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

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

1000 ft B 2 1 Blue Ridge Parkway A

5000 ft A B New York Thruway

5000 ft B 2 1 A Merritt Parkway

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. http://www.bombardier.com/en/transportation/products-services/rail-vehicles/high-speed-trains/x2000---sweden?docID=0901260d80010605#

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. www.lococarriage.org.uk/x2000.htm Norman W. Garrick

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.   www.lococarriage.org.uk/x2000.htm Norman W. Garrick 8

Cornering Cars Does you every day car need to handle like the EXIGE? http://paultan.org/2006/01/11/top-gear-tests-cornering-ability/ Does you every day car need to handle like the EXIGE?

Forces on Cornering Car

mv2/r ma = mg Nf Normal Force http://www.nascar.com/kyn/101/glossary/index.html

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

Rate of superelevation is ‘e’ in %

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

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.

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

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

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)

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*6 + 0.13) = 3600/15*(0.19) = 1264 feet I-95 East Lyme

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

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

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*8 + 0.18) = 1225/15*(0.26) = 314 feet Blue Ridge Parkway