![]() The spreadsheet is available for the curious here. ![]() For greater accessibility, I performed a simple Euler integration in Excel. This can be turned into a differential equation and solved numerically, and is easily done with a number of tools including Matlab or LabView. The result of these two considerations is an equation for the radius of the curve based on the starting velocity, height, and angle of the track around the curve. So to counteract the variable effects of gravity based on angle by adding or subtracting an equivalent amount of centripetal acceleration, we must further decrease the radius at the top and increase it at the bottom of the loop. While travel vertically either up or down the sides or the loop, the gravitation component is zero. Travelling horizontally at the top of the loop, gravity gives a negative 1G component. Thus when the rider is traveling horizontally at the bottom of the loop, gravity gives him a 1G load. The amount that gravity pushes the rider into the seat is the gravitational constant multiplied by the cosine of the angle the rider is traveling. To account for problem 2, we must also vary the radius, but this time as a function of the angle of travel instead of the height. So to account for problem 1 and maintain constant acceleration, we must take our circular loop and bend it so that it has a smaller radius as the height increases. However, if an entire loop were a circle with constant radius, there would be two big problems:ġ. The roller coaster slows down as it climbs the loop, so centripetal acceleration would drop near the top.Ģ. Gravitational acceleration and centripetal acceleration are additive at the bottom of the loop, where they both push the rider into the bottom of the seat, but opposite at the top of the loop, where centripetal acceleration pushes the rider into the seat, but gravity tries to pull him out. Where A is the acceleration, V is the velocity, and r is the radius. The centripetal acceleration around a circle is expressed as: So, like gravity, the centripetal force can be expressed as acceleration and applied to any sized person. The force is a function of speed and radius, but, just like gravity, is proportional to the rider’s body mass. Traveling around a circle creates a centripetal force that the rider experiences as a G-force. To create a constant G-force loop, you can start with the basic shape of a circle. We asked what shape to start with, and how to modify it to make the loop. But the banking is so severe that an inversion seems imminent, and when the train doesn't invert the result is wonderful confusion.Last month's challenge was define the shape of a roller coaster loop that would create a constant G-force experience. ![]() Again, from the queue or the loading station this looks like just another banked curve. The coaster negotiates a banked drop, at the bottom of which are some fairly heavy positive G's, and then swoops into another great element, the horseshoe. Suddenly riders are staring 115 feet straight down and, though they can see the coaster's massive purple supports flanking them, they have no clue where they will be going next. I was told that eventually the seat lowering will take place while the train ascends the hill, but for now it happens in the station.Īfter cresting the lift hill, a slight curve leads into a 180 degree inversion and the ride's most spectacular moment. Riders begin seated but are immediately lowered to the prone position, facing up, where they will remain all the way up the lift hill. I'll briefly describe Batwing's basic course, but even knowing basically where this ride is going ill-prepares riders for its chaotic actualization. ![]() The best compliment to give this ride is that while from a distance it looks extremely simple, almost innocuous, it is actually an intense, disorienting (in a good way), and surprise-filled ride. Surprise, and all its attendant anxiety and exhilaration, is Batwing's crowning achievement.
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