Transcript Slide 1
Geometric Design (II) Learning Objectives • To calculate minimum radius of horizontal curve • To understand design concepts for transition curves and compute min length • To understand the role of SSD in horizontal and vertical design • To define and apply grade considerations • To develop vertical curves (Chapter 6.1 ~ 6.4) Horizontal Curve • Minimum Curve Radius – Curve requiring the most centripetal force for the given speed – Given emax, umax, Vdesign min R( ft ) V (2mph ) 15e u R Horizontal Curve Properties Based on circular curve Point of Curvature Point of Tangency • • • • • • • • R: radius of curve D: degree of curve : central angle T: length of tangent L: length of curve LC: long chord M: middle ordinate dist E: external dist Horizontal Design Iterations • Design baseline – Curve radius above the minimum – Superelevation and side-friction factor not exceeding the maximum values • Design is revised to consider: cost, environmental impacts, sight distances, aesthetic consequences, etc. Horizontal Curve Sight Distance V2 Recall SSD 1.47Vt r a 30 G 32.2 • R 28.65 SD M R 1 cos R • Sight line is a chord of the circular curve Sight Distance is curve length measured along centerline of inside lane Horizontal Curve Sight Distance Figure 6-10 Transition Curves • Gradually changing the curvature from tangents to circular curves Without Transition Curves With Transition Curves Transition Curves • Gradually changing the curvature from tangents to circular curves – Use a spiral curve L: min length of spiral (ft) V: speed (mph) R: curve radius (ft) C: rate of increase of centrifugal accel (ft/sec3), 1~3 3.15V 3 L RC Transitional Curves • Gradually changing the cross-section of the roadway from normal to superelevated (Figure 6-9) Keep water drainage in mind while considering all of the available cross-section options Vertical Alignment Reduced Speed Increased Speed Vertical Alignment • Grade – measure of inclination or slope, rise over the run – Cars: negotiate 4-5% grades without significant speed reduction – Trucks: significant speed changes • 5% increase on short descending grades • 7% decrease on short ascending grades Grade Considerations • Maximum grade – depends on terrain type, road functional class, and design speed Rural Arterials Terrain 60mph 70mph Level 3% 3% Rolling 4% 4% Mountainous 6% 5% Grade Considerations • Critical length of grade – Maximum length which a loaded truck can travel without unreasonable speed reduction – Based on accident involvement rates with 10mph speed reduction as threshold Grade Considerations General Design Speed Reduction Vertical Curves • To provide transition between two grades • Consider – Drainage (rainfall) – Driver safety (SSD) – Driver comfort • Use parabolic curves • Crest vs Sag curves Vertical Curves Vertical Curves Given – G1, G2: initial & final grades in percent – L: curve length (horizontal distance) Develop the actual shape of the vertical curve PVI point of vertical intersection point of vertical curvature G1% point of vertical tangency G2% Vertical Curves • Define curve so that PVI is at a horizontal distance of L/2 from PVC and PVT • Provides constant rate of change of grade: r G2 G1 L A G1 Ax2 EP EPVC x 100 200L G1% G2% Example • • • • • G1 = 2% G2 = -4% Design speed = 70 mph Is this a crest or sag curve? What is A? Vertical Curves • Major control for safe operation is sight distance • MSSD should be provided in all cases (use larger sight distance where economically and physically feasible) • For sag curves, also concerned with driver comfort (large accelerations due to both gravitational and centrifugal forces) Crest Vertical Curves • Critical length of curve, L, is where sight line is tangent to the crest • Assume driver eye height (H1) = 3.5 ft and object height (H2) = 2.0 ft and S=MSSD Sag VC - Design Criteria • • • • Headlight sight distance Rider comfort Drainage control Appearance