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Curve studies look at two types of curvature, horizontal and vertical. Horizontal curves affect the handling of the car and their postings are based on driver comfort and the ability of vehicles to stay on the road. Vertical curves affect how far a driver can see obstructions in the road or other vehicles.

Horizontal Curve Studies
On horizontal curves the tires of the vehicle must counter the vehicle's centripital force (sideways force). If the vehicle's speed is too great the vehicle will slide off the side of the road. Superelevation (banking) of curves helps to hold the vehicle on the road and allows higher safe speeds than on a curve with no superelevation. The safe speed on a curve does not account for the effects of snow, ice, sand, or other substances on the road which may affect the tire's ability to grip the road.

Horizontal curves are tested using a device called a ball-bank indicator. the ball- bank indicator has been widely used by research groups, local agencies, and highway departments as a uniform measure for the point of discomfort to set safe speeds on curves. It consists of a steel ball in a steel glass tube. The ball is free to roll except for the damping effect of the liquid in the tube. With such a device mounted in a vehicle in motion, the ball-bank reading at any time is indicative of the combined effect of the body roll angle, the centrifugal force angle, and the superelevation angle. Based on tests it was concluded that safe speeds on curves where indicated by ball-bank readings of 14 degrees for speeds of 20 mph or less, 12 degrees for speeds of 25 and 30 mph, and 10 degrees for speeds of 35 through 50 mph, and provide ample margin of safety against skidding.

During the study a vehicle is driven through the study area at varying speeds and the reading from the ball-bank indicator is recorded. Based on the ball-bank indicator readings a reasonable safe speed for the curve is determined. If the safe speed is lower than the posted speed limit a curve or turn sign may be posted with an advisory plate to warn the driver. In most cases where the safe speed is at or greater than the speed limit no signing is done.

Vertical Curve Studies
The safe speed for vertical curves is determined by the available sight distance at the curve. Stopping sight distance is based on being able to view a 6 inch high object from a point 42 inches (3.5 feet) above the pavement (assumed to be the driver's eye height in a small vehicle). As a vehicle travels faster, the distance it requires to stop also goes up. The minimum stopping sight distance for a particular vehicle speed includes two distances: the distance traveled by the vehicle from the instant the driver sights an object requiring a stop to the instant the brakes are applied and the distance required to stop the vehicle from the instant brake application begins. The table below gives the stopping sight distance for various speeds.

Speed
(mph) 		Stopping Sight
Distance (feet)
20 125
25 150
30 200
35 250
40 325
45 400
50 475
55 550
60 650
65 725
70 850

If there is more than an isolated vertical curve or two which do not meet the stopping sight distance requirements, the speed limit may be reduced to reflect this condition.

Vertical curve studies can also determine whether or not there is adequate sight distance for passing or pulling out from a stop sign. In this case the driver's eyes remain at 3.5 feet above the pavement, but the target object is 4.25 feet (51 inches) corresponding to the height of a small car.

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