The BBC reports on a Boeing 777 that crash-landed at Heathrow Airport on January 17. Crash investigators have found that the 777's engines were still running, but failed to respond when the pilot tried to throttle up two miles out and at 600 feet altitude. The aircraft was not low on fuel. Six previous engine failures have been reported in 777s since the type debuted in 1995; not a high rate, but high enough that they're beginning an intensive analysis of the entire fuel system.
Here's the handy diagram from the article (vertical scale is exaggerated in the diagram):

So, why does this mean the 3° approach is unsafe? For that matter, why is a 3° approach the "standard" airline approach?
Well, basically, it comes down to this: Airlines fly a 3° approach because a steeper descent may make the passengers feel uneasy. But there's a problem: the 3° approach is below the glide path. It takes power all the way in to maintain the correct descent rate. Lose power on final — like this 777 did — and you have a serious, often fatal, problem.
Military pilots fly a 9° approach. Nine degrees vs. three isn't really that much steeper. But there's a crucial difference: On a 9° approach, you're on the dead-stick glide path. That means you're not using power to control your sink rate, you're gliding with the throttles at idle. You can lose an engine, or all engines, on final and scarcely care, because you can still glide all the way to landing with no power.
But a 9° approach "may upset the passengers", or so say the airlines.
I don't know about you, but if I were an uninformed airline passenger and was given the choice of a safer, steeper approach, or a shallower approach that might be a little more comfortable but risks crashing if the aircraft loses power on final approach, I know which I'd pick.
A hearty "Job well done" goes to British Airways Senior First Officer John Coward, by the way. Despite losing engine power less than a minute before landing, he put the bird down without a single serious casualty among the 136 passengers and 16 crew. (One passenger broke a leg while evacuating the aircraft after the crash-landing.) They say any landing you walk away from is a good one, and 151 people out of 152 walked away from that one.
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(bad typo. no donut.)
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I do wish they'd talk more about how the pilot managed to keep that tube upright on no power as it plowed across a field. Freaking amazing, is what it is.
And also perhaps talk about why the plane "suddenly had no power". My personal guess is "software", but perhaps that's a sausage-factory-worker problem.
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It was obvious that the passenger next to me--a young woman in her late teens or early twenties--was seriously panicked. "OMG what's happening?" So I explained it to her, that there was probably something or someone on the runway and that it wasn't safe to land, and that this is standard procedure when that happens and every pilot knows how to do it safely. Sure enough the captain comes on, "Uh, ladies and gentlemen, apologies for the discomfort there and for the delay in landing...the aircraft in front of us hadn't cleared the runway."
It doesn't take much to panic the passengers.
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With a 3 degree path the engines are already mostly spooled up. There's a lag time while the turbines increase in power (like turbo lag in a car). With a 9 degree path the engines would either have to be at a lower power setting, or the drag elements (flaps, speed brakes) would have to be redesigned to provide more drag.
Also, the descent has to be arrested to near zero in a normal landing, so the 3x descent rate of the 9 degree path would result in either 3x the G forces in the flare or a longer duration flare, started higher above the ground.
I guess we'd have to consider the number of total power failures per year versus the number of go-arounds and normal landings to really see the total impact.
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The airspeed required on the final segment of an instrument approach is determined by multiplying the aircraft's stall speed by some constant factor, usually 1.3. For most heavy transport-category aircraft this is about 150 knots. If you are maintaining 150 knots on a three-degree approach, your descent rate is about 750 ft/min (relatively healthy). On a nine-degree approach, it'd be a rather brisk 2,250 ft/min. Now, a Category I (the lowest precision) ILS requires visual contact with the runway environment by 200 feet above ground level. On a three-degree approach, you have about 12 seconds to impact; plenty of time to spool up the engines, clean up the airplane by retracting the flaps and landing gear, and execute the missed approach. On a nine-degree approach, you're down to 4 seconds.... You now also have to figure out how to arrest a significant descent rate in the landing flare itself, or when encountering downbursts or wind shear, when the cards are already stacked against you.
Okay, having said all that, two other observations.
1. Twin-engine transport-category aircraft are permitted to fly up to 120-180 minutes (depending on type of aircraft and operating procedures) from land during over-water flights.
2. A nine-degree approach does not guarantee that you will arrive on the runway in the event of simultaneous engine failure: the winds aloft will make a tremendous difference in the aircraft's position over the ground.