Name: designing smooth road grade transitions
Uploaded: 2025-03-26T15:36:50.000Z
Duration: 1 min 24 s
Channel: JoVE

K12 Standards

Alabama Course of Study Science

9-12

Earth and Space Science

Earth's Systems

9-12.ESS.2.8.a

Introduction to Vertical Curves

Vertical curves provide smooth transitions between varying grades on highways and railroads, improving safety and comfort.&#160;These curves are parabolic and can be symmetrical or nonsymmetrical, depending on the lengths of the tangents.They connect the back tangent, representing the initial grade, to the forward tangent, representing the following grade.The transition begins at the Point of Vertical Curvature or P.V.C., where the back tangent meets the curve. The curve rises or falls gently, guided by its geometry, and eventually connects to the forward tangent at the Point of Vertical Tangency or P.V.T.The point where the extensions of the back and forward tangents intersect is called the Point of Vertical Intersection or P.V.I.Tangent offsets, the vertical distances from tangents to the curve, help calculate elevations and define the curve's profile.At the curve&#8217;s midpoint, the elevation is halfway between the P.V.I. and the midpoint of a straight line joining the P.V.C. and P.V.T.Vertical curves are carefully designed to ensure smooth alignment, proper sight distance, and balance between cutting and filling, enhancing the functionality of roadways.

introdução às curvas verticais

As curvas verticais s&#227;o transi&#231;&#245;es parab&#243;licas que conectam diferentes inclina&#231;&#245;es em rodovias e ferrovias, garantindo um alinhamento suave entre as tangentes traseiras e dianteiras. A tangente traseira representa a inclina&#231;&#227;o inicial, enquanto a tangente dianteira define a inclina&#231;&#227;o subsequente. Essas curvas podem ser sim&#233;tricas, com comprimentos de tangente iguais, ou assim&#233;tricas, com comprimentos variados. Os pontos-chave que definem uma curva vertical incluem o Ponto de Intersec&#231;&#227;o Vertical (P.V.I.), onde as tangentes se encontram; o Ponto de Curvatura Vertical (P.V.C.) no in&#237;cio da curva; e o Ponto de Tang&#234;ncia Vertical (P.V.T.), marcando o fim da curva.
Os deslocamentos de tangente, dist&#226;ncias verticais medidas das tangentes &#224; curva, s&#227;o essenciais para c&#225;lculos de eleva&#231;&#227;o e perfil. No ponto m&#233;dio da curva, sua eleva&#231;&#227;o &#233; determinada pela m&#233;dia da eleva&#231;&#227;o no P.V.I. com o ponto m&#233;dio de uma linha reta conectando o P.V.C. e o P.V.T. Esta propriedade simplifica o layout geom&#233;trico de curvas verticais.
Os princ&#237;pios matem&#225;ticos das curvas verticais dependem de propriedades parab&#243;licas, onde os deslocamentos tangentes variam com o quadrado da dist&#226;ncia dos pontos de tang&#234;ncia, e as segundas diferen&#231;as permanecem iguais em esta&#231;&#245;es uniformemente espa&#231;adas. Essas propriedades s&#227;o essenciais para verificar os c&#225;lculos de curvas.
O projeto de curvas verticais equilibra fatores como dist&#226;ncia de visibilidade, terraplenagem ideal e declives adequados. Ajustes no comprimento da curva ou gradientes garantem a efici&#234;ncia e a seguran&#231;a do alinhamento. Essas curvas s&#227;o cruciais para alcan&#231;ar projetos de rodovias funcionais e econ&#244;micos e atender &#224;s demandas da infraestrutura de transporte moderna.

Introdução às Curvas Verticais

Vertical curves are parabolic transitions that connect different grades on highways and railroads, ensuring a smooth alignment between back and forward ...

Education

JoVE Core

Civil Engineering

Engenharia Civil

Unit 1

Unidade 1

Horizontal and Vertical Curves

Curvas Horizontais e Verticais

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

designing smooth road grade transitions

Vertical curves are parabolic transitions that connect different grades on highways and railroads. They help create a smooth alignment between the back tangent and the forward tangent. The back tangent is the first grade, and the forward tangent is the next grade.

These curves may be symmetrical or nonsymmetrical. In a symmetrical vertical curve, the tangent lengths are equal. In a nonsymmetrical curve, the tangent lengths are different. The main points used to describe the curve are the Point of Vertical Intersection, or P.V.I., where the tangents meet, the Point of Vertical Curvature, or P.V.C., where the curve begins, and the Point of Vertical Tangency, or P.V.T., where the curve ends.

Tangent offsets are important in curve calculations. A tangent offset is the vertical distance from a tangent line to the curve. These offsets help determine elevation and profile values. At the midpoint of the curve, the elevation can be found by averaging the elevation at the P.V.I. with the midpoint of a straight line connecting the P.V.C. and P.V.T. This rule makes the geometric layout easier to work with.

Vertical curves also follow key parabolic rules. Their tangent offsets change with the square of the distance from the tangency points. Evenly spaced stations on the curve have equal second differences, which helps check calculations. Engineers use these properties, along with sight distance, earthwork needs, and suitable grades, to choose a curve length or adjust the gradients. These choices help make roadway designs safer, more efficient, and more economical.

Designing Smooth Road Grade Transitions

introduction to horizontal curves

Horizontal Curve Parts and Road Alignment

Horizontal curves connect straight road or railroad segments and help vehicles move safely through a change in direction. They are used in highway and railroad design to create smooth transitions between tangents, which are the straight path sections before and after the curve. By reducing abrupt changes, these curves can support steadier travel speed and help lower the chance of accidents. A simple horizontal curve is defined by its geometry around the intersection point, or P.I., where two...

degree of curvature and radius of curvature

degree-of-curvature-and-radius-of-curvature

Curvature Measures in Civil Engineering Curves

Degree of curvature and radius of curvature help describe how sharply a curve bends in civil engineering. The degree of curvature measures the steepness of the bend. The radius of curvature shows how tight or smooth the curve is. The degree of curvature can be found by the chord basis or the arc basis. In the chord basis method, the degree is the central angle subtended by a chord of 30.48 meters. In the arc basis method, it is the central angle subtended by an arc of length 30.48 meters. <br...

curve equations

Curve Measurements and Arc Length

Curve measurements describe the key parts of a curved line. The main values are tangent distance, chord length, middle ordinate, and total arc length. These measurements help explain a curve’s shape and size using its radius and central angle. Tangent distance, or T, is the straight-line distance from the point where two tangents meet to the start or end of the curve. It depends on the curve radius, R, and the central angle, I. These two values work together to set the curve’s layout. Chord...

horizontal curve: problem solving

Setting Out a Horizontal Curve

A horizontal curve is set out by using its radius, intersection angle, and stationing of key points. In this example, the radius is 400 meters, the intersection angle is 30 degrees, and the station of the point of curvature, or P.C., is 0 + 150 meters. The goal is to find the station values for the point of intersection, or P.I., the point of tangency, or P.T., and the midpoint of the curve. The length of the long chord is also needed. The first step is to calculate the tangent distance, T,...

field procedure for staking out curves

Surveying Curve Layout with Deflection Angles

Surveying curve layout with deflection angles turns a designed curve into stakes placed in the field. In construction, this step helps keep structures aligned along a curved path. Surveyors use calculated positions so the physical markers match the plan. The process starts by finding the curve’s geometric values. These include the radius, central angle, and tangent distances. Surveyors also identify the Point of Curvature (PC), the Point of Tangency (PT), and the midpoint of the curve. These...

introduction to vertical curves

Vertical curves are parabolic transitions that connect different grades on highways and railroads. They help create a smooth alignment between the back tangent and the forward tangent. The back tangent is the first grade, and the forward tangent is the next grade. These curves may be symmetrical or nonsymmetrical. In a symmetrical vertical curve, the tangent lengths are equal. In a nonsymmetrical curve, the tangent lengths are different. The main points used to describe the curve are the Point...

vertical curve: problem solving

Calculating Elevations on a Vertical Curve

Vertical curves connect two roadway grades and help make the road safer, smoother, and more functional. To find the elevation at specific stations on the curve, engineers follow a set of steps based on the curve length, the grades, the Point of Vertical Intersection, or P.V.I., and the P.V.I. elevation. The first step is to locate the Point of Vertical Curvature, or P.V.C., and the Point of Vertical Tangency, or P.V.T. The P.V.C. marks the start of the curve, and the P.V.T. marks the end.

elevation of intermediate points on vertical curves

elevation-of-intermediate-points-on-vertical-curves

Finding High and Low Points on Vertical Curves

Vertical curves help roadways move smoothly from one grade to another. Engineers use them to connect changing slopes and keep the road profile safe and even. To design these curves, they calculate intermediate elevations and find the highest or lowest point on the curve. Intermediate elevations on a vertical curve are found with the tangent offset method. This method uses the starting elevation, the grades at each end, and the curve shape. It gives the elevation of any point along the curve by...

sight distance in a vertical curve

Road Safety on Crest and Sag Curves

Road safety on crest and sag curves depends on how far drivers can see ahead. In roadway design, vertical curves must give drivers enough sight distance to notice hazards and react in time. This affects safety, driver comfort, and how efficiently the transportation network works. Vertical curves are grouped into two main types: crest curves and sag curves. A crest curve is shaped like a hilltop, so the road can block the view of what is beyond it. For these curves, sight distance is based on...

design example: setting a curve using design data

design-example-setting-a-curve-using-design-data

Plotting a Horizontal Curve from Field Data

Plotting a horizontal curve from field data starts with careful geometric design. The curve in this example has a radius of 200 meters and an intersection angle of 20 degrees. Engineers use the method of perpendicular offsets from the long chord to place the curve on the ground. The long chord is the straight line between the two ends of the curve. Here, its length is calculated as 69.46 meters. To improve accuracy, 3-meter intervals are marked along the chord. Offset distances at each point...

key terms and concepts

Learn how vertical curves connect road grades with parabolic shape, key points like PVI, PVC, and PVT, and the math used in roadway design.

Designing Smooth Road Grade Transitions | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

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Physical Properties Of Minerals I: Crystals and Cleavage

Source: Laboratory of Alan Lester - University of Colorado Boulder
The physical properties of minerals comprise various measurable and discernible ...

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Physical Properties Of Minerals II: Polymineralic Analysis

Source: Laboratory of Alan Lester - University of Colorado Boulder
The physical properties of minerals include various measurable and discernible ...

Types of Building Stone

Building stones are sourced by extracting rock from natural rock deposits and shaping it into the specific forms and dimensions needed for building ...

4. Obtain, evaluate, and communicate information about the geologic conditions and processes that form different Earth materials.

9-12.ESS.2.4

Igneous Intrusive Rock

Source: Laboratory of Alan Lester - University of Colorado Boulder
Igneous rocks are products of the cooling and crystallization of high temperature ...

Igneous Volcanic Rock

Source: Laboratory of Alan Lester - University of Colorado Boulder
Igneous rocks are the products of cooling and crystallization of magma. Volcanic rocks ...

Quarrying of Stone

Quarrying involves the meticulous extraction of stone from a quarry by either using controlled explosions or precision cutting techniques to remove the ...

a. Plan and carry out investigations to explore the processes that form plutonic (intrusive) and volcanic (extrusive) igneous rocks of differing compositions and textures. Example: Conduct a crystallization experiment to determine how speed of cooling affects crystal size.

9-12.ESS.2.4.a

Acid Attack on Concrete

Acids interacting with concrete dissolve the hydrated cement paste, leading to a softened and structurally weakened material.
Acidity breaks down the ...

Abrasion Resistance of Concrete

Concrete abrasion can occur from vehicular wear on surfaces or abrasive solids in water, which erodes canal linings.
The shot-blast test evaluates ...

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Turbidity and Total Solids in Surface Water

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
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b. Analyze and interpret data to explain the effects of mechanical and chemical weathering and erosion on Earth's materials by wind, water, ice, and gravity.

9-12.ESS.2.4.b

Making a Geologic Cross Section

Source: Laboratory of Alan Lester - University of Colorado Boulder
Geologic maps were first made and utilized in Europe, in the mid-to-late 18th century. ...

c. Construct an explanation using evidence from experiments, models, or data of the processes that create and transform igneous, sedimentary, and metamorphic rocks.

9-12.ESS.2.4.c

Pore Size Distribution

Capillary pores are considerably larger than gel pores, and various pore sizes exist within the hardened cement paste.
In conditions of partial hydration, ...

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Determination of Moisture Content in Soil

Source: Laboratories of Dr. Ian Pepper and Dr. Charles Gerba - The University of Arizona
Demonstrating Author: Bradley Schmitz
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Non-destructive Tests for Concrete Strength

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d. Plan and conduct an investigation on water's effect on surface and subsurface processes. Examples: Use particles of varying sizes to determine how the speed of water impacts particle distribution. Use the porosity and permeability of particles of various sizes to determine how the size and sorting of particles affects water movement.

9-12.ESS.2.4.d

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GIS Software, Hardware, and Sources of GIS Data

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Manipulation and Analysis

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Using GIS to Investigate Urban Forestry

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e. Obtain and communicate information about significant geologic characteristics in Alabama and the southeastern United States. Examples: types of rocks, caves, sinkholes, minerals, energy resources

9-12.ESS.2.4.e

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The Evidence for Evolution

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5. Obtain, evaluate, and communicate information about major events in Earth's history.

9-12.ESS.2.5

Radioactive Decay and Radiometric Dating

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Isotopes

Elements have a set number of protons that determines their atomic number (Z). For example, all atoms with eight protons are oxygen; however, the number ...

a. Analyze and interpret data to sequence events in Earth's history, including relative and absolute dating techniques, principles of superposition and crosscutting relationships, igneous intrusions, radiometric dating, and the fossil record.

9-12.ESS.2.5.a

Extinction

The History of Life on Earth
Fossils of organisms that were different from anything alive today had been documented as early as the 17th century, but it ...

b. Construct an explanation based on evidence of how catastrophic and long-term events have impacted life on Earth, including mass extinctions.

9-12.ESS.2.5.b

The Colonization of Land

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The Carbon Cycle

Carbon is the basis of all organic matter on Earth, and is recycled through the ecosystem in two primary processes: one in which carbon is exchanged among ...

What is Photosynthesis?

Photosynthesis is a multipart, biochemical process that occurs in plants as well as in some bacteria. It captures carbon dioxide and solar energy to ...

c. Construct explanations from evidence of how the flow of energy through Earth's systems has changed over time. Example: Earth's oxygen level was lowest during the Cryptozoic Eon (Precambrian) and highest in the Carboniferous.

9-12.ESS.2.5.c

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An Overview of bGDGT Biomarker Analysis for Paleoclimatology

Source: Laboratory of Jeff Salacup&#160;- University of Massachusetts Amherst
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An Overview of Alkenone Biomarker Analysis for Paleothermometry

d. Obtain, evaluate, and communicate information about important tectonic and geologic events that have occurred in Alabama over geologic time. Examples: geologic ages and types of rocks, fluctuations in sea levels, temperature changes

9-12.ESS.2.5.d

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Determining Spatial Orientation of Rock Layers with the Brunton Compass

Source: Laboratory of Alan Lester - University of Colorado Boulder
Most rock units exhibit some form of planar surfaces or linear features. Examples ...

Properties of Transition Metals

Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3&#8211;12 are ...

6. Obtain, evaluate, and communicate information about the theory of plate tectonics.

9-12.ESS.2.6

a. Construct an evidence-based explanation of continental drift, basing conclusions on comparisons of coastlines, fossils, ages of rocks, climate, and magnetic patterns.

9-12.ESS.2.6.a

b. Construct an explanation, based on evidence, of tectonic plate movement, types of plate boundaries, and how boundary type relates to specific tectonic features, including mountain ranges, earthquakes, volcanism, volcanic islands, hotspots, mid-ocean ridges, and faults.

9-12.ESS.2.6.b

c. Develop and interpret a model of Earth's internal structure and composition, including inner core, outer core, asthenosphere, lithosphere, mantle, and crust.

9-12.ESS.2.6.c

d. Analyze data to interpret seismic activity and assess the risk of volcanic eruptions and earthquakes in Alabama and other areas in the United States.

9-12.ESS.2.6.d

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Mechanisms of Heat Transfer II

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Phase Changes

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7. Obtain, evaluate, and communicate information about the role of energy transfer in wind, precipitation, cloud formation, and front formation.

9-12.ESS.2.7

a. Obtain and communicate information to explain how water cycles through the atmosphere, including condensation, evaporation, clouds, types of precipitation, relative humidity, and dew point.

9-12.ESS.2.7.a

Specific Heat

The specific heat capacity of a substance refers to the energy required to increase the temperature of one gram of that substance by one degree Celcius. ...

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Quantifying Heat

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b. Plan and carry out an investigation to determine the differential heating of land and water and explain how these differences create changes in local and global weather. Example: Heat water and soil under lamps for 10 minutes and allow water and soil to cool for 10 minutes, then apply the results to explain land and sea breezes.

9-12.ESS.2.7.b

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Ideal Gas Equation

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c. Construct an explanation of how air masses, source regions, fronts, weather changes associated with frontal passage (including cold, warm, occluded, and stationary fronts), air pressure, air density, temperature, cloud types, and precipitation are related to each other.

Designing Smooth Road Grade Transitions

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