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碓氷峠EF63

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【与えられた条件 / Given Parameters】

grade = 0.0667 # 勾配(66.7‰ = 6.67%)
m = 400000 # 列車質量 [kg]
g = 9.81 # 重力加速度 [m/s²]
f_r = 0.002 # 転がり抵抗係数
F1 = 196000 # EF64牽引力(1両あたり)[N]


【計算式 / Formulas】

① 勾配抵抗(Gradient resistance)
F_g = m × g × sinθ ≈ m × g × grade

② 転がり抵抗(Rolling resistance)
F_r = m × g × f_r

③ 合計抵抗(Total resistance)
F_total = F_g + F_r

④ 機関車の総牽引力(Total locomotive traction)
F_loco = 2 × F1

⑤ 登坂可能条件(Climbing condition)
条件: F_loco > F_total
余裕牽引力 ΔF = F_loco − F_total


【代入計算 / Substitution】

F_g = 400000 × 9.81 × 0.0667 = 261,828 N
F_r = 400000 × 9.81 × 0.002 = 7,848 N
F_total = 261,828 + 7,848 = 269,676 N
F_loco = 2 × 196,000 = 392,000 N
ΔF = 392,000 − 269,676 = +122,324 N


【判定 / Result】

F_loco > F_total → 登坂可能(Theoretically Possible)


【補足 / Remarks】

現実の運転では以下を考慮する必要がある:
・粘着係数 μ ≈ 0.25〜0.33 により牽引力は制限される
・曲線抵抗(1〜2‰程度の追加抵抗)が加わる
・速度変化による加減速抵抗、風圧、天候の影響
したがって理論上は可能でも、実際には余裕を確保するため
補助機関車 EF63 が併用されていた。

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