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Calculation of length of a train passing through a bridge/tunnel

작성자 Uploader : picktime 작성일 Upload Date: 2018-09-06변경일 Update Date: 2018-09-08조회수 View : 289

There is a train which completely passes through a bridge of length LB (m) by the time Bs (s).
If it takes the time Ts(s) for this train to completely pass by a

There is a train which completely passes through a bridge of length LB (m) by the time Bs (s).
If it takes the time Ts(s) for this train to completely pass by a train of length LT (m) running at speed VT (m/s) in the opposite direction, the length of train can be calculated as below.

Letting the train length and speed as L (m) and V (m/s) respectively,

and from the condition of passing the bridge,
V = (L+LB)/Bs

From the condition of passing the train running in the opposite direction

V+VT = (L+LT)/Ts

Removing L in the above two equations and rearranging,,

(L+LB)/Bs+VT = (L+LT)/Ts

(L+LB+VT*Bs)*Ts = (L+LT)*Bs

L*(Ts-Bs) = LT*Bs-LB*Ts-VT*Bs*Ts

L = (LT*Bs - LB*Ts - VT*Bs*Ts) / (Ts-Bs)


*** 참고문헌[References] ***
L = (LT*Bs - LB*Ts - VT*Bs*Ts) / (Ts-Bs)
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변수명 Variable 변수값 Value 변 수 설 명 Description of the variable


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