Force, acceleration, velocity, speed, gravity, weight, G-force, Newton, meters/sec, meters/sec/sec, medium, centrifugal force, radius, circumference, inertia
Next Generation Science Standards:
- HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass and its acceleration.
Article Guide: X-wing part 2 Article Guide
Ever wonder what it would be like to be an X-wing pilot? By using knowledge of basic, Newtonian physics and a calculator, we can find out exactly what that would feel like
In our last post, we discussed how the force exerted on an object is a function of its acceleration; if that object is speeding up, slowing down, or changing direction. We also discussed how if an X-wing can only accelerate so quickly without killing the pilot. The average person loses consciousness when they experience around 10 to 12 times their body weight in force (called a G-force, check out the previous post for a more thorough explanation) and experiencing more than 20 G-forces would likely cause death.
But our essential question remains: How many G’s would you experience in an X-wing and would the human body be able to handle it? Before we answer this we need to find out how many Newtons a pilot would experience in a 1 G-force environment. Once we have that number, we can establish how quickly an X-wing could speed up or change direction without our pilot becoming an Obi-Wan Kenobi force ghost.
How much force can you take?
Since there are no other volunteers and because I’ve always wanted to fly an X-wing, I am going to select myself for this thought experiment. My mass is around 77 kg, which means I experience a weight of about 754.6 N (my mass of 77 kg multiplied by 9.8 meters/sec/sec – the acceleration due to gravity on Earth). This gives us a baseline for how many G-forces a pilot of my same mass would experience. If a pilot of my mass experienced a force of 2 G’s, it would mean they are accelerating at 19.6 meters/sec/sec (double that of Earth’s gravitational pull) and that a force equal 1,509.2 N is being exerted on them (1509.2 N/754.6 N = 2 G).
However, we don’t have any information on how quickly an X-wing can accelerate; there’s nothing in Star Wars canon that provides any specifications on how quickly an X-wing can reach its top speed of 100 MGLT or 29,997 meters/sec. What we do know is the upper limit of how many G’s a human body can handle. At around 10 G’s, humans begin to blackout due to forces being too strong for the heart to get blood to the brain. I’m going to use this as our upper limit on how much force our pilot can take. Below I have calculated the amount Newtons a 10 G force would feel like on me.
Now that we know the upper limits of force that a pilot of my mass could take, we can use Newton’s Second Law of Motion to calculate how quickly the X-wing would accelerate with that amount of force.
For these calculations, we are going make two assumptions: the pull of gravity from any nearby moon, planet, or star is negligible and there is no friction force in space due to a lack of media such as air or water. Remember that forces are only exerted when an object accelerates. Our pilot will feel 0 G-force as they sit idly in the X-wing cockpit and again once they reach top speed. It doesn’t matter how fast you are going; unless you are accelerating, you’ll feel nothing.
Let’s find out how quickly we can get up to our top speed. Since we know the pilot’s mass (77 kg) and how much force their body could take (7,546.0 N), we can work backward to find out how quickly our X-wing can safely accelerate.
If 98.0 meters/sec/sec sounds fast, that’s because it is. But it doesn’t give us any idea of how long it would take for our X-wing to get to top speed. Let’s take our calculations one step further. Acceleration is the change in velocity divided by the change in time. If we know our acceleration, our final speed, and our initial speed, we can easily find how long it would take to get to top speed.
In the previous post, we converted the Star Wars unit of speed, MGLT, into something useful in a physics equation. According to Wookiepedia, the top speed of an X-wing is 100 MGLT, which we have given a very rough estimate to be 29,997 meters/s (107,925 km/h or 67,061 mph). Since our pilot is starting a rest, the X-wing’s speed is initially zero. Using the equation below, we can easily find the time.
Based on our math, it would take about 5 minutes for an X-wing to accelerate to its top speed of 100 MGLT or 29,997 meters/sec. While this may seem kind of long based on what we see in the Star Wars movies, accelerating any faster would mean our pilot would be slipping in and out of consciousness, the human body didn’t evolve to take ten times the Earth’s gravitational force. Maybe things get more interesting once we fly around at top speed.
Turn, turn, turn
Forces are applied when objects accelerate. This can mean a change in speed, but it also can mean a change in direction. Imagine you are a car making a quick turn; you feel a force that pushes you towards the outside of the turn. This is due to inertia, the property of matter that resists a change in motion unless a force acts on it. Your body is moving straight and wants to continue to do so, even though your car is making a turn at a high rate of speed.
In order for an object to follow a circular path without changing speed, a continuous force must be applied. The force that pulls an object towards the center of a circle is called centripetal force. We can use this as an approximation for the forces being exerted on our pilot when making a turn in their X-wing.
Centripetal force requires a slightly different equation because we have to factor account for our X-wing moving in a circle. As before, let’s start with the amount of G’s my body could handle to see how sharp our turn can be. We also know how fast our X-wing can go at top speed, 100 MGLT or 29,972 meters/sec. We can then use the centripetal force equation to find out how tight a turn our X-wing could take without killing our ace pilot by solving for the radius.
To give some perspective, the radius of our turn is longer than a direct flight from Los Angeles to London. However, this really doesn’t give us a clear picture of how sharp that turn would be. Let’s find out how big the circle of our turn is by finding the circumference, which we can do by multiplying the radius by 2 π.
That’s a big circle, about 50% more than the circumference of the Earth. However, we are moving pretty fast, nearly 30,000 meters/sec. Let’s find out how long would it take to make that complete loop. We know our speed and our distance, so time is a pretty easy calculation.
A little less than 2 seconds to make a loop bigger than the Earth is pretty impressive. However the maneuvering starfighters are able to perform in the battle we see in Star Wars far tighter. That’s just not realistic when you are account for forces being exerted on the pilot’s body. Any attempt to make a tighter turn would cause a dangerous amount of centripetal force to be exerted on the pilot.
Doesn’t this make flying an X-wing kind of lame?
The physical reality flying and turning at high speeds is much less exciting than what we see in the movies. If starfighters had to make giant, planet sized turns would make for some pretty awkward battle scenes. If we are correct in our assumption that 1 MGLT is equal to 1/1,000,000 the speed of light (and who’s to say we are), then there is no way the human body would be able to handle the forces being exerted on them if X-wings moved they way they do in the Star Wars films.
Moreover, it would still take a really long time to get anywhere in the inconceivable vastness of space, even traveling at the speeds we calculated. Most of space is just that: empty space. It would take over 15 months to get from Earth to Saturn at top X-wing speed. Getting to another star system would take even longer. If you were in an X-wing traveling at 100 MGLT, it would take you over 4380 years to get to Alpha Centauri, the closest star to Earth. Unless we find a way to bend the spacetime continuum, we won’t be able to zip across the galaxy in a few hours or days as ships can do in the hyperspace of Star Wars.
This doesn’t mean that Star Wars is devoid of scientific principles. Despite the inaccuracies, there are some Star Wars inspired technologies that are being developed. NASA is working on perfecting ion engines that have already been used in the DAWN probe and researchers at Darpa have been working on a prosthetics that can feel. Popular Science magazine wrote a nice article on 6 other emerging technologies and IBM has a YouTube series on the Science of Star Wars that’s worth checking out.
What this thought experiment does do is illustrate the forces acting on someone during space travel. It’s easy for us to watch a movie and assume that when our civilization develops interplanetary travel that it will function like driving a car; just get in a spaceship, turn the key, hit the gas, and go wherever you want. Our bodies just didn’t evolve to take the huge amounts of forces needed to accelerate as much as we see in the pop culture. It also serves as a reminder how important our current planet is to our survival. There’s little chance of us traveling to another habitable planet within the next hundred years, if ever.
Until then, we’ll have to satisfy our need for epic space battles by watching Stars Wars.