Judul: Review of Morning Glory Type Service Spillway Dimensions Considering the Seroja Tropical Cyclone at Manikin Dam
Abstrak: Munculnya siklon tropis seroja pada tanggal 5 – 12 April 2021 menyebabkan bencana alam banjir bandang dan angin puting beliung di pulau Timor. Kejadian siklon tropis seroja tersebut perlu dipertimbangkan dalam desain Bendungan Manikin dan infrastruktur lainnya untuk mengantisipasi potensi melimpasnya air di atas main dam. Desain bendungan harus aman dari kegagalan hidrolis dengan cara membangun bangunan pelimpah yang mampu mengalirkan debit banjir. Tujuan penelitian ini adalah untuk melakukan kajian ulang dalam perhitungan debit rencana dengan mempertimbangkan kejadian siklon tropis seroja. Metode yang dilakukan terdiri atas analisis curah hujan, analisis debit banjir rencana bangunan pelimpah utama, penelusuran banjir, dan analisis dimensi pelimpah utama (morning glory). Hasil perhitungan debit banjir rencana QPMF sebesar 949.19 m3/detik. Dengan besaran debit rencana tersebut, nilai elevasi muka air banjir setinggi +152.10 mdpl serta debit outflow maksimal yang dapat dialirkan sebesar 540.25 m3/detik. Hasil kaji ulang menunjukkan bahwa dimensi bangunan pelimpah utama yang direncanakan cukup memadai untuk mengalirkan QPMF yang diakibatkan siklon tropis seroja, The emergence of seroja tropical cyclone on 5-12 April 2021 caused natural disasters of flash floods and tornadoes on the island of Timor. The seroja tropical cyclone event needs to be considered in the design of the Manikin Dam and other infrastructure to anticipate the potential for water overtopping the main dam. The design of the dam must be safe from hydraulic failure by constructing a spillway that is capable of conveying the flood discharge. The purpose of this research is to conduct a reassessment in the calculation of the discharge plan by considering the seroja tropical cyclone event. The method consists of rainfall analysis, flood discharge analysis of the service spillway building plan, flood tracing, and dimension analysis of the service spillway (morning glory). The result of the calculation of the design flood discharge QPMF is 949.19 m3/second. With the amount of the design discharge, the value of the flood water level is as high as +152.10 masl and the maximum outflow discharge that can be flowed is 540.25 m3/second. The review results show that the planned dimensions of the service spillway building are adequate to drain the QPMF caused by tropical cyclone Seroja.
Keyword: design discharge, morning glory, seroja tropical cyclone

Judul: Kajian Dimensi Bangunan Spillway
Abstrak: Bangunan spillway merupakan bangunan hidrolika dari suatu bendungan yang berfungsi pada saat keadaan darurat (emergency), yaitu keadaan muka air pada saat volume tampungan banjir maksimum. Penelitian ini bertujuan untuk melakukan kaji ulang bangunan spillway pada Bendungan Randugunting berdasarkan kajian terhadap desain existing bangunan spillway, debit rencana bangunan spillway, kedalaman aliran kritis, dan profil muka air bangunan spillway. Tipe bangunan spillway yang direncanakan adalah tipe side spillway dengan tipe mercu Ogee. Hasil analisis luas catchment area Sungai Banyuasin adalah 17.39 km2 dengan panjang sungai 8.52 km. Nilai curah hujan rencana dengan periode ulang 1000 tahun adalah sebesar 180.40 mm. Hasil analisis debit rencana metode rasional sebesar 124.07 m3/det, sedangkan dengan metode HSS Nakayasu distribusi hujan 2 jam sebesar 207.40 m3 /det. Kedalaman aliran kritis di atas mercu bendung bangunan spillway diperkirakan setinggi 1.39 m. Elevasi muka air pada saat banjir maksimum adalah 95.66 mdpl di atas mercu bendung spillway, 88.78 - 90.11 mdpl di segmen saluran samping, 88.23 - 88.78 mdpl di segmen saluran transisi, 61.34 - 88.62 mdpl di segmen saluran peluncur, dan 66.28 mdpl di segmen akhir peredam energi., Spillway is a hydraulics building of a dam that functions during an emergency, when the water level of the maximum flood storage volume. This study aims to review the spillway building on the Randugunting Dam based on a study of the existing design of the spillway building, the design discharge of the spillway building, the critical flow depth, and the water level profile of the spillway building. The planned type of spillway building is a side spillway type with an Ogee crest type. The analysis of Banyuasin River catchment area are 17.39 km2 with the river length of 8.52 km. The result of the planned rainfall with a return period of 1000 years is 180.40 mm. The result of discharge with rational method is 124.07 m3/s, while with the Nakayasu HSS method the 2-hour rain distribution is 207.40 m3/s. The critical depth above the weir crest is estimated to be 1.39 m. The maximum water level during flooding is 95.66 masl above the spillway weir crest, 88.78 - 90.11 masl in the side channel segment, 88.23 - 88.78 masl in the transition channel segment, 61.34 - 88.62 masl in the drop channel segment, and 66.28 masl in the stilling basin segment.
Keyword: Critical flow depth, design discharge, water surface profile

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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