CELE Transportation & Highway Engineering — Highway Engineering and Geometric DesignCheat Sheet
Highway Engineering and Geometric Design cheat sheet for CELE aspirants. If you could only take one sheet of paper into your review session, this is what it would look like. Professional Regulation Commission (PRC) — Board of Civil Engineering's most-tested concepts, all in one place.
Exam context
On the CELE 2026, the Transportation & Highway Engineering subtest carries a "Core" weight in Professional Regulation Commission (PRC) — Board of Civil Engineering's pattern. Highway Engineering and Geometric Design lands at position 1st out of 4 in the standard review order. Target score is 70% weighted average, no sub-test below 50%, and roughly a meaningful share of items come from Transportation & Highway Engineering on a typical CELE paper.
Highway Engineering and Geometric Design - Cheat Sheet
Your last-minute revision companion for Highway Engineering and Geometric Design. This cheat sheet covers stopping sight distance, horizontal and vertical alignment, superelevation, cross-section design, and key formulas for the PRC Civil Engineer Licensure Examination.
Sections
Formulas
Formula
SSD = 0.278Vt + V²/[254(f ± G)]
Meaning
V = design speed (km/h); t = reaction time (s); f = longitudinal friction coefficient; G = grade (decimal, + for upgrade, − for downgrade)
Watch Out
Grade sign REVERSES effect: +G shortens SSD (uphill helps braking), −G lengthens it (downhill resists braking). Most common error is forgetting the grade term entirely or using wrong sign.
When To Use
Every problem involving safe stopping distance on a roadway, level or graded
Common Values
Value
2.5 s
Symbol
t
Quantity
Standard reaction time
Value
0.30–0.40
Symbol
f
Quantity
Friction coefficient (dry asphalt)
Value
0.20–0.30
Symbol
f
Quantity
Friction coefficient (wet asphalt)
Section Title
Stopping Sight Distance (SSD)
Important Facts
- Reaction time t is typically 2.5 s (range 1.5–3.0 s depending on alert/drowsy driver).
- Friction coefficient f varies by pavement: 0.30–0.40 (dry asphalt), lower when wet or icy.
- Constants 0.278 and 254 embed unit conversion (km/h to m/s, gravity g).
- SSD is the BASIS for minimum sight distance at horizontal and vertical curves.
- Downgrade (−G) significantly increases stopping distance; critical safety issue on steep roads.
Key Definitions
Term
Stopping Sight Distance (SSD)
Example
For V = 80 km/h on level ground, SSD ≈ 128 m including 2.5 s reaction and braking distance.
Definition
Minimum length of road visible to a driver to stop a vehicle safely before a hazard at design speed.
Term
Perception-Reaction Distance
Example
At 80 km/h: 0.278 × 80 × 2.5 = 55.6 m.
Definition
Distance travelled during the 2.5 s reaction time before braking begins.
Term
Braking Distance
Example
At 80 km/h with f = 0.35: V²/[254(f ± G)] = 6400/88.9 = 72 m.
Definition
Distance required to stop the vehicle from design speed using maximum friction available.
Diagrams To Know
- SSD profile diagram showing reaction phase (straight) and braking phase (deceleration curve).
- Distance vs speed plot showing SSD increasing as V².
- Grade effect comparison: level, uphill, downhill SSD curves.
Formulas
Formula
e + f = V²/(127R)
Meaning
e = superelevation rate (decimal); f = side friction; V = speed (km/h); R = curve radius (m)
Watch Out
The constant 127 = (g × 3.6²)/1000 uses SI + km/h. If speed is in m/s, constant changes to 9.81. Both superelevation AND friction provide centripetal support; don't drop either.
When To Use
Find safe speed on a curve or minimum radius for a design speed.
Formula
R_min = V²/[127(e_max + f_max)]
Meaning
Minimum curve radius at design speed, maximum superelevation, and maximum side friction.
Watch Out
e_max and f_max are DESIGN LIMITS (typically e_max = 0.06–0.10, f_max = 0.10–0.16), not actual values. Check DPWH or AASHTO standards for the specific project.
When To Use
Verify if a horizontal curve meets design standards; common board exam question.
Formula
V_safe = √[127R(e + f)]
Meaning
Safe speed for an existing curve with known radius, superelevation, and friction.
Watch Out
Speed increases as √R, not linearly. A doubling of radius gives only √2 ≈ 1.4× speed increase.
When To Use
Given R, e, f; solve for maximum allowable speed.
Common Values
Value
0.08–0.10 (8–10%)
Symbol
e_max
Quantity
Maximum superelevation (rural)
Value
0.04–0.06 (4–6%)
Symbol
e_max
Quantity
Maximum superelevation (urban)
Value
0.10–0.16
Symbol
f_max
Quantity
Maximum side friction
Section Title
Horizontal Alignment & Superelevation
Important Facts
- Centripetal acceleration on a horizontal curve is provided by superelevation (gravity component) and friction (tire grip).
- Maximum superelevation on rural highways: typically 6–10% (steeper is uncomfortable and risky in snow/ice).
- Maximum superelevation on urban streets: typically 4–6% (balance between safety and accessibility).
- Transition curves prevent sudden change in superelevation; abrupt change causes tire scrub and discomfort.
- Minimum radius for no superelevation (e = 0): R_min = V²/(127f_max); much larger than with superelevation.
Key Definitions
Term
Superelevation (e)
Example
e = 0.08 (or 8%) means 0.08 m rise per 1 m horizontal distance across the lane.
Definition
Inward banking of the road surface on a curve, measured as rise/run (decimal) or percentage.
Term
Side Friction (f)
Example
f ≈ 0.10–0.16 typical; higher on fresh asphalt, lower on wet or worn surfaces.
Definition
Maximum lateral friction between tire and pavement available before skid on a banked curve.
Term
Transition (Spiral) Curve
Example
Clothoid spiral; length L_s ≈ V²/(46.656R) (V in km/h).
Definition
Curve segment that gradually develops superelevation from 0% at the tangent to full rate at the circular arc.
Diagrams To Know
- Cross-section of banked curve showing superelevation angle.
- Superelevation development along transition curve (length L_s).
- Force diagram: centripetal force = N sin(e) + f·N·cos(e), N perpendicular to road.
Formulas
Formula
K = L/A
Meaning
K = curve parameter; L = vertical curve length (m); A = algebraic difference in grades (%).
Watch Out
A = |G₁ − G₂| (algebraic difference, e.g., +3% to −2% gives A = 5%). Confusing signed grades causes wrong L.
When To Use
Determine if a parabolic vertical curve provides adequate sight distance; design curve length.
Formula
L_crest = AS²/(658 + 50S)
Meaning
L = minimum crest curve length (m) for sight distance S (m); A = algebraic grade change (%).
Watch Out
Constant 658 assumes driver eye height ≈ 1.08 m and object height ≈ 0.6 m. Different assumptions change constant.
When To Use
Crest curves over a hill where sight distance is limited by horizon.
Formula
L_sag = AS²/(120 + 3.5S)
Meaning
L = minimum sag curve length (m) for headlight distance S (m); A = algebraic grade change (%).
Watch Out
Constant 120 assumes headlight angle ≈ 1° above horizontal. Daytime sag curves may be longer due to comfort (vertical acceleration limit).
When To Use
Sag curves in valley where night headlight throw is the constraint.
Common Values
Value
4–6%
Symbol
G
Quantity
Grade limit (major highways)
Value
8–10%
Symbol
G
Quantity
Grade limit (local/urban roads)
Value
1.08 m
Symbol
h_e
Quantity
Driver eye height
Value
0.6 m
Symbol
h_o
Quantity
Object height (crest curve)
Section Title
Vertical Alignment & Grades
Important Facts
- Vertical curves are ALWAYS parabolic (ACI/AASHTO standard for ride comfort and sight distance geometry).
- Crest curves are limited by sight distance; sag curves by headlight throw (night visibility).
- Long grades (>4–5%) reduce truck speed; may require climbing lanes or escape ramps.
- Grade exceeding 6% is typically avoided on major routes; 8–10% permissible on local roads.
- Point of curvature (PC), vertex (PVI), point of tangency (PT) terminology is crucial for vertical curve calculations.
Key Definitions
Term
Vertical Curve (Parabolic)
Example
Crest curve connecting +2% upgrade to −3% downgrade over L = 200 m.
Definition
Smooth transition between two different grades using a parabola; ensures safe sight distance and passenger comfort.
Term
Grade (G)
Example
G = +0.04 (or +4%); G = −0.03 (or −3%).
Definition
Slope of the road; positive (upgrade) or negative (downgrade), expressed as decimal or percentage.
Term
Algebraic Grade Difference (A)
Example
From +2% to −3%: A = |2 − (−3)| = 5%.
Definition
Absolute change in grade between the two tangent segments joined by a vertical curve.
Diagrams To Know
- Crest curve profile: convex upward; sight line passes over top.
- Sag curve profile: concave downward; headlight beam angle is constraint.
- Vertical curve length vs algebraic grade change graph.
Common Values
Value
3.5 m
Symbol
W_lane
Quantity
Standard lane width (expressway)
Value
3.0 m
Symbol
W_lane
Quantity
Standard lane width (local road)
Value
3.0–3.5 m
Symbol
W_shoulder
Quantity
Outer shoulder width (expressway)
Value
2–4%
Symbol
Crown
Quantity
Camber (crown slope)
Section Title
Cross-Section Design
Important Facts
- Cross-section is the 'template' for the entire road; all geometric elements (width, camber, superelevation) are fixed here.
- Pavement layers (asphalt, base, subbase) are designed for traffic load and climate; not directly part of geometric design.
- Median (if present) provides safety and separates opposing traffic; width ≥ 2 m typical.
- Curbs and gutters on urban roads; no curbs on expressways and rural highways.
- Drainage slope (camber) is essential even on curves; superelevation ADDS to the crown slope.
Key Definitions
Term
Lane Width
Example
Expressway: 3.5 m per lane. Local street: 3.0 m.
Definition
Clear width allocated to one direction of traffic; typically 3.0–3.75 m for highways.
Term
Shoulder Width
Example
Expressway: 3.0–3.5 m outer shoulder. Local: 1.0–2.0 m.
Definition
Paved strip beside the travel lanes; provides emergency stopping, drainage, and lateral clearance.
Term
Camber (Crown)
Example
Two-lane road: −2% slope from center to each edge (forms a crown).
Definition
Transverse slope for drainage; typically 2–4% toward the edges.
Term
Superelevation Transition
Example
Transition length L_s ≈ 100–300 m for a highway curve.
Definition
Gradual taper of superelevation from 0% at tangent to full rate at curve; prevents edge drop and tire scrub.
Term
Clear Zone
Example
Expressway: 10 m clear zone; rural two-lane: 6–9 m.
Definition
Obstacle-free area on either side of the roadway; improves safety by reducing crash severity.
Diagrams To Know
- Typical cross-section of a two-lane rural highway (crown camber, shoulders, clear zone).
- Divided expressway cross-section (dual lanes, median, shoulders).
- Urban street section (sidewalks, curbs, lanes, gutters).
- Superelevation transition from straight to curve (normal crown rotating to banked curve).
Formulas
Formula
V_design = percentile speed + buffer
Meaning
Design speed should be close to the 85th-percentile operating speed; add buffer for conservative design.
Watch Out
Design speed is NOT the posted speed limit. It is the speed for which geometric design is calculated. Posted limit may be lower for safety/policy reasons.
When To Use
Select the design speed for a new or upgraded roadway.
Common Values
Value
100–120 km/h
Symbol
V
Quantity
Design speed (expressway)
Value
70–100 km/h
Symbol
V
Quantity
Design speed (arterial)
Value
30–50 km/h
Symbol
V
Quantity
Design speed (local/residential)
Section Title
Design Speed & Traffic Parameters
Important Facts
- All geometric parameters (SSD, curve radius, grade, sight distance) are tied to ONE design speed.
- Design speed must be consistent with the road's functional classification (expressway, arterial, local).
- Traffic composition (% trucks, buses) affects vertical/horizontal geometry (long grades, turning radii).
- Climate (rain, snow, ice) reduces effective friction; conservative f should be used in design.
- Posted speed limit is an enforcement tool; design speed is a SAFETY baseline.
Key Definitions
Term
Design Speed (V)
Example
Rural expressway: V = 100–120 km/h. Urban arterial: V = 60–80 km/h. Residential street: V = 30–40 km/h.
Definition
Maximum speed at which vehicles can safely operate on a roadway under ideal conditions; governs all geometric elements.
Term
85th-Percentile Speed
Example
If measured speeds on an existing road show 85th percentile = 75 km/h, design speed ≈ 75–80 km/h.
Definition
Speed below which 85% of traffic travels; upper bound of safe operating speed for the road's users.
Term
Traffic Volume (ADT)
Example
ADT = 5,000 vehicles/day → 2 lanes. ADT = 20,000 → 4 lanes (divided or undivided).
Definition
Average daily traffic (vehicles per day); affects number of lanes, shoulder design, and intersection capacity.
Diagrams To Know
- Functional classification hierarchy (expressway → arterial → collector → local) with typical design speeds.
- Speed vs radius relationship showing safe operating speed regions.
- Traffic volume categories and corresponding lane configuration.
Formulas
Formula
SSD = 0.278Vt + V²/[254(f + G)] [UPGRADE, +G]
Meaning
On an uphill grade, friction is AIDED by the gravity component; braking distance is SHORTER.
Watch Out
Use (f + G) in the denominator. Forgetting the + sign is the #1 mistake.
When To Use
Vehicle braking uphill (gravity aids deceleration).
Formula
SSD = 0.278Vt + V²/[254(f − G)] [DOWNGRADE, −G]
Meaning
On a downhill grade, gravity opposes braking; braking distance is LONGER.
Watch Out
Use (f − G) in the denominator. Writing (f + |G|) or (f − (−G)) causes sign errors.
When To Use
Vehicle braking downhill (gravity opposes deceleration).
Common Values
Value
~10–15% reduction vs level
Symbol
ΔG
Quantity
SSD shortening factor (upgrade)
Value
~20–30% increase vs level
Symbol
ΔG
Quantity
SSD lengthening factor (downgrade)
Section Title
SSD on Grades — Detailed Calculation
Important Facts
- An upgrade shortens SSD by ~10–15% vs level; a downgrade lengthens it by ~20–30% for typical grades.
- Steep downgrades (e.g., −8%) can DOUBLE the braking distance vs level ground.
- Always check SSD on downgrades; critical for sight distance design on mountain roads.
- The grade effect is most pronounced at high speeds (V² term dominates).
Key Definitions
Term
Grade Notation (Signed)
Example
Road rises 4 m over 100 m horizontal: G = +0.04 (or +4%). Road falls 3 m: G = −0.03 (or −3%).
Definition
+G = uphill (positive grade); −G = downhill (negative grade).
Diagrams To Know
- Graph of SSD vs speed for three cases: level, +3% upgrade, −3% downgrade.
- Stopping distance breakdown on downgrade showing extended braking phase.
Reactions Or Equations
Note
Shows that downgrade SSD − upgrade SSD is proportional to grade change and V².
Equation
ΔSSD = V²/254 × [1/(f − G) − 1/(f + G)]
Conditions
G > 0; grade difference between downgrade and upgrade.
Formulas
Formula
m = R − √[R² − (S/2)²]
Meaning
m = perpendicular distance from curve center to sight line (middle ordinate); S = sight distance along arc; R = curve radius (m).
Watch Out
S is the arc length along the centerline, NOT the chord. For large R and small S, approximation m ≈ S²/(8R) is often used (simpler but less accurate).
When To Use
Determine the clear zone width required on a horizontal curve to ensure sight distance S.
Common Values
Value
5–15 m inward
Symbol
m
Quantity
Clear zone requirement (typical curve)
Section Title
Sight Distance on Horizontal Curves (Circular Arc)
Important Facts
- Inside edge of a horizontal curve requires a 'clear zone' free of sight-blocking objects.
- m increases as R decreases (tighter curves need wider clear zones).
- Trees, poles, buildings on the inside radius are common sight obstructions on curves.
- Clear zone is often not achievable in urban areas; road markings and speed reduction are alternatives.
Key Definitions
Term
Sight Distance on Horizontal Curve
Example
R = 300 m curve requires S ≥ 128 m (SSD at 80 km/h) → clear zone m ≈ 11 m inside the curve.
Definition
Line-of-sight length along the centerline of a horizontal curve; obstructed by objects (buildings, trees, cut slope) on the inside of the curve.
Diagrams To Know
- Horizontal curve plan view showing sight line, middle ordinate m, and clear zone boundary.
- Cross-section of curve at sight-blocking object showing obstruction height.
Reactions Or Equations
Note
Error is <5% if S < 0.2R. Use exact formula if S/R is large (tight curves with long sight distance requirement).
Equation
m ≈ S²/(8R) [for small S relative to R]
Conditions
S << R; approximation simplifies calculation.
Must Remember
- SSD formula: 0.278Vt + V²/[254(f ± G)]. Grade sign is CRITICAL: +G shortens, −G lengthens. This is the #1 exam mistake.
- Minimum radius R_min = V²/[127(e+f)]. Both superelevation AND friction contribute. Constant 127 is fixed for V in km/h.
- On downhill grades, SSD can increase by 20–30% vs level. Always check critical downhill stretches for sight distance compliance.
- Crest curves use L = AS²/(658 + 50S); sag curves use L = AS²/(120 + 3.5S). Different sight constraints (horizon vs headlight).
- Design speed governs ALL geometric elements: SSD, curve radius, grade limits, sight distance, and cross-section.
- Transition (spiral) curves gradually develop superelevation to prevent abrupt edge drop and tire scrub; length ≈ V²/(46.656R).
- Clear zone on inside of horizontal curves must be free of obstructions; m ≈ S²/(8R) for required width.
- Friction coefficient varies widely: f = 0.30–0.40 (dry asphalt), 0.20–0.30 (wet), lower on ice/gravel. Conservative design uses lower values.
- Camber (crown) is 2–4% transverse slope for drainage, SEPARATE from superelevation on curves.
- Functional classification (expressway → local) sets design speed range; always verify with DPWH/AASHTO guidelines for your project type.
Last Minute Tips
- GRADE SIGN IN SSD: Write it as SSD = 0.278Vt + V²/[254(f ± G)], then substitute +G or −G. Don't memorize two separate formulas; one formula with careful sign substitution avoids errors.
- R_min vs R_existing: If problem gives a curve radius and asks 'is this safe?', compare to R_min. If R_actual > R_min, it's safe. Always solve V_safe = √[127R(e+f)] as check.
- Downgrade SSD: On any −G (downhill) problem, the braking distance INCREASES. Always expect SSD_downgrade >> SSD_level. If your answer is shorter on downgrade, you used the wrong sign.
- Sight distance at curves: The formula m = R − √[R² − (S/2)²] is exact but ugly. Use m ≈ S²/(8R) for quick approximation on the exam if time-pressed. For S = 150 m, R = 300 m: m ≈ 150²/(8×300) ≈ 9.4 m.
- Cross-section memory aid: Lanes (3.0–3.75 m) + shoulders (1.5–3.5 m) + clear zone (5–15 m) + median (if divided). Total typical cross-section width = 12–20 m. Know one example for each road type.
Comparison Tables
Rows
Values
- 54
- 48
- 62
Property
40
Values
- 86
- 75
- 101
Property
60
Values
- 128
- 113
- 150
Property
80
Values
- 180
- 157
- 212
Property
100
Values
- 242
- 210
- 290
Property
120
Columns
- Design Speed (km/h)
- Level, f=0.35 (m)
- +3% Grade, f=0.35 (m)
- −3% Grade, f=0.35 (m)
Table Title
SSD vs Design Speed & Grade Conditions
Rows
Values
- 63
- 80–100
Property
40
Values
- 141
- 160–200
Property
60
Values
- 250
- 300–350
Property
80
Values
- 394
- 400–500
Property
100
Values
- 569
- 600–800
Property
120
Columns
- Design Speed (km/h)
- R_min (m)
- Practical Design (m)
Table Title
Minimum Curve Radius by Design Speed (e_max=0.08, f_max=0.12)
Rows
Values
- 3.5–3.75
- 3.0–3.5
- 1.5–2.0
Property
Expressway
Values
- 3.5
- 2.5–3.0
- 1.0–1.5
Property
Primary Arterial
Values
- 3.0–3.5
- 2.0–2.5
- 0.5–1.0
Property
Secondary Arterial
Values
- 3.0
- 1.5–2.0
- —
Property
Collector Road
Values
- 3.0
- 1.0–1.5
- —
Property
Local Street (Urban)
Columns
- Road Type
- Lane Width (m)
- Outer Shoulder (m)
- Inner Shoulder (m)
Table Title
Lane & Shoulder Widths by Functional Class (DPWH Guidelines)
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