Technicalities: Speaking of Jets

Whether jets can exceed their exhaust velocity.

Certain universal questions pop up over and over, like “Why is there something, when there could be nothing?” or “Can a jet fly faster than its own exhaust velocity?” Let’s look at the second one; I’ll get back to the first in a future column.

Reciprocating engines inhale about 15 pounds of air for every pound of fuel they burn. This is the so-called “stoichiometric ratio” — the ratio at which every oxygen molecule in the air gets combined with a hydrocarbon molecule in the fuel, leaving no unconsumed oxygen or fuel at the end. Chemically combining the oxygen and fuel releases energy in the form of heat — which makes the engine go — as well as, in the ideal case, just carbon dioxide and water.

The hot gas produced in an internal-combustion engine is called its “working fluid.” (The word fluid applies to gases as well as liquids.) Since atmospheric air is only about one-fifth oxygen, the bulk of the working fluid is just miscellaneous gases, mostly nitrogen, that have been heated and expanded by the combustion of the fuel. In a reciprocating engine, the heat-induced expansion of the working fluid moves the pistons, which move the crankshaft, and so on. In a jet, expansion increases the velocity of the exhaust stream. The acceleration of its working fluid is the source of the thrust of a jet engine.

Jet engines run on a much leaner mixture than recips do — three times leaner, in fact, the air-fuel ratio in a turbojet or turbofan being typically on the order of 50:1. Spreading the heat of combustion through a greater mass of air lowers the overall temperature to a point that the internal components of the engine can support. Since a 50:1 mixture will not ignite, the burners are designed to mix the fuel with just a portion of the air at first, and add the rest of the air only once the fuel is burning.

Now, as for whether the jet can go faster than its own exhaust, this is one of those puzzlers that sound more complicated than they really are. Deep thoughts about inertial frames of reference, or about how the air slows down and speeds up inside the engine and how its pressure changes as the engine processes it, just complicate the matter unnecessarily. The basic principle is straightforward. The mass of the working fluid remains essentially unchanged between when the engine sucks it in and when it spits it out. True, it is very slightly increased by the addition of fuel; but fuel is only around 2 percent of the exhaust mass, and so for all practical purposes, the same mass leaves the tailpipe as entered the inlet. Only its velocity changes. Since the thrust of the engine results from nothing other than the acceleration of the working fluid, a jet airplane can not exceed its own exhaust velocity. If it did, the engine’s inlet velocity would be greater than its outlet velocity, no acceleration of the working fluid would have taken place, and there would be no thrust.

The same is not true of a rocket. A rocket carries its working fluid with it. At any given instant, both the fuel and the oxidizer of a rocket are already moving at the speed of the rocket; speed added to them by combustion is all profit — pure thrust.

The inability to exceed their own exhaust velocity is not a severe constraint upon jets. The exhaust velocity of a subsonic or transonic jet engine is limited by nozzle shape to the speed of sound, but since the temperature in the exhaust is extremely high — say, 1,500 degrees Fahrenheit — the speed of sound there is much higher than it would be at the ambient temperature. The exhaust velocity therefore exceeds the flight speed by a wide margin, and ample thrust is available up to and beyond the speed of sound in air.

In the interest of forestalling needless letters to the editor, let me add that the foregoing applies to a turbojet, not to a turbofan. A turbofan engine is a hybrid combining a turbojet core with a ducted propeller, and only the core operates by adding heat to its working fluid. Since the thrust contribution of the fan is produced aerodynamically, the general principle that I have described does not apply. But no matter — the duct and fan are even less able to approach the exhaust velocity of the core engine than a pure turbojet is.

And now for a sudden sidestep. The subject of jet engines has been on my mind lately because of the project of Austin Meyer, the creator of the remarkable, and at $29.95 remarkably inexpensive, flight simulation program X-Plane. Meyer wants to build a four-seat jet for his own use, with an eye to eventually producing it in the form of a kit for homebuilders.

This project got its start in a misunderstanding. Seeing the published specific fuel consumption of the Williams FJ-33 engine, about .49 pounds of fuel per hour per pound of thrust, Meyers — who until recently owned two Cessna Columbia 400s himself and, quite irrelevantly, is Dick Collins’ cousin — very naturally concluded that a jet of the general size and weight of a Lancair IV-P or the Columbia could rival a recip’s fuel consumption while far surpassing its speed. Unfortunately, the .49 figure applies only to an engine running at full power while standing still at sea level. In cruise, the sfc, or specific fuel consumption, is much higher, and best-economy fuel flows — I’m guessing here, since Williams does not reveal performance tables — are going to be in the 200- to 250-pound-per-hour range.

Requesting more information about the FJ-33 from Williams, Meyer learned that it would not sell an engine, or even provide information about its performance, to anyone but an established airframe manufacturer. (Its reticence may be due to its having suffered a public-relations mauling by Eclipse as the weight of the latter’s Very Light Jet outran the capabilities of the tiny Williams FJ-22 engine.) Meyer then turned to Pratt & Whitney, as Eclipse had; the 900-pound-thrust 610F used in the Cessna Mustang and Phenom 100 is actually more suitable for a very basic single-engine four-seater than the slightly larger and considerably more powerful FJ-33. Pratt & Whitney’s response seemed a little friendlier, but the availability of suitable state-of-the-art engines for use in homebuilts remains problematic.

Nonetheless, discussing this with Meyer got me thinking about how I would design a four-seat jet for amateur builders. The packaging is tricky. A conventionally configured recip’s combination of short, heavy nose and long, light tail makes for an airplane that is naturally balanced and aerodynamically stable. But a single jet engine has to be behind the cabin, and air has to get to it without a lot of tortuous ducting. The engine has to be reasonably accessible, and its exhaust can’t blast the empennage. Meyer’s own first sketch looked like an Eclipse 400, with a V tail and a single engine on a pylon above the aft fuselage. Unlike the designers of airliners and business jets, however, designers of single-engine personal jets have not yet reached consensus. A quick survey of existing and proposed single-engine jets (most of which have more than four seats) finds engines that are buried, semi-buried or propped up on pylons, with intakes direct, single or bifurcated. Since the engine tends to sit so far aft, the CG creeps back and the tail surfaces grow in order to preserve stability.

Noodling over design ideas is a contagious disease. My friend Hans Kandlbauer, who flies for Swiss International Air Lines and teaches aerodynamics in Zurich, caught it and came up with an Avanti-like three-surface arrangement. We both put the engine inside the fuselage; I used an S-duct with a single overhead intake, and he favored intakes at 10 and 2 o’clock, like those of the VisionAire Vantage. But it may well be that, as a practical matter, putting the engine in a nacelle up on the roof really is the best compromise. Perhaps those endplate fins beloved of Lockheed in the olden days could find a new home on a jet, requiring an overhaul of our aesthetic preconceptions about fast airplanes.

These imaginary airplanes have dimensions similar to those of four-seat single-engine recips: 36-foot span, a fuselage length of about 26 feet and a wing area of about 145 square feet. A pressurized recip that size would weigh less than 4,000 pounds. A jet is heavier, largely because of its greater fuel requirement; 4,500 pounds may be optimistic.

Meyer, who has announced the project on his X-Plane website (x-plane.com/x1/x1.html), will fly various designs in his program, which gives a very persuasive illusion of flying the actual airplane and is an excellent tool for initial assessments of stability and performance. He is designing a new avionics interface, by the way, since he considers that of his Garmins insufficiently intuitive. No doubt advice will come pouring in from many sources, some even less qualified than I am. Perhaps the end result, if the age of miracles has not yet passed, will be a technological first: a Wikiplane.


New to Flying?


Already have an account?