Photo A woman was hit by a motorcycle and died = Soka City

### Woman died ... 18-year-old boy was hit by a motorcycle at 9 pm on a straight road in Soka, Saitama, arrested on suspicion

** ***If you write the contents roughly*

According to the office, the site is a straight road 6.2 meters wide.** **

Around 18 pm on the 9th, an unemployed woman (64) was hit by a motorcycle on a prefectural road in Yatsukakami-cho, Soka City, Saitama Prefecture.** → Continue reading**

**Saitama newspaper**

Saitama Prefecture's only local newspaper. Carefully selected news from the prefecture!

### Wikipedia related words

If there is no explanation, there is no corresponding item on Wikipedia.

# Linear (route)

**linear**(Senkei,*alignment*) Is道路,TrainThe shape of the route such as.That is, what is the shape of the flat line?Straight lineとcurveIs a combination of, uphill, downhill, etc.SlopeIt shows how is configured.

## Overview

When a road or railroad connects a starting point (starting point) to a destination (ending point), it is not common that the shape is composed only of straight lines or that they are all flat.If there is an obstacle on the way, it is necessary to insert a curve in the line to avoid it, and if there is a height difference between the start point and the end point, it is necessary to provide a slope on the line.The shape of such a line is called linear.

Linear indicates a combination of planar straight lines and curves**Horizontal alignment**, Shows the slope along the route**Alignment**In addition, it is provided so that the vehicle can run smoothly in the curved section.**One-sided gradient / Kant**And so on, these individually**Alignment element**It is called.In general, horizontal alignment is mainly composed of straight lines and loose curves.Longitudinal slopeIs near flat**Linear is good**On the contrary, routes with many sharp curves and steep slopes are called**Bad alignment**Is called.The quality of the alignment affects the running performance of the vehicle, and a route with a good alignment can comfortably run at high speed.

In addition to railroads and roads, linearRiverIt is also used to indicate the shape of.

## Horizontal alignment

### Straight line and radius of curvature / curvature

Alignment is a linear element that indicates the planar shape of a line.The basics of horizontal alignment are straight lines and arc curves, both of which are arcs.radius*R*Shown with.The smaller the radius R, the steeper the curve, and the straight line*R*= ∞ (infinity).Also, the horizontal alignment iscurvature*k*Can also be indicated by the reciprocal of the radius*k=*1/*R*There is a relationship of.Therefore, the larger the curvature, the sharper the curve, and if the straight line is indicated by the curvature,*k*= 0.

When the traveling vehicle approaches the curved section of the route, the vehicleCentrifugal forceWorks.The centrifugal force at this time can be expressed by the following equation.

here,

*F*- Centrifugal force*m*--Vehicle mass*v*--Vehicle running speed*R*- curvature radius*k*--Curvature

.

From this, it can be seen that the centrifugal force increases as the traveling speed of the vehicle increases, and increases as the radius of curvature decreases.When the centrifugal force becomes excessiveRide comfortIn addition to damaging the vehicle, the vehicle capsizes, derails, deviates from the road, etc.ACCIDENTCauses.Therefore, in order for the vehicle to comfortably travel at high speed, it is necessary to increase the radius of curvature (decrease the curvature).If it is unavoidable to have a small radius of curvature, a speed limit is set for the traveling vehicle.

### Relaxation curve

As mentioned above, the basics of horizontal alignment are straight lines and arc curves, and the arc curve is the radius of curvature (curvature radius) in the curve section.curvature) Is constant.However, when directly shifting from a straight section to a curved section, the traveling vehicle suddenly changes.handleIt adversely affects ride comfort and safety, such as being required to operate and suddenly applying a large centrifugal force.In particular, a sudden transition to a sharp curve with a small radius of curvature has a large effect.

So a straight line (radius of curvature)*R = ∞* / Curvature*k = 0*) May insert a curve that gradually changes to the curvature of a given arc curve.**Relaxation curve**Called.The transition curve improves driving operation and riding comfort, and will be described later.One-sided gradient / KantTo change smoothly (Kant's diminishing)^{[1]}) Can be done.Further, the transition curve is inserted not only when connecting a straight line and a curve but also when connecting arc curves having different radii of curvature.In railways, there is no arc curve part and only the transition curve part.*Total transition curve*May be used.

In the case of roads, the gradual decrease in curvature is constant, but in the case of railways, it gradually decreases linearly.*Straight line diminishing*And gradually decrease in a curve*Curve diminishing*There is.In the case of linear diminishing, the curvature cannot be differentiated at the start and end points of the transition curve, but in the case of curving diminishing, the start and end points of the transition curve become differentiable, so it is used in high-speed railways (Shinkansen, etc.).

Generally, the following curve is used as the transition curve.

- Clothoid curve Straight line diminishing (perfect straight line)
- It is a curve in which the curvature changes at a constant rate.
- At a constant speed while driving at a constant speedhandleCorresponds to the locus when operating.
- It is used as a transition curve for roads.
- In the case of railways, the calculation for maintenance is relatively difficult.Labor saving trajectoryIt is often adopted in the case of.

- 3rd order curve (3rd order parabola) Straight line diminishing (not a perfect straight line)
- Alignment curve used in railways
^{[2]}..Because the calculation for maintenance is easier than the clothoid curveBallast orbitThen this is often adopted.

- Alignment curve used in railways
- Sine half-wavelength diminishing curve Curve diminishing
- Used on railroads
^{[2]},JapanThen.ShinkansenIt is used for sections that travel at 120 km / h or more.

- Used on railroads
- McConnell curve

## Alignment

### Slope

Design speed (km / h) | Gradient limit (%) | |
---|---|---|

Specified value | Special value | |

120 | 2 | 5 |

100 | 3 | 6 |

80 | 4 | 7 |

60 | 5 | 7~8 |

: | : | : |

20 | 9 | 11~12 |

Road structure ordinanceAn example of a Japanese ordinary road by.The special value is the upper limit when it is unavoidable. |

When a line connects two points with different heights, the line between them isSlopeWill have.Especially to distinguish this gradient from the one-sided gradient described later.**Longitudinal slope**Sometimes called.

The degree of gradient is generallypercentageorPer milleIs expressed using.The slope of the road is generally a percentage, and if it is 5%, it is a slope with a height difference of 100 m when traveling 5 m horizontally.On the other hand, for railways with a smaller slope than roads, it is shown as a fraction, and for 10 per mil, the slope has a height difference of 1000 m when traveling 10 m horizontally.Also, especially that the gradient is 0, that is, flat.**Level**Called (level).

Large gradients affect the speed of the traveling vehicle.A steep uphill puts a burden on the acceleration of the vehicle, and a steep downhill makes the braking effect worse, so it is not suitable for high-speed driving.Therefore, the maximum value of the gradient is generally set according to the design speed of the route.Further, as in the case of planar alignment, a speed limit may be set when a steep slope is unavoidably set.

The table on the right shows examples of Japanese roads.Road structure ordinanceIndicates the "limit value of the longitudinal gradient with respect to the design speed" defined by.It can be seen that the higher the design speed, the stricter the limit value is set for the longitudinal gradient.

### Longitudinal curve / vertical curve

Top-If there is no vertical curve. Bottom-If there is a vertical curve. |

At a point where the slope changes, if the slope is suddenly changed at one point, a "break" will occur on the route, which is not preferable, such as hindering the running performance or contacting the bottom of the vehicle with the road surface.Therefore, at the change point of the gradient, a curve is inserted in the longitudinal direction, and the gradient is gradually changed.This curve**Longitudinal curve**, Or from English notation**Vertical curve** (*vertical curve*), Especially in railways**Vertical curve**Call^{[4]}..The vertical curve is a quadratic curve (parabola) Is used, but since it can be approximated by an arc, its size is expressed using a radius.

As shown in the right figure, the vertical curve also has the effect of ensuring the visibility of the vehicle.The upper part of the figure on the right is the case where there is no vertical curve, and the vehicle running in front of the gradient change point cannot see the vehicle running ahead due to the blind spot caused by the gradient change point.On the other hand, if a vertical curve is inserted as shown in the figure below, the blind spot becomes smaller and the vehicle in front can be visually recognized.The distance at which visibility can be ensured from such a linear state**Viewing distance**Call it (Shikyo).Since it is necessary to take a large viewing distance on a route with a high design speed, it is required to take a large radius of the longitudinal curve.

## One-sided gradient / Kant

### Slope given to the curved part

Horizontal alignmentAs described above, a centrifugal force that tries to push the vehicle out of the curve acts on the vehicle traveling on the curved portion.Excessive centrifugal force hinders riding comfort and adversely affects stable driving.

Therefore, by lowering the inside of the curved portion or raising the outside of the curved portion to give the vehicle an inclination in the direction opposite to the centrifugal force, the traveling of the curved portion of the vehicle is made comfortable and smooth.On the road, this is because the entire road surface is tilted inward of the curve.**One-sided gradient**(Katakoubai)**bank** (*bank*).The one-sided gradient is expressed as a percentage (percentage) like the longitudinal gradient.On the other hand, in railways, the same effect can be obtained by making a height difference between the rails inside and outside the curve.this**Cant** (*cant*), Which is indicated by the height difference of the rail (millimeter in Japan).

### Effect

The roles of one-sided gradient and Kant are as follows.

- Work to reduce the force due to centrifugal force
- When centrifugal force acts on a vehicle, a force that tries to cause skidding between the tire and the road surface acts on the automobile, and a lateral pressure that pushes the rail by the wheel acts on the railroad vehicle.When these become excessive, automobiles begin to skid, and railcars can derail their wheels over the rails.On the other hand, the one-sided gradient and the cant exert a force in the opposite direction to the centrifugal force due to the inclination, and have a function of reducing these effects.
- Work to prevent falls and capsizes
- Centrifugal force acts on the center of gravity of the vehicle.Therefore, in a vehicle having a high center of gravity, a rotational force (moment) that tries to overturn or capsize acts due to centrifugal force.On the other hand, the one-sided gradient and the cant have the effect of moving the position of the center of gravity of the vehicle to the inside of the curved portion, and give a moment in the opposite direction.This has the effect of reducing the rotational force of overturning and overturning.
- Work to improve ride comfort
- Centrifugal force acts not only on the vehicle but also on passengers and passengers in the vehicle.Excessive centrifugal force also affects ride comfort, but proper one-sided slopes and cants also improve ride comfort.For example, if the centrifugal force and the rotational force due to the one-sided gradient / cant match, the person in the car does not feel the centrifugal force.If you are careful, you may notice a change in vertical acceleration (change in gravity you feel), but the effect on riding comfort is much smaller than when you receive horizontal acceleration.

### Water gradient (road)

One-sided gradients and cants are basically provided in curved sections where centrifugal force acts, and theoretically it is not necessary to provide them in straight sections where the curvature is 0.However, if the slope of the road surface is horizontal on the road, water tends to collect on the road surface in rainy weather and drainage is not good. Therefore, a slope (about 1.5% to 2%) is provided so that water can flow even in a straight section. ing.

Also (on the left side),MotorcycleIt is this water gradient that tends to reduce the right side of the tire.

### Synthetic slope (road)

Longitudinal slopeThe gradient that combines and one-sided gradient (crossing gradient) is called the combined gradient, and is the steepest slope of the road surface.A composite slope occurs when there is a plane curve in a section of the road with a vertical slope.Here, the automobile receives gradient resistance and curve resistance at the same time, and the resistance becomes larger than usual.Especially when the slope is steep and the radius of the curve is small, driving danger is likely to occur.

Its size is

here,

*S*: Composite gradient (%)*i*: One-sided gradient (%)*j*: Longitudinal gradient (%)

Obtained at.

## Other

Description example | 距離 (From the starting point) | Use |
---|---|---|

No.22 + 2.0 | 442.0 m | 道路 |

STA.5 + 12.0 | 512.0 m | highway |

12k573 | 12,573 m | Train |

Other terms related to linearity are outlined.

- Widening element
- In the curved section of the roadInner ring differenceA linear element that widens the inside of the curved part in order to absorb the influence of and secure the viewing distance.
- slack
- A linear element that facilitates curved running of railway vehicles by slightly moving the rails inside the curved section to widen the rail spacing in the curved section of the railway.
- Sokuten and kilometers
- It shows the distance from the starting point to the ending point along the route.
- Sokuten
- It is installed on the road.In Japan, every 20 meters
**No.**In addition to assigning (number) in order, every 100 meters on the highway**Sta.**(Station) may be used.When indicating a position other than the station, the distance from the station in front is used.MetersAdd in units,**Sokuten + ○○**It is shown in the form of. - About a kilo
- The distance from the starting point by railKilometersShown in units.After the distance
**k**Is added, and if there is a fraction less than a kilometer, a number in meters is added after k.on the other hand,Imperial imperialIn countries where the unit system of is used, "mileage" is used, and even in Japan, it was based on miles before the transition to the metric system.

## footnote

**^**Kant's diminishing --Track Maintenance Wiki (Tuesday, August 2015, 8 11:09 version) Retrieved August 54, 2018- ^
^{a}^{b}"Railway Engineering" pp.51-52 **^**Highway Curves and Test Track Design American Academy of Sciences KA Stonex, William A. McConnell 1957**^**"Railway Engineering" p.54

## References

- "Explanation and Operation of Road Structure Ordinance" Japan Road Association, February 2004, revised edition.ISBN 978-4-88950122-3.NCID BA66671474.
- Kamiura, Masaki, Onoda, Shigeru, Sucho, Makoto "Railway Engineering" Morikita Publishing, 2000, 1st edition.ISBN 978-4-62748471-9.

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