Here are some pictures from Kennedy Space Center of Space Shuttle Atlantis.
Here are some pictures from Kennedy Space Center of Space Shuttle Atlantis.
In 2011, a person from Raytheon called me up out of the blue and asked if I wanted to be involved in a project to help eliminate space debris. I was interested.
A little background (the first): The majority of space is not really a vacuum. There are particles pretty much everywhere in space. The question really is what is the density of those particles – or how many particles are there in a given volume. The atmosphere of Earth is a relatively narrow shell around the Earth. We know that if we climb Mt. Everest there is not much air up there. But, to us, “not much air” is still a whole lot of air.
We think of space as having no air at all. Astronauts have to wear space suits to protect them from the “vacuum of space” after all. There are a number of very interesting things about this, but it should really be a totally separate post. Let’s simply leave it that there is, indeed, atmosphere up in space where the International Space Station (ISS) orbits.
Since there is air up there, objects such as satellites and the ISS feel a drag force, as we have discussed in a few other posts. The density in the atmosphere up there is very very small, but the objects in orbit are moving extremely fast. This means that the drag force that the objects feel is not really large, but it can strongly affect their orbital motion.
As a rule of thumb, objects that are orbiting below about 200 km (120 miles) will deorbit extremely quickly, in a matter of days to weeks, because of the atmospheric drag. The atmosphere is so thick there that the objects just can’t stay aloft and they ultimately decrease their altitude rapidly and (hopefully) burn up in the atmosphere around 70 km altitude.
Satellites above about 700 km (420 miles) or so will basically never deorbit because of atmospheric drag. The atmospheric density there is so low that drag is not an important force on objects in orbit. Don’t get me wrong – there is still an atmosphere, but it is so tenuous that orbiting objects don’t care about it.
Between these two altitudes, drag is important. In fact, the ISS, which orbits at around 400 km (240 miles) altitude has to be moved up every couple of weeks, because atmospheric drag pulls it down. The ISS is constantly being pulled back towards the Earth due to drag, and we lift it back up to 400+ km using propulsion to keep it in orbit. If we didn’t do this, the ISS would fall back to Earth and burn up in the atmosphere in 6-12 months.
A little background (the second): Space is filled with a lot of crap. There are about 20,000 objects in orbit around the Earth that are about the size of a softball or larger. This stuff is pretty dangerous, since it is moving at speeds of 7,600 m/s (17,000 MPH). It can cause a lot of damage (Gravity, anyone?). Here is a picture of the space shuttle window after being hit with a piece of debris that was significantly less than a millimeter in size:
There is a realization that we need to do something about all of this space debris. One of the worst things that has happened because of the amount of debris is that an Iridium satellite was destroyed due to a collision with a retired Russian spy satellite. This caused the creation of thousands more pieces of debris, which could then impact other objects. There is real concern.
I was called by this guy from Raytheon to see if I wanted to help solve this problem. I said, sure, that would be great. We wrote a proposal to NASA to see if we could get money for it. They gave us some seed money to see if the idea could pan out. The project was called “Space Debris Elimination (SpaDE)”.
The general idea of the project was to see if we could increase the atmospheric drag in front of an object in orbit around the Earth enough to cause it to deorbit. Here is a graphic to illustrate the idea:
At first, this idea seems very interesting and plausible. My main profession is a modeler of the upper atmosphere. A long time ago, I wrote a large-scale model of the atmosphere that looks at what happens when large amounts of energy is added to the atmosphere in the form of the aurora (i.e., the northern/southern lights). I continue to work on this model today, and have a bunch of graduate students who use the model to do research. For project SpaDE, I took the model and made it so we could run it over a very small area (like a couple of hundred kilometers by a couple of hundred kilometers) and inject a huge amount of energy quite low in the atmosphere. The model then simulated what would occur.
You might ask, what is “a huge amount of energy”? Well, that is a good question. The model can handle almost any amount of energy, but for this project we were looking at roughly nuclear bomb types of energies. The general idea would be to take a large explosive device to the stratosphere, or about 30 km, and explode it there. We would use some sort of device to direct the majority of the energy upwards, creating a very large density perturbation that would propagate upwards to the upper atmosphere where a piece of debris would travel through the density enhancement and deorbit.
When people find out about this project, they always ask: why did you stop working on it? Well, this is really the point of this post – to describe why this type of debris mitigation strategy is unlikely to work.
Problem, the first: You have to take an extremely large explosive device up on a balloon and explode it in the atmosphere. That is unlikely to be ok with pretty much anyone. Also, directing the blast so that the majority of energy would go upwards could be rather heavy, making the balloon quite big. Basically, there would be a lot of logistical problems. You could envision that each balloon launch could run upwards of several hundreds of thousands of dollars or more. For comparison, if you wanted to do something like capture debris with a satellite and deorbit it, it might cost 10s of millions of dollars. So, a balloon with a large bomb is much cheaper, but a logistical nightmare.
Problem, the second: This is somewhat more technical. The atmosphere breathes. When it warms up, it expands, and when it gets cooler, it contracts. The upper atmosphere absorbs a bunch of energy from the aurora. The aurora deposits about 40 Giga-Watts of energy into the upper atmosphere continuously. During extremely disturbed times, it can deposit over 500 GW of energy for several hours. Those are big numbers, so what does it mean? Let’s say we have an extremely disturbed aurora (500 GW) for 6 hours. That is about 1e16 Joules of energy, which is 2.6 megatons of TNT, which is roughly 10 times LESS energy than a very large nuclear bomb. With the aurora, it is distributed over a very large region, and will cause an increase in density at around 400 km altitude of about a factor of 10. That is a pretty big increase in density. A coworker noted to me that a hurricane is caused by a density change of about 10%. This is a 1000% change in the thermosphere due to the aurora. The thermosphere is a pretty interesting place!
A nuclear bomb will cause a much larger change in the density, clearly. But, the problem is that it will change is only in a very small volume. You get a mushroom cloud that goes up into the atmosphere and causes a (lets say) 100 times increase. By the time the mushroom cloud gets up to orbital altitudes, it will be about 200-ish km across. A satellite will pass through this mushroom cloud in about 25 seconds. Then the density is back to normal. For a large auroral event, the entire atmosphere is increased by a factor of 10 for 6 hours, meaning that the satellite goes through 6 hours of 10 times larger drag. This is enough to change the satellite’s orbit. Definitely. But, it will really only change the altitude of the satellite by a meter or two. Not much in the grand scheme of things. So, a 100 times increase in the density for 26 seconds doesn’t change the orbit very much at all. Simplistically, you would need about a 1 million times increase in the density at satellite altitudes over the 26s in order to get the same effect as a 10 times increase for the storm over six hours. That would be a very large bomb indeed. And it would only cause something like a meter or two altitude change. Not deorbiting. For that you would need on the order of a hundred or so of these events. That is a lot of bombs.
Hopefully that was not too technical. Sorry if it was.
Problem, the third: In order to actually effect the single piece of debris, you would have to launch the balloon several hours before hand to allow it to get to a high enough altitude, and be over the pretty much the exact spot in which an object will be orbiting. Then you have to time the explosion perfectly, so that the orbiting object passes directly through the shock front of the blast. This is probably the easiest of the three problems, since with a model, you can pretty easily determine how quickly the blast wave will move through the atmosphere in all directions. Controlling the path of the balloon is more of a challenge, but I have actually written software that will allow you to figure out the trajectory of high altitude balloons, since this is a sort of a hobby or mine. (I will say that I have never exploded a nuclear device on one of our balloons!) Check out a video of one of our balloon launches where we launched two balloons at the same time.
What basically happened with Project SpaDE is that we did not get selected for funding for round two. This was not too surprising, since the concept is just not very scalable. You could actually see this working if you wanted to slightly nudge a small object that was going to hit a major satellite or something. If you perturbed the orbit a couple of days before the collision was supposed to occur, it could actually change things. Possibly. But, it would not be able to deorbit anything.
Sorry that this post was so long. Hopefully it was still entertaining.
Hopefully, over the past few posts, I have convinced you that using chemical rockets to get to space is a pretty horrible way of doing it. And, just as I am certain that I will continue to post about this technology, I am certain that we will continue to use them, since it is really the only way to actually climb out of this gravity well that we call home (at this time!). But, my friends, trust me when I tell you that there is something better. Actually, there are a number of technologies that are being worked on that may be better. All of them have some really major issues, but it is good that we are trying.
This is the first post in a series that is going to explore some alternate ways of getting around the solar system and off of this rock. And, because I like you guys, I am not going to start off with #10 and work up to #1. I am going to start off with the craziest possible way of getting us into space. (There are crazier ways of getting around the solar system, though!) Let’s get started.
Once upon a time, there lived a guy named Gerald Bull. Yes, he was sort of short and stocky. And Canadian. Here is a picture of him:
Gerald Bull came up with a fantastic idea. In 1961 he bought a 16-inch battleship gun from the US Navy for about $2000. That isn’t 16 inches long, that is 16 inches in diameter. He moved it to Barbados and started running tests with it. He put atmospheric sensing instruments into the noses of the shells, and then fired them into the atmosphere. These shells were about 150 kg and could go to altitudes of about 100,000 ft, or about 20 miles. In the air. By the way, these “rockets” were called Martlets. His program was called the High Altitude Research Program, or HARP.
Ok, let’s step back for a minute and think about this. Bull was firing a gigantic cannon straight up in the air with things that weighted about 300+ pounds. I launch weather balloons. These go up to the same height with packages that weigh 12 lbs. Bull was doing some crazy stuff! Interestingly, there is really not a great way of sampling this part of the atmosphere, since it is really hard for airplanes to fly this high. Satellites can’t orbit this low because the atmosphere is incredibly “thick” there. So, rockets are about the only good way to take in situ measurements in this area (well, above about 100,000 ft, or 30 km to about 200+ km) of the atmosphere. Bull fired about 1,000 of these Martlets into the atmosphere in just a year or so.
But it really doesn’t stop there.
In 1963, Bull created the Martlet-3, which reached over 100 km altitude. He could launch a “rocket” that could go up to space for about $5000. Considering that rockets can cost over a million dollars that do the same thing, this is super freaking cheap.
He then extended the length of the cannon to about 110 feet with the ultimate goal of launching things into orbit. (The reason that you extend the length of the cannon is because you can get the force of the expanding gas for longer, allowing the projectile to accelerate for longer.) His idea was to build a rocket that would be shot up to about 100 km, and then the rocket would fire and take the payload into orbit. This would be extremely cheap, since the majority of the mass to get something into orbit is used up just to get up to the right altitude. If you can get the “third-stage” of a rocket up to 100 km altitude with a big gun, then it is super cheap to get to orbit! His Martlets got up to 180 km altitude for a world record that is still in existence.
Unfortunately, Bull never reached this goal. There was a ton of red tape, with the US and Canadian government involved. Bull did not really believe in red tape and so he left the program. Bull continued to love big guns and started working for some shady people, developing highly accurate guns that could be used by one country against another. Ultimately, he worked for Iraq in helping them develop the Scud missiles that were supposed to be used against Israel. It turns out that Israel doesn’t really like this type of behavior, and Bull ended up with a few bullets in him in March of 1990.
The moral of the story (besides “don’t screw with Israel”) is that we could actually use a big gun to get us to outer space and ultimately into orbit. We don’t even need gunpowder to do this anymore – we can use the same technology that drives super-fast roller coasters and trains: linear induction motors. This technology has led to the development of rail guns by the Navy. You seriously have to watch this video. This is a massive increase in our technological capabilities. Basically, you accelerate the “bullet” up to speeds of about 4,000 miles per hour in the barrel of a gun. Serious horsepower.
If we can use this technology to knock things out of the sky, why aren’t we using it to put things into orbit? That is a fantastically good question!
There are two problems with this idea (beyond Israel killing you for trying):
There are researchers who are working on techniques that could be used independently or in conjunction with a big gun, so that you wouldn’t have to actually take fuel to get to orbit either. While that is interesting, it is no where as cool as the Martlet. Seriously. Gerald Bull. What a guy.
One of the big problems with rockets is their size. They need to be truly humungous to get anything into orbit. Interestingly, the reason for this was explained back before modern day rockets were even invented. A Russian scientist named Konstantin Tsiolkovsky described why rockets need to be really big way back around the turn of the last century (like 1900).
The graphic below helps to understand what is going on. Let’s say you want to lift a blue cube into space. The blue cube has some mass to it. In order to accelerate the blue cube up to some speed it takes a total of two bricks of red fuel. Let’s put some pretend numbers to this to make it a bit easier to understand. Let’s say that you want to reach a speed of 4, and using two bricks of red fuel will give you a speed of 1. That is too slow. So, we need more fuel.
Now the problem is that we have the blue cube plus two red bricks of fuel, which is more massive than just a blue cube. So, we will need even more fuel to accelerate this. In order to accelerate the blue cube plus two red bricks by 1, we will need four red fuel bricks:
We can keep going on this. Now we have a blue cube and 6 red bricks. In order to accelerate all of them by a speed of 1, you need 8 red bricks of fuel.
After that, we will be going at a speed of 3. We are very close to 4! To accelerate all of those red bricks (we have 14 now!) plus the blue cube by another 1, it takes 16 red bricks of fuel! Yikes! This is growing out of control!
For a rocket, what would happen is that the 16 red bricks would burn to allow the rest of the fuel plus the blue cube to be accelerated by 1. Then the 8 red bricks would fire, accelerating the 6 red bricks plus the blue cube by 1, giving a total speed of 2. Then the four red bricks would burn and accelerate the two red bricks and blue cube by 1, giving a total speed of 3. Finally, the last two red bricks would burn, accelerating the blue cube by 1 and giving a total speed of 4.
The point of all of the above is that the amount of fuel that you need grows very quickly, since you have to have more fuel to lift the other fuel that lifts the other fuel which lifts the other fuel, etc. Tsiolkovsky realized this more than 110 years ago and came up with a formula that describes this phenomena (of course, he knew calculus, which helps to explain things a bit). There are two forms of his equation:
They are exactly the same equation (but probably don’t look like it because of the “e” and the “ln”), but just re-arranged to allow two different questions to be answered:
One detail that I left out, which was talked about in the last post about chemistry, is that there is a term in the equation that represents the exhaust velocity of the rocket (Ve). If we take the top equation above, there are simplistically two terms of the right hand side: the exhaust velocity and the ratio of the full mass of the rocket to the empty rocket. What this multiplication means is that if you want to reach a given speed (V), you can use less fuel (smaller ratio of masses) if you have a larger exhaust velocity (Ve). The amount of fuel still exponentially increases (this is sort of what the “ln” means), but if you use a fuel with a higher exhaust velocity, you can use significantly less of that fuel. So, you want to get a fuel that will really leave the rocket with as much speed as possible. Then you can use less of it!
You can also use these equations to prove that a rocket with stages is much more efficient that a single-staged rocket. I won’t do this here, but you can think of it conceptually given the diagrams above. Let’s pretend that the black boxes around the fuel and blue cube are different stages of the rocket and that they have mass, which is pretty much exactly how it works. For the biggest rocket (with the blue cube and the 30 red fuel bricks), the rocket will be quite heavy and it will really be hard to get the fuel and everything up into the air. When we burn the 16 red bricks, we then get to drop the gigantic storage tank and some motors and plumbing and all sorts of stuff. The rocket then has significantly less mass. The next 8 red cubes have a MUCH easier job to do in this case, and they can accelerate the rocket much faster. The same is true when the 8 red cubes are done burning and the rocket drops the second stage with the motors and plumbing and stuff for that.
Rockets typically have three or four stages, each with smaller motors (or less motors) and smaller fuel tanks, just as illustrated above. The most efficient rocket in the world would destroy itself as it burned, having an infinite number of stages. That is quite difficult to engineer, though.
Chemical rockets that use fuel like this are about the only thing that we have ever used to get something off the ground. But, there are other methods. Some of them are just scary, and could get you killed by the CIA. Let’s talk about that next time.
In the last post, I talked about how it was basically impossible for humanity to get to another star using modern technology. For this post, I would like to talk about why that is, and why we don’t have space hotels or moon bases yet.
The whole reason comes down to chemistry. The vast majority of rockets that exist and all rockets that take anything into outer space use chemistry to make the rockets go. A few posts ago, I talked about thrust. Thrust is a pretty simple concept – basically, a rocket moves forward by expelling things quite quickly out the back. There are two terms in the thrust equation, the mass flow rate (how much stuff the rocket spits out), and the exhaust velocity (how fast it spits it out). Simple.
The mass flow rate is pretty easy to understand also. It basically is just how much fuel the rocket uses per second. In some ways, it is like hitting the gas pedal on your car: the harder you push on the gas pedal, the more gas flows into the engine and the faster you go. That is a pretty simplified version, but it is about right. A larger rocket really just has a larger mass flow rate. The space shuttle had pipes that fed into the main engines that were about a foot in diameter. That is a LOT of fuel! The Saturn V used roughly 1000 gallons of fuel per second. They actually had a very hard time mixing the fuel with oxidizer on the Saturn V, since the flow rate was so high (they didn’t have great fuel injectors in the 60s!), and they would get explosions in the engines. Instead of giving up, they simply made the combustion chambers more sturdy to handle the explosions.
Anyways, the mass flow rate is how much fuel the rocket uses per second. This is set by how big the engine is, and there is no real limit, except how big you can build the engines (or how many engines you can stick on a rocket – yes, I am talking to you Space-X with your 27-engine Falcon Heavy rocket).
The other term in the equation is the really tricky one – this is the exhaust velocity, which is how fast you can expel the mass out the back. Simplistically, you would think that this would be easy to turn up, but it is not. There has not really been any big revolutions in the exhaust velocity in a long time (like the 60s). The most common way to make a large exhaust velocity is to make an extremely hot gas, and direct it into a nozzle. You mix fuel with an oxidizer, and you get an explosion. Then you turn the explosion into directed energy using a nozzle.
We can design pretty good nozzles. They can be something like 90%+ effective at turning the thermal energy into kinetic energy. That is great. There is no factor of 10 improvement or anything that can be gained from nozzles.
The big problem behind this is chemistry. Let’s take the space shuttle’s main engine. This engine used two of the most abundant elements we have on Earth: Hydrogen and Oxygen. You cool them both down until they are liquids, store them until the rocket is ready to fly, then combine them in the engine. What is the result? Water! The space shuttle’s main engine exhaust is water! Crazy, eh? The amount of energy that is released when 2 molecules of Hydrogen are introduced to one molecule of Oxygen is exactly the same every time – about 6 eV, which is a tiny bit of energy. The fundamental issue here is that we get only a very specific amount of energy out of the reaction. If we take the 6 eV of energy and we turn that into an exhaust velocity, it ends up being about 3,000 m/s. This is very fast at first glance, really it is not.
This small amount of energy totally limits us so that rockets have to be huge. If the chemistry were such that these elements released 10 times more energy, then we could (in theory) make rockets that were much smaller (more than 10 time – by a lot). In fact, we play around with different chemicals to try to make a larger exhaust velocity, but the problem is that the chemicals that produce the most wickedly large exhaust velocities are horrific to work with – like super caustic and really, really bad for humans. So, there has to be a balance between safety (which costs a LOT of money or lives) and exhaust velocity too. This huge Russian rocket explosion that killed over 100 people, was while they were trying out new fuels that would have larger exhaust velocities.
We have not invented a better way to get off the ground than using a chemical rocket engine. There are a TON of other ideas out there, but it is this fundamental limitation of the exhaust velocity that limits our ability to actually go very many places far away from Earth.
Next time, I will go through a simple formula that was invented in the early 1900s that predicted this whole problem. It was a good 40 years before modern rockets were even invented! And then, I will start posting about all of the absolutely crazy ideas that could possibly get us to the stars. Well, ok, maybe not. But, they are awesome anyways!
Given the news of the finding of an Earth-like planet around one of our nearest stars, as described here, it is interesting to see if we could ever actually get to this planet. I am going to start a small series on the idea of getting to another star. I will cover a few topics such as the problem with getting to another star with our current technologies, what new technologies we could use, and why getting some satellites to another star might not even help.
Right then. Why can’t we get to another star now?
Let’s say that we want to get to a star that is about 4.5 light years away. A light year is actually a distance – it is the distance that light travels in an Earth year (as opposed to a Martian year). It is roughly 9.5×10¹² km. That is a long distance. To give some perspective, it takes just over 8 minutes for light to get from the sun to the Earth. To reach Pluto, it takes light 5.3 hours. Given that it took New Horizons 9.5 years to get to Pluto, you can see that it will take us a fair bit of time to go all the way to another star.
But, let’s try.
How would you get a satellite to another star? Well, you would have to accelerate it up to some speed, then cruise for a long time, and then decelerate it once it gets to the other star. Ideally.
Since we would want to actually see what this thing measures in our lifetime, let’s assume that we can get it up to about 1/3 light speed (a nice round number of 100,000,000 m/s), and let’s assume that we can accelerate at roughly the gravity of Earth, which is about 10 m/s². If we do a tiny bit of math, we can see that it will take us 10,000,000s to reach this speed, which seems like a huge amount of time. But, considering that there are 86,400s in a day, this is only about 116 days or about 4 months.
So, if we wanted to get to another star, we would take about 4 months to accelerate up to about 1/3 the speed of light, cruise for about 12 years, and then decelerate for about 4 months, with a total trip time of about 13 years total. Not that long! Why aren’t we packing our backs now (or building a satellite for the 13 year journey)?
The problem with this is that we don’t have the technology to accelerate something at 10 m/s² for 4 months. If you watch a rocket launch, you will see that the rocket accelerates for only a few minutes – like 10. In fact, to reach orbital speeds (7,600 m/s) , if you accelerate at 10 m/s², it will take about 13 minutes. To break away from the Earth, which is much harder, it will take about 20 minutes. Even with math, that is significantly shorter than 4 months.
One of the reasons that I brought up New Horizons before is because it is one of the fastest satellites ever launched. It left our orbit going about 36,000 MPH, which is about 16,260 m/s.
Let’s put this speed in the context of getting to that other star which is 4.5 light years away. 16,260 m/s is about 0.0000542 times the speed of light. So, to get to another star, New Horizons would take about 83,000 years. That, my friends, is a long time, and why no one is packing any bags.
It will be a long time before we can make this journey in any reasonable amount of time. Next time, let’s talk about why we will never be able to get to another star using our current rocket technology. I am not even joking here. Using modern rocket technology, it would more mass for fuel that there is matter in the entire universe to accelerate us up to anywhere close to the speed of light. But, let’s talk about that next time.
One of the interesting things about learning about thrust for a rocket, is that we can use the same types of formulas for airplanes. So, let’s take a few minutes and figure out how much fuel an airplane uses to travel from one place to another. We can also look at why airplanes fly at the altitudes that they do, and how the wind affects the fuel used.
How to actually do this? Well, we need two equations that we have talked about on different posts: (1) the equation for thrust; and (2) the equation for the drag force. When a plane is traveling between two places at a constant altitude, we can ignore the forces in the vertical direction, since the gravity of Earth is balanced by the lift from the wings. In the horizontal direction, the forces are also balanced (since we are traveling at a constant velocity), namely the thrust of the airplane is balanced by the drag force from the airplane moving through the air.
So, what is the drag force on an airplane? Well, we can calculate it using the formula: F=0.5*Rho*Area*DragCoefficient*Speed², where Rho is the mass density of air, Area is the frontal area of the airplane, DragCoefficient is the Drag Coefficient of the airplane, and Speed is the speed of the airplane (with respect to the wind). Let’s do a simple example, and take the Boeing 747, like the plane shown above. Some assumptions about the 747:
Area = 158.3 m² (that is pretty big!)
Drag Coefficient = 0.05 (that is pretty small!)
Velocity = 562 miles per hour = 250 m/s
I basically found these by looking around on the web.
The surface mass density is 1.23 kg/m³. The density decreases pretty rapidly as you go up in the air. At 30,000 ft, the density is roughly 38% of the surface density (0.467 kg/m³). At 40,000 ft, the density is about 25% (0.308 kg/m³).
Ok, that was a lot of numbers. Sorry. What does this mean? Well, we could talk about the drag force that the 747 experiences. If we do all of the math, and we assume that the 747 is cruising at 40,000 ft, we get a force of 75,750 N, which is 17,030 lbs. If the airplane were to be flying just 10,000 ft lower, the force would be 25,885 lbs, which is much (50%) larger, showing that the altitude that the airplane flies is pretty important.
Now, let’s calculate how much fuel is used during a 6 hour flight (say New York to London). If we assume that it is all cruise (which is a bad assumption, since a lot of fuel is used to take off), how much fuel does the 747 use?
Well, we have to calculate how much fuel a 747 uses each second at cruise speed and at altitude. Remember that Thrust = MassFlowRate * ExhaustVelocity. For a rocket engine, the Exhaust Velocity is really the speed at which the gas comes out of the engine. For a jet engine, that is not really the case, and it is a bit more complicated. But, let’s skip over that and just take my word that the “ExhaustVelocity” of a jet engine is about 35,000 m/s. (If the exhaust velocity were really that large, it would be pretty dangerous to be around the backend of an airplane!)
To get the MassFlowRate, we can just divide the thrust by the ExhaustVelocity. At 40,000 ft altitude, the MassFlowRate would be 2.16 kg/s. A gallon of jet fuel is about 2.7 kg. So, a 747 uses just under (80%) a gallon of jet fuel every second. Depending on your point of view, this is either a lot (a car uses a gallon every few hours), or a tiny bit (a rocket uses a hundreds of gallons each second).
Over the course of a 6-hour (6*3600 seconds) flight, the airplane would use about 17,300 gallons of fuel (not counting takeoff and landing) if it flew at 40,000 ft.
If the airplane were to fly at 30,000 ft and keep the same exact speed (562 mph), the airplane would use 26,300 gallons! That is 9,000 gallons of jet fuel more, just for flying at 30,000 ft.
Hopefully this helps you understand why airplanes fly as high as they can. If you are on a very large airplane that is flying a long way, then the airplane may raise the altitude a couple of times as it uses fuel. A super heavy 747 can’t fly at 50,000 ft, since its wings can’t support the lift at 50,000 ft. As the 747 uses fuel and is less mass, it can fly at higher and higher altitudes. The best track would be to fly at the highest altitude all of the time, increasing altitude all of the time, but rules stop this – there are certain altitude “lanes” that planes can fly in.
Just for fun, if the airplane is at 40,000 ft, it gets about 0.195 miles per gallon. At 30,000 ft, it gets about 0.128 miles per gallon. If the flight had 400 people on the 747, and it flew at 40,000 ft, then each person would get the equivalent of about 78 MPG. Not really that bad! It would be hard to drive somewhere for this type of fuel economy!
Interestingly, if a 747 were to fly at ground level the entire flight, it would use 69,000 gallons of fuel to fly from New York to London, or would get about 0.05 miles per gallon. Yikes!
Finally, how does wind effect the amount of fuel used? Well, a 747 goes 562 MPH not with respect to the ground, but with respect to the background wind. So, if the 747 is flying in the jet stream, which can be about west-to-east at 100 MPH, then the ground speed of the 747 flying from New York to London would be 652 MPH, but coming back from London to New York, the ground speed would be 452 MPH. This doesn’t cause the amount of fuel used per second to change, but it changes the number of seconds the airplane is in the air. From New York to London, the flight would be shortened to 5:10, and back to New York, it would be lengthened to 7:30. The amount of fuel used would be 14,700 gallons (saving 2,600 gallons, NY to London) or 21,000 gallons (costing about 3,700 more gallons, London to New York).
Ah, physics. I love you.
Oh, on a side note, think about in the first Iron Man movie when he (Iron Man) flew from Los Angles to the Middle East in his suit. Obviously it must have been pressurized, since he would have to fly at incredibly high altitudes. Iron Man is quite a big smaller than a 747, but he probably was flying about twice as fast as a 747. So, if you do the calculations, he would have had to use about 147 kg of fuel. If this was jet fuel (which it was not, but that is a separate discussion) it would be about 55 gallons. Where did he put all of this fuel??? Marvel Fans want to know!