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Thermodynamics for Pilots

Aero

William Thomson, 1st Baron Kelvin was an Irish mathatical physiscist and engineer who died right around the time the Wright Brothers were first using the compressibility of air to temporarily escape the pull of gravity. Kelvin, besides disovering where absolute zero is — at 0° Kelvin of course, was also the first to postulate the field of thermodynamics, henceforth dooming engineering students to the first of many "make it or break it" courses on the way to their degrees.

So what's all this mean to a pilot? Lots. Thermodynamics is what allows a jet engine to turn fuel into thrust. It also rules the roost in your air conditioning and pressurization systems. You don't need all those formulas and fancy theorems, but it does help to understand why gases behave they way they do if you ever need to trouble shoot that jet engine or air conditioning pack of yours.


 

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Photo: Lord Kelvin, from Wikimedia Commons

The First Law of Thermodynamics

The increase in internal energy of a closed system is equal to the difference of the heat supplied to the system and the work done by it.

A closed system is anything you want it to be, say a jet engine or an entire airplane, but it is easier to understand the theory if you consider something smaller. A drop of water, for example. The water itself has an amount of stored energy in terms of its temperature. If you were to place the drop onto a colder surface, the drop will tend to raise the temperature of the cold surface, increasing its stored energy while lowering its own. The warm water does work on the cold surface by releasing its stored energy. We call this stored energy "potential energy" and the transfer of energy is work.

There are other forms of potential energy, such as that found stored in jet fuel, which is chemical energy. That stored energy is released when the conditions are right to ignite the fuel.

The Principal of Conservation of Energy

Energy can be transfered from one form to another, but cannot be destroyed or created.

The closed system can absorb energy — say the drop of water is heated, or can give up energy — say the drop of water heats something else up. But the energy either came from someplace or went someplace. It wasn't created or didn't disappear.

Back to our drop of jet fuel: sitting in the fuel tank it has chemical potential. Once ignited in the burner can of your engine, that energy is converted to the work done on the engine propelling it forward and to the heat thrown out the tail pipe. All of the energy is accounted for, even if you don't reap all of the benefit.

So how about an example? Here is a typical air conditioning pack from a Gulfstream G450. The pack itself requires no electrical power and does not have any refrigerant, yet it turns 400°F bleed air into 35° conditioned air. How does it do this?

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Figure: Air conditioning pack thermodynamics, from Eddie's notes.

There are two inputs: hot engine bleed air and cold ram air. The engine bleed air has thermal energy (it is very hot) and kinetic energy (it is being thrown at the pack with a lot of pressure). The ram air also has significantly less thermal energy (it is relatively colder) and kinetic energy (the pressure is much lower).

The pack has two heat exchangers which are little more than radiators which raise the temperature of the colder air and lower the temperature of the hotter air. The result is the bleed air loses energy while the ram air gains energy.

The pack also has an air compressor. The air enters the compressor at a given energy in the form of heat and pressure. The compressor exerts work on the air and that work becomes heat. (Remember it cannot be destroyed so it must transform itself into heat.) Why raise the heat only to cool it again? Two reasons:

  • The heat exchanger works best when the difference in temperatures is greatest. It will subtract more energy from air that is much hotter than air that is only slightly hotter.
  • The compressor is connected to a turbine that converts the bleed air's kinetic energy into the mechanical energy required to spin the compressor. The reduction in kinetic energy is greater than the increase in thermal energy so the net effect is less energy in the resulting conditioned air.

There is another player involved: the pack itself. The kinetic energy of the bleed air drives a turbine which spins a compressor and a ram air fan. That kinetic energy subtracts kinetic and thermal energy from the bleed air. The pack also has inefficiencies to consider. The bearings generate heat and the enclosure itself becomes warmer. Both of those subtract energy from the bleed air.

The last stage of the air conditioning pack allows the air to expand. Just as compressing a gas causes it to heat, expanding a gas causes it to cool. The gas expends energy when it expands and that energy comes from the stored heat.

So once you've subtracted all the mechanical, thermal, and pressure energies you end up with cooler conditioned air.

The Second Law of Thermodynamics

Heat cannot spontaneously flow from a colder location to a hotter location.

Kinetic and potential energy dissipate. Over time, temperature, pressure, and chemical potential tend to even out. This process is known as entropy and is often stated thusly: things go from order to disorder.

[Coram, pg. 127] The second law is unique to thermo and puts limits on what is physically possible in the conservation of energy. It is called the "law of entropy" and applies to all systems but is most easily introduced by its effects on a closed system — that is, one not acted upon by outside forces. The second law postulates that the expenditure of energy does not ebb and flow. It says that in a closed system, the transfer of heat goes only in one direction, from a high temperature to a low temperature.

[Coram, pg. 128] The second law was the first nonreversible law in physics — something almost beyond the pale of science. It says the universe goes from order to disorder. . . . Some even use the second law to try to prove the existence of God. This argument has it that God established order (low entropy), and since then the universe as progressed and continues to progress to disorder (high entropy).

So what does this mean for us pilots? Charles E. Cooper was a 19 year old majoring in aeronautical engineering when he happened to sit in class next to then Captain John Boyd, the Air Force fighter pilot who almost singlehandedly changed the art of war. Boyd wanted to better understand the second law of thermodynamics:

[Coram, pg. 131] Cooper began talking about the second law, explaining how more usable energy always goes into a system than goes out, because there is unavailable energy called entropy. All entropy means, Cooper said, is that no system is one hundred percent effective; if it were, you would have a perpetual-motion machine.

In terms of a fighter pilot's need to out maneuver an advisary, the aircraft has energy in terms of altitude and speed and can add to that energy using the engine's thrust, which converts the chemical energy of fuel. Much of the fuel's energy does not translate into energy for the pilot because it is expended in heat thrown aft or absorbed by engine components.

But let's consider an even simpler idea: an airplane is steady cruise flight with a constant thrust setting. If the pilot pushes the nose over to descend the aircraft will necesarily pick up speed. If the pilot levels momentarily and then climbs back to the original altitude, the aircraft will end up at a lower speed unless enough fuel was burned to increase the thrust to weight. Why is that? It is because an amount of speed (energy) was consumed by the g-load needed to level off at the bottom of the descent and then to begin a climb. And that leads us to Boyd's:

Energy-Maneuverability Theory

[Coram, pg. 147] In an equation, specific energy is denoted by "PS," (pronounced "p sub s"). The state of any aircraft in any flight regime can be defined with Boyd's simple equation:

PS = ( T - D W ) V

or thrust minus drag over weight, multiplied by velocity. This is the core of E-M.

This elegant equation explains much of what you might intuitively know about flying airplanes:

  • At any given moment, you can increase speed by increasing thrust, decreasing drag or weight
  • You can also decrease speed by decreasing thrust or increasing drag (and those of us who could air refuel, by increasing weight)
  • You can also change speed by changing the specific energy, PS, by trading altitude (up or down), which trades potential energy (altitude) for kinetic energy (velocity).
  • You have another lever to pull in this energy-maneuverability equation: G loading, which impacts the "W" term directly; increasing G-loading will decrease V, decreasing G-loading will increase V.

The Third Law of Thermodynamics

As a system approaches absolute zero the entropy of the system approaches a minimum value.

While not really germane to us pilots, this law just tells us it is impoossible to get to absolute zero or to the point where the energy of everything has completely scattered so it is all at the minimum value. (It can approach the value, it cannot reach it.)

References

Coram, Robert, Boyd: The Fighter Pilot Who Changed the Art of War, Back Bay Books, New York, NY, 2002

Revision: 20130926
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