The Issue With Rotating Spacecraft


Although it would be fantastic if humans could live in space, a "weightless" environment presents several significant difficulties. The surface of the Earth, where gravity effects are constant, is where humans perform at their best. Without it, long-term exposure to microgravity has well-known effects such as muscle atrophy and loss of bone mass.

Therefore, we will need to develop an artificial gravity environment if we want to live in space. We can only achieve it by creating a vehicle that accelerates continuously. The most typical idea is to build a rotating spacecraft. But it's not as simple as it seems. This is why.

Feeling heavy

The fundamentals of gravity and what it means to feel your weight will be discussed first.

The attraction between mass-containing objects is known as gravity. There is an attracting force that draws you toward the Earth and maintains you on the ground since both your body and the Earth have mass. You are continually being pulled by this force, but you are not aware of it since the Earth is concurrently pulling on every area of your body.

You may be saying to yourself, "I'm sitting here on this chair, and I can definitely feel my weight," and I understand. Gravity isn't really what you're feeling, though. It's the chair's and the ground's force pushing up on you. This upward-pushing force is referred to as your "apparent weight."

Taking a brief elevator ride can help us better understand the idea of seeming weight. Starting at rest, the elevator. But when you press a button, it starts to rise. That implies that there must be an upward acceleration, at least for a brief period of time before the elevator reaches its travel speed. You feel a little heavier as the upward acceleration continues. The elevator must then slow down once it is close to the floor specified in the programming. This indicates that it is accelerating downward. You feel lighter at this moment.

However, your real weight never changed. Your actual weight, which is determined by the combination of your mass (m), the mass of the Earth, and your distance from its center, is a gauge of the force gravity applies to your body. On Earth, gravity pulls on a kilogram with a force of 9.8 newtons. (Since mass and weight are separate concepts, on a planet with a different gravity, your mass would still be the same, but your weight would be different.)

None of these things alter when using an elevator. It does alter your outward weight, though. Although it seems unusual, this effect is quite beneficial for a spacecraft.

Continuum Acceleration

Let's imagine that you are in a "weightless" environment such as space, where there is no gravitational pull, or even in low Earth orbit, where there is microgravity. Imagine having a massive elevator on your spacecraft that continuously accelerates upward. Your weight would feel exactly the same as it does now if the elevator's acceleration were equal to the gravitational field at Earth's surface.

Unfeasible, of course, is a starship with an endless elevator. It would be simpler to simply accelerate the entire vehicle. That would unquestionably produce fake gravity. In reality, The Expanse, a science fiction television series, uses this as the main approach on spacecraft.

However, there is an issue. A spacecraft's rockets must be continuously fired in order to maintain constant acceleration. That would demand absurdly large amounts of gasoline. However, you can't stop using the rockets because doing so would cause your acceleration to become zero. What a waste of your lovely fake gravity. The "Epstein drive," which may as well be magic, is how they solve this issue in The Expanse.

We will need another kind of acceleration for modern humans in order to create artificial gravity.

Roundabout Motion

The pace at which velocity changes is what we refer to as acceleration. Therefore, an automobile would accelerate at a rate of 10 meters per second per second if it went from 10 meters per second to 20 meters per second in the span of one second. (We commonly spell that as 10 m/s2).

But in reality, velocity is a vector. As a result, the velocity not only indicates how quickly something is traveling, but also its direction.

Let's say an automobile is traveling west at 20 m/s. Then it makes a turn, moving 20 m/s to the north after one second. The car experienced an acceleration even if it is going at the same speed because it changed lanes. If we know the speed and the radius (R) of the path the car follows in this turn, we can compute the amount of acceleration (v).

You don't actually need this math, though. You can feel something pushing you to the side of the car as it turns, just like you can feel the acceleration in a moving elevator. This is how you intuitively know that turning in a car is an acceleration.

Because of this, we are able to produce artificial acceleration using a rotating object. The spaceship or space station doesn't need to be forced to turn in a circle like a car would. Instead, picture a big rotating thing with people inside it. The appearance would be similar to this:

In this picture, three people are positioned within a turning cylinder. Each of them has an acceleration and a sense of gravity because they are all going in circular routes. (For them, the cylinder's core represents the "up" direction.)

It turns out that, rather than their velocities, we can describe their motion using the spacecraft's angular velocity (). (v). Each person would experience an acceleration of:

Radians per second are used to express the angular velocity (). One would virtually feel as though they were standing on the surface of the planet if this acceleration were 9.8 m/s2, which is the same as the gravitational field on the Earth's surface. (We'll discuss the distinctions soon.)

A revolving spacecraft or space station has the advantage of not requiring additional rocket fuel once it has started to rotate. It won't cease until something intervenes. Because of this, science fiction TV shows and films like The Martian, Babylon 5, 2001: A Space Odyssey, Interstellar, and many others use this technique for creating artificial gravity.

And this equation provides us with crucial information for designing spacecraft. With a little R and a huge, you could create a small vehicle that spins extremely quickly, or you could create a large ship that rotates slowly.

Most compact rotating spacecraft

A rotating spaceship must increase its angular velocity in order to achieve the appropriate acceleration if its radius is reduced. (Permit's use 9.8 m/s2. The acceleration corresponding to standing on Earth's surface is 1 g.)

The issue is back, albeit this time it's with people. Yes, there are some rotational issues we have. (I personally find spinning rides in amusement parks, such as the Mad Tea Party at Disney World, to be too much to handle. Just imagining it makes me feel a bit queasy.) According to scientific studies, the majority of people can tolerate rotation rates of approximately 1 rpm. An angular velocity of up to 4 rpm may be conceivable, according to additional evidence. Another study came to the conclusion that humans could be able to function at 26 rpm if they are exposed to increasing durations of greater and higher rotation rates.

Assumedly, we have a few astronauts who can withstand a rotational speed of 26 rpm. (Perhaps the teacup ride is where they rehearse.) What size spaceship could you make to create an artificial gravity of 1 g?

The angular velocity must first be changed from revolutions per minute to radians per second. A value of = 2.72 radians/second would result from that. (Remember that 2 radians are equal to 1 revolution.)

Next, we simply solve for R using an acceleration of 9.8 m/s2 (the radius). This results in a 2.6-meter-diameter, circular spacecraft with a 1.3-meter radius. That is very small. Its diameter, which is around 4.2 meters, is even smaller than a module of the International Space Station. If you choose an angular velocity of 4 rpm, which is more feasible, the spacecraft would have a diameter of 112 meters. That is significantly larger, about the size of a soccer or football field.

There is a small method you can utilize if you don't want to build a revolving spaceship that is 112 meters wide. Use two smaller vessels connected by a cable in place of one larger one. Then, these two smaller components would revolve around a single mass center. Humans can be placed in one (or both) of these components to simulate a gravitational field. In the Netflix film Stowaway, an illustration of this kind of revolving ship may be found.

Separation of Gravity

However, there are two events that could take place on a rotating spacecraft to convince you that you are not on Earth's surface. The first is that it's conceivable for the strength of the artificial gravity field at your head to differ from that at your feet. Let's imagine a human standing in a somewhat modest rotating spacecraft to understand why this might occur.

The person is in a revolving vehicle, so their head and feet are moving at the same speed. They do not, however, move in an identically sized circle. The circular path radius of the head (Rh) is less than that of the feet because it is closer to the spinning craft's center (Rf). Keep in mind that when the radius of motion increases, the acceleration (and hence, the artificial gravity) decreases. The gravitational field will be less intense at the person's feet than at their head. That is a little strange.

However, it is possible for it to be worse. Consider the 1.3-meter-radius spaceship from the previous example. Being shorter than the average human, the astronaut's head might extend past the axis of rotation. In this scenario, their feet would be drawn to the opposite side of the spacecraft, which we can refer to as the floor, and their head would be pulled towards the one side (let's call it the ceiling). This strange artificial gravity would definitely make this astronaut queasy if spinning extremely quickly wasn't enough already.

With larger rotating ships, this "differential gravity" doesn't provide as much of a challenge. Let's revisit the 112 meter wide rotating craft from the last example. Its radius is 55.8 meters, and its angular velocity is 4 rpm. At the "bottom," the gravitational field would be 9.8 m/s2, identical to that of Earth. An astronaut's head would move in a circle with a radius of 54.1 meters if they were 1.75 meters tall. This indicates that the gravitational field would be 9.49 m/s2 at their head. That's only 3.2 percent less than the field underneath them, which is not a significant problem.

Conical Force

The Coriolis force, which is another effect of living in a rotating object, exists. Since this force is somewhat complex, let's begin with an illustration utilizing a rotating merry-go-round. Assume that this merry-go-round has two people standing on it, A and B, one at the outside and B near the center. A top view is shown here:

Observe how both individuals are following the same angular velocity around the circles. However, in order to complete the circle in the same amount of time as person A, person B must travel a greater distance. As a result, B will move more quickly along a line than A.

That won't cause a problem until B chooses to travel closer to the circle's center. Person B will be moving too quickly for the new radius if they switch to a new circular path with a smaller radius. This person's path will probably tend to curve to the side because of the faster speed at the new circular radius. The Coriolis force is the name for this additional force.

A ball would roll along a curved path if person B rolled it to person A, looking like this:

The speed of the moving object (relative to the rotating frame) and the angular velocity of the revolving merry-go-round are both factors that affect the amount of the Coriolis force. And in a spacecraft, the same thing would occur.

The Coriolis force is difficult to calculate because of a number of variables, but I'll still put it in writing as an equation:

This force is always perpendicular to the velocity, and it is zero if the object is stationary in the rotating frame. This is an important point to remember.

What sort of effects would that have on a spaceman in a rotating craft? If the person were to remain motionless, nothing would occur. However, what if they get up? Since the person's center of mass is going upward as they move from sitting to standing, they would have a velocity toward the center of the circle during the standing up process.

In proportion to their velocity, the Coriolis force would push them in a sideways direction. Additionally, this force may push them in various directions depending on how the chair is positioned. The Coriolis force will cause the individual to be propelled forward when they stand up if the chair is facing in the same direction as the spaceship is rotating. They will be pushed backward by the chair if it is facing that direction. They will be pushed to the other side of the chair if it is facing one way. And it goes beyond simply standing. Your hand will experience a sideways force if you move it. There will always be a sideways force on the liquid when you attempt to pour a drink into a glass. Maybe you can get used to a sideways force with every motion, but that would be really annoying.

Can you do something about the Coriolis force? Yes. By building a spaceship with a lower angular velocity, which means it takes longer to complete one rotation, you can reduce this sideways-pushing force. But less artificial gravity would result from that.

You simply need a larger spacecraft if you want artificial gravity that is similar to Earth's and a diminished Coriolis effect. You have to decide between building a massive, expensive spaceship with all the amenities of home, which will be big and expensive, or building a small, inexpensive spacecraft and dealing with obtrusive Coriolis forces.

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