BEAST PHYSICS TIPS
with Ashok Dibbawalla
Some Intermediate Pressure Calculations Involving Centripetal Force and County Executive Joel Giambra
What would happen if we put Erie County Executive Joel Giambra in a centrifuge?
Ever taken one of those spinning carnival rides? The ones where the floor drops out, and the riders are stuck to a vertical wall? (If you haven't, imagine riding inside a giant top loading washing machine on spin cycle.) This is a low speed centrifuge. As the drum turns faster and faster, the riders find themselves plastered to the sides.
Most people know that heavy items will press against the edges of a spinning container. Still, there remains a lot of confusion as to why this happens, or what happens at extreme speed. In this article, we'll explore the phenomena in a thought experiment, using Joel Giambra as our test subject.
Let's imagine an extremely powerful carnival ride, with Giambra, fresh from calling for an additional $45 million in loans for the county to build a new Youth Detention center, is riding alone. For the sake of discussion, we'll assume that Giambra weighs about 220lbs, and that the radius of the drum is 25 feet. We'll start by turning the drum at a stately 1 RMP (1 revolution per minute).
If we only glance for a moment, we see that Giambra appears to be moving in a straight line. If we observe over a longer period of time, we can see that his direction of travel is actually continuously changing. The definition of acceleration is the rate of change of velocity. Therefore, the more rapidly his direction of travel changes, the greater the acceleration he's experiencing. Some elementary calculus will tell us that the acceleration is proportional to the radius of the drum, and proportional to the square of the rate of rotation. Accelerating a massive object implies a force, and this force is proportional to the product of the acceleration and this mass.
In layman's terms, this means that every time we double the rate that the drum spins, we quadruple the force that the drum wall exerts on this back to keep him moving in a circle. At 1 RPM, less than two pounds of force is needed to keep him moving in a circle. Of course, he must still support his own weight, so the acceleration he feels is the normal 1 G we all live with.
Let's dial up the speed. At 4 RPM, he's pressing against the wall of the drum with 30 lbs of force. This is at a right angle to gravity, so his total weight feels as if it's only gone up by 2 lbs. At 10 RPM, he's reached 1.3 G's. He's also traveling about 10 MPH. If the drum had a hanging weight, it would now hang at 40 degrees to the vertical. 15 RMP takes him to 2.2 G's, approximately the force of gravity at the cloud tops of Jupiter. The force holding him against the wall is now stronger than the earth's gravity pulling him down. If you placed a scale between him and the wall, it would read about 420 lbs.
Remember what we discussed about the force being proportional to the square of the rate of rotation? Well... here is where things start to take off. At 20 RPM, much faster than any speed he experiences in County meetings, our scale reads 750 lbs. The weight of this own chest makes breathing labored; he's at 3.6 G's. 25 RPM brings 5.4 G's. Fighter jet pilots are exposed to this level of acceleration, but they won't tell you it's fun. At 30 RPM the G force reaches 7.7. County executive Giambra will not be awake for the rest of the ride.
We're up to 60 RPM now, once around every second, and 31 G's. His body is pressing against the drum with a force of 3.4 tons. I confess that I don't have detailed data on bone strength, but I would imagine that he's at least cracked some ribs by now.
350 RPM takes us to 1,000 G's, and once again, Giambra—as he was at the bottom of the ocean floor—is liquefied. The flesh has long since peeled away from bone. We notice something else, too. The liquid is forming layers. The tissue is no longer strong enough to support its weight, and the heavier chemicals are settling to the walls of the drum.
You can rev your car to 5,000 RPM, but at that rate, the unfortunate Giambra is finished. We've exceeded a staggering 200,000 G's. Assuming that drum is 6 feet tall, Giambra's remains are a slick on the wall mere 45 thousandths of an inch thick. (See my previous article for calculations of Giambra's volume.)