This isn’t actually a real Iron Man suit. But it does fly. It’s a flying suit made by Gravity Industries, a young British startup that builds what they call ‘jet suits.’ The system uses six kerosene-powered jet thrusters to let a human fly around. Honestly, it just looks cool.

This tweet states that it takes 1,000 horsepower to fly—how about an estimation to check this number?

### The Physics of Flight

Let’s start off with some fundamental physics. How does this jet suit fly? I’m going to say it’s all about the momentum principle. This says that the net force on an object changes its momentum where momentum is the product of mass and velocity. Here is the equation form of this idea.

There is one other important idea about forces—they are an interaction between two objects such that for every force there is an equal and opposite force.

OK, now for flying. Suppose I have a human that is hovering above the ground. There is of course the gravitational force pulling down on the human so that there must also be an upward force to make the total force zero (so the human stays hovering). This upward force comes from the thrust of the micro jets. But how does a jet produce thrust? The answer comes from the momentum principle.

Basically, this jet engine takes stationary air from above the engine and pushes it down so that it is moving with some new speed. This change in speed means that there is a change in momentum of the air such that it requires a force. If you push down on the air, the air pushes *up* on the human—and that is the trust.

It’s not too difficult to derive (and I did so here if you want to see it), but this thrust force depends on a number of factors:

- The density of air (this will probably be some constant value around 1.2 kg/m
^{3}). - The speed of the air coming out of the jet engines—I will call this “thrust speed.”
- The area of the jet thrust (that comes out of the engine).

Notice that all three of these factors change either the mass or speed of the air—which changes the momentum of the air. As an equation, it would look like this:

If you want a flying human to hover, this thrust force would have to be equal to the human’s weight. But I don’t really care so much about the thrust force: What I want is the power. Power is a measure of the rate at which you do work—the work in this case is going into the increase in kinetic energy of the air. Putting this together (again, refer to the human-powered helicopter post for the details), I get the following expression for power.

You can use these two expressions together to calculate the hovering power. First use the thrust force to calculate the speed of the air to hover and then use this speed to calculate the power.

### Estimations

Now I need some values to calculate the power. Here are my estimations.

- Mass of human (plus all the gear) = 90 kg (total guess).
- Number of jet engines = 6. Technically, I think the newest suit has five jet engines and one of them is larger.
- Area of jet engine = 0.0079 m
^{2}(based on a engine diameter of 10 cm).

With these values, I get a thrust air speed of 176 m/s (394 mph)—just in case you want to see, here are my calculations in python. I’m embedding them right in this page to help promote the idea that python makes an excellent calculator. You can even change the values and rerun it to get new values. It’s awesome.

Using this thrust speed, I get a power of 77,889 Watts or 104 horsepower. Yes, this is quite a bit lower than the listed 1,000 hp in the video but I think this is OK. I have calculate the hovering power, not the flying power. But there is another reason that I will now describe.

### Components of Thrust

One of the cool things about this flight suit is the method that is used to control vertical thrust. Of course there is a throttle for the jet engines so that you could increase or decrease the thrust, but you don’t need to do that. Instead, the human pilot can increase the angle of arms so that the jet engine thrust is directed only partially down. Here, let me draw a force diagram.

Each of these hand jets has a thrust force in which part of the force (the x-component) pushes inward and part (the y-component) pushes upward. If the arm angle is θ degrees (as measured from the vertical), then the vertical component of force would be the total force multiplied by the cosine of θ. Yes, you need to be careful here. I see physics students make this mistake quite often. Just because it’s a y-component doesn’t automatically mean that it depends on the sine of θ—you have to look to see how the angle is measured. Just be careful.

OK, let’s assume that the arm angle is at 40° from the vertical. That means the total thrust (ignoring the jet engines on the back) would have to be greater in total magnitude to get a component to balance out the gravitational weight. If I include this in the power calculation, I get a thrust speed of 202 m/s with a power of 116 thousand Watts (115 horsepower).

That’s still lower than the listed power, but this is a calculation based on a bunch of estimates. I suspect my value for the diameter of the jet engine is too large—but you can change that in python calculations if you like (see above). Also, this is the theoretical power with no energy losses. I assume that an actual engine wouldn’t be perfect. But even if I get the wrong answer, it’s still fun to make these estimations.

Oh, how about one homework question? If you assume my estimations are close to being legitimate, how high could this jet suit fly? Hint: As you increase in altitude, the density of air decreases.

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