Now for some physics. How do you control this flying suit? This suit has one main jet engine on the pilot's back with two smaller jets on each arm. That means the pilot can control the suit by just changing the arm positions and not even having to adjust the jet engine thrust. It's a cool design.
Let's see how you would position your arms (for that day when you are the pilot) for different motions.
Hovering and vertical motion
When starting off, the pilot keeps his or her arms out at an angle. That means there are essentially four forces on the human. There is the downward gravitational force and the upward (and at a slight angle) force from the back jet. Finally, there are the two angled forces from the arm jets. Here is a simplified force diagram for when the suit is in a hover (stationary and off the ground):OK, hold on. Before we talk about these forces, let's go over some very basic physics. First, there is the gravitational force. On the diagram, this appears as mg where m is the mass of the human flier and g is the gravitational field. On the surface of the Earth, the gravitational field has a magnitude of about 9.8 Newtons per kilogram.
But what do forces even do? The most basic force-motion relationship says that the total vector force (the net force) on an object is proportional to the object's acceleration. That means that for a pilot to hover in place, the total force must be zero. If the net force is in the upward direction, the human will accelerate upward.
Since we need the net force, let's write the net force as the following equation:
There are some important notes for this equation.
- The "arrows" over the variables mean that they are vectors. Vectors are variables with more than one piece of information. If you want to think about these two parts of the variable as "magnitude" and "direction," that's not too bad. But it is indeed important that these are vector quantities.
- Why is mg positive and not negative? Aha! This is a common student error that I see. The vector direction for the gravitational field (g) is pointed down. That's already in the variable. You don't need to add another negative to it—that would just mess up all of the equations.
- Woah! The "left" jet force is on the right of the pilot! No, in my diagram, the pilot is facing the screen. The pilot is not backwards, you are backwards.
- What the heck is the arrow over the zero? That is the zero vector. It's different than plain zero. The zero vector is a force of zero Newtons in all directions. It has a zero x-component, a zero y-component, and a zero z-component. Trust me—the zero vector is important. Most introductory textbooks just avoid this.
But if you don't change the jet thrust, how can you go from hovering to accelerating upward? The key is the thrust angle of the jet arms. Let's say the pilot is in hovering mode. That means that the net force in the y-direction must be zero. Note: When we are talking only about the components of forces, they are one-dimensional and thus not vectors. So, for this hover we have 4 forces in the y-direction. There is the back thrust and gravity—but then there is a component of vertical force from the two arm jets. Let me draw just one of these arm jets.
Any vector force can be split into separate forces. It's useful to break a force into a part that is pointing in the x-direction and a part in the y-direction. (Also you can do the z-direction since real life is in 3D.) Since x and y are perpendicular to each other, these components form the sides of a right triangle. That means that you can find the magnitude of these component forces by using that trigonometry stuff you learned in middle school. The x- and y-components of the force depend on the jet engine thrust angle.
Big deal, right? Yes, it's a big deal. Now you can see how to accelerate upward. You would need more vertical thrust. Without changing the jet engine throttle, you can just pull your arms in closer to your body. Doing this will produce a smaller force angle (θ in the diagram above) to produce a greater y-component of force. Now there is a going to be a net upward force and you will accelerate.
Going forwardNo one just wants to hover. If you are Iron Man, you always want to actually fly and go places, right? To accelerate forward, you need to aim your jet hands towards the back—just a little bit. Depending on the angle of the back jet, you might even be able to point your arms straight down. Here is a diagram looking from the side of the flying Iron Man:
Notice that there is now a forward component of force from the back jet. If the jet arms don't push back, this x-component of force for the back jet will be the only force pushing forward. The pilot will then accelerate. If there are no other forces, the flying human would continue to increase in speed in this position. Once at the desired speed you would put your arms back to the same position as hovering. Remember, you don't need a net force while moving at a constant speed—you just need it to accelerate. OK, if there is a significant air drag force acting on you, this will change your forces a little bit. I'm just guessing you aren't going to be flying super-fast on your first try.
Oh, you might have to adjust your arms during this acceleration. It's possible that by moving your arms back and leaning forward, you change the vertical forces. Don't worry, just pull your arms in closer to your body to give a greater upward arm jet force to compensate.
What about rotating and moving side to side? Sideways motion is the same as above. You just want a net force in that direction to accelerate. When you are ready to stop, you would need to have a net backward force to slow yourself down.
For the rotation, you would also need to consider the net torque on the pilot—where torque is sort of like a rotational force. But don't jump too far ahead. Just keep it basic for now. Once you have mastered hovering, we can talk about torque and rotations.
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