Part 2: Airtime!

Alright, let's move on to part 2, airtime hills. These elements are specially designed hills to drop the normal force of the coaster seat on its riders to zero (or, as we'll see later, into negative forces). Weightlessness is a feeling that fascinates many. Falling is scary but exhilarating, providing an appearance of danger through speed and sensation. The feeling of weightlessness derived from such a fall became very popular, and was one of the main attractions behind many of the rollercoasters from both yesterday and today. Airtime hills were some of the first elements developed for coasters as, once a ride got up in the air, it made perfect sense to drop back to the ground. The first airtime hills were based more on experimentation than dynamics problems, but modern coasters take complex approaches to providing perfect hills. Before we add such a hill to our ride, I'll give some background on airtime hills over time.
The year is 1976, and Arrow Dynamics is building the first truly modern coasters. Each has a series of elements, usually culminating in the popular double corkscrew. Now, as an Arrow Dynamics engineer, how would we go about designing an airtime hill? The norm for the day were constant radius curves attached in series. A small curve up, a long arc pointing downwards to create airtime, and a small curve bringing the train back to the horizontal. From our coursework, we can easily calculate the speed required to float over the crest of a hill given a path curvature or desired force. I'll walk through a relatively simple example. We'll assume I can target a speed of 15m/s (54 km/hr) at the top of our example curve. What radius should we create for perfect weightlessness? It's easy enough, as shown here:

Now that we have a suitable radius, I'll build a short test track with the specifications above. Here's an editor side view of our hill. You can see the three separate sections of the hill. I've added 2 support columns to further illustrate how the center section has a constant radius.

Now let's simulate our track, using the track and train style of the time. Riding in the middle of the train, we can see that, at the crest of the hill, we have a perfect 0.0 vertical g reading. This is the weightlessness we were looking for! Note that, because the train does not travel at a constant speed over the curve, the g force will vary over course of the hill.

We also note that, even in the position we based our radius calculation off of, the front of the train holds a -.1 force, as shown below:

Why the difference? The entire train is constrained to move as a single unit, and the speed of the train as a whole over the hill is higher when the front and rear of the train traverse the top. This is due to a lower center of gravity for the entire train (translating to higher kinetic energy). For the first half of the hill, the front of the train will get less than the target g force, having stronger airtime. However, on the second half, these seats actually experience the opposite effect, having slightly more than 0 g. Such differences are less important import for smaller trains but a critical issue for larger ones. From this idea, it's clear that the front and back seats of a coaster will have slightly greater airtime spikes but will also experience times where airtime is less strong. The middle seats will have the most consistent airtime. This principle, of course, only applies to symmetrical elements.

Alright, now that we've designed the perfect airtime hill for 1976, why don't we just put it in our ride? Well, for starters, this element is slightly painful. The change from positive gforce in the first section of the hill to weightlessness in the next is extremely abrupt (with, in fact, absolutely no transition between them), leading to a jerky, unnatural motion. This jerk is best illustrated in this onride video of Cedar Point's Corkscrew ride (it's right after the lift hill). Note the instantaneous shift from an upwards slope to the airtime section. In order to keep our vertebrae in their proper order, we need to move to the current age of design.

Modern airtime hills contain several improvements over their forerunners. First and foremost, they are parabolic in shape. The radius of the airtime section decreases as it nears the crest, allowing for a continuous stretch of the target weightlessness. The curve tightens as the train slows, keeping the acceleration of the passengers the same. Modern hills also feature sweeping transitions from positive g force to weightlessness, giving a smoother ride and a much safer one. For our track, I'll use a technique developed by a pair of German students called 'force vector design.' This system inputs a series of g force formulas and time intervals, and generates a perfect ride path based on the desired effects. Unfortunately, beyond this basic concept it's a bit too hard to formulate a model for the hill, mostly because our dynamics-fu is not yet advanced enough. I don't have experience relating multiple dynamic iterations such as is needed here. I am, however, currently working on an attempt at this. A new post will follow sometime this week, and hopefully together we can get something working. For today we'll just skip ahead to the result; a modern, parabolic airtime hill creating a constant -0.5 g force. Wait a minute, you may say, how does a coaster experience such a strong negative force? What's to keep the train from flying and crashing into the ground? The solution is a complex wheel assembly involving, in the case of our Intamin train, 6 wheels per point of contact. The two wheels underneath the track can take the force created by the rider's upward acceleration, keeping the ride on track. Here's a real-life example on the world's second fastest coaster, Top Thrill Dragster:

So why do we want less than weightlessness? The sensation of 'ejection' airtime, or an experience of being thrown from the train causes an even stronger force and feeling of danger. This type of airtime is my absolute favorite. A major concern for ejection airtime is the restraint system; it needs to be comfortable and extremely reliable. The system needs to contain the passenger in the car without bruising while hopefully allowing freedom of movement. Luckily, Intamin trains are among the most comfortable in the business, utilizing either a unobtrusive 't-bar' as seen in Top Thrill Dragster above or a newer OTSR (over the shoulder restraint) design which is still quite comfortable. Here's Hershey Park's Fahrenheit with such a design.

Alright, after justifying our hill, let's see it in action! Note again that our g force is off the target because the front car has passed the crest of the hill.

Hooray, we've got ourselves a solid element. This is, however, just one example of a modern airtime hill. We could have used hills with varying amplitudes and speeds to create a variety of effects. Here's an example of a slower hill which holds its airtime for a longer period of time. This is one of my finished rides, for the final round of a design tournament (I ended up winning).

There also exist speed hills, as illustrated in this picture from 'Thunder Dolphin' in Tokyo. This type of hill has less airtime but a much higher velocity, leading to a unique sensation. It's at the very bottom of this picture (Sorry, it's partly obscured as I couldn't find a better picture):

Ok, that was part two. Our coaster's still very basic, but we'll work on more complex things when we return. I'll describe most of the common track elements and implement several of them in our design. Until next time!