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交通工程·道路
12
engines
交通流基本图
Traffic flow fundamental diagram
q=k·v · 抛物线q(k) · 临界密度kc处qmax=3000 · 自由流/拥挤
Flow q, density k and speed v: q = k · v
格林希尔兹模型
Greenshields model
v=vf(1−k/kj) · q=vf(k−k²/kj) · qmax=vf·kj/4在kj/2 · v(60)=50
Linear speed-density v = v_f·(1 − k/k_j) and the parabolic flow it implies
交通冲击波
Traffic shockwave
uw=(q2−q1)/(k2−k1)=弦斜率 · 停车波−16.7km/h逆行 · 时空图
The boundary between two traffic states travels at u_w = (q2 − q1)/(k2 − k1)
跟驰模型:安全距离与通用汽车(GM)模型
Car-following: safe distance & the GM model
安全间距s=s0+vT · GM a=λ·Δv · s(20)=32m · k=31veh/km
s = s0 + v·T — equilibrium spacing grows linearly with speed; a = λ·(v_lead − v_follow) is the stimulus–response
韦伯斯特法:定时信号最佳周期与绿信比
Webster's method: optimal cycle & green split
C0=(1.5L+5)/(1−Y) · gi=(yi/Y)(C0−L) · Y=0.55→C0=37.8s
C0 = (1.5·L + 5) / (1 − Y), gi = (yi/Y)·(C0 − L)
信号交叉口的确定性排队与延误图
Deterministic queueing & delay diagram at a signal
累积到达/离去 · 竖=排队长横=延误面积=总延误 · λ=0.2红30s
Cumulative arrivals A(t) & departures D(t): vertical gap = queue, horizontal gap = per-vehicle delay, area between = total delay
高速公路服务水平 · 交通密度分级
Highway Level of Service · density grading
LOS A–F按密度pc/mi/ln · A≤11/E≈能力/F>45 · 带状图
Grade a basic freeway segment A–F by traffic density (pc/mi/ln), per the HCM
停车视距 SSD · 反应 + 制动
Stopping Sight Distance · reaction + braking
SSD=0.278Vt+V²/(254(f±G)) · V=80→127.6m · 上坡助/下坡增
Stopping sight distance = reaction distance + braking distance, versus speed and grade
无信号支路通行能力 · 间隙接受
Unsignalized Minor-Road Capacity · gap acceptance
cm=vc·e^(−vc·tc/3600)/(1−e^(−vc·tf/3600)) · tc6.5/tf3.5 · 460veh/h
Minor-road potential capacity falls as conflicting major flow rises
干道信号协调与绿波带
Signal Progression & Green-Wave Bandwidth
绿波时空图 · 理想相位差=L/v=26.7s · 通过带宽 · 错时遇红
Time-space diagram: coordinated signal phases and a platoon trajectory
HCM 高速公路通行能力:流率与 v/c
HCM Freeway Capacity: Flow Rate & v/c
PHF高峰系数 · vp=V/(PHF·N)=2222 · 能力2400 · v/c=0.926
From hourly volume and PHF to design flow rate, compared with the 2400 pc/h/ln capacity
路面当量单轴载 ESAL 与四次方定律
Pavement ESAL & the Fourth-Power Law
LEF=(轴载/18kip)^4四次方律 · 36kip=16/18=1/9=0.0625 · ΣESAL
Load equivalency factor LEF = (axle load / 18 kip)^4 — damage rises with the fourth power of load