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# الباب الثانى

chapter 2

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### الباب الثانى

1. 1. Railway Engineering Chapter (2) Eng: Mohamed Ismail Kotb
2. 2. ‫اﻟرﺣﯾم‬ ‫اﻟرﺣﻣن‬ ‫ﷲ‬ ‫ﺑﺳم‬ ( ‫اﻟﻣﻧﺣﻧﯾﺎت‬ ) ‫اﻟﺛﺎﻧﻰ‬ ‫اﻟﺑﺎب‬ ‫إﻟﻰ‬ ‫اﻟﻣﻧﺣﻧﯾﺎت‬ ‫ﺗﻧﻘﺳم‬: 1(‫اﻟرأﺳﯾﺔ‬ ‫اﻟﻣﻧﺣﻧﯾﺎت‬2(‫اﻷﻓﻘﯾﺔ‬ ‫اﻟﻣﻧﺣﻧﯾﺎت‬ ‫اﻟرأﺳﻰ‬ ‫اﻻﺳﺗدارة‬ ‫ﻟﻣﻧﺣﻧﻰ‬ ‫ﺑﮫ‬ ‫اﻟﺗﺧطﯾط‬ ‫ﯾﻣﻛن‬ ‫ﻗطر‬ ‫ﻧﺻف‬ ‫أﻗل‬ ‫اﻟﻣرﻛزﯾﺔ‬ ‫اﻟطﺎرد‬ ‫اﻟﻘوة‬FC = = ∝ ∝ = 2% ‫ﺑﺎﻟﻤﺘﺮ‬ ‫أﺳﻲ‬‫ﺮ‬‫اﻟ‬ ‫اﻻﺳﺘﺪارة‬ ‫ﻣﻨﺤﻨﻰ‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬:Rv : V‫اﻟﺴﺮﻋﺔ‬(km/h) ‫اﻟﺳﻠس‬ ‫اﻟﺳﯾر‬ ‫ﻟﺗﺣﻘﯾق‬ ‫ﻟﻠﻣﻧﺣﻧﻰ‬ ‫ﻗطر‬ ‫ﻧﺻف‬ ‫أﻧﺳب‬Rv =0.4 V2 ‫ﯾﻘل‬ ‫أﻻ‬ ‫ﯾﺟب‬ ‫و‬Rv‫ﻋن‬)(‫أو‬2000‫أﻛﺑر‬ ‫أﯾﮭﻣﺎ‬ ‫ﻣﺗر‬. ≥‫ﻛﺑﯾرة‬ ‫ﺑدرﺟﺔ‬ ‫اﻟﺳﻛﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺿﻐط‬ ‫ﯾزﯾد‬ ‫ﻻ‬ ‫ﺣﺗﻰ‬. 2000 m≥Rv‫ﻣروﻧﺗﮭﺎ‬ ‫ﺣدود‬ ‫ﻋن‬ ‫اﻟﻔﺧذ‬ ‫ﻛﻣرة‬ ‫ﻓﻰ‬ ‫اﻹﺿﺎﻓﯾﺔ‬ ‫اﻟﺿﻐوط‬ ‫ﺗزﯾد‬ ‫ﻻ‬ ‫ﺣﺗﻰ‬ ‫ﻣﺗر‬. ‫اﻟرأﺳﯾﺔ‬ ‫اﻟﻣﻧﺣﻧﯾﺎت‬ FC w FC w w
3. 3. ‫اﻟرأﺳﯾﺔ‬ ‫اﻟﻣﻧﺣﻧﯾﺎت‬ ‫ﻗواﻧﯾن‬ 1(‫ﻷﻋﻠﻰ‬ ‫رأﺳﻰ‬ ‫ﻣﻧﺣﻧﻰ‬ = 0.4 ∆ = | − | 1000 . = ∗ ∆ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻨﺴﻮب‬a: = ˋ − 2 × | | 1000 ‫ﻧﻘﻄﺔ‬ ‫ﻣﻨﺴﻮب‬b: = ˋ − 2 × | | 1000 ‫اﻟﻣﻧﺣﻧﻰ‬ ‫ﻣﻧﺗﺻف‬ ‫ﻣﻧﺳوب‬c: = 2 = ˋ − cˋ g 1 %o g 2 %o
4. 4. 2(‫ﻷﺳﻔل‬ ‫رأﺳﻰ‬ ‫ﻣﻧﺣﻧﻰ‬ = 0.4 ∆ = | − | 1000 . = ∗ ∆ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻨﺴﻮب‬a: = ˋ + 2 × | | 1000 ‫ﻧﻘﻄﺔ‬ ‫ﻣﻨﺴﻮب‬b: = ˋ + 2 × | | 1000 ‫اﻟﻣﻧﺣﻧﻰ‬ ‫ﻣﻧﺗﺻف‬ ‫ﻣﻧﺳوب‬c: = 2 = ˋ + LV RV x Y y a b c -6‰ +5‰ Dg bˋ g 1 %o g 2 %o
5. 5. ‫اﻟﺑطن‬ ‫ﻋن‬ ‫اﻟظﮭر‬ ‫ارﺗﻔﺎع‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫اﻟﺒﻄﻦ‬ ‫ﻋﻦ‬ ‫اﻟﻈﻬﺮ‬ ‫ﺗﻔﺎع‬‫ر‬‫ا‬ ‫ﻗﻴﻤﺔ‬ ‫اﺳﺘﻨﺒﺎط‬ ‫ﻳﻤﻜﻦ‬E)‫ﻣﻢ‬(‫اﻟﻘﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ﺑﺪﻻﻟﺔ‬R)‫ﻣﺘﺮ‬(‫واﻟﺴﺮﻋﺔ‬V)‫ﻛﻢ‬/‫اﻟﺴﺎﻋﺔ‬(‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﻮﺟﻪ‬ ‫ﻋﻠﻰ‬. FC× Cos = W×sin + DFC sin = G E , Cos 1 FC = W × + DFC × = w × + m × a × = m × g × + m × a a = − × ‫اﻷﻓﻘﯾﺔ‬ ‫اﻟداﺋرﯾﺔ‬ ‫اﻟﻣﻧﺣﻧﯾﺎت‬ ν ‫م‬/‫ث‬ ‫ق‬‫ر‬ = ‫ﻛـ‬.‫س‬2 ‫ر‬ R G E h    FC FC Cos FC sinw w Cos wsin ‫اﻟﻌﺮﺑﺎت‬ ‫ﺛﻘﻞ‬ ‫ﻣﺮﻛﺰ‬ )+ )-( ‫ﻋﺠﻠﺔ‬ ‫اﺗﺠﺎه‬ ‫اﻟﻄﺮد‬ ‫اﻟﻤﺮﻛﺰﯾﺔ‬ FC = R Vm 2 
6. 6. ‫ﺣﻴﺚ‬a=‫ﻛﺰﻳﺔ‬‫اﻟﻤﺮ‬ ‫اﻟﻄﺮد‬ ‫ﻋﺠﻠﺔ‬)‫داﺧﻠﻴﺔ‬ ‫أو‬ ‫ﺧﺎرﺟﻴﺔ‬(‫م‬/‫ث‬2 ‫داﺋﺮي‬ ‫ﺧﻂ‬ ‫ﻋﻠﻰ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺘﺤﺮك‬ ‫ﻣﺎ‬ ‫ﻛﺘﻠﺔ‬‫ﻋﻠﻰ‬ ‫ﺗﺆﺛﺮ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻘﻮة‬ ‫ﻣﻘﺪار‬ ‫ﻋﻠﻰ‬ ‫ﺗﺪل‬ ‫وﻫﻰ‬ ، ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ذو‬R. ‫وﻟﻜﻦ‬ 6.3 )/( hrkmV = ν(m/s)،G=1500‫اﻟﻌﺎدي‬ ‫اﻻﺗﺴﺎع‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ‫ﻣﻢ‬ a = 12.96 − 9.81 1500 a = 12.96 − 153 / (1) OR ∴ = 11.8 − 153 (2) ‫ﻟﻠﻤﻌﺎدﻟﺔ‬ ً‫ﺎ‬‫وﺗﺒﻌ‬)1(‫ﻛﺎﻧﺖ‬‫إذا‬a‫اﻟﺪاﺧﻞ‬ ‫إﻟﻰ‬ ‫ﺗﺆﺛﺮ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫أن‬ ‫ﻋﻠﻰ‬ ‫ﺗﺪل‬ ‫ﻓﺈﻧﻬﺎ‬ ‫ﺳﺎﻟﺒﺔ‬ ‫ﻛﺎﻧﺖ‬‫وإذا‬ ‫اﻟﺨﺎرج‬ ‫إﻟﻰ‬ ‫ﺗﺆﺛﺮ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫أن‬ ‫ﻋﻠﻰ‬ ‫ﺗﺪل‬ ‫ﻓﺈﻧﻬﺎ‬ ‫ﻣﻮﺟﺒﺔ‬. = . × ‫ﺣﺎﻻت‬ ‫ﻓﻰ‬ ‫ﺗﺳﺗﺧدم‬: ، ‫ﺿواﺣﻰ‬ ، ‫ﻣﺗرو‬ ‫ﺧط‬ ‫ﺳرﻋﺔ‬‫ﺛﺎﺑﺗﺔ‬. = × = . × ∑ × × ∑ ‫ﻗطﺎرات‬ ‫ﺳﯾر‬ ‫ﺣﺎل‬ ‫ﻓﻰ‬ ‫ﺗﺳﺗﺧدم‬ ‫أ‬ ‫و‬ ‫ﻣﺧﺗﻠﻔﺔ‬ ‫ﺑﺳرﻋﺎت‬‫ﻣﺧﺗﻠﻔﺔ‬ ‫وزان‬. = ‫اﻟﺣﺻول‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫ﺗﺳﺗﺧدم‬ ‫ﯾﻣﻛن‬ ‫ﺳرﻋﺔ‬ ‫أﻋﻠﻰ‬ ‫ﻋﻠﻰ‬ ‫ﺑﮭﺎ‬ ‫ﯾﺳﯾر‬ ‫أن‬ ‫ﻟﻠﻘطﺎر‬. ‫ﺣﺎﻟﺔ‬ ‫وﻓﻰ‬Emax < E = . × − ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫ﺗﺳﺗﺧدم‬Emin > E
7. 7. ‫ﺳﺮﻋﺘﻪ‬ ‫ﻛﺎﻧﺖ‬‫إذا‬ ‫اﻻﻧﻘﻼب‬ ‫وﺷﻚ‬ ‫ﻋﻠﻰ‬ ‫ﻳﻜﻮن‬ ‫أﻧﻪ‬ ‫ﻓﺄﺛﺒﺖ‬ ، ‫ﺑﻄﻦ‬ ‫ﻋﻦ‬ ‫ﻇﻬﺮ‬ ‫ﺗﻔﺎع‬‫ر‬‫ا‬ ‫ﺑﺪون‬ ‫ﻣﻨﻔﺬ‬ ‫أﻓﻘﻰ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫ﻋﻠﻰ‬ ‫ﻗﻄﺎر‬ ‫ﺳﺎر‬ ‫إذا‬: ≅ 8 ∙ ℎ ‫ﺣﻴﺚ‬ G :‫اﻟﺴﻜﺔ‬ ‫اﺗﺴﺎع‬)‫اﻟﻘﻀﺒﺎن‬ ‫ﻣﺤﺎور‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬-‫ﻣﺘﺮ‬( R :‫اﻟﻤﻨﺤﻨﻰ‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬)‫ﻣﺘﺮ‬( h :‫اﻟﻘﻀﺒﺎن‬ ‫ﺳﻄﺢ‬ ‫ﻋﻦ‬ ‫اﻟﺜﻘﻞ‬ ‫ﻛﺰ‬‫ﻣﺮ‬ ‫ﺗﻔﺎع‬‫ر‬‫إ‬)‫ﻣﺘﺮ‬( ‫اﻟﺣ‬‫ــــ‬‫ل‬ ‫اﻟﻮزن‬ ‫ﻧﺘﻴﺠﺔ‬ ‫اﻟﻔﻌﻞ‬ ‫رد‬Re 2 w = ‫ﻛﺰ‬‫اﻟﻤﺮ‬ ‫اﻟﻄﺎردة‬ ‫اﻟﻘﻮة‬ ‫ﻧﺘﻴﺠﺔ‬ ‫اﻟﻔﻌﻞ‬ ‫رد‬‫ﻳﺔ‬DRe × = ‫ـﺪاﺧﻠﻲ‬‫ـ‬‫ﻟ‬‫ا‬ ‫ـﻴﺐ‬‫ـ‬‫ﻀ‬‫اﻟﻘ‬ ‫ـﻰ‬‫ـ‬‫ﻠ‬‫ﻋ‬ ‫ـﻞ‬‫ـ‬‫ﻌ‬‫اﻟﻔ‬ ‫رد‬ ‫ـﺒﺢ‬‫ـ‬‫ﺻ‬‫أ‬ ‫إذا‬ ‫ـﻼب‬‫ـ‬‫ﻘ‬‫اﻻﻧ‬ ‫ـﻚ‬‫ـ‬‫ﺷ‬‫و‬ ‫ـﻰ‬‫ـ‬‫ﻠ‬‫ﻋ‬ ‫ـﺎر‬‫ـ‬‫ﻄ‬‫اﻟﻘ‬ ‫ـﺒﺢ‬‫ـ‬‫ﺼ‬‫ﻳ‬ ‫ﺻﻔﺮ‬ ‫ﻳﺴﺎوي‬ Re = DRe × = × × . × . × × = . × × = ≅ × G h FE w ReRe DReDRe
8. 8. ‫ارﺗﻔﺎع‬ ‫ﻣﻧﺣدر‬‫اﻻﻧﺗﻘﺎل‬ ‫وﻣﻧﺣﻧﻰ‬ ‫اﻟﺑطن‬ ‫ﻋن‬ ‫اﻟظﮭر‬  =  = × = 150  = × /ℎ  L = 1000 10 )()( ff EV   Sh = R LS 24 2 ‫اﻟ‬‫ﻣﻧﺣ‬‫اﻟﻣرﻛب‬ ‫ﻧﻰ‬  IF (R2 > R1 )  = × = 150  = × /ℎ ( v is the future speed)  = ×
9. 9. L = 10 ( ) ( ) 1000 L = 10 ( ) ( ) 1000 L = L − L Sh = 1 2 24 1 Sh = 2 2 24 2 Sh = Sh − Sh ‫إ‬‫اﻟظﮭر‬ ‫رﺗﻔﺎع‬‫اﻟﺣﺎﻟﻲ‬ ‫اﻟﺑطن‬ ‫ﻋن‬ = 8 × = × (V is present speed ) ‫اﻟﻌﻛﺳﻲ‬ ‫ﻟﻠﻣﻧﺣﻧﻰ‬ ‫اﻟﺑطن‬ ‫ﻋن‬ ‫اﻟظﮭر‬ ‫ارﺗﻔﺎع‬ ‫ﻣﻧﺣدر‬ ‫ﺗﻧﻔﯾذ‬ ‫طرق‬: 1(‫ﻣﺳﺎﻓﺔ‬ ‫ﺗرك‬ ‫ﻣﻊ‬ ‫اﻟﺧﺎرﺟﻲ‬ ‫اﻟﻘﺿﯾب‬ ‫رﻓﻊ‬‫اﻟﺛﺎﻧﻲ‬ ‫اﻟﻣﻧﺣدر‬ ‫وﺑداﯾﺔ‬ ‫اﻷول‬ ‫اﻟﻣﻧﺣدر‬ ‫ﻧﮭﺎﯾﺔ‬ ‫ﺑﯾن‬ ‫ﻣﺳﺗﻘﯾﻣﺔ‬. .ً‫ا‬‫ﺟد‬ ‫ﻗﻠﯾل‬ ‫زﻣن‬ ‫ﻓﻲ‬ ‫اﻟﻣﺳﺗﻘﯾﻣﺔ‬ ‫اﻟﻣﺳﺎﻓﺔ‬ ‫وﻧﮭﺎﯾﺔ‬ ‫ﺑداﯾﺔ‬ ‫ﻋﻧد‬ ‫ﺻدﻣﺔ‬ ‫ﺣدوث‬ : ‫ﻋﯾﺑﮭﺎ‬ 2(‫اﻟﺛﺎﻧﻲ‬ ‫اﻟﻣﻧﺣﻧﻰ‬ ‫ﻓﻲ‬ ‫اﻟداﺧﻠﻲ‬ ‫اﻟﻘﺿﯾب‬ ‫وﺧﻔض‬ ‫اﻷول‬ ‫اﻟﻣﻧﺣﻧﻰ‬ ‫ﻓﻲ‬ ‫اﻟﺧﺎرﺟﻲ‬ ‫اﻟﻘﺿﯾب‬ ‫رﻓﻊ‬. : ‫ﻋﯾوﺑﮭﺎ‬ -‫اﻟﺻﻌب‬ ‫ﻣن‬ ‫ﻟﻛن‬ ‫اﻟﻘﺿﯾب‬ ‫ﻣﻧﺳوب‬ ‫رﻓﻊ‬ ‫اﻟﺳﮭل‬ ‫ﻣن‬‫ﻣﻧﺳوﺑﮫ‬ ‫ﺧﻔض‬ ً‫ا‬‫ﺟد‬. -‫اﻟﻣﻧﺣﻧﻰ‬ ‫ﻓﻰ‬ ‫ﺗﻌطﻰ‬ ‫اﻟﻣﻘﺎرﻧﺔ‬ ‫ﻧﻘط‬ ‫ﻣﻧﺎﺳﯾب‬)2(‫إذ‬ ، ‫اﻟﺻﯾﺎﻧﺔ‬ ‫ﻟﻌﻣﺎل‬ ‫ﻣﻌﺗﺎد‬ ‫ھو‬ ‫ﻣﺎ‬ ‫ﺧﻼف‬ ‫ﻋﻠﻰ‬ ‫اﻟﺧﺎرﺟﻰ‬ ‫اﻟﻘﺿﯾب‬ ‫ﻋﻠﻰ‬ ‫اﻟداﺧﻠﻰ‬ ‫اﻟﻘﺿﯾب‬ ‫ﻋﻠﻰ‬ ً‫ﺎ‬‫داﺋﻣ‬ ‫ﺗﻧﺳب‬ ‫أﻧﮭﺎ‬. 3(‫ﻓﻲ‬ ‫وﺿﻌﮭﻣﺎ‬ ‫ﯾﺗﺑدل‬ ‫ﺣﺗﻰ‬ ‫اﻟوﻗت‬ ‫ﻧﻔس‬ ‫ﻓﻲ‬ ‫اﻟداﺧﻠﻲ‬ ‫اﻟﻘﺿﯾب‬ ‫ﻣﻧﺳوب‬ ‫رﻓﻊ‬ ‫ﻣﻊ‬ ‫اﻟﺧﺎرﺟﻲ‬ ‫اﻟﻘﺿﯾب‬ ‫ﻣﻧﺳوب‬ ‫ﺗﺧﻔﯾض‬ ‫اﻟﺛﺎﻧﻲ‬ ‫اﻟﻣﻧﺣﻧﻰ‬. .ً‫ﺎ‬‫داﺋﻣ‬ ‫اﻟﻣﺗﺑﻌﺔ‬ ‫اﻟﺳﻠﯾﻣﺔ‬ ‫اﻟطرﯾﻘﺔ‬ ‫وھﻰ‬ ‫اﻟﺳﺎﺑﻘﺔ‬ ‫اﻟﻌﯾوب‬ ‫ﺗﺗﻼﻓﻰ‬ : ‫ﻣﻣﯾزاﺗﮭﺎ‬ ‫اﻟﻌﻛﺳﻰ‬ ‫اﻟﻣﻧﺣﻧﻰ‬
10. 10. ‫اﻟﻌﻛﺳﻰ‬ ‫اﻟﻣﻧﺣﻧﻰ‬ ‫ﺗﺻﻣﯾم‬  IF (R2 > R1 )  = × = 150  = × /ℎ ( v is the future speed) R1 R2 E1 LS E2 LS 1:n 1:n E1 LS1 E2 LS2 1:n 1:n V 10  E1 LS E2 LS ym yn En xn ‫ﻟﻠﻤﻨﺤﻨﯿﯿﻦ‬ ‫اﻷﻓﻘﻰ‬ ‫اﻟﻤﺴﻘﻂ‬ ‫أ‬(‫ﻓﻰ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﺗﺮك‬ ‫ب‬(‫اﻟﻈﮭﺮ‬ ‫ﻋﻦ‬ ‫اﻟﺒﻄﻦ‬ ‫ﺗﺨﻔﯿﺾ‬‫ﻓﻰ‬ ‫ﺟـ‬(‫اﻟﻌﻜﺴﻰ‬ ‫اﻟﻤﻨﺤﺪر‬ ER1 SR1 SR2 ER2
11. 11.  = × L = 10 ( ) ( ) 1000 L = 10 ( ) ( ) 1000 = .5 (L + L ) ≥. ( + ) < .5 ( + ) = .5 (L + L ) > .5 ( + ) L = 8 ( ) ( ) 1000 L = 8 ( ) ( ) 1000 L +L = 2X AB … … .1 = 2 1 ………2 solve <. ( + ) Reduce the speed L +L = 2X AB 80 ( ) 1000 1 + 80 ( ) 1000 2 = 2X AB ّ‫اﻟﻠﻲ‬‫اﻟذى‬‫واﺣد‬ ‫إطﺎر‬ ‫ﻓﻲ‬ ‫ﻣﺛﺑﺗﯾن‬ ‫ﻣﺣورﯾن‬ ‫ذات‬ ‫ﺑﺿﺎﻋﺔ‬ ‫ﻋرﺑﺔ‬ ‫ﻟﮭﺎ‬ ‫ﺗﺗﻌرض‬ ‫ﺑﻣﻘدار‬ ‫اﻷﺧرﯾﺎت‬ ‫ﻋن‬ ‫ﺗﻧﺧﻔض‬ ‫أو‬ ‫اﻟﻌﺟﻼت‬ ‫إﺣدى‬ ‫ﺗرﺗﻔﻊ‬ ‫اﻟﻣﻧﺣدر‬ ‫ﻋﻠﻰ‬ ‫ﻣﺣورﯾن‬ ‫ﻣرور‬ ‫ﻧﺗﯾﺟﺔ‬ ، ‫اﻟﻣوﺿﺢ‬ ‫اﻟرﺳم‬ ‫ﻣن‬‫ﺔ‬‫زاوﯾ‬ ‫ﺗﺻﺑﺢ‬ ‫وﺑذﻟك‬ ّ‫اﻟﻠﻲ‬‫ﻛﺎﻵﺗﻲ‬:(rad) = nG d  IF AB (given) E G d 1:n d
12. 12. ‫اﻟﺣدﯾدﯾﺔ‬ ‫ﻟﻠﺳﻛك‬ ‫اﻟدوﻟﻲ‬ ‫اﻻﺗﺣﺎد‬ ‫ﻟﻣواﺻﻔﺎت‬ ً‫ﺎ‬‫طﺑﻘ‬ ‫اﻟﺧﺷن‬ ‫اﻟﺳﯾر‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ nmin = 8V 8V = 400 V = 50 km/hr ‫اﻟﺳﻠس‬ ‫اﻟﺳﯾر‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ nst = 10V 10V = 400 V = 40 km/hr ‫اﻟرأﺳﻰ‬ ‫اﻟﻣﻧﺣﻧﻰ‬ ‫ﻣﻊ‬ ‫اﻷﻓﻘﻰ‬ ‫اﻟﻣﻧﺣﻧﻰ‬ ‫اﻟرأﺳﻰ‬ ‫اﻟﻣﻧﺣﻧﻰ‬ ‫أﻻﯾﺗداﺧل‬ ‫ﯾﺟب‬‫اﻻﻧﺗﻘﺎل‬ ‫ﻣﻧﺣﻧﻰ‬ ‫ﻣﻊ‬  AB = .5X (LS + LV) ≥. ( + ) < .5 ( + ) = .5 (L + L ) > .5 ( + ) L = 8 ( ) ( ) 1000 L = L +L = 2X AB … … .1 <. ( + ) Reduce the speed L +L = 2X AB 80 ( ) 1000 + ( )X θ = 2X AB IF AB (given)
13. 13. ‫ﺑطن‬ ‫ﻋن‬ ‫ظﮭر‬ ‫ارﺗﻔﺎع‬ ‫ﺑدون‬ ‫اﻟﻣﻧﺣﻧﯾﺎت‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫ﻟﻠﺧط‬ ‫اﻟﻘﺻوى‬ ‫واﻟﺳرﻋﺔ‬ ‫اﻷﻓﻘﯾﺔ‬ ‫اﻟداﺋرﯾﺔ‬ ‫اﻟﻣﻧﺣﻧﯾﺎت‬ ‫أﻗطﺎر‬ ‫أﻧﺻﺎف‬ ‫ﺑﯾن‬ ‫اﻟﻌﻼﻗﺔ‬‫اﺗﺻﺎل‬‫رة‬‫ﻣﺑﺎﺷ‬ ‫ﮭﺎ‬‫ﺑﺑﻌﺿ‬ ‫ﺎت‬‫اﻟﻣﻧﺣﻧﯾ‬ ‫ھذه‬ ‫ﻣﻧﺣﻧﯾﺎت‬ ‫ﺑدون‬‫اﻧﺗﻘﺎل‬‫ﺗﻧﻔﯾذ‬ ‫أو‬‫ارﺗﻔﺎع‬‫ﺑطن‬ ‫ﻋن‬ ‫ظﮭر‬. a = R V 96.12 2 - 153 E ‫ﺣﺎﻟﺔ‬ ‫وﻓﻲ‬E=‫ﺻﻔﺮ‬ a = R V 96.12 2 = 100096.12 2   KV Δa = 12960 2 KV D ‫أن‬ ‫ﺑﺎﻟﺘﺠﺮﺑﺔ‬ ‫وﺟﺪ‬ ‫وﻗﺪ‬Δa‫ﻋﻦ‬ ‫زادت‬ ‫إذا‬ ‫ﺧﻄﺮة‬ ‫ﺗﺼﺒﺢ‬0.7‫م‬/‫ث‬2 ΔK  2 7.012960 V   2 9000 V ‫ﻣﻧﺣﻧﯾﺎت‬ ‫ﺑدون‬ ‫ﺑﺑﻌﺿﮭﺎ‬ ‫اﻟﻌﻛﺳﯾﺔ‬ ‫اﻷﻓﻘﯾﺔ‬ ‫اﻟداﺋرﯾﺔ‬ ‫اﻟﻣﻧﺣﻧﯾﺎت‬ ‫اﺗﺻﺎل‬ ‫ﻋﻧد‬ ‫ﺗواﻓرھﻣﺎ‬ ‫اﻟواﺟب‬ ‫اﻟﺷرطﺎن‬‫ھﻣﺎ‬ ‫اﻧﺗﻘﺎل‬: 1) ΔK  2 9000 V 2) ΔK  10 1(‫ﻣرﻛب‬ ‫و‬ ‫ﺑﺳﯾط‬ ‫ﻣﻧﺣﻧﻰ‬  a = R V 96.12 2 ( a≯.65 )‫اﻟﻣرﻛزﯾﺔ‬ ‫اﻟطرد‬ ‫ﻋﺟﻠﺔ‬ ‫ﺷرط‬ = . 2(‫ﻋﻛﺳﻰ‬ ‫ﻣﻧﺣﻧﻰ‬  a = R V 96.12 2 a≯.65 = .
14. 14.  Δa = 12960 2 KV D )‫اﻟﻣرﻛزﯾﺔ‬ ‫اﻟطرد‬ ‫ﻋﺟﻠﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺗﻐﯾر‬ ‫ﺷرط‬Δa≮.7‫م‬/‫ث‬2 ( ΔK  2 7.012960 V   2 9000 V ‫ﺣﺎﻟﺔ‬ ‫وﻓﻰ‬R‫اﻟﻌﻜﺴﻰ‬ ‫اﻟﻤﻨﺤﻨﻰ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﻳﺔ‬ ΔK = 2 9000 V = . ‫ﺣﺎﻛﻢ‬ ‫اﻧﺤﺪار‬ ‫وﺟﻮد‬ ‫ﺣﺎﻟﺔ‬ ‫وﻓﻰ‬ ‫اﻟﻣﻧﺳوب‬ ‫ﻓرق‬=‫اﻷﻓﻘﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺎت‬+‫اﻟﻤﻨﺤﻨﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫اﻟﺛﻼﺛﺔ‬ ‫اﻟﺷروط‬ ‫ﺗﺣﻘﯾق‬ ‫ﻋﻠﻰ‬ ‫ﯾﻌﻣل‬ ‫ﻗطر‬ ‫ﻧﺻف‬ ‫أﻗل‬ ‫ﻋﻠﻰ‬ ‫اﻟﺣﺻول‬ ‫ﯾﺗم‬ ‫وﺑذﻟك‬: 1(‫اﻟﻣرﻛزﯾﺔ‬ ‫اﻟطرد‬ ‫ﻋﺟﻠﺔ‬ ‫ﺷرط‬a≯.65 2(‫اﻟﻣرﻛزﯾﺔ‬ ‫اﻟطرد‬ ‫ﻋﺟﻠﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺗﻐﯾر‬ ‫ﺷرط‬Δa≮.7‫م‬/‫ث‬2 3(‫اﻟﺣﺎﻛم‬ ‫اﻻﻧﺣدار‬ ‫ﺷرط‬