Last week the White House unveiled the flag for the new branch of the US military, the Space Force. But wait! There’s more: The president also said the US is developing a new “super-duper missile” that will be 17 times faster than the ones we have today.
I don’t know everything there is to know about rockets and missiles, but I do know basic physics. And I’ll be honest, this seems crazy. For comparison, among current missiles, the UGM-133 Trident II might be the speediest. It’s a submarine-based missile that hits about 8.06 kilometers per second (18,000 mph for you imperial unit people). Yes, that’s already insanely fast.
So what if you raise that by a factor of 17? That means a super-duper missile would have a velocity of 137 kilometers per second. That’s about 400 times the speed of sound—Mach 400. It could travel across the country, coast to coast, in 30 seconds. Is that even possible? Let’s do an estimation to see what it would take.
No details were offered, but I assume we’re talking about a ballistic missile here. Unlike a cruise missile, which is propelled by a jet engine over its entire flight, a ballistic missile uses a rocket engine to reach much higher speeds. But the rocket only burns for a few minutes. After the initial boost phase, it’s basically an unpowered projectile, like a bullet, moving in an arc-like trajectory under the influence of gravity.
Also, we can safely assume it travels at an altitude where there is very little air. I just don’t think anything can go 137 km/s in the atmosphere—the air drag forces would be too great. If you look at the missiles that clearly only travel in the atmosphere, the MIM-104 Patriot is the fastest with a speed of Mach 5. So if we want a super-duper fast missile, it’s going to have to be in space.
Actually, we really only need two things to model this new fast missile. The first is a better name. I’m not going to keep calling it the super-duper missile—that’s silly. Instead, inspired by the Trident II, I’m going to call it the Zoom Spear I.
Second, we need a mass. This is tougher than the name, because most of the mass of a missile is in the fuel. If you want a missile to go faster, you need more fuel, which will increase the mass. On most rockets, the payload is just 2 to 5 percent of the total mass of the vehicle; that’s called the payload fraction. Let’s say the Trident II has a mass of 59,000 kg with a payload fraction of 5 percent. This puts the payload at about 3,000 kg. (That might be high, but just stick with me.) That’s the part I want to get going really fast.
If you have a payload moving at 8.06 km/s like the Trident II, it requires energy to get it that fast. We can calculate this as the kinetic energy—a quantity that depends on both the mass and the velocity of the payload.
With the listed values, the Trident II payload would need 97 billion joules of energy. That’s the equivalent of 23 tons of TNT.
But what about Zoom Spear I? If it has the same payload mass but 17 times the speed, it will require much more energy, since the kinetic energy depends on the square of the velocity. Not 17 times as much energy, but 172 times more, or 2.8 x 1013 joules. That’s a ridiculous amount of energy.
Assuming this Zoom Spear I uses the same kind of fuel as the Trident II, the energy density (energy per unit volume) would also be the same. This means it would need 289 times more fuel (that’s 17 squared), so it would have to be much, much larger. The Trident II is already about 45 feet long; this thing would have to be enormous.
But it’s even worse than that. Increasing the mass of the fuel means you need more fuel to push the extra mass. It’s a runaway problem, where carrying more fuel means you need to carry even more fuel. This is why some of these rockets, like the Saturn V, get so darn big.
Oh sure, maybe there is a new way to fly missiles. That’s possible, but let’s just wait and see if this missile really goes that fast. If it does, I hope they adopt my name of Zoom Spear I.
Would It Ever Come Down?
On a related note, Scott Manley has some absolutely awesome videos about all things related to rockets. He had this to say about the Zoom Spear I (I’m sticking with this name):
Is this true? Would this missile be faster than the escape velocity? What the heck is the escape velocity anyway?
Suppose I take a baseball and throw it straight up with an initial speed of 10 meters per second. As it ascends, the ball will slow down because of the downward-pulling gravitational force. It will eventually get to some maximum height and then fall back down. With this speed, that max height would be 5 meters. If I double the initial velocity, it will go 20 meters before falling down. The faster I throw it, the higher it goes.
So what if I throw it really fast, with an initial velocity of 4,000 m/s (9,000 mph)? If I ignore air resistance, and I ignore why I’m throwing this ball up instead of pitching in the majors, I calculate that it’ll reach a height of 816 kilometers. But that’s wrong. That assumes the gravitational force has a constant value. Actually, as the ball gets farther from the center of the Earth, the gravitational force decreases. Taking that into account, it will actually reach a height of 934 km.
Since the gravitational force decreases with distance, it actually turns out that there is a certain speed you can throw the ball such that it will never return, never. That’s called the escape velocity. You can calculate the escape velocity by looking at the conservation of energy. I’ll skip the details, but it looks like this:
In this expression G is the universal gravitational constant with a value of 6.67 x 10-11 N×m2/kg2, ME is the mass of the Earth (5.972 x 1024 kg), and R is the radius of the Earth (6.37 x 106 m). Putting in these values, the escape velocity for the Earth is 11 km/s. This is way lower than even the lowest estimates for the speed of the Zoom Spear I. Ergo, Scott was correct (not surprising).
Now if it were some type of cruise missile, it could still work—assuming it were possible to make a cruise missile reach such stupid-crazy speeds, which I doubt, because it would need even more fuel to maintain propulsion throughout the flight. But anyway, then you could use the thrust to push the missile back down to Earth to hit its target.
But if it’s a ballistic missile, you are going to have a problem. Remember, the “ballistic” part means that it will move under the influence of gravity. But at that speed it wouldn’t come back to the surface—it wouldn’t even make a complete orbit. It would just keep moving away from Earth and never come back. Never.
Dear friends, this is my last month as a regular contributor for Wired Science. But the physics fun won’t stop! Going forward, you’ll find my stuff on Twitter, as well as on Medium and YouTube. See you on the platforms! —Rhett Allain
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