Unformatted text preview: Horizontal Alignment NOTES AND ASSIGNMENT #1 BACKGROUND
Created by John Caruano Created by John Caruano Horizontal Curves Horizontal Curves Created on a horizontal plane and allow for a smooth transition between two straight tangents. Allows for directional changes. Horizontal curves are necessary wherever two tangents intersect. Horizontal Curve Types Horizontal Curve Types – Brokenback – Reverse Simple – single curve of constant radius Compound – two or more simple curves in succession Spiral – curve with a constantly changing radius. This type is used to enhance driver comfort Simple Curve Simple Curve Compound Curve Compound Curve Spiral Curve Spiral Curve Horizontal Curves Horizontal Curves Page 81 of the text displays a diagram of a simple curve and the means to calculate the elements of a simple curve Simple Curve Components Simple Curve Components and Calculations PC = Point of Curvature (start) PT = Point of Tangency (end) PI = Point of Intersection (of tangents) R = Radius (of the curve) Δ = Delta = Angle formed between two tangents T = Tangent Length T = R tan (Δ/2) Simple Curve Components Simple Curve Components and Calculations E= External Distance E = R[(1/cos(Δ/2)) – 1] M = Middle Ordinate M = R[1 – cos (Δ/2)] L = Length of Curve L = Δ*R *Note: Δ is in Radians When to use Δ in Radians When to use or Degrees? When Δ is used in a function, it is used in degrees. (i.e. T, E, or M) For the calculation of the Length of Curve (L), Δ is in radians. The conversion between radians and degrees is as follows:
– Radians = Degrees * π/180 – Degrees = Radians * 180/ π Compound Curve Stationing Compound Curve Stationing (along the centerline) When given the following, compound curve stationing can be completed:
– BS = Beginning Station – ES = Ending Station – X1 = length of first tangent – X2 = length of second tangent – X3 = length of third tangent PI1 = BS + X1 T1 = R1*tan(Δ1/2) PC1 = PI1 T1 L1 = R1 * Δ1 (in radians) PT1 = PC1 + L1 PI2 = PT1 + (X2 T1) PC2 = PI2 – T2 T2 = R2*tan(Δ2/2) L2 = R2 * Δ2 (in radians) PT2 = PC2 + L2 ES = PT2 + (X 3 – T2 ) Assignment #1 Assignment #1 Background This assignment entails the development of a horizontal alignment for a new rural collector connecting two existing roads. The design criteria will be specified in the laboratory manual. An AutoCAD drawing will be submitted and should clearly show the roadway centerline, edges of traveled way and shoulders, and limits of right of way. Include all relevant information such as stationing, location of PCs, PTs, tangent and curve data, and cross section dimensions. Horizontal curve calculations are to be done by hand (done on previous slides) and handed in with your CAD drawings on engineering paper. Be sure to include a scale and north arrow. Plot the drawing on 11”x17 paper (We will discuss next week). ...
View Full Document
- Spring '02
- Osculating circle, John Caruano, Curve Compound Curve