CEE 3604 Transportation Geometric Design Others

CEE 3604 

Transportation Geometric 

Design 

Others 

Transportation Engineering (A.A. Trani) 

1

Horizontal Curves (Highways) 


2

Note Some Differences with Vertical 

Alignments 

• The length L is defined along the curved 

path 

• In vertical curve L was defined along the x 

axis 

• The transition curve is a circle in horizontal 

alignments vs a parabola 


3

Fundamental Equations 

T 

R = tan Δ 2 

T = R tan Δ 2 

E = external distance 

M = middle ordinate 

T = tangent length 


4

Example # 1 


5

Example # 1 Solution 


6

Turning Radius (Highway Design) 

R = 

v 2 

g(e + f ) 

Source: NYSDOT 

http://downloads.transportation.org/SuperelevationDiscussion9-03.pdf 


7

AASHTO Design Values 


8

AASHTO Design Tables 


9

Example # 2 

• Calculate minimum radius for a design speed 

of 120 [km/h]. The superelevation rate is 

limited to 0.06 due to icing effects in winter 

R = 

v 2 

g(e + f ) 


10

Example # 2 Solution 

• Using Table 7.8 we extract the necessary 

information 


11

How to Achieve Superelevation? 

• Superelevation requires 

a smooth transition 

from a flat highway to a 

curved highway with 

the desired 

superelevation 

• Several concepts have 

can be applied 

• Linear superelevation 

rate concept is used 


12

Example # 3 

A horizontal curve requires a 100 meter transition length to achieve 

the full superelevation of 0.08 (see Figure). A suggested 

superelevation schedule is shown in the Figure. 

Note that we start with the standard road with a crown and two 

1.5% transverse slopes at station 0+0.00. 

The left offset point (green point) transitions to a flat surface at 

station 0+15.80 

Finally, at station 0+100.00 the full superelevation is reached 

Plot the elevation of the left offset, the crown centerline and right 

offset elevations every 10 meters. In your plot the x-axis is the station 

number and the y-axis the elevation. 


13

Example # 3: Design for Superelevation 

Figure 1. Problem 3. 


14

Solution to Example # 3 

The sample stations shown in Figure 1 indicate a rate of change 

of elevation of the left offset in the first 15.80 meters is 

(0.015*w)/15.8 per meter (0.0035 meters per meter of station) 

After the station 0+15.8 is reached, two possible solutions are 

provided in Figures 2 and 3. 

Figure 2 assumes the rate of change of the left offset of 0.0035 

m/m applies up to station 0+31.6 meters 

The rate increases to 0.0063 m/m after station 0+31.6 to reach 

the desired superlevation of 0.08 at station 0+100.00 metric. 

The solution shown in Figure 3 assumes rate of superelevation 

of the Left Offset increases to 0.0063 m/m after station 0+15.8. 


15

Solution (Figure 2) 

• Solution assumes 0.0035 meter/meter elevation 

change of Left Offset up to station 31.6 meters. 

Then rate increases to 0.0063 meters per meter 

of station. 


16

Solution (Table 1) 


change of Left Offset up to station 31.6 meters. 

Then rate increases to 0.0063 meters per meter 

of station. 


17

Solution (Figure 3) 


of Left Offset up to station 15.8 meters. Then 

rate increases to 0.0069 meters per meter of 

stationing up to station 0+100.00. 


18

Solution (Table 2) 


of Left Offset up to station 15.8 meters. Then rate 

increases to 0.0069 meters per meter of 

stationing up to station 0+100.00. 


19

Horizontal Design vs. Stopping Sight 

Distance 


20

Horizontal Alignment vs SSD 


21

SSD in Horizontal Curve 


22

Other Modes of Transportation 

• All vehicles used in transportation turn 

• Airport automated people movers have 

modest turning radii (due to low speeds) 

• High-speed rail vehicles have large turning 

requrements 

• TGV has design radii of 4,000 meters 

• Aircraft turn to fly routes and avoid 

obstacles 


23

High-Speed Rail 

• Side forces cannot be very large or damage can 

occur to the steel wheels 

• Tilting mechanisms are used to add passenger 

comfort and help manage side forces 

A JR Hokkaidō DC283 tilting train 

5 degrees normal 

8 degrees maximum 

source: Wikipedia Commons 


24

Definition: Degree of a Curve 

• A useful unit to specify a horizontal curve 

employed by the railway industry is the degree of 

the curvature (d) 

• The definition of degree of curvature is the 

number of degrees traversed by the curve per 

100 feet (or 30 meters) 


25

Example # 4: degree of Curve Calculation 

• What is the degree of the curve for a 4,000 meter 

radius horizontal curve for the French TGV high 

• A 4,000 meter radius turn yields 

69.81 meters per degree (i.e., 

25,133 meter circumference) 

• The degree of the curve is 

calculated over a 30 meter 

segment (100 feet) 

• The degree of the curve is then: 

0.4297 degrees per 30 

meters 


Source: http:// 

en.wikipedia.org/wiki/ 

File:TGV-Duplex_Paris.jpg 

26

TGV Design Criteria 

• Tight tolerances and smooth curves 

Source: AREMA 


27

Example # 5: TGV Track Design Speed 

Find the maximum design speed (in mph) of the TGV 

railway track using the equation presented in the 

previous Figure(i.e., AREMA document) using the 

degree of curvature found in Example # 4. 

In France (as in most Europe) the maximum elevation 

of the outside rail is never to exceed 7.1 inches (180 

mm). 


28

Example # 5: TGV Track Design Speed 


29

Aircraft Turning Performance 

L cos(φ) = mg L sin(φ) = mV 2 

R 


30

Nomenclature 

• L = lift generated by the aircraft wings (N) 

• R = turning radius (m) 

• mg = aircraft weight (N) 

• 

φ bank angle (radians) 

• 

Γ turn rate (radians per second) 

• n = load factor 

• T = thrust 

• D = drag 


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33

Example # 6: Aircraft Turning 

An airport engineer is helping with the design an approach 

procedure to a regional airport with a single runway as shown 

in Figure 4 

The procedure tries to avoid the community to the South of 

the airport and calls for a constant radius of turn as the 

approaching aircraft fly over at 2,500 feet and 200 mph 

The turn is expected to limit the bank angle to 20 degrees to 

avoid excessive loads on the vehicle and passengers. 

Find the distance d if the parameters of the turn are followed 

as stated in Figure 2. The neighbors in the “Green” community 

want to be at least 1100 meters from the flight path. 


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CEE 3604 Transportation Geometric Design Others

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