The new lane management since EEP16 has completely changed the habits acquired since the previous versions when it came to curving, bending or adopting a particular shape for curved lanes. We now have additional properties at our disposal that give us much greater construction possibilities.

## In summary

We will detail each type of curve proposed in EEP16. As we can see in the image below, no less than 6 types of curves are offered in the drop-down list. For each type of curve selected, different properties will appear in the Characteristics frame:

Note : Dans EEP16, la Clothoïde est disponible à partir du plugin 1 et la courbe Spline à partir du plugin 4.

Important : before tackling the different types of curves, each parameter modified in the Start of position frame of the track properties window has an impact on the configuration of the track and the parameters specific to each type of curve.

## The different types of curves

### The arc

The arc is a completely flat section of track which can’t have a slope. Three parameters: angle, length, radius are used among the following three double-combinations:

#### Angle + length

By entering a positive value in the Angle input box, the track is bent to the left.

Conversely, to bend the track to the right, enter a negative value in the Angle input box.

Here, the angle is still positive 9 ° and EEP automatically calculated a radius of 381.97 meters. Why 381.97? This figure corresponds to the trigonometric calculation of a curved section with an angle of 9 ° for a given length of 60 meters.

If you enter a negative angle of 9 °, EEP will always calculate a radius of 381.97 meters. To understand, imagine a full circle. Our section of track is only a small part of the total circumference of the circle. Indeed, regardless of the direction, for a length of 60 meters and a positive or negative angle of 9 °, the radius will always be 381.97 meters

We always have a radius of 381.97 meters for a given length of 60 meters. Now we are going to enter a new length of 90 meters in order to get a bigger radius because we want to build a rail line used by faster trains.

Well, the radius value has remained the same. Why ? quite simply because we have chosen to make the modification in the 3rd pair Length + radius! This makes sense since we are asking EEP to change the length while keeping the same radius! So this is not the right solution to build a rail line dedicated to faster trains.

Let’s think about it … If the value of our radius remained the same for a different length, another of the values ​​of the Length – Angle – Radius trio has necessarily been modified. In our case, after having eliminated those for the length and the radius, then must remain that of the angle. To check this, we will re-select the double combination Angle + length and check if the value of our angle has been modified:

Effectively ! our angle has changed to -13.5 degrees. Obviously, in our example in order to build a railway line adapted to fast trains, this is not at all the right idea to follow for higher traffic speeds. Indeed, these tracks must have the lowest angle as possible, which requires a much larger radius.

Now if we enter -9 ° as the new angle value, logically our radius should increase:

Which, after selecting the Angle + Radius characteristics is effectively the case at 572.95 m.

Important : Modifying a value following the selection of a double-combination always influences the other values ​​and this is valid whatever the type of curve used. Always ask yourself the following question: “What kind of value do I need to change? Length, radius or angle?” Once you have determined the relevant parameter (s), building the lanes will become easier and more logical.

### The rotator

The rotator is a curved or straight section of track with an upward slope (positive value) or downward slope (negative value). Four parameters angle, length, radiusslope (°) are used among the following three combinations, but these do not necessarily use all four parameters together :

#### Angle + length + Deflection

With the rotator, we are only going to be interested in the parameter of the deflection. Logic would have wanted this parameter to be called Slope, but the Trend editor decided otherwise. The other three parameters are identical to the arc.

We are going to change the parameter for the deflection and enter a value of 10 degrees:

As we can see, we see the rising path. If we had entered a negative value, it would sink into the ground. This is the preferred method if you want to create a depression so that the track passes under a bridge for example.

Now we can change the angle of the track, which gives us:

The other two combinations available are:

• Angle + radius + Deflection
• Length + radius + Deflection

The same principles apply here as well as for the arc we saw above. Depending on the desired result, we can act on this or that parameter depending on the construction needs.

### The helix

The helix is a curved section of track with a constant slope. This makes it the ideal curve for building helical ramps such as turning loops, although unlike model railroading, it is possible to use virtual connections in EEP. Four parameters angle, length, radius, slope (in ° or in meters) are used among the following two combinations:

• Angle + Length + Slope(°)
• Angle + Radius + Slope(m)

For the slope, you can choose a value in degrees or in meters. Below, a first example:

Do not rely on the small value of 0.5 degrees for the slope because the purpose of the helix is to set the 1st section of the track and then use one of the following two commands:

1. Via the 2D window, in the Add an extension frame, the Duplicate forward button,
2. Via the 3D window, the Add once at the end command in the contextual menu of the selected track.

Now we are going to duplicate this first section until we form a complete circle and look in the 3D view to see the result:

The first section is laid at 0.60 m at ground level. After a first circle, the last section just above the first is 17.34 meters above ground level. Let’s continue our helix to perform an additional revolution:

The last section is 25.73 m above ground level. It is faster to use the Duplicate Forward 2D Window function than the Add Once command at the end of the context menu in the 3D Window.

Now here is a second example:

The first section is laid at 0.60 m at ground level. After a first revolution, the last section just above the first is 17.34 meters above ground level. Let’s continue our helix to perform an additional revolution:

Here, the angle is doubled compared to the first example, the track is shorter and the slope is greater. This results in a smaller but steeper helix. Indeed, the last section is found at the height of approximately 34 meters from ground level.

These two examples perfectly illustrate the close links between each parameter. It is up to you to choose the most relevant according to your construction needs.

### The cubic

The cubic is an elaborate curve to connect two points and keep the two tangents. It is also relatively complex to understand. We will try to explain it with simple words. If the subject interests you and you have the soul of a mathematician, there are excellent resources on the internet on the subject. No less than seven parameters Angle Y, Angle Z, Offset X, Offset Y, Offset Z, Overshoot start, Overshoot end can be used together to construct the desired curve. As for the other types of curves, the parameters present in the Start  position frame must also be taken into account.

These are the default settings when we first display the properties window. So far we have a completely straight track:

We will start by modifying the Y Offset parameter and together see the modification made to the track:

We have entered in the Y offset parameter (red box) a value of 15 °. We can see that our track is curved to the left at an angle of 15 °. Granted, this is not a linear curve, but that is not the point here. For now, let’s take care of understanding the Y offset with a 2D diagram:

In this orthonormal diagram, we immediately see that the track has been deflected at an angle of 15 ° on the coordinate axis (Y axis). The track has as a point of origin [0, 0] which corresponds to the center of the circle (mark O). The white line represents the direction of the angle, from the center of the circle to its circumference.

We also find the length of our track represented by the radius of the circle which is here 60 meters. In the properties window, the length of the track is defined by the X Offset property.

We also find the length of our way represented by the radius of the circle which is here 60 meters. In the properties window, the length of the track is defined by the X Offset property.

While keeping our Y Offset, we’re going to change the Z Offset parameter to an angle of 6 °:

We can see that the 6 ° angle in the Z Offset property acts on the height at the end of the track.

Below is the same track seen from another angle:

We notice the difference in level between the start and the end of the section. This difference corresponds to our Z Offset property of 6 °.

After the Y and Z offsets, the unit of which is the degree, we are going to modify the X Offset which, unlike its two brothers, is expressed in meters. Indeed, this parameter acts only on the length of the track:

As you can see in the image above, only the track length has been divided by 2 compared to the previous image.

The parameters of the X, Y and Z offsets are the easiest to understand. We will now move on to the main course and without delay with the Angle Y parameter:

What exactly does the Angle Y parameter do? The Y angle (in the cubic and not the Y angle of position) returns the tangent of the X and Y axes. Here, The tangent is the result of the opposite side by the adjacent side. The opposite side is the Y axis symbolized in EEP by a green circle at the right end of the track section. The X axis is symbolized by the red double arrow line. The white dotted lines symbolize a cube to help you mentally reproduce a projection in space.

Therefore, at the starting point of the tangent with an angle of 20 °, the track describes a curve at a height of 20 ° symbolized in the diagram by a dotted green line. Here we have a positive value of 20 °, that’s why the track starts to descend (for the sake of clarity, I raised the track above the ground surface) because the angle pushes the track outwards. Conversely, if we had entered a negative angle of -20 °, the track would start to climb.

Now let’s move on to the Z angle. Like the Y angle, here we change the angle of the Z axis. Let’s illustrate this with a small diagram:

We still have the X axis as the adjacent side, but this time the Z axis is the opposite side. As you can see in the diagram, the Z axis is symbolized in EEP by a blue colored circle at the start of the section of the track (right in the image). Imagine that the blue circle on the right is a spinning top. You will gently rotate the spindle in the center of the router. Suppose the left end of the section simultaneously copies the same rotational motion of the router, so the end of the section on the left will rotate according to the angle of rotation of your router and that’s exactly what happens. here, the curve at the end of the section on the left corresponds to the tangent of the Z angle of 20 °. The white line is there to materialize the end of the track.

In the example below, we are cumulating the effects of the parameters of angle Y and angle Z. You will notice that this time, we have intentionally entered a negative angle for angle Y so that the track climbs, unlike the example of angle Y.

We are now going to study the Overshoot start and  Overshoot end properties. These two properties are closely related to the X Offset property. These two peculiarities should be noted:

1. The sum of the values ​​of these two properties can never be less than the total value of the X Offset property. Example: if the length of the track is equal to 60 meters (X Offset = 60 m), Start and End can’t be less than 30 meters,
2. The same applies to the maximum permitted value. Either of these properties can’t contain a value greater than twice the length of the track defined by the X Offset property. Example: if the track length is equal to 60 meters (X Offset = 60 m ), the Start or End property can’t be greater than the value 120.

At first glance, the number expressed in these two properties is confusing, as it is by no means a value expressed in meters. This number is used in a Cartesian equation to calculate a level 3 algebraic curve (also called a cubic parabola). We will keep it simple and summarize the situation as follows with the following image:

The default is 60 for both properties. In the image above, you see the track overlay with four different settings and the corresponding values ​​indicated by arrows. We must therefore remember :

1. The smaller and equal the two values, the flatter the track will be,
2. The greater and equal the two values, the more the slope on each side of the central axis (double yellow arrow) will be accentuated,
3. The more the start value is lower than the end value, the more the track will be raised on either side of the central axis,
4. The more the start value is greater than the end value, the lower the track will be on either side of the central axis,

Note that these properties also see their behavior modified according to the other properties of the cubic.

The three properties circled in red in the Start position frame allow you to orient the track on the three axes.

### The clothoid

The clothoid (from plugin 1 for EEP16), is a flat curve with a curvature which gradually increases. To put it simply, the clothoid is used to blend a straight section to a curve but changing the entry and exit angles to soften the start and end of the curve. Indeed, it is not recommended to directly connect a straight line to a curved track. This suddenly causes a radial acceleration for the passengers which can be measured by the square of the speed divided by the radius of the curve (V² / r). Three parameters Radius A or Angle A, Length, Radius B or Angle B are used among the following two combinations:

• Angle + length

Here is a small diagram to demonstrate the validity of this curve which should now be used systematically (except in special cases) between straight – curve transitions:

Here you see two superimposed curves; At the top with the clothoid property and the one below with the arc property. We easily notice the smoother transition with the clothoid. By using a clothoid after a straight section, your passengers will not experience the discomfort of radial acceleration. It also results in a visually smoother curve. The double red arrow shows the relation with the angle of curvature which is the same in both types of curves. We have intentionally exaggerated the angle to 30 ° for the clarity of the drawing. In this example, we start again at the end of the clothoid with another curve endowed with the arc property of the same value as the angle B.

Now let’s change the value of angle A to a value of 10 °:

The entry of the curve is smoother, because the starting angle changes the initial curvature. Please note : Angles A and B are related to the level of the sign. They are both positive or negative, but one can’t be positive and the other negative.

### The spline

Appeared with plugin 4 in EEP16, this curve is different from the others because it has control points (materialized by nodes) whose positioning can be modified at will in order to adapt the curve according to your construction needs. You can edit it in both 2D and 3D editing modes.

#### In the 2D editor(planning window)

1. Place a section of track in your layout,
2. To make your work easier later, you can bend the track from one end:
1. Choose the Track properties command in the contextual menu:
1. Select the Type of curve: Spline and then click on the OK button at the bottom of the window:
1. After validation, we can see in the 2D editor, the track with additional nodes materialized by green circles:

This curve has only one active parameter in the Characteristics frame which is the Scale:

The nodes can be moved easily according to your construction needs. The mouse cursor changes to a hand when you hover over a node:

It is also possible to add or remove nodes allowing you to shape the track according to your wishes. To perform the operation, click on the track with the right mouse button to display the contextual menu and choose the Add / remove a control point command:

After clicking on the command, the cursor changes with a + and – as well as a small white circle:

From now on, nothing could be simpler, if you click on an already existing node, it is deleted. If you click between two nodes, a new node is created.

#### In the 3D editor

In this mode, modifying the track layout is identical to 2D editing mode.

To start, right-click on the track in question to bring up the context menu. Select the Edit, move object option:

You will see 4 white arrows appear to move the node horizontally in the direction of your choice and a green arrow to move it vertically.

Important : if the match object position height to surface option is activated, the nodes can not be moved vertically!

If this option is disabled, you can easily move a node vertically by holding one of the two [Ctrl] keys down. This key behaves like a toggle: once pressed, the four horizontal white arrows turn green and the vertical green arrow turns white:

Of course, as in the 2D editor, you can add or remove nodes. To perform the operation, right-click on the track to open the contextual menu and select the Add / remove control point command:

The procedure remains identical to that of the 2D editor for adding or removing a node.

### The line

We saved the most difficult for the end: the line! Nonsense exists for the line which is anything but curved! Two parameters are used and concern, on the one hand, the Scale and, on the other hand, the length:

The unit of measure is the meter. The minimum and maximum lengths are between 1 and 120 meters.