A big or sudden change in speed or direction can make a bigger acceleration. To keep these forces at safe levels, the designer has to stretch out the time and the distance it takes to navigate the curve at the bottom of the hill. This spreads the change out over time, decreasing the force you feel. The top of the next hill has to be high enough to slow the coaster down, or stretched out to a gentler or banked curve, so the car doesn't fly off the track. Space is a problem.
Coasters go forward two feet for every foot they climb.
If the highest hill is 100 feet, it takes about 200 horizontal feet to get the car that high. If the highest hill is 200 feet, it takes 400 feet. Since land is expensive, the designers have to be creative about the use of space. A track shaped into a curve takes up less space than one left in a straight line. Connections Creators of amusement park rides apply their knowledge of physics in their designs.