting environment. So my search for a better plotting environment continues. I know that such environments are supported by Matlab and Mathematics, but these packages are too expensive for my limited software budget. References Ripples in Mathematics: the Discrete Wavelet Transform by Jensen and la Cour-Harbo, 2001 So far this is the best book Ive found on wavelets. I read this book after I had spent months reading many of the references that follow, so Im not sure how easy this book would be for someone with no previous exposure to wavelets. But I have yet to find any easy reference. Ripples in Mathematics covers Lifting Scheme wavelets which are easier to implement and understand. The book is written at a relatively introductory level and is aimed at engineers. The authors provide implementations for a number of wavelet algorithms. Ripples also covers the problem of applying wavelet algorithms like Daubechies D4 to finite data sets (e.g. they cover some solutions for the edge problems encountered for Daubechies wavelets). Wavelets and Filter Banks by Gilbert Strang and Truong Nguyen, Wellesley Cambridge Pr, 1996 A colleague recommend this book, although he could not load it to me since it is packed away in a box. Sadly this book is hard to find. I bought my copy via abebooks, used, from a book dealer in Australia. While I was waiting for the book I read a few of Gilbert Strangs journal articles. Gilbert Strang is one of the best writers Ive encountered in mathematics. I have only just started working through this book, but it looks like an excellent, although mathematical, book on wavelets. Wavelets Made Easy by Yves Nievergelt, Birkhauser, 1999 This books has two excellent chapters on Haar wavelets (Chapter 1 covers 1-D Haar wavelets and Chapter 2 covers 2-D wavelets). At least in his coverage of Haar wavelts, Prof. Nievergelt writes clearly and includes plenty of examples. The coverage of Haar wavelets uses only basic mathematics (e.g. algebra). Following the chapter on Haar wavelets there is a chapter on Daubechies wavelets. Daubechies wavelets are derived from a general class of wavelet transforms, which includes Haar wavelets. Daubechies wavelets are better for smoothly changing time series, but are probably overkill for financial time series. As Wavelets Made Easy progresses, it gets less easy. Following the chapter on Daubechies wavelets is a discussion of Fourier transforms. The later chapters delve into the mathematics behind wavelets. Prof. Nievergelt pretty much left me behind at the chapter on Fourier transforms. For an approachable discussion of Fourier transforms, see Understanding Digital Signal Processing by Richard G. Lyons (below). As Wavelets Made Easy progresses, it becomes less and less useful for wavelet algorithm implementation. In fact, while the mathematics Nievergelt uses to describe Daubechies wavelets is correct, the algorithm he describes to implement the Daubechies transform and inverse transform seems to be wrong. Wavelets Made Easy does not live up to the easy part of its title. Given this and the apparent errors in the Daubechies coverage, I am sorry to say that I cant recommend this book. Save your money and buy a copy of Ripples in Mathematics . Discovering Wavelets by Edward Aboufadel and Steven Schlicker At 125 pages, this is one of the most expensive wavelet books Ive purchased, on a per page basis. It sells on Amazon for 64.95 US. I bought it used for 42.50. If Discovering Wavelets provided a short, clear description of wavelets, the length would be a virtue, not a fault. Sadly this is not the case. Discovering Wavelets seems to be a book written for college students who have completed calculus and linear algebra. The book is heavy on theorms (which are incompletely explained) and very sort on useful explaination. I found the description of wavelets unnecessarily obscure. For example, Haar wavelets are described in terms of linear algebra. They can be much more simply described in terms of sums, differences and the so called pyramidal algorithm. While Discovering Wavelets covers some important material, its coverage is so obscure and cursory that I found the book useless. The book resembles a set of lecture notes and is of little use without the lecture (for their students sake I hope that Aboufadel and Schlicker are better teachers than writers). This is a book that I wish I had not purchased. Wavelet Methods for Time Series Analysis by Donald B. Percival and Andrew T. Walden, Cambridge University Press, 2000 Im not a mathematician and I dont play one on television. So this book is heavy going for me. Never the less, this is a good book. For someone with a better mathematical background this might be an excellent book. The authors provide a clear discussion of wavelets and a variety of time series analsysis techniques. Unlike some mathematicians, Percival and Walden actually coded up the wavelet algorithms and understand the difficulties of implementation. They compare various wavelet families for various applications and chose the simplest one (Haar) in some cases. One of the great benifits of Wavelet Methods for Time Series Analysis is that it provides a clear summary of a great deal of the recent research. But Percival and Walden put the research in an applied context. For example Donoho and Johnstone published an equation for wavelet noise reduction. I have been unable to find all of their papers on the Web and I have never understood how to calculate some of the terms in the equation in practice. I found this definition in Wavelet Methods . The World According to Wavelets: The Story of a Mathematical Technique in the Making by Barbara Burke Hubbard, A.K. Peters, 1996 This book provides an interesting history of the development of wavelets. This includes sketches of many of the people involved in pioneering the application and mathematical theory behind wavelets. Although Ms. Hubbard makes a heroic effort, I found the explaination of wavelets difficult to follow. The Cartoon Guide To Statistics by Larry Gonic and Woollcott Smith, Harper Collins I work with a number of mathematicians, so its a bit embarrassing to have this book on my disk. I never took statistics. In college everyone I knew who took statistics didnt like it. Since it was not required for my major (as calculus was), I did not take statistics. Ive come to understand how useful statistics is. I wanted to filter out Gaussian noise, so I needed to understand normal curves. Although the title is a bit embarrassing, The Cartoon Guide to Statistics provided a very rapid and readable introduction to statistics. Understanding Digital Signal Processing by Richard G. Lyons. This book is fantastic. Perhaps the best introductory book ever written on digital signal processing. It is the book on signal processing for software engineers like myself with tepid mathematical backgrounds. It provides the best coverage Ive ever seen on DFTs and FFTs. In fact, this book has inspired me to try FFTs on financial time series (an interesting experiment, but wavelets produce better results and Fourier transforms on non-stationary time series). See my web page A Notebook Compiled While Reading Understanding Digital Signal Processing by Lyons My web page on the wavelet Lifting Scheme. The Haar wavelet algorithm expressed using the wavelet Lifting Scheme is considerably simpler than the algorithm referenced above. The Lifting Scheme also allows Haar wavelet to be extended into a wavelet algorithms that have perfect reconstruction and have better multiscale resolution than Haar wavelets. Emil Mikulic has published a simple explaination of the Haar transform, for both 1-D and 2-D data. For those who find my explaination obscure, this might be a good resource. The Wavelet Tutorial . The Engineers Ultimate Guide to Wavelet Analysis, by Robi Polikar. The ultimate guide to wavelet analysis has yet to be written, at least for my purposes. But Prof. Polikars Wavelet Tutorial is excellent. When it comes to explaining Wavelets and Fourier transforms, this is one of the best overviews Ive seen. Prof. Polikar put a great deal of work into this tutorial and I am greateful for his effort. However, there was not sufficient detail in this tutorial to allow me to create my own wavelet and inverse wavelet tranform software. This Web page (which is also available in PDF) provides a nice overview of the theory behind wavelets. But as with Robi Polikars web page, its a big step from this material to a software implementation. Whether this Web page is really friendly depends on who your friends are. If you friends are calculus and taylor series, then this paper is for you. After working my way through a good part of Wavelets Made Easy this paper filled in some hole for me. But I would not have understood it if I had read it before Wavelets Made Easy . Wim Sweldens, who has published a lot of material on the Web (he is the editor of Wavelet Digest ) and elsewhere on Wavelets is a member of this group. An interesting site with lots of great links to other web resources. Lifting Scheme Wavelets Win Sweldens and Ingrid Daubechies invented a new wavelet technique known as the lifting scheme . Gabriel Fernandez has published an excellent bibliography on the lifting scheme wavelets which can be found here. This bibliography has a pointer to Wim Sweldens and Peter Schroders lifting scheme tutorial Building Your Own Wavelets at Home . Clemens Valens has written a tutorial on the fast lifting wavelet transform. This is a rather mathematically oriented tutorial. For many, Wim Sweldens paper Building Your Ownh Wavlets at Home may be easier to under stand (although I still found this paper heavy going). Gabriel Fernandez has developed LiftPack . The LiftPack Home Page publishes the LiftPack software. The bibliography is a sub-page of the LiftPack Home page. Wavelets in Computer Graphis One of the papers referenced in Gabriel Fernandezs lifting scheme bibliography is Wim Sweldens and Peter Schroders paper Building Your Own Wavelets at Home . This is part of a course on Wavelets in Computer Graphics given at SigGraph 1994, 1995 and 1996. The sigGraph course coverd an amazing amount of material. Building Your Own Wavelets at Home was apparently covered in a morning. There are a lot of mathematically gifted people in computer graphics. But even for these people, this looks like tough going for a morning. Ive spent hours reading and rereading this tutorial before I understood it enough to implement the polynomial interpolation wavelets that it discusses. D. Donoho De-Noising By Soft-Thresholding . IEEE Trans. on Information Theory, Vol 41, No. 3, pp. 613-627, 1995. D. Donoho Adapting to Unknown Smoothness via Wavelet Shrinkage . JASA. 1995. CalTech Multi-Resolution Modeling Group Publications The Wavelets in Computer Graphics page, referenced above, is one of the links from the CalTech Multi-resolution Modeling Group Publications web page. The wavelet publications referenced on this page concentrate on wavelet applications for computer graphics. This is yet another introductory tutorial by a mathematician. It gives a feeling for what you can do with wavelets, but there is not enough detail to understand the details of implementing wavelet code. Amara Graps web page provides some good basic introductory material on wavelets and some excellent links to other Web resources. There is also a link to the authors (Amara) IEEE Computational Sciences and Engineering article on wavelets. Wave from Ryerson Polytechnic University Computational Signals Analysis Group Wave is a C class library for wavelet and signal analysis. This library is provided in source form. I have not examined it in detail yet. Wavelet and signal processing algorithms are usually fairly simple (they consist of a relatively small amount of code). My experience has been that the implementation of the algorithms is not as time consuming as understanding the algorithms and how they can be applied. Since one of the best ways to understand the algorithms is to implement and apply them, Im not sure how much leverage Wave provides unless you already understand wavelet algorithms. Wavelet Compression Arrives by Peter Dyson, Seybold Reports, April 1998. This is an increasingly dated discussion on wavelet compression products, especially for images. The description of the compression products strengths and weaknesses is good, but the description of wavelets is poor. Prof. Zbigniew R. Struzik of Centrum voor Wiskunde en Informatica in the Netherlands has done some very interesting work with wavelets in a variety of areas, including data mining in finance. This web page has a link to Prof. Struziks publications (at the bottom of the Web page). Prof. Struziks work also shows some interesting connections between fractals and wavelets. Disclaimer This web page was written on nights and weekends, using my computer resources. This Web page does not necessarily reflect the views of my employer (at the time this web page was written). Nothing published here should be interpreted as a reflection on any techniques used by my employer (at that time). Ian Kaplan, July 2001 Revised: February 2004Howto: Performance Benchmarks a Webserver You can benchmark Apache, IIS and other web server with apache benchmarking tool called ab. Recently I was asked to performance benchmarks for different web servers. It is true that benchmarking a web server is not an easy task. From how to benchmark a web server : First, benchmarking a web server is not an easy thing. To benchmark a web server the time it will take to give a page is not important: you don8217t care if a user can have his page in 0.1 ms or in 0.05 ms as nobody can have such delays on the Internet. What is important is the average time it will take when you have a maximum number of users on your site simultaneously. Another important thing is how much more time it will take when there are 2 times more users: a server that take 2 times more for 2 times more users is better than another that take 4 times more for the same amount of users. 8221 Here are few tips to carry out procedure along with an example: Apache Benchmark Procedures You need to use same hardware configuration and kernel (OS) for all tests You need to use same network configuration. For example, use 100Mbps port for all tests First record server load using top or uptime command Take at least 3-5 readings and use the best result After each test reboot the server and carry out test on next configuration (web server) Again record server load using top or uptime command Carry on test using static htmlphp files and dynamic pages It also important to carry out test using the Non-KeepAlive and KeepAlive (the Keep-Alive extension to provide long-lived HTTP sessions, which allow multiple requests to be sent over the same TCP connection) features Also don8217t forget to carry out test using fast-cgi andor perl tests Webserver Benchmark Examples: Let us see how to benchmark a Apache 2.2 and lighttpd 1.4.xx web server. Static Non-KeepAlive test for Apache web server i) Note down server load using uptime command uptime ii) Create a static (small) html page as follows (snkpage.html) (assuming that server IP is 202.54.200.1) in varwwwhtml (or use your own webroot): ltDOCTYPE HTML PUBLIC quot-W3CDTD HTML 4.0 TransitionalENquotgt lthtmlgt ltheadgt lttitlegtWebserver testlttitlegt ltheadgt ltbodygt This is a webserver test page. ltbodygt lthtmlgt Login to Linuxbsd desktop computer and type following command: ab -n 1000 -c 5 202.54.200.1snkpage.html Where, -n 1000: ab will send 1000 number of requests to server 202.54.200.1 in order to perform for the benchmarking session -c 5. 5 is concurrency number i.e. ab will send 5 number of multiple requests to perform at a time to server 202.54.200.1 For example if you want to send 10 request, type following command: ab -n 10 -c 2 somewhere Repeat above command 3-5 times and save the best reading. Static Non-KeepAlive test for lighttpd web server First, reboot the server: reboot Stop Apache web server. Now configure lighttpd and copy varwwwhtmlsnkpage.html to lighttpd webroot and run the command (from other linuxbsd system): ab -n 1000 -c 5 202.54.200.1snkpage.html c) Plot graph using Spreadsheet or gnuplot. How do I carry out Web server Static KeepAlive test Use -k option that enables the HTTP KeepAlive feature using ab test tool. For example: ab -k -n 1000 -c 5 202.54.200.1snkpage.html Use the above procedure to create php, fast-cgi and dynmic pages to benchmarking the web server. Please note that 1000 request is a small number you need to send bigger (i.e. the hits you want to test) requests, for example following command will send 50000 requests : ab -k -n 50000 -c 2 202.54.200.1snkpage.html How do I save result as a Comma separated value Use -e option that allows to write a comma separated value (CSV) file which contains for each percentage (from 1 to 100) the time (in milliseconds) it took to serve that percentage of the requests: ab -k -n 50000 -c 2 -e apache2r1.cvs 202.54.200.1snkpage.html How do I import result into excel or gnuplot programs so that I can create graphs Use above command or -g option as follows: ab -k -n 50000 -c 2 -g apache2r3.txt 202.54.200.1snkpage.html Put following files in your webroot (varwwwhtml or varwwwcgi-bin) directory. Use ab command. Sample test.php file Run ab command as follows: ab -n 500 -c 5 202.54.200.1test.php Sample test.pl (perl) file usrbinperl commandperl -v title quotPerl Versionquotprint quotContent-type: texthtmlnnquot print quotlthtmlgtltheadgtlttitlegttitlelttitlegtltheadgtnltbodygtnnquotprint quotlth1gttitlelth1gtnquot print commandprint quotnnltbodygtlthtmlgtquot Run ab command as follows: ab -n 3000 -c 5 202.54.200.1cgi-bintest.pl Sample psql.php (phpmysql) file lthtmlgt ltheadgtlttitlegtPhpMySQLlttitlegtltheadgt ltbodygt ltphp link mysqlconnect(quotlocalhostquot, quotUSERNAMEquot, quotPASSWORDquot) mysqlselectdb(quotDATABASEquot)query quotSELECT FROM TABLENAMEquot result mysqlquery(query)while (line mysqlfetcharray(result)) mysqlclose(link) gt ltbodygt lthtmlgt Run ab command as follows: ab -n 1000 -c 5 202.54.200.1psql.php Your support makes a big difference: I have a small favor to ask. More people are reading the nixCraft. Many of you block advertising which is your right, and advertising revenues are not sufficient to cover my operating costs. So you can see why I need to ask for your help. The nixCraft, takes a lot of my time and hard work to produce. If you use nixCraft, who likes it, helps me with donations: Become a Supporter rarr Make a contribution via PaypalBitcoin rarr Dont Miss Any Linux and Unix Tips Get nixCraft in your inbox. Its free: Better Programmer June 10, 2006, 4:24 am 1689ms per page view That8217s 1.7 secords, and an appalling figure for a production website8230 Doctor, heal theyself You really need to spend some time profiling your web app. Repeat after me: It 8216just works8217 is not enough 8212 it must work well LOL the above output is not from a real box. It is just includes so that readers can understand the output. Thanks for the look at 8220ab8221. I agree the more important metric is the average response time under production load. Based on some scripts I use myself, I wrote a tutorial on how to monitor the response time of a real world load (though there8217s nothing saying it couldn8217t be used alongside ab or siege) I8217ve also got an article going up on the same site in the near future that uses trussstrace to profile Apache and the configuration, in case you8217re really concerned about performance. Thanks for sharing information and tutorial. There is lot of discussion going on about Sun Solaris dtrace sunbigadmincontentdtrace Unfortunately, it is not available for Linux :( Zydoon June 13, 2006, 2:20 am for better monitoring of the webserver behavior, you can take a look at ganglia, it8217s more accurate than ps, top or uptaime (even if it is better used for clusters) I suggest you httperf, I find it better than ab, just because I can play scenarii for testing. And finally, thank you for this introduction of ab, I8217m giving it a try (I8217m benchmarking a web cluster). Zydoon. Thanks for suggestion. I wonder if you know about an script for gnuplot to process the information obtained with the g option. Thanks for the post good work Sakthi November 23, 2007, 12:26 pm Sir, Now i am using Apache ab to benchmark the search server in an websit. Now currently i can use n number of request and n of cuncurrency to search a same word.My problem is i want search n number of words with n number of request and cuncurrency, give me a s olution. Thanks in advance M.Sakthi I am getting different result for the same command ab -n 300 -c 2 203.168.1.15KAPILqueryTest.php and at different time. May I please know why it happends like this Thanks amp Regards Kapil Krishnan CPK Here is a way to let ab produce a CSV file that covers a range of concurrencies (like 0-1,000) . saving you the hurdle of running ab 1,000 times (and merging results). It has been used to benchmark Apache, IIS 5.1 and 7.0, Nginx, Cherokee, Rock and TrustLeap G-WAN, see: You just have then to import the CSV file into Open Office to generate Charts include include include include include include include for(i0 i res.txt, ii:1) for(best0, j0 jltITER j) system(str) Sleep (40) get the information we need from res.txt if((ffopen(quotres.txtquot, quotrbquot))) printf(quotCan039t open filenquot) return 1 memset(buff, 0, sizeof(buff)-1) fread (buff, 1, sizeof(buff)-1, f) fclose(f) nbr0 if(buff) char p(char)strstr(buff, quotRequests per second:quot) if(p) quotRequests per second: 14,863.00 sec (mean)quot while(p039 039) p nbratoi(p) if(bestltnbr) bestnbr Trilitheus September 7, 2009, 2:08 pm I8217ve changed this slightly 8211 I think the. ffff: is something to do with IPV6 8211 with from remote host or localhost 8211 I may be wrong 8211 anyhoo8230. I changed the netstat line to this: netstat -ntu awk 8216 8217 sed 8216s::ffff:8217 cut -f1 -d: sort uniq -c sort -nr note the extra sed 8216s::ffff8217 which converts the lines with the funny bits in to the same as the others. This was the simplest and fastest way I could think off to strip it out so the rest of the code works as expected. Hope this helps anyone who was getting a headache with this. Jek October 16, 2009, 12:51 am Your server is really slow8230 My results on my server: Here is the PHP page it uses: ltphp algos hashalgos() foreach (algos as hash) echo hash.quot: 8220.hash(hash, GET8216s8217).82218221 gt Here is AB8217s results: Benchmarking 192.168.1.70 (be patient)8230..done Server Software: Apache2.2.9 Server Hostname: 192.168.1.70 Server Port: 80 Document Path: test.php Document Length: 3109 bytes Concurrency Level: 10 Time taken for tests: 2.788 seconds Complete requests: 1000 Failed requests: 0 Write errors: 0 Total transferred: 3444000 bytes HTML transferred: 3109000 bytes Requests per second: 358.74 sec (mean) Time per request: 27.875 ms (mean) Time per request: 2.788 ms (mean, across all concurrent requests) Transfer rate: 1206.55 Kbytessec received Connection Times (ms) min mean-sd median max Connect: 2 13 4.1 12 41 Processing: 5 15 4.5 14 43 Waiting: 5 14 4.4 13 43 Total: 13 28 5.6 26 59 Percentage of the requests served within a certain time (ms) 50 26 66 28 75 29 80 30 90 33 95 38 98 48 99 52 100 59 (longest request) andreas November 13, 2009, 3:19 pm thanks for the tips
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