🛣️ Highway & Railway Engineering

Superelevation Calculator

Design the full superelevation transition for highway curves — superelevation rate, runoff length, tangent runout, total transition development and edge-of-pavement profile — using the AASHTO maximum-relative-gradient method, with NHA Pakistan, IRC and BS limits.

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Superelevation Calculator

e Rate · Runoff Length · Tangent Runout · Transition Development · Edge Profile

⚙️ Settings

Unit System

Design Standard

📐 Superelevation Rate

How is the superelevation rate set?

Curve Radius R (m) Radius of the horizontal curve

Design Speed (km/h)

Max Superelevation e_max

Side Friction f

🛣️ Transition Geometry (Runoff & Runout)

Lane Width w (m) Width of one traffic lane

Number of Lanes Rotated n₁ Lanes rotated about the axis

Normal Crown / Cross-Slope (%) Adverse cross-slope removed in runout

Max Relative Gradient Δ

Axis of Rotation

Runoff on Tangent (proportion) Fraction of runoff placed before PC

📋 Transition Table Interval

Station Interval (m)

📊 Superelevation Results

✅ Calculated

Station	Distance (m)	Outer-Lane Cross-Slope	Region

📐 Designing the curve geometry itself (PC, PT, tangent, degree of curve)? Use the Horizontal Curve Calculator — this page focuses on the superelevation transition that develops into that curve.

📖 Method

How Superelevation & Its Transition Are Designed

Superelevation is the banking of the carriageway toward the inside of a horizontal curve so that a component of gravity helps balance centrifugal force. But the curve cannot jump from a flat cross-slope to full banking instantly — it is developed gradually over a transition made of the tangent runout and the superelevation runoff. This calculator sizes that whole transition.

Determine the Design Superelevation Rate e

From the point-mass equation e + f = V²/(127R) (metric). Solve for e using the design speed, radius and the side-friction factor f. The rate must not exceed e_max for the region (0.07 on NHA highways).

Read the Maximum Relative Gradient Δ

Δ is the steepest allowable longitudinal slope between the pavement edge and the axis of rotation. It decreases with design speed (AASHTO Table 3-15): 0.60% at 60 km/h down to 0.38% at 120 km/h. A flatter Δ at high speed forces a longer, gentler transition.

Compute the Superelevation Runoff L_r

The length to rotate the pavement from zero cross-slope to full superelevation: L_r = (w · n₁ · e_d / Δ) · b_w, where w is lane width, n₁ the number of rotated lanes, e_d the design rate, and b_w the multilane adjustment factor.

Compute the Tangent Runout L_t

The length to remove the adverse (normal) crown before runoff begins: L_t = (e_NC / e_d) · L_r, using the same edge-rotation rate. The total transition length is L_t + L_r.

Position the Transition Relative to the Curve

For an unspiralled curve, about two-thirds of the runoff (AASHTO: 0.67–0.80) is placed on the tangent before PC and the remainder on the curve, so full superelevation is reached just inside the curve.

Plot the Edge-of-Pavement Profile

The development diagram shows the outside and inside edges rotating about the chosen axis through normal crown → runout → runoff → full superelevation, which is what the field crew sets out.

∑ Core Superelevation Formulas

SUPERELEVATION DESIGN — AASHTO max-relative-gradient method Design rate: e + f = V² / (127·R) (V km/h, R m) Solve for e: e = V²/(127R) − f (cap at e_max) Minimum radius: R_min = V² / [127·(e_max + f)] Multilane factor: b_w = (1 + 0.5(n₁ − 1)) / n₁ Superelev. Runoff: L_r = (w · n₁ · e_d / Δ) · b_w Tangent Runout: L_t = (e_NC / e_d) · L_r Total Transition: L_total = L_t + L_r Runoff on tangent: L_r,tan = p · L_r (p ≈ 0.67) Runoff on curve: L_r,crv = (1 − p) · L_r w = lane width n₁ = lanes rotated e_d = design superelevation Δ = max relative gradient e_NC= normal crown slope p = proportion on tangent Imperial: replace 127 with 15 (V in mph, R in ft).

🛣️ Reference

The Four Stages of Superelevation Development

Every superelevation transition moves the pavement through these stages in order.

Stage	What Happens	Length	End Condition
Normal Crown	Both lanes drain away from centerline at the normal cross-slope	—	Outer lane at −e_NC
Tangent Runout	Outer lane rotates up from −e_NC to level (0%)	L_t	Pavement is a single flat plane
Superelevation Runoff	Whole section rotates from 0% to full e_d	L_r	Full superelevation e_d reached
Full Superelevation	Constant banking maintained around the curve	(curve)	Held until the exit transition

For NHA Pakistan motorways, AASHTO development applies with e_max=0.07 and rotation usually about the median edge or centerline. On divided carriageways each direction is treated separately. The axis of rotation changes which edges move, but the runoff length L_r depends on the number of lanes rotated, not the axis.

📊 Standards

AASHTO Maximum Relative Gradient (Δ) by Design Speed

The maximum relative gradient between the pavement edge and the axis of rotation. Lower values at higher speed produce longer, smoother runoffs. From AASHTO Green Book 2018, Table 3-15.

Design Speed	Max Relative Gradient Δ	Typical Runoff (e=0.06, 2 lanes)	Use
50 km/h	0.65%	≈ 50 m	Collector
60 km/h	0.60%	≈ 54 m	Arterial
70 km/h	0.55%	≈ 59 m	Secondary highway
80 km/h	0.50%	≈ 65 m	National highway
90 km/h	0.47%	≈ 69 m	NHA highway
100 km/h	0.44%	≈ 74 m	Motorway
110 km/h	0.41%	≈ 79 m	Motorway
120 km/h	0.38%	≈ 85 m	M-roads (M-1, M-2)

💡 Runoff column assumes lane width 3.6 m, e_d=0.06, 2 lanes rotated (b_w=0.75). Always confirm Δ and e_max against the project authority's manual.

📝 Worked Example

Superelevation Transition — NHA Motorway Curve

Problem: A 2-lane (each direction) motorway curve has R = 400 m, design speed 100 km/h, e_max = 0.07, lane width 3.6 m, normal crown 2%. Rotation about centerline, 0.67 of runoff on tangent. Find e, runoff, tangent runout and total transition.

Given:
 R = 400 m   V = 100 km/h   e_max = 0.07   w = 3.6 m
 n1 = 2   e_NC = 0.02   Δ = 0.44%   p = 0.67   f = 0.12

Step 1 — Design Superelevation Rate:
 e = V²/(127R) − f = 100²/(127·400) − 0.12
   = 10000/50800 − 0.12 = 0.1969 − 0.12 = 0.0769
 e exceeds e_max 0.07 → adopt e_d = 0.07 (curve near minimum radius)

Step 2 — Multilane Adjustment Factor:
 b_w = (1 + 0.5(n1−1))/n1 = (1 + 0.5)/2 = 0.75

Step 3 — Superelevation Runoff:
 L_r = (w·n1·e_d/Δ)·b_w
     = (3.6·2·0.07 / 0.0044)·0.75
     = (0.504 / 0.0044)·0.75 = 114.55·0.75 = 85.9 m

Step 4 — Tangent Runout:
 L_t = (e_NC/e_d)·L_r = (0.02/0.07)·85.9 = 24.5 m

Step 5 — Total Transition:
 L_total = L_t + L_r = 24.5 + 85.9 = 110.4 m

Step 6 — Position Relative to PC:
 Runoff on tangent = 0.67·85.9 = 57.6 m  (before PC)
 Runoff on curve   = 0.33·85.9 = 28.3 m  (after PC)

ANSWER: e_d = 0.07 | L_r = 85.9 m | L_t = 24.5 m
 Total transition = 110.4 m
 Place 57.6 m of runoff before PC, 28.3 m beyond PC.

💡 Practice

Expert Tips for Superelevation Design

Rate & Limits

Cap e at e_max (0.07 NHA). If the required e exceeds it, the radius is too sharp — lengthen the curve, don't over-bank
Below a minimum-radius threshold for the speed, AASHTO keeps the road at normal crown — no superelevation needed

Runoff Length

Use the max-relative-gradient method, not a fixed length — high-speed roads need much longer runoffs
More rotated lanes increase L_r, but the b_w factor keeps it less than proportional
Round the final L_r up to a practical setting-out length

Positioning

Place ~0.67–0.80 of runoff on the tangent so full superelevation is just reached inside the curve
On spiralled curves, develop the full runoff along the spiral length instead

Drainage & Comfort

Watch the zero-cross-slope point in the runoff — flat pavement drains poorly; keep a min profile grade ≥ 0.5%
Avoid placing the cross-slope reversal on a low point of the vertical profile

⚠️ Final superelevation and transition design must be verified and signed by a licensed Civil / Transport Engineer. This calculator is for preliminary design and checking only.

❓ FAQ

Frequently Asked Questions

Tangent runout (L_t) is the length needed to rotate the outside lane from its normal adverse crown up to a level (zero) cross-slope. Superelevation runoff (L_r) is the length needed to then rotate the whole pavement from level up to the full design superelevation. The full transition is the sum of both, L_t + L_r.

By the AASHTO maximum-relative-gradient method: L_r = (w · n₁ · e_d / Δ) · b_w, where w is lane width, n₁ the number of lanes rotated, e_d the design superelevation rate, Δ the maximum relative gradient for the design speed, and b_w = (1 + 0.5(n₁−1))/n₁ the multilane adjustment factor.

Δ is the maximum allowable longitudinal slope of the pavement edge relative to the axis of rotation. AASHTO tabulates it against design speed — for example 0.60% at 60 km/h falling to 0.38% at 120 km/h. The lower value at higher speed forces a longer, smoother runoff for ride comfort and appearance.

For curves without a spiral, AASHTO recommends placing about 0.67 to 0.80 of the runoff length on the tangent ahead of PC, with the remainder on the curve. This means full superelevation is achieved a short distance inside the curve, which gives the smoothest driver path.

Pakistan's NHA follows AASHTO geometric design with maximum superelevation e_max = 0.07 for motorways and national highways. Provincial roads also reference IRC, which allows up to 0.10 in hilly terrain. The runoff and runout are developed by the AASHTO max-relative-gradient method in both cases.

No — the runoff length depends on the number of lanes rotated (through n₁ and b_w), not on whether you rotate about the centerline, the inside edge or the outside edge. The axis only changes which edges move and the resulting edge-elevation profile, which is why the development diagram differs by method even when L_r is identical.

Superelevation Calculator