PE Transportation cheat sheet

Fundamental flow identity: q = k × u, where flow is in veh/h, density in veh/mi, and speed in mi/h; any two variables determine the third in uninterrupted flow.

Freeway basic segment LOS is set by density (pc/mi/ln): A ≤ 10; B >10–20; C >20–28; D >28–35; E >35–45; F >45.

Signalized intersection LOS is set by average control delay (s/veh): A ≤ 10; B >10–20; C >20–35; D >35–55; E >55–80; F > 80.

Two-way stop-controlled minor-street capacity: c = v·e^(−v·t)/(1 − e^(−v·t_f)), with v the conflicting flow rate, t the critical gap, and t_f the follow-up time.

HCM base saturation flow is 1900 pc/h/ln for through lanes; adjustments cover lane width, heavy vehicles, grade, parking, bus blockage, area type, and turning movements.

Webster optimal cycle length: C_o = (1.5L + 5)/(1 − Y), where L is total lost time per cycle in seconds and Y is the sum of critical flow ratios.

Peak hour factor: PHF = peak-hour volume / (4 × peak 15-min volume); values range from 0.25 to 1.00, and the 15-min flow rate equals the hourly volume divided by PHF.

Greenshields linear model: u = u_f(1 − k/k_j); capacity occurs at k = k_j/2 and u = u_f/2.

Yellow change interval: y = t + v/(2a + 2gG), with t ≈ 1.0 s perception-reaction, v in ft/s, a ≈ 10 ft/s², and G the approach grade.

Stopping sight distance: SSD = 1.47Vt + V²/[30(f ± G)], with V in mph, brake reaction time t = 2.5 s, and the grade term added on upgrades and subtracted on downgrades.

Minimum horizontal curve radius: R = V²/[15(e + f_s)], with V in mph and superelevation e and side friction f_s as decimals.

Typical maximum superelevation is 4% to 8% (commonly 6% in urban areas, 8% in rural); the allowable side friction factor drops as design speed rises.

Crest vertical curve with S < L: L = A·S²/2158, where A is the algebraic grade change in percent and S is stopping sight distance in feet (eye 3.5 ft, object 2.0 ft).

Sag vertical curve with S < L: L = A·S²/(400 + 3.5S), based on headlight sight distance with the headlamp 2 ft above pavement at a 1-degree upward angle.

Vertical curve K = L/A is the horizontal distance for a 1% grade change; larger K produces flatter curves, and minimum K is tabulated by design speed for SSD.

Normal pavement crown is 2%; maximum grades for level terrain are roughly 3% to 4% at high design speeds and increase for rolling and mountainous terrain.

Intersection sight triangles use legs measured along each approach, with the length along the major road set by the stopping sight distance of the major-road approach.

Passing sight distance on two-lane highways is tabulated by design speed (for example about 2,135 ft at 60 mph and 2,480 ft at 70 mph).

The four-step model runs sequentially: trip generation, trip distribution, mode choice, and route assignment, producing link volumes and ridership estimates.

Gravity distribution: T_ij = P_i·A_j·F_ij / Σ_k(A_k·F_ik), where F is an impedance (friction) factor typically decaying with travel time or cost.

Federal law requires a metropolitan planning organization for every urbanized area with population of 50,000 or more.

ITE Trip Generation data provide an independent variable (e.g., 1,000 sq ft GFA), an average rate, a regression equation, the R², and the number of data points; rates are preferred unless the equation fits better.

Functional classification - arterial, collector, local - balances mobility against access and drives design standards, federal funding eligibility, and reporting.

Transportation conformity requires long-range plans and TIPs to not worsen air-quality violations relative to the state implementation plan for NAAQS.

Demand elasticity = percent change in demand divided by percent change in price, fare, or travel cost; short-run fuel elasticities are small, long-run values are larger.

Volume-to-capacity ratios and planning LOS thresholds are used for sketch-level screening before detailed HCM analysis.

Travel demand management measures - parking pricing, transit subsidies, rideshare programs, telework - target peak-period single-occupant vehicle trips.

Crash rate per million entering vehicles: R = (N × 1,000,000)/(ADT × 365 × T), where N is the number of crashes in T years.

Roadway segment rate per 100 million vehicle-miles: R = (N × 100,000,000)/(ADT × 365 × L × years), with L the segment length in miles.

Critical crash rate: Rc = Ra + K·√(Ra/M) + 1/(2M), where Ra is the average rate of similar sites, M is exposure in million entering vehicles, and K sets the confidence level.

HSM predictive method: N_predicted = N_SPF × CMF1 × CMF2 × … × C, multiplying the safety performance function output by crash modification factors and a calibration factor.

A crash modification factor below 1.0 indicates a crash reduction; above 1.0 indicates an increase, and combined CMFs are multiplied together.

Empirical Bayes: N_EB = w·N_predicted + (1 − w)·N_observed, with w = 1/(1 + k·N_predicted); this corrects for regression to the mean in observed counts.

KABCO severity scale: K fatal, A suspected serious (disabling) injury, B minor (evident) injury, C possible injury, O property-damage-only.

EPDO analysis converts injury crashes into property-damage-only equivalents using severity weighting factors so sites with different severity mixes can be ranked.

Before-after evaluations use comparison groups or the empirical Bayes method to separate treatment effects from crash count trends and regression to the mean.

Structural number: SN = a1·D1 + a2·m2·D2 + a3·m3·D3, with typical layer coefficients near 0.44 for asphalt concrete and 0.14 for granular base.

AASHTO 1993 flexible design: log10W18 = ZR·S0 + 9.36·log10(SN+1) − 0.20 + log10[ΔPSI/(4.2 − 1.5)]/[0.40 + 1094/(SN+1)^5.19].

AASHTO 1993 rigid design uses slab thickness D and a serviceability loss of (4.5 − 1.5) rather than (4.2 − 1.5) in the performance equation.

An 18,000-lb single axle with dual tires equals one ESAL; the truck factor is the ESALs per truck and is multiplied by design-lane truck volume and growth.

Resilient modulus for fine-grained subgrade soils with CBR ≤ 10: Mr (psi) ≈ 1500 × CBR.

Performance-graded binder such as PG 64-22 must satisfy a high pavement temperature of 64 °C for rutting and a low temperature of −22 °C for thermal cracking.

Superpave volumetric design targets 4% air voids at the design traffic level and checks VMA, VFA, and dust-to-binder ratio (typically 0.6 to 1.2).

Rigid pavement design uses the modulus of subgrade reaction k (psi/in) and concrete modulus of rupture; dowel bars transfer load across transverse joints.

Reliability enters AASHTO design through ZR: 50% ≈ 0, 90% ≈ −1.282, 95% ≈ −1.645, 99% ≈ −2.327, with S0 about 0.45 flexible and 0.35 rigid.

Dense-graded asphalt mixtures are typically accepted at 92% or more of maximum theoretical specific gravity (Gmm), determined from cores or gauges and reported as lot averages.

MUTCD merging taper length: L = W·S²/60, where W is the lateral offset in feet and S is the speed limit in mph.

Tack coat is applied to the existing surface at roughly 0.05 to 0.15 gal/yd² of emulsion, with the rate reduced for open, coarse surfaces versus tight surfaces.

Quality assurance acceptance commonly uses percent within limits (PWL), which credits both the lot mean and lot variability relative to specification limits.

Pavement condition index ranges from 0 to 100, with 100 for new pavement and 0 for failed pavement; it drives treatment selection in pavement management systems.

Concrete joint sawing must begin within the window before random cracking develops, often about 4 to 12 hours after placement depending on weather and mix.

Preventive maintenance treatments include crack sealing, fog seal, chip seal, slurry seal, microsurfacing, and thin overlays; each addresses a specific distress.

Recycled asphalt pavement is routinely allowed at 15% to 25% in hot-mix surface courses, with higher percentages in base layers and cold recycling.

Work zone activity areas require a buffer space plus longitudinal buffer based on speed, and drop-offs at milled edges must be controlled before opening to traffic.