A Personal Blog

forewarning: this post is much longer than what is appropriate for a blog post, has some physics discussion, has only been proofread once, probably should not be cited for any sort of report, doesn’t have any fun pictures, ignores the convention of using the third person in narrative, probably has some run on sentences, and is very interesting to me. I hope you enjoy the one sided discussion.

Approximately 3 years ago, I was on my way back to Oregon after spending a year living on the island of St Thomas, and on this journey I stopped to visit a friend who lived in Seattle, lets just call him Scott, who eventually drove me the last leg of the trip back to Oregon. I spent a few weeks with him up there though, and one of the activities we did was go to The Museum of Flight at Boeing Field. I don’t remember exactly what initiated the trip, but I imagine that it was the result of me liking museums, aviation, and wanting to do something, and Scott had never gone there.

This museum has one of the supersonic Concorde aircraft on display, and a discussion began concerning the different configuration of the engines on the Concorde as compared to conventional airliners. The Concorde utilizes turbojet engines, which are mounted directly to the body of the aircraft, and are much narrower compared to conventional airliner engines. Normal airliners utilize turbofan engines, located in separate nacelles attached to the wings of the aircraft. I believe at the time I was telling him that turbofans were more efficient at providing thrust to an aircraft, but did not function well at the high air velocities the Concorde traveled at. Unfortunately at the time, I lacked much explanation to my argument. I believe Scott came from the perspective of chemical energy in – kinetic energy out – from both engines, why should one be more effective than the other? Not to mention the Concorde was much more streamlined and with the narrower engines, had a smaller cross sectional area and therefore less drag.

So, last night, or the other night depending on when I finish this, while I was falling asleep, this all came back to me in a flash, and I thought of a good way to explain it, and about half a dozen related tangents, generally related to physics and thermodynamics, as I am finishing my B.S. In mechanical engineering, and here I am about to share with Scott and whoever else finds it. I might also mention that though I speak as if everything I say is fact, I might easily have a thing or two wrong in this discussion. Keep in mind that these are the words of a student, not the professor.

First, a turbofan and a turbojet are both intimately related forms of “jet” engines, both utilizing a Brayton thermodynamic cycle. A thermodynamic cycle is a system in which thermal energy and useful work are exchanged through processes usually involving changing the state of a working fluid, such as air, in a cyclic manner. A power cycle changes thermal energy into work, where a refrigeration cycle uses work to transfer thermal energy from one place to another. A Brayton cycle is similar, though not identical to another power cycle which many people are familiar with, the Otto cycle, which powers 4 stroke gasoline engines. The Brayton cycle compresses air taken from the engine intake, adds heat to the compressed air through combustion of fuel, and extracts work from the increased energetic state of the air through the turbine blades. This “work” is then used to turn the compressor to compress more incoming air. Work is also done through the increased velocity of the exhaust gases from the engine, pushing the aircraft forward. This is a basic description of a turbojet.

A turbofan can be described simply as a turbojet in which some of the blades of the compressor only move air through the engine and out the back, bypassing the turbine, aka the part of the engine that extracts work after the heat has been put into the system, and just pushing the air out the back of the engine. It could be described as a “fan.” It is able to do this because it is harnessing the work collected by the turbine portion of the engine. As this air has not been heated, it does not reach as high of velocities as the heated and compressed air coming out from the turbine portion. These streams diffuse momentum to each other so that the average exhaust flow velocity is much slower than if there were no fan and all of the exhaust stream came from the turbine alone, as in a turbojet. However, the rate of mass flow is now much higher because of the additional air being pushed by the fan.

What does this all mean? Well, this is the comparison that came to me as I was attempting to fall asleep. Imagine I am free floating in space, and have two ways to propel myself. I can shoot a small 22 rifle, using the reaction force of the gun to propel me, or I throw a rock, but am limited to only putting the exact same amount of energy into throwing that rock. According to Wikipedia, a standard 22 round has a muzzle velocity of 330 m/s (I’m not sure what barrel length that might be based on, but it doesn’t matter), and has a mass of 2.6 grams. This means the bullet has a kinetic energy of 1/2*m*v^2 = 1/2*.0026*330^2 = 141.5 joules of energy. This quantity represents the amount of energy which was transferred from the thermal expansion of the ignited gunpowder to the bullet, and will also be my limit for how much energy I can put into the rock.

How much thrust do I get from the bullet? Momentum is always conserved, and is represented by the quantity mass * velocity. Therefore, the mass * velocity of the bullet will be equal to the change of my mass * velocity in the other direction. .0026*330 = 105 kg*V, V therefore equals .0082 meters per second in the opposite direction. Not very fast, but it is a very small bullet, so what do you expect?

What about my rock? Lets imagine a 1 kg rock, that I can push or throw, but I am limited to only applying the same amount of energy to the rock, 141.5 joules. This would give the rock a velocity as follows, 141.5=1/2*1*v^2, v=(141.5*2)^(1/2) = 16.8 meters per second. Wow, that is actually quite a throw. Again, using conservation of momentum, 16.8*1 = 105*V, V=6.25 meters per second for me in the opposite direction. Yes, that is correct, same amount of energy, but I will get propelled to a speed nearly 800 times faster than using the rifle. This is the same concept in the difference in efficiency between a turbojet and a turbofan, more thrust for the fuel dollar.

However, now to complicate things. The Concorde was actually very fuel efficient once it reached altitude and speed. As you may have gathered from above, reaching twice the velocity of a standard airliner requires 4 times the energy input, and the Concorde flew higher than a normal airliner as well, requiring more energy to reach that altitude, but once it was at speed and altitude, it had two major advantages in efficiency.

First, remember how average exhaust speeds were slower in the turbofan engine? I believe average is in fact slower than the speed at which the Concorde traveled at (supersonic exhaust flows are very loud and turbofans avoid this if possible to make their engines quieter). There is a common misconception that this means they would not have provided thrust at all, because they wouldn’t be pushing against the atmosphere. This is incorrect, as if one looks at the problem from the frame of reference of the airplane, mass is being thrown from the back, and the plane will be pushed forward, even if the mass coming from the back is still moving forward in the frame of reference of the atmosphere. However, it does increase drag of the plane, creating what might be called a “wake” behind the aircraft, sucking atmospheric air along with the craft. Air will also back up in front of the motor, as the motor can’t suck it in fast enough. The turbojets of the Concorde however, where ideal in this environment, pushing exhaust gases rearward quickly enough to be moving backward in the frame of reference of the atmosphere, reducing wake. Also, the engines of the Concorde had intake ramps, which accounts for the triangular nature at the front of its engines. These ramps served the major purpose of slowing and limiting the air entering the engines. This reduces that back up at speed, but is also critical as the engines would be damaged if supersonic air entered them directly.

Secondly, the aircraft was designed to be very aerodynamic at the speeds and altitude in which it traveled. This is a tricky comparison with conventional airliners, as drag force is characteristically related to the square of velocity, similar to the way energy compared to velocity. This means an object traveling twice as fast will tend to generate 4 times the drag force. However, the Concorde was designed to have excellent aerodynamics at its cruise speed, which is apparent in its delta wing design, sharp nose, and streamlined shape. Also, as the Concorde traveled at higher altitudes, the atmosphere was thinner and generated less drag in general. Basically the comparison is that if at cruise speed the amount of drag between a normal airliner and a Concorde was similar, it took a similar amount of energy per second (power) to maintain that cruise speed, but the Concorde could cover twice as many miles. This comparison is pretty rough, requiring many assumptions, but arguably, the Concorde at speed could get very good “miles per gallon.”

Now, all of this relates with another conversation I once had with my father. This was several years ago, and we were discussing the war in Iraq. He was wondering why American forces had to use fuel guzzling jets for operations, and that he wouldn’t mind seeing WW2 style piston powered aircraft put into use, supporting the men and women on the ground. It would be significantly cheaper and more efficient, he said. At the time, I knee jerked responded that I believed turbofan’s were more efficient than piston engines and that this was one reason that his plan was not put into use.

The truth of it is, in terms of thrust per unit energy, a propeller powered aircraft has similar advantages as did the turbofan to the turbojet. It produces higher mass flow traveling at slower velocities out the back of the aircraft, producing more thrust for less energy.

However, similar to the comparison of the turbojet to the turbofan, a turbofan can get better “miles per gallon” when traveling at cruise speed. I might also add that the factor of mass is important here, that for the turbofan comparison with piston engines, it might be better to say better “miles per gallon per airplane mass.” Further, turbofan’s have a major advantage in terms of power density. This is to say that a turbofan produces much more power per unity mass than a piston engine is capable of, allowing for either a lighter aircraft or additional aircraft equipment for a given amount of thrust.

What does this all mean? Well, Dad was right about one thing for sure, piston engines do provide advantages in terms of thrust per unit energy efficiency at low speeds. This is especially useful in terms of providing support to ground troops due to loiter time, the amount of time an aircraft can remain overhead. The idea has actually been utilized in the unmanned aircraft known as the Predator. This aircraft uses a piston engine, and can loiter over a battlefield for nearly a day if necessary, something possible by efficient use of energy.

However, the evolutionary replacement to the Predator, known as the Reaper, has moved to a turbo-prop engine. I haven’t discussed this design yet, but it utilizes a Brayton cycle, similar to a Turbofan, but the thrust is almost entirely produced by a propeller, rather than the stream of air leaving the engine. The compressor-combustor-turbine is primarily used to turn heat energy into work, which then turns the propeller. In terms of performance, this might be seen as point between turbofans and piston engines, pushing more mass and having higher thrust efficiency than a turbofan, but still higher exit velocities (and higher power density) than a piston powered engine. The Reaper can travel at higher speeds, getting better “miles per gallon per mass,” and carry a heavier payload. It does pay a price of reduced thrust efficiency, resulting in requiring significantly more fuel to loiter similar times as the Predator is capable of.

Ok, well up to know, I have kept this fairly on topic so far, and if you are good and tired of engine talk probably time to stop reading and call it a night. But if you are not, it’s now time to talk about something I can’t remember if I read it first or it arose organically between a combustion theory course and a power generation course, concerning thermal efficiency of a cycle. Thermal efficiency refers to how much heat energy I put into an engine, and how much of the energy I can get out as work. Energy cannot be created or destroyed, and at least in any case I intend to ever worry about, it will not be turned into and out of mass. So any energy put into the engine is either turned into work, or is released as waste heat that could not be harnessed. All thermodynamic cycles are limited by something known as the Carnot cycle. The Carnot cycle is not an actual defined cycle, rather it defines the maximum amount of energy between to thermal states that may be harnessed as work. If I put 1000 Joules worth of heat energy in, I will never be able to get 1000 Joules of work energy out. However, I can increase the Carnot efficiency by increasing the difference between thermal states of my engine. These thermal states represent a high energy state, and a low energy state, and work is harnessed as the energy flows from that high state to the low state. The high state in a Otto cycle is the high temperature and pressure right after ignition, and the low state is represented by atmospheric conditions. Work is extracted as the energy flows between these two states. I’m really not doing the Carnot cycle justice here, as defining it also requires going into concepts of entropy, which sort of concerns the state of how concentrated and ordered a piece of mass is, and that a thermodynamic process will always move from a state of lower entropy to higher entropy. This leads to concepts such as exergy and/or availability. Really I can’t say my understanding of it is perfect, but just remember that if you are in a Thermodynamics course, always answer “entropy is increasing,” or “because entropy is increasing,” and you will always be right.

So, Carnot efficiency, and therefore the efficiency of any engine can be increased by increasing the high energy state of the cycle. This does not mean putting more energy into the system, but having the energy at a higher thermal state. In other words, have your high state at 1000 degrees instead of 500, with a constant incoming of 1000 watts of thermal energy. It doesn’t necessarily make intuitive sense, but (with a material that has a constant specific heat, which is relatively common (this means it takes the same amount of energy to increase the temperature of something from 0 to 100 as it does 100 to 200 degrees)), raising steel from 500 degrees to 600 degrees takes the same amount of energy as it does to go from 900 to 1000. So, same amount of energy flow, but higher temperature.

Where I am going with this? An engine that operates at the highest possible temperature will be very efficient. However, there are limits to our systems in terms of material properties. Turbines, which I have so far talked about as generally being an efficient choice, are inherently limited by the temperatures their blades can withstand. This is because their blades are constantly in contact with the hot combustion gases from which they extract power. Turbine technology improvements have largely been a process of building the blades from better materials so as to operate at a higher temperature.

What’s the point of this? Well, an interesting thing about piston engines, using the Otto cycle, is that the process is not as inherently limited by combustion temperature. This is do to the cyclic nature of the 4 stroke motor, where combustion temperatures are reached on only one stroke. During the other strokes materials are not subject to the high temperature of combustion, and the temperature of cylinder walls are actively cooled so that they never reach those combustion temperatures, and therefore do not melt or fall apart or whatever.

This means that fuel air mixture can be burnt at its adiabatic flame temperature, which is basically as hot as possible, leading to more efficient conversion of heat energy to work energy due to the increase in the difference of thermal states, increasing the Carnot cycle limit. Further, this means the piston engine can be build from much cheaper conventional materials and manufacturing techniques.

However, this comes at the price of energy being drawn into the cooling system to keep material temperatures down, as well as requiring what really is a more mechanically complex system (though cheaper to build) than a turbine based engine. A piston engine has more moving parts and work transfer through additional parts, such as pistons moving up and down. In comparison, a turbine, though expensive to build due to required materials and manufacturing requirements, is mechanically simpler, as well as highly reliable.

Interestingly, future turbine technology is likely to incorporate cooling technology on turbine blades, in principle similar to the idea utilized in piston engines, allowing for higher combustion temperatures while keeping the blades from reaching those temperatures. As discussed above, this would increase efficiency and therefore performance. Strategies include micro channel flows of a cooling fluid within the turbine blade, or manipulation of a boundary layer at the turbine blade surface through air bled from ports on the blade.

Finally if you have stuck with me all this time, I would like to discuss an propulsion solution that may seem completely contrary in terms of thrust efficiency with everything thus far discussed: ion engines. Ion engines are no longer the realm of science fiction, as they have been successfully utilized now on several satellites and space probes. Ion engines function by accelerating ionized gases through electrical or magnetic field manipulation to very, very high speeds out the back of the craft. If you followed the discussion above concerning turbojets and turbofans, this would lead you to believe that ion engines are not energy efficient for the amount of thrust they produce, which is indeed correct.

Why use them if they suck? Well though they are very energy inefficient, the are very “mass” efficient. Normal chemical powered engines such as jet turbines and chemical rockets get the energy for their thrust from the mass that is being used to create thrust, therefore for more energy, you need more mass and bigger fuel tanks. Ion engines get their energy from other sources, and the ionized gas is only used as the reactive mass to push the vehicle forward. The source of energy is generally solar panels, which can provide constant power for the engine, with no mass cost for the power, and will not ever run out of power, till they wear out anyway. This means that the ion engine will produce much more thrust per unit of fuel mass compared to other options, allowing the craft to be much lighter, which again results in more efficient propulsion.

The drawback to ion propulsion? These engines are very limited by the amount of power available. 1000 Watts from a set of solar panels or RTG is not a lot of power, and means that though the ion engines will be very fuel efficient, they cannot produce very much thrust at any time. If an ion propelled craft wants to get somewhere, it has to leave the engines on for a very long time. 1000 Watts of power turned into thrust for 3 years however can result in high velocities just as well as a chemical rockets and use significantly less mass to do it.

I believe that theoretically, if man one day chooses to do so, a craft could be built with a nuclear reactor, powering ion engines, and this could be a viable method of manned interplanetary travel. Nuclear fuel provides incredible power density, while ion engines provide excellent “thrust density,” or amount of thrust per unit mass, could combine to a comparatively lightweight viable solution to space travel. Finding a medium where the craft was both energy efficient and mass efficient would be the challenge, as well as the hundreds of other challenges in getting nuclear reactor into space… making it work in zero g…. keeping the astronauts/cosmonauts from killing each other while in transit for 6 months, etc etc etc.

Well, I hope that you enjoyed this one sided discussion that occurred while falling asleep. Again, I would suggest against citing anything in this article, as I did not cite any sources, nor did I use many, only occasionally looking at wikipedia to verify a definition or understand something better. That is the joy of a blog, sharing information in the same way I would at the dinner table, except that I don’t get any feedback from the listeners to stop, and therefore keep going…. and going….. and going…… and going…… and done!