Physics of disneyland's space mountain?

Question

someone please tell me a bit of the physics in this ride

Answer 1

The Physics of Disneyland's Space Mountain:

In April 1975, a few months after Space Mountain opened at Walt Disney World and proved to be popular, it was decided that there would be a Space Mountain at Disneyland. Because of space limitations at Disneyland, an entirely new design would be required and it had to fit in a 200-foot diameter building that would be less than half the volume of the WDW version.

For a popular ride such as Space Mountain was certain to be, the ride capacity needs to be 2,000 passengers per hour or more. With room for only one track instead of the two-track system at WDW, a larger vehicle would be required. So instead of the WDW type vehicle, which has tandem seating, a new, larger vehicle with side-by-side seating was indicated. With two-car trains in each case, this increased the seating from eight to 12 passengers for each dispatch. It also allowed the use of lap bars instead of seat belts and eliminated the need for two people to share the same seat, a real problem when strangers are involved and resulting, in the extreme case, in some trains being dispatched with as few as four passengers onboard. So, with a 20-second dispatch interval, the theoretical hourly capacity (THC) would be 2,160 as opposed to 2,400 at WDW. But the actual ride capacity would be more nearly the same due to the improved seating arrangement.

A wealth of data was gained from the Walt Disney World experience which was useful for the new design. As I discussed in George's article about WDW's ride system (link), the goal for a ride with a space theme is that it be smooth and flowing; thus proper curve banking and smooth transitions from level to fully banked is essential. We found at WDW that some of the transitions had roll rates that were a little severe, so we set a new standard for Disneyland that was only half that of the WDW worst case (we also went back and altered the WDW track.)

Next, we designed and built a prototype vehicle and a test track because the track design is dependent on vehicle performance. We decided to use nylon wheels with ball bearings rather than the polyurethane wheels with roller bearings that had been used on the Matterhorn and WDW Space Mountain because they have lower and more consistent rolling resistance. Step one was to run the vehicle and measure such factors as rolling resistance, bearing and seal drag, wheel skidding, and aerodynamic drag so that new data could be plugged into the track design program that we had developed for the WDW project. Step two was to run endurance tests to detect any structural problems with the vehicle or track.

On to track design. This isn't rocket science; it may be more complicated than that. Once a rocket leaves the Earth's atmosphere, there is little drag to contend with. Sure, there are some issues with gravity from the various planets and moons but, hey, they don't have to worry about getting a Mickey Mouse hat caught in their wheels. And furthermore, they have little vernier rockets attached that can make corrections, whereas we, who are trying to design a pure gravity ride, can make no corrections. It's the difference between a guided missile and a ballistic one.

Now for a little physics (those of you who hated Physics in high school may want to skip the next three paragraphs; if, in fact, you've read this far.) Gravity rides are all about potential energy vs. kinetic energy. As a vehicle goes downhill, it is trading its “head” (or elevation) for speed. The speed (in feet per second) as the train leaves the lift is proportional to the square root of the decrease in head (in feet) multiplied by a gravitational force of 2G (about 64.4 feet per second squared), plus a little bit more because of the speed of the lift. As the trains go uphill they give back speed to gain head. That's the simple part. The complicating factor is the various drag factors. If we didn't have drag our Space Mountain train, which starts at a height of 68 feet, we would be going about 45 mph when it returned to the station. But we do have drag, and it is the job of the designer to manage that drag so that the head losses will be about equal to the height of the lift.

We like to return to the station at about five feet per second, which is the same speed as the train was moving on the lift when we started out. So that means we have to lose the entire 68 feet. We know from past studies that, on the average, as we travel along a length of track, we will lose head equal to about three percent of that length due to the several drag factors. We don't know exactly how much until we do our calculations because some losses are dependent on track configuration, others on speed, yet others on weight and some on all three. But we now can estimate that we have to squeeze about 2,267 feet of track (68/.03) plus lifts, station, and storage into a 200-foot-diameter building.

We also know that track crossovers have to be a minimum of 9.5 feet center-to-center so that passengers won't bump their heads, that banked curves will not have a G-force of more than 2.5, and that there will not be negative Gs at crests that will raise passengers off their seats. Further we need to have braking stations at elevated positions less than 20 seconds apart (remember the dispatch interval?) and satisfy George by zooming past the queue line (part of this is to let people know what they are in for so that the “chickens” will take the next exit out). And, as an aside, about that Mickey Mouse hat. If something slows a train down so that it does not get out of its zone in time, brakes will close so that the following train will not hit it.

So the fun begins, and it is fun if you like puzzles. Track routings are laid out on paper and checked on the computer to make sure that the speeds, the timing, and the G factors are all within limits. There is a lot of trial and error involved and the layout drawings—with all the erasures—are not very pretty when they're done. It takes a few months before the track data can be sent to the shop for fabrication and to the structural engineers to design the supports.

Next comes installation and then Test & Adjust (T&A). First, we send empty trains. The biggest worry is that an empty train will stall at the top of some hill and the only solution would be to make expensive track changes or to add one of those dreaded “energy wheels” (see the earlier story linked above), thus violating the pure gravity ride concept. Fortunately, the train came back without incident. Then there are a few runs with sandbags and finally with the designer on board so that he can assess the ride quality (and get his picture in the company newspaper).

At this point I have to confess that, at the end of the ride in the reentry tunnel, there are a series of devices that could be called “energy wheels” although we call them “retarders.” I submit that this does not violate the pure gravity ride principle because we are now down (nearly) at station level and it's important to fine-tune the vehicle speed before it enters the station. The heavily loaded vehicles will approach faster than the light ones. After a break-in period it became clear that the loaded vehicles were approaching the retarders at about twice the desired speed and the retarders were overloaded. Understand here that doubling the speed from five to ten feet per second represents just a few inches of head loss, a small percentage of the 68-foot drop. So, what to do about it? We ran a series of tests with cast members on board, and replaced some of the nylon wheels with more and more of the softer polyurethane wheels until we got the reentry speed down to a level that the retarders could handle.

With all these cast members exposed to these tests, the rumors were flying. One day on the way to Disneyland, I stopped at the Red Cross in Los Angeles to donate blood. One of the nurses asked me what I did at Disney and I told her. “Well”, she said, “Why are you slowing down the ride?” The rumor seemed to be that the ride was too wild and that we had to tame it down. The fact is—and you can see it if you study the formula above for speed as a function of head—that although we cut the reentry speed in half, the speed in the fastest parts of the ride would drop by less than three percent, which is not noticeable.

Disneyland's Space Mountain opened on May 28, 1977 and was reproduced at Tokyo and, recently, Hong Kong. During those same years and later (1969 to 1986), we also designed the Big Thunder Railway (working title) rides at Walt Disney World, Disneyland, Tokyo Disneyland, and Euro Disneyland using the same principles and techniques. The Disneyland Space Mountain was recently reopened with a new, but identical, track. 171 million people had ridden on the old track, a total of more than 8 million miles.