The regs requirements are pretty explicit in all states. The 4 engine aircraft comes closest to the end of the runway under all normal operations due to the factoring used. Having said that, it is pretty much self evident but usually glossed over, that the aircraft needs to be able to meet at least the engine out case screening height to have been anywhere near meeting the certification requirements. So... getting to OEI screen height at the end of the smooth stuff, before the ruff is probably a nice thing to achieve. Does the plane do that? As an industry and as professionals, we have for years come back from a takeoff where everything went right, and we barely have made the OEI screen heights, if indeed they were made. This isn't just the old wet takeoff cases which were always entertaining. Have a look at a certain B744 pax aircraft taking off out of SFO many years back, where coincidentally the flight crew were berated for the engine out path they flew. Given that the aircraft wasn't near its marks anyway, it seems somewhat callous to beef about the crew barely missing the hill. There was the B742F out of Brussels National which also beat up the crew for their abort. The data of course shows that the point where the aircraft was supposed to get to V1 was so far down the runway that they were not likely to go flying that day, barely with all 4 engines going. Cathays B742F photo taking off out of Kai Tak is interesting, they are below the OEI screen height, but on 4 engines (look at the rudder and aileron... no input, no yaw/roll... ergo, no failure). The A340 is in a league of it's own, it has been seen disappearing over the roadway on the north side of CLK off runway right with no more than the gear height clearance from the top of busses on the causeway. The latest images of the A340-600 takeoff out of SAM is entertaining, crew clothes change sort of territory.
Are these from being overweight? A simple check is whether the aircraft after a takeoff performance failure gets to planned destination, if they dont they may well have been heavier than planned. IF they do, then perhaps the environmental conditions are not quite as advertised. At high temps, the performance drop off becomes pretty impressive with just minor temperature changes. The reported temperature is not that temp that the aircraft engines and airframe are immersed in on the runway, yet there is no correction for that, it is assumed to not alter the outcome. The original testing should have mitigated that change, where the testing was done in similar conditions to what the real world experiences, but, if that was the case, then you would not get the wild rides that occur where there is no change in wind on the roll.
2 engine planes are much nicer, if you get a wild takeoff on a normal takeoff, then be assured you probably didn't want to meet a bird on that roll. The 4 engine case is just more obvious to the pilots, but we as a group have failed to stand up for the punters and get the performance right. Many of the takeoffs that end with some excitement involve errors by the crews, such as the Halifax B742F, which was unusual, there was a latent risk factor in the process. The IL76 CBR departure was just wrong all round.
But..
hotshots,
When you roll your quadrapuffs down the runway, some simple figures should come to mind. Simple stuff, but beyond the Ken of many management pilots, regulators and some safety boards...
An engine out aircraft has a minimum screen height of 35' using dry values. Yes, 15' is applied if you use a reduced V1, as the reject case is protected at the cost of the go case screen height case, but energy is energy, if you get to normal dry V1 and can only achieve 15' screen height, don't think that things were rosy.
The minimum distance for all engines is limited in part to being 115% of the OEI case... that is not limiting for the 2 or 3 engine aircraft but sure as heck makes the 4 engine normal case interesting. Restating that case, you can argue directly that a 4 engine aircraft should achieve a minimum of the 35' case at 1/1.15= 87% of the TODA. That means that 13% of the TODA distance as a bare minimum has to be available logically to climb higher than the 35' height. This is pretty basic, disregarding the fact that the screen height of 35' is required to be achieved on 3 engines, with a continued acceleration from a minimum speed of V1-1 second, though to Vr, and then targeting V2 for the screen height point. Big planes have big speeds; a rotate is over 160Kts, say, 170+, which is... 85msec approx. Once you get to rotate, it takes a finite period of time for the attitude to change, and then you get enough CL to get the V'2*ro to give enouff lift on the total S you have to make magic happen. How long? look at the FCTM, FCOM, or time it in a sim some day, or look out at other planes, or read your QAR data before it is needed from a DFDR. Plan on 6 seconds to break ground from the first movement of the elevators. You have target rates, but that is an "S" bend to achieve, it takes some time, and that is some distance, 6 seconds +/- x speed. Speed then is Vr+ a bit, you are pulling towards holding V2, which is usually a few knots higher, say +8-10 on Vr. For smaller aircraft, there are minimum fractions that will come into play but then you tend to avoid the end fence by more on most takeoffs. Once the wheels are off the pavement, for the normal case, you will develop a rate of climb which will stabilise as the aircraft stabilises on the target speed. That is pretty simple to determine. Call that 1800FPM for stamps, which is 30ft/sec ROC. So, from 35' at 87% of the way down the runway, the plane will continue to climb at about 30FPS for the additional time it has to cross the end of the TODA, which is 13% of the total TODA. Your speed for that climb is V2-V2+10 for big toys, a bit more for smaller jets. For the big guys, that gives you... about... 180+kts (less your HWC of course, but 0WC is the limiting case) or just on 92msec.
For a 12000' runway, you have about 5.14 seconds from 87% of the TODA at 35' to climb higher... which is another 154'. Be kind, drop that a little, and call it 150'. Add the 35' and you have 185' That is around about a large fraction of the length of the aircraft above the ground when you get to the end of the TODA and out over the rough. It is a lot more than 35'. A heck of a lot more. It is not "exciting", "sporty", "thrilling" or any other adjective indicating a near run thing.
If you barely got airborne on 4 engines, it is fairly certain you don't want to try it again on 3 from V1-1second in the same conditions. To that end, and given the amount of interest that the regulators, safety bureaus and manufacturers have in sorting out performance, one should be careful in having wind that is not as advertised, temps that exceed the targets, or wasting runway on lineups etc. Yes, JAR/EU ops does a better job of runway allowance, but when seat 1A looks out the window from a parked position prior to roll that is down range of the 1000' markers, on a limit takeoff, then frugality is in order. If you consider that the "margins" are there for your protection, sit down and do the maths form the last limit case takeoff that you did and see what you come up with.
While you are at it, consider the statement that exists in the AFM on thrust setting, next time you consider margins. The OEM's AFM approved by the state of manufacture states what a a static, standing and rolling takeoff is. It then states that the difference between standing and rolling is negligible, (great). What it doesn't state is what the difference is between static and standing, yet it does state that the takeoff performance is predicated on static method. Oddly, not all engines can do a static thrust setting, you get surges. Remember that the original figures used for the charts (bless them all) are based on measured performance from a point where power is set, and then calculated for the earlier bit to give a total solution. (That was a procedure, it may have been changed, data is better recorded today). Be careful out there. A pretty good group of operators sorted out performance on one jet a number of years ago, it appears no one is around anymore that really cares that much about the continuing issues. The great news is that engine failures at V1 don't happen every day, and when they do, they don't happen on limiting cases too often. That is a wonderful thing, but then there was the available data of the Brussels B742 where the aircraft was already in peril before the engine quit. Blame the pilot, everyone else does. Chuck Yeager wasn't going to get that plane off the ground in one piece, but who cares at the end of the day. Unless it is your aircraft that you are in.
When you watch the next heavy jet departures off a limiting day of operations, stand in line with the TODA (OK, fence) and watch the height above ground. Have a look and determine what you have for your own confidence. If you have the time, say, survey 8 to 10 takeoffs out of one location in limit cases, and determine if they all are well above the OEI screen height, as above. If not, then you may have some further digging to do. If all of them fail to get to 35'. you might want to do something courageous, like do your job as it is entrusted to you. If some of them barely get off the concrete, then some thought should be applied to the inherent risk of the operation. Oddly, most companies and regulators have takeoff performance failure as a mandatory reporting event. For you 4 holer drivers, how often have you had a failure to get above 35' (without an engine failure) and not reported it?
Performance failures occur for benign reasons, they also can occur because there are issues. The data sorts out which is which.