1. Design Speed and Horizontal Alignment
Norman W. Garrick
Lecture 10
Street and Highway Design

2. How do we determine the curve radius?
I-95 East Lyme

3. 1000 ft B 2 1
Blue Ridge Parkway A

4. 5000 ft A B
New York Thruway

5. 5000 ft B 2 1 A
Merritt Parkway

6. Swede High Speed Tilt Train
The first high-speed tilting train, X 2000, was delivered to Swedish State Railways in 1990 on the Stockholm - Gothenburg route.
Travel time for this route was reduced by more than 25 percent with only minor upgrading of the infrastructure.
The key to increased speeds lie in the radial self-steering bogies whereby track forces are reduced, allowing up to 50 percent higher speed through curves.
Microprocessor-controlled, active passenger car tilting technology assures passenger comfort in curves.

7. Cornering Forces Soft Bogies!
Radial-steered bogies on their own allow an increase in operating speeds by 40% or up to 180Km/h (112mph) without increasing rail/wheel forces compared with conventional bogies. 
This reduces wear on both the rail and wheels - wheel life is increased by up to six times.  However, the increase in speeds allowed by these bogies would be uncomfortable to the passengers without tilt.
Norman W. Garrick

8. Cornering Forces Tilting Trains
Tilt is used primarily for comfort.  
An accelerometer is fitted in the first bogie of the train in the direction of travel and measures lateral forces as the train enters a curve.  Computer-controlled hydraulic ram tilt each coach into the curve, up to a maximum inclination of 6.5º.  The tilting system compensates for up to 75% of the lateral force of a curve.
Incidents of 'sea-sickness' or 'tilt nausea’ can occur as 25% of lateral forces are still felt by the passengers.  
Norman W. Garrick 8

9. Cornering Cars Does you every day car need to handle like the EXIGE?
Does you every day car need to handle like the EXIGE?

10. Forces on Cornering Car

11. mv2/r ma = mg Nf Normal Force

13. Road Superelevation (e)
What is largest superelevation rate practical?
Depends on Climate, Speed, Vehicle Type
Maximum superelevation in practice – 12%

14. Rate of superelevation is ‘e’ in %

15. mV2/R = (0.01e+f)/(1-0.01ef) = V2/gR Forces in = mV2/R Simplify givesNf =
Normal Force
Forces in = mV2/R
Simplify gives
(0.01e+f)/(1-0.01ef) = V2/gR
note: f is in fraction, e is in %

16. What Value of f should be used?Nf
Normal Force
The road is designed so that the expected value of side friction is much less than the value that would cause sliding.
The value of ‘f’ used is equivalent to that which would
cause a minimum level of discomfort to the vehicle occupants.

17. Maximum and Assume Side Friction
Maximum side friction for smooth tires and wet concrete – 0.35 at 45 mph
The value decrease as speed increase
The assumed value of side friction for design varies from 0.1 to 0.25 depending
on the design speed (higher values for lower speeds)
AASHTO
Norman W. Garrick

18. Determining Rmin This equation is used to calculate Rmin
(0.01e+f)/(1-0.01ef) = V2/gR
f is in fraction, e is in %
What value of e and f and V?
e – is the rate of superelevation to be used
f – is the allowable level of side friction selected to cause a specified level of discomfort to vehicle occupants and to ensure that the operator is not surprised by a very sharp curve
V – design speed

19. Rmin = V2 / g{(0.01emax+fmax)
Calculating Rmin
(0.01e+f)/(1-0.01ef) = V2/gR
f is in fraction, e is in %
Since 0.01ef is tiny, it can be ignored
So equation simplifies to
(0.01e+f) = V2/gR
Rmin = V2 / g{(0.01emax+fmax)
If we use g in ft/s and V in mph
Rmin = V2/15 (0.01emax+fmax)

20. I-95: Calculating Rmin I-95 East Lyme Rmin = V2/15 (0.01emax+fmax)
Assume
V = Design Speed = 60 mph
emax = 6 %
fmax = 0.13
Rmin = 602 / 15 (0.01* )
= 3600/15*(0.19)
= 1264 feet
I-95 East Lyme

21. R versus Rmin I-95 East Lyme R3 > Rmin R2 > Rmin R4 > Rmin

22. Same Design Speed as I-95, Same Rmin
R2 > Rmin
R1 > Rmin
R4 > Rmin
R3 > Rmin
New York Thruway

23. Blue Ridge Parkway: Calculating Rmin
Rmin = V2/15 (0.01emax+fmax)
Assume
V = Design Speed = 35 mph
emax = 8 %
fmax = 0.18
Rmin = 352 / 15 (0.01* )
= 1225/15*(0.26)
= 314 feet
Blue Ridge Parkway