When designing a hill in a road, what special number helps figure out how long the curve should be for safe sight?

When designing a hill in a road, the special number that helps determine how long the curve should be for safe sight is called the K-value. The K-value represents the horizontal length of the vertical curve required for each one percent of algebraic difference in grade. A vertical curve is a parabolic arc used to smoothly connect two intersecting road grades, which are the slopes of the road, typically expressed as percentages. For example, a +3% uphill grade connecting to a -2% downhill grade would have an algebraic difference in grade of |+3 - (-2)| = 5%. The K-value is essential because it directly relates the curve's length to the necessary Stopping Sight Distance (SSD). Stopping Sight Distance is the minimum distance needed for a driver to see an obstacle on the road, perceive the hazard, react, and bring the vehicle to a complete stop safely before reaching the obstacle. This distance is calculated based on the road's design speed, typical driver reaction time, vehicle braking performance, and road surface conditions. For a crest vertical curve, which is the curve at the top of a hill, the K-value is derived from a formula that incorporates the required Stopping Sight Distance, the standard driver's eye height, and the height of a typical object that needs to be seen on the road. A higher K-value signifies a longer, more gradual vertical curve for a given change in grade, thereby providing a greater line of sight over the hill's crest and enhancing safety by ensuring drivers have sufficient distance to react and stop.