All rides and attractions have height requirements, as well as a set of rider admission policies. These safety standards ensure that the rider conforms to the restraint device safely, and is developed enough to experience various forces exerted on them. But who makes up this number, and what factors come into play when determining that restriction?
1. ASTM Standards
First and foremost, the committee that oversees all ride manufacturers, parks, inspectors, and operators is the American Society of Testing and Materials (ASTM). As they do with EVERY industry, their Volume 15.07 covers Amusement Devices and other recreational attractions. They are the ones who make "the rules" for everyone involved to follow.
From the moment that a ride concept is designed, to its fabrication, to construction, and finally operation/maintenance, ASTM has set standards to govern these bodies. One of their articles covers forces and acceleration exerted on riders. With the use of acceleration and G-Force graphs, they show the maximum boundaries and limits that can be subjected to a rider. There's a reason why many rides have similar height requirements (36", 42", 48", 52", 54"). ASTM suggests that a rider be a specific height as an average indicator for age and development. The higher a force range is on a rider, the taller they should be (which of course height isn't always a good metric for age, but it provides an average).
2. Ride Manufacturers and Restraints
When designing ride vehicles and restraint devices, a ride manufacturer needs to design a device that will be able fit the largest audience as possible, but also do so safely. I will use Intamin as an example. We all know and have heard about how unforgiving their T-bar restraint can be for larger riders. Intamin has tried many sizes and shapes of those restraints over the years to be able to safely hold more riders of larger proportions. But the larger a restraint becomes, the more you have to sacrifice riders of a lower height requirement who cannot fit.
Therefore, there is a balance in trying to achieve the greatest amount of potential riders as possible. Force-wise, ASTM standards may give a lower number, say 48", but a ride manufacturer can easily bump that number up, if their restraint device requires riders of a taller stature or with longer legs or torsos.
3. Park, State, Insurance Reasons
This one is more of a grey area, but parks themselves, state regulations, and (indirectly) raised insurance fees can all factor into the final decision for a height requirement. Similar ride models or trains may even have different height requirements from park-to-park in many cases.
Insurance companies charge fees to insure rides based off of risk, intensity, restraint type, etc. This is a very similar system to how pricing on car insurance, home insurance, and life insurance work. A ride that has a very high intensity or thrill factor will have a larger cost to insure than the teacups. If a park boosts the height requirement above the ASTM or manufacturer minimum, they could help alleviate insurance costs due to more mature riders taking part (lower risk). Another scenario is a ride with a dual-redundant locking mechanism being supplemented with a seatbelt, to add more factors of safety.
Millennium Force at Cedar Point is over 300 feet tall, built by Intamin. Although it is 100 feet shorter in height, and has the exact same train design as Millennium Force, Ride of Steel at Darien Lake has a 54" requirement, vs MF's 48". Insurance costs and the park's personal opinion on the issue played a role into this ride's increased requirement, despite being a smaller ride.