# Supplementary Information

## K Value

Vertical curves (sag or summit) can also be designed using the value K as an input parameter instead of the minimum Radius/Length defined at Design Standard.

## Activating K - Value as input

Run the function Options and activate the tab Vertical. Mark the check box K - Value as input. Figure 1: User Interface for Circular Curves Figure 2: User Interface for Parabolic Curves

## K - Value concept Figure 3: K - Value concept and details ## Design Criteria - Vertical Curves

### Sight Distance Requirements

The horizontal length of the vertical curve (L) for a given sight distance (Ls) is calculated by the following expressions:

Where,

Substituting the vertical curve parameter K for L/A in EQ(2) gives:

K = (Ls2)/C — — — — — EQ(3)

Sight distance formula:

Ls = (0.284*V*tr)+(V2)/(254.3*(f+s)) — — — — — EQ(4)

Where,

Sightline constant (C) for summit curves:

C = 200*[√(h1)+√(h2)]2 — — — — — EQ(5)

Where,

Sightline constant (C) for sag curves:

C = 200*[h+Ls*Tan(q)] — — — — — EQ(6)

Where,

Sightline constant (C) for sag curves at overhead obstructions:

C = 200*[√(H-h1)+√(H-h2)]2 — — — — — EQ(7)

Where,

Using the above equations, the value of K can be obtained for the following conditions:

### Parabolic Curves

Enabling 3rd-degree (parabolic curves) for the summit and sag curves. By default 2nd-degree curves will be used for the curve elements (sag/summit) of vertical alignment. Parabolic curves can also be used instead of 2nd-degree curves. To activate parabolic curves, use the following procedure:

Step 1: Open the dialog box System Properties and select the tab Advanced:

Start > Control Panels > System

Or activate the shortcut menu of the icon My Computer and select Properties.

Step 2: Click the button Environment Variables. The dialog box Environment Variables will pop up.

Step 3: System variables: Click the button New. The dialog box New System Variable will pop up.

Step 4: Define the value VIPS at the field Variable Name: and value P at the field Variable Value:.

The change made will come in the act once the computer is rebooted.

The newly created system variable will be listed.

Note: To switch back to simple curves for vertical alignment, delete the system variable VIPS.

### Scale Symbols

The construction objects are drawn like symbols or print, e.g. example fixed points, radius, clothoid, etc. The drawing scale determines the size of the symbol. If the scale is changed from, for example, 1:1000 to 1:4000 the symbol size will increase.

If the drawing scale is changed while the Alignment design is running, the CAD command Redraw or Regen is recommended to update the symbol size to the new scale.

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