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June 25, 2015

Four Engines vs. Two: The Surprising Mathematical Guarantee of Safety

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Written by: David J. Williams
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Jesse Pinkman may never have understood clearly the exact science behind his craft, but he learned to trust it and respect it as a way to improve his product. The science of the production and operation of the modern airliner is extensive and far reaching, with limited understanding by the public and even many aviation personnel. However, there is a basic principle in the hotrod community that applies equally to aviation – put a big enough engine on it, and it will fly.

As discussed in a previous article, an air crew must be able to guarantee that the airliner will be able to either stop on the runway, or safely continue the takeoff even after the failure of one of the engines. Though the plane may have lost half of the power (if it has only 2 engines, for example), it can still safely climb out on the remaining engine(s) after exceeding the “decision speed” (typically around 150mph), and continuing to accelerate to 175 mph and climb out.

The current fleet of airliners in the United States is dominated with products from Boeing, Airbus, Embraer, Bombardier and Douglas. Though the design, design philosophy and personal opinions vary widely, the general performance is all highly similar. The cruise speeds, minimum flying speeds (stall speed), cabin pressurization ratios and flight control metrics only vary by small margins, regardless of aircraft type or size.

One widely different area is takeoff and climb performance, which is the measurement of feet climbed per mile. When operated at or near the maximum weight, the climb performance of the 50-seat Canadair CRJ will be similar to that of the 450-seat Boeing 777. Though the maximum takeoff weight of the 777 is a massive 775,000 pounds, its engines put out a combined thrust of 230,000 pounds, or a 1 to 3.3 thrust-to-weight ratio. The difference is evident when each of these aircraft are operated with light loads (small amount or removal of passengers, bags, cargo and fuel). Lightly loaded, the CRJ’s thrust-to-weight ratio is 1 to 2.4, while the Boeing 777’s is an astounding 1 to 1.7. This affords the 777 a very short takeoff distance with a steep climb-out gradient.

Recently there was a video (below) that went viral with a Boeing 787 in Vietnam Airlines livery, showing the aircraft rotating to a near-vertical climb after takeoff. Mathematically this isn’t possible since it would require approximately a 1 to 1 thrust-to-weight ratio. A vertical (or even very steep) climb would therefore result in fast decreasing speed and the eventual stall of the aircraft. However, a lightly loaded 787 does have a ratio of around 1 to 2.1, allowing a much steeper than normal climb gradient. The pilots also momentarily climbed at a steeper angle than normal, surely lost some speed, then pushed the nose down after gaining just a couple hundred feet of altitude, and then resumed accelerating. This is safe, but if done in revenue operations, the steep climb gradient would scare the passengers, followed by a low-G sudden nose-down pitch. However, the steep climb combined with the clever camera angle, gave the illusion of a near-vertical climb.

Comparison of 3 aircraft when heavily loaded.

Comparison of 3 aircraft when heavily loaded.

One would think that an aircraft with additional engines would provide even better performance on normal takeoffs, but the extra engines actually reduces it! Airliners are designed to be able to adequately climb with the failure of one engine. In addition, FAA regulations require that three- and four-engine airliners must be able to meet slightly steeper climb gradients with the loss of an engine on takeoff compared to the twin-engine airliners.

Comparison of 3 aircraft when lightly loaded.

Comparison of 3 aircraft when lightly loaded.

Let’s take a look at the basic math. Certain models of the McDonnell MD-11 (three engines), the Boeing 747 (four engines), and the Boeing 767 (two engines) were all equipped with General Electric’s CF6 engines. With an engine failure, each of these widebodies will climb out on a similar angle, with a slightly steeper climb angle for the three and four engine models (as required by the regulation). However, with all engines running, the Boeing 767 will climb the steepest. That is because the two-engine 767 on a normal takeoff has twice as much power as required, while the MD-11 has one half as much more while the 747 only gains a third more power with all engines running. As you can see from the table to the right, mathematically a 747 will be able to out climb an MD-11 and B-767 with the loss of one engine. However, the B-767 will out-climb the MD-11 and B-747 with all engines running.

This can be seen by watching the departures of the heavily laden intercontinental widebodies on departure. The twin-engine models will have a climb angle similar to the lighter, narrowbody domestic airliners and regional jets, while the four-engine Boeing 747s, Airbus A340s and A380s will have a shallower climb angle and longer takeoff roll.

Watching the four engine leviathans depart for destinations on the other side of the planet gives the impression that they are dangerously low and slow. In fact, like other airliners they are accelerating through 200 mph, and although the climb angle isn’t as dramatic as the more common twin-engine airliners, it is adequate, even if one of the engines were to fail.

The Boeing pilots at the controls of the Boeing 787 were given a machine with incredible performance. They took it to the safe limits without fear of startling the passengers. Combined with a strategically placed camera, the result was a terrific piece of marketing with the illusion of what could not be.

fbd

David J. Williams is a former airline captain and currently involved with aviation safety.



About the Author

David J. Williams
David Williams, an aviation safety expert and aviation historian, living in New York City.




 
 

 

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  • speedbird1

    Always thought that 4 engines were safer; who would suspect?

    • Neither is more or less safe than the other. They just perform differently.

  • Frederick Miller

    The more engines you have on and airframe equals more potential for failure, if you have four engines that have a reliability factor of let’s say one in every 10 years, a two engine airplane will have twice the reliability as it only has half the potential of failure. You would think a four engine aircraft would be safer but in terms of engine loss, it is twice as likely of a 747 engine failure than a 767 with like engines. (I do realize the 747 and 767 do not have the same engines and was only using it for a comparison)

    • xtmar

      On a four engine plane, you’re more likely to have an engine fail, but also less likely to reach a critical failure, because you have more redundancies.

      Historically, the Constellation was revered/mocked as the most reliable three engined plane, because it could still fly decently with three engines and continue the flight (as can a 747, and indeed BA flew a few years ago from LAX to LHR with three engines after one of them failed shortly after takeoff), whereas the loss of an engine in a single or twin engine aircraft causes an immediate flight abort.

    • Doug

      On the contrary, the 747 and 767 often do have the same engines and they are interchangeable with minor modifications. Our GE powered 747s and 767s shared engines although the new engines would go on the 767 as a general rule.

  • Thomas Jones

    I’ve really tried to care, but to be honest, I don’t. After reading the article and deeply searching all my internals I still don’t give two hoots in heck about a airplane with one, two or ninety-nine motors. I just plane don’t care.

  • So if you have two engine failures on two engine aircraft and a four engine aircraft, which aircraft is safer to fly and be on?