Ride Physiology

Background
Imagine a passenger riding through a loop on a roller coaster. The passenger's head is towards the inside of the circle.

Her feet are to the outside of the circle. In order to keep blood in the passenger's head, a centripetal force needs to be applied to the blood to push it upwards toward the head and the center of the circle. The heart applies the centripetal force on the blood. A passenger can experience many g's in a loop. Recall that a g is the number of times heavier an object becomes. A 7 g experience means that the passenger feels 7 times heavier. Everything about the passenger becomes 7 times heavier. Her 3 pound brain now weighs 21 pounds. Every ounce of blood becomes 7 times heavier. If the blood feels too heavy the heart cannot apply enough force to push it towards the head. If the brain does not get any blood it will not get the oxygen the blood carries. The passenger will pass out within a second.

The Extreme Experience
You are riding a new untested roller coaster when something goes wrong. As you enter the first big loop, a great pressure pushes you down. You slouch down in the seat from the extra weight. Over the top of the loop the roller coaster car slows down. The extra weight on your legs, lap, and shoulder make it impossible to sense that you are upside down. Out of the loop, over a hill and into another loop. This loop has a smaller radius. The car is traveling much faster now. As the g forces climb up toward 7 g's, you sink further still in the seat. You can no longer see color. Everything appears in black and white. An instant later, the passenger next to you disappears from view. Your field of vision is shrinking. It now looks like you are seeing things through a pipe. The front corner of the car disappears from view as your peripheral vision disappears. The visual pipe's diameter is getting smaller and smaller. You sink into the seat further still as the number of g's climb further. In a flash you see black. You have just "blacked out." You are unconscious until the number of g's are reduced and the blood returns to your brain.
Amusement park owners and insurance companies do not want the previously described situation to occur. It would limit repeat riders and the number of potential consumers who can safely ride the coaster. Most roller coasters keep the g's felt under 5 g's on an inside loop or the bottom of a dip after a hill. When a rider travels over a hill at a high rate of speed, he experiences negative g's. A negative g is the multiple of a person's weight that is needed to keep a rider in his seat. Negative g's also force the coaster car to try to come up off the track. Negative g's are a rider's heaven and a designer's nightmare. Negative g's are avoided as much as possible.
A negative g has a different effect on a rider than a positive g. Both negative and positive g's can cause a rider to pass out. But negative g's cause a rider to "red out." A red out condition occurs when there is too much pressure on the brain caused by too much blood in the head. The extra pressure can cause blood vessels to burst and kill the rider. This is a sure way to limit the number of repeat riders.

There is another way for a rider to experience negative g's. It is related to the length of the train. The roller coaster track is designed for the dynamics at the center of mass of the coaster train. Negative g's are experienced by the rider at the back of the train as he travels over a hill. For an empty train, the center of mass is in the middle of the train.Whatever speed is acquired by the center of the train is the speed for the entire train. After the center of a train passes over a hill it begins to gain velocity. As the center speeds up so does the back of the train. This means that the rear of the train will travel over the hill faster than the middle of the train. If the rider travels over the hill faster than the designed velocity of the hill the rear car will be whipped over the hill.

Some "g" Determinators:

Calculation of the g's felt

To calculate the g's felt, a formula from circular motion will be utilized. Since energy relationships do not utilize time, the circular motion formula used will also not utilize time.

Where "v" is the velocity of the body and "R" is the radius of the circle traveled. To calculate the velocity a body is traveling, use energy relationships to solve for the kinetic energy and the associated velocity. One more thing. To calculate the g's felt remember that the g's felt by the rider is the normal force on the seat of the rider divided by the mass then converted into g's. As a rider enters a loop he will feel 2 forces.

The real number of interest is the number if g's felt by the passenger traveling in the vertical circle. The g's felt are calculated below.
SF_y = m(a_c) = (Normal Force) - Weight
SF_y = mv²/_R = (Normal Force) - mg
(Normal Force) = mv²/_R + mg
recall that... (Normal Force)_/mg = g's felt by the rider
thus... (Normal Force)/g = mv²/R/mg + mg/mg
g's felt by the rider = (centripetal acceleration in g's) + 1 at the bottom

These results can be summarized as follows...

These results can be interpreted easily. As a rider enters the loop, the track has to exert a normal force upwards to supply the necessary centripetal force and acceleration to make the rider travel in a circle. But because the loop is vertical and the rider is at the bottom the normal force not only has to supply the centripetal force but must also overcome the pull of gravity. That's why 1 g is added in the equation. At the top of the loop, 1 g is subtracted from what is felt because the pull of gravity is helping the normal force exerted by the track instead of needing to be overcome.