CELE Transportation & Highway Engineering — Ports, Harbors, Airports and RailroadsRevision Notes

Formulas

Exam Tips

• Memorize e = GV²/(127R) — the constant 127 appears in both highway and railway formulas. For railways, G is always in the numerator.
• If the problem gives gauge in mm (e.g., 1435 mm), convert to meters first before substituting.
• When asked for cant in mm, compute in meters first then multiply by 1000.
• For board exams, standard gauge = 1.435 m unless the problem explicitly states otherwise.
• Ruling gradient questions often ask which gradient limits train load — always the steepest (not the average) grade on the line.

Key Points

• Standard gauge (Philippine and international) = 1.435 m (distance between inner faces of rail heads).
• Narrow gauge (used in some older Philippine lines) = 1.067 m; this value may appear in legacy board problems.
• Superelevation (cant) of the outer rail on a curve is provided to counteract centrifugal force and improve passenger comfort.
• The equilibrium cant formula: e = GV²/(127R), where G is gauge (m), V is speed (km/h), R is curve radius (m).
• The constant 127 ≈ 2g/3.6² × 10⁻³ and applies consistently when V is in km/h and R in m — same constant as road superelevation.
• Ruling gradient is the steepest grade that limits the load a locomotive can haul; it governs train capacity on a line.
• Transition curves (spirals) are inserted between tangent track and circular curves to allow gradual introduction of curvature and cant.
• Check rails (guard rails) are placed on sharp curves (small R) to prevent derailment by constraining wheel flanges.
• Ballast (crushed stone) provides drainage, distributes load from sleepers to subgrade, and maintains track geometry.
• Maximum permissible cant in practice is limited to about 150–180 mm on most rail lines to avoid excessive discomfort for slow trains.

Definitions

Section Title

Railroad Engineering

Common Mistakes

• Using the road superelevation formula (e = V²/127R without gauge G) instead of the railway cant formula — always include G in the numerator for railways.
• Forgetting to keep V in km/h and R in meters; the constant 127 is only valid for these units.
• Confusing maximum cant (practical limit, ≈150–180 mm) with the computed equilibrium cant — the actual cant set is the lesser value.
• Mixing up gauge values: 1.435 m (standard) vs. 1.067 m (narrow) — read the problem carefully.
• Applying the chord-definition degree-of-curve formula with a 20-m chord (highway) instead of a 30-m chord (railway).

Formulas

Exam Tips

• Always apply the three corrections in order: (1) Elevation → (2) Temperature → (3) Gradient. The problem may give only one or two corrections — apply only those specified.
• Compute T_ISA = 15 − 6.5×(H/1000) first, then ΔT = T_ART − T_ISA. If ΔT ≤ 0 (cool airport), no temperature correction is needed.
• The elevation correction per 300 m is exactly 7% (0.07). For non-multiples of 300 m, use the proportional formula: factor = 0.07 × (H/300).
• For wind rose questions: the runway heading that intercepts the largest arc of the wind rose (covering ≥ 95% of observations within allowable crosswind limits) is selected.
• Remember: corrections always increase runway length (never decrease) because all three factors (altitude, heat, gradient) reduce aircraft performance.

Key Points

• Runway orientation is determined by the wind rose to maximize 'wind coverage' — the percentage of time crosswind components are within the allowable limit; ICAO requires ≥ 95% coverage.
• The wind rose is a polar diagram showing wind speed and direction frequency; the runway is aligned along the dominant wind direction to minimize crosswind.
• ICAO Annex 14 governs airport design; Philippine airports follow CAAP (Civil Aviation Authority of the Philippines) standards aligned with ICAO.
• Basic runway length is determined from aircraft performance data (balanced field length) at sea level, ISA (International Standard Atmosphere) conditions, zero gradient.
• Three successive corrections are applied to basic runway length: (1) Elevation, (2) Temperature, (3) Gradient.
• Elevation correction: +7% per 300 m of airport elevation above MSL (ICAO standard). Applied first.
• Temperature correction: +1% per °C of airport reference temperature (ART) above the standard atmosphere temperature at that elevation (ISA temperature = 15°C − 6.5°C per 1000 m of elevation). Applied to the elevation-corrected length.
• Gradient correction: +10% per 1% of effective gradient (ICAO). Applied last to the elevation-and-temperature-corrected length.
• If elevation + temperature correction exceeds 35%, ICAO recommends a detailed study — this is a knowledge point, not a recalculation procedure for board exams.
• Runway strips, clearways, stopways, and runway end safety areas (RESA) are additional runway protection zones.
• Taxiways connect runways to aprons; aprons (ramps) are parking/servicing areas for aircraft.
• Runway pavement is designed for critical aircraft (ACN–PCN method): Aircraft Classification Number vs. Pavement Classification Number.
• ILS (Instrument Landing System) precision approach categories (CAT I, II, III) determine obstacle limitation surfaces and visibility minima.
• Runway declared distances: TORA (Take-Off Run Available), TODA (Take-Off Distance Available), ASDA (Accelerate-Stop Distance Available), LDA (Landing Distance Available).

Definitions

Section Title

Airport Engineering

Common Mistakes

• Applying the temperature correction as 1% per °C above 15°C (sea-level ISA) instead of above the ISA temperature at the airport's actual elevation — T_ISA = 15 − 6.5×(H/1000).
• Applying corrections additively (adding percentages) instead of multiplicatively (successive multiplication). Each corrected length becomes the input for the next correction.
• Using effective gradient as rise-over-run of the entire runway, but forgetting to express it as a percentage before multiplying by 10%.
• Forgetting the order of corrections: Elevation first, Temperature second, Gradient last.
• Confusing TORA with physical runway length — TORA may be shorter if a displaced threshold exists.

Formulas

Exam Tips

• Channel depth formula is simple: D = draft + UKC. Memorize it and watch the datum reference in the problem statement.
• Board problems usually give draft and UKC directly — just add them. If tidal range is given, the problem should specify at what tide level UKC is required.
• Know the distinction: wharf/quay = parallel to shore; pier = perpendicular to shore; dolphin = isolated structure in water.
• DWT is carrying capacity; displacement is total weight of vessel (carrying capacity + vessel weight). For depth calculation, only draft matters.
• For breakwater type questions: rubble-mound is more common in moderate depths with available rock; vertical (caisson) is used in deep water.

Key Points

• A harbor is a naturally or artificially sheltered body of water where ships can anchor, load, and unload safely.
• Key structures: breakwaters (wave protection), wharves/quays (alongside berthing), piers (projecting from shore), dolphins (isolated mooring structures), bollards (mooring points).
• A berth is a designated space where a vessel moors; a turning basin is an open water area where vessels maneuver to enter/exit berths.
• Minimum channel depth = design vessel draft + under-keel clearance (UKC). Typical UKC = 0.5–1.5 m depending on bottom type and wave conditions.
• All depths are referenced to a tidal datum — typically Lowest Low Water (LLW) or Mean Lower Low Water (MLLW) in Philippine practice.
• Tidal range affects available depth: at high tide, depth increases by the tidal range; design is governed by worst case (low tide).
• Breakwaters may be rubble-mound, composite, or vertical (caisson) type; selection depends on water depth, wave climate, and available materials.
• Dredging is the excavation of underwater material to achieve the design channel depth; maintenance dredging restores depth lost to sedimentation.
• Quay walls resist horizontal earth/water pressure and vertical ship loads; they may be gravity, sheet-pile, or anchored types.
• Port planning considers: vessel size (length, beam, draft, DWT — deadweight tonnage), traffic volume, cargo type (bulk, container, RoRo, liquid bulk), and landside connections.

Definitions

Section Title

Ports and Harbors

Common Mistakes

• Forgetting to reference channel depth to tidal datum — stating depth as 'below water surface' when water surface varies with tide.
• Adding UKC to the vessel's deadweight tonnage instead of to the loaded draft — DWT and draft are different quantities.
• Confusing a pier (perpendicular to shore) with a wharf/quay (parallel to shore) in definitional questions.
• Using displacement tonnage instead of deadweight tonnage to describe vessel size — they differ by the vessel's light weight.
• Neglecting squat effect (vessel sinks slightly when moving due to Bernoulli effect) when UKC seems adequate at rest — this is a conceptual caution, not usually numerically tested at board level.