B747-200: Vref, V2 and Vmcg
 

I quote from one of my books:

"Vref is included on the takeoff data card as a reference for computing enroute climb speeds. Vref varies directly with gross weight and simplifies the additives for climb speeds while V2 is influenced by Vmcg at low gross weights and would require a wider range of additives for the various speeds."

Can someone please explain how "V2 is influenced by Vmcg at low gross weights and would require a wider range of additives for the various speeds".

Thanks.

At light weights the 747 will have the V speeds below Vmcg & Vmca, so we use a minimum set of figures regardless of the weight.

Without knowing the source of your information, it is difficult to know just where the author is coming from. Possibly the text meant to say Vmca rather than Vmcg and is just a typo. Alternatively, Vmcg-limited V1 could lead to a similar incidental effect on V2 at low weights.


However, it is useful to review the generic story from time to time as there are some traps here for young players which can bite hard and Mutt and I like to run it past the new people in the forum every now and again.

If I may talk twins, which is what I normally play with (only the factors change .. not the basic story).......

V2 normally is scheduled as the minimum permissible V2 to keep the takeoff distances down.

The certification rules require, for the configuration, that minV2 (or V2min - take your pick) be not less than

(a) 1.2 x Vs for the weight

(b) 1.1 x Vmca

Typically, for any aircraft,

(a) at lower weights, the Vmca requirement will become limiting. By this one means that 1.1Vmca is greater than 1.2Vs. In this region, V2 doesn't vary with weight.

If Vmca is very low, this effect may not be seen .. the Citation, if I recall correctly, is an example. However, I would be very surprised if a wing-mounted four-motored bird did not exhibit the effect.

(b) as the weight increases Vs increases and, at some point, 1.2Vs increases above 1.1Vmca ..... now V2 increases as weight increases.

To check this out, have a look at your standard speed schedule with weight. At low weights, V2 is constant and doesn't vary with weight .. you are Vmca-limited. As the weight increases, you get to a point where V2 starts to increase as weight increases.... you are stall-limited.

A consideration which often is overlooked in training is that the handling problems with a failure, say, halfway through the rotation flare are VERY critical if V2 is Vmca-limited and, depending on Type yaw-roll coupling characteristics, you might need a lapful of wheel rotation to control bank ... Vmca is very bank-dependent ... if you don't control bank, Vmca increases rapidly due to slip ... and you SUDDENLY find yourself in the middle of a Vmca departure ... crash, burn, die. Well worth investigating this in the sim ... just a confidence and co-ordination training exercise ... but to experience it in the aircraft for the first time is not a good thing. Those who haven't played with it might be non-believers ... those who have will smile knowingly ....

As we back up a little on the takeoff, VR is relevant. In essence, VR is a convenient speed chosen so that the OEI rotation will result in somewhere near V2 at screen height. VR will sit somewhere between V1 and V2.

Backing up further, we have to concern ourselves with V1. V1 is limited on the high side by VR and on the low side by Vmcg.

If Vmg is sufficiently high, then minV1 may be high enough at low weights to require that VR be increased which, in turn, might require that V2 be increased. (This may be what the original text was referring to).

If the aircraft is typical ..., in the same way that the speed schedule shows a constant Vmca-limited V2 at low weights, there will be a constant Vmcg-limited V1 at low weights. So, even if Vmca were not going to be a problem, in the scenario described in the previous paragraph, we could see the Vmcg-limited V1 imposing an incidental non-weight-related limitation on V2 at low weights.

As with Vmca-limited V2, there is a trap associated with Vmcg-limited V1 takeoffs.

For the US case, certification Vmcg is determined for NIL WIND. However real world actual Vmcg is highly crosswind dependent. Typically, the effect of crosswind might be to increase the real world Vmcg by half the crosswind for a twin, to more than the entire crosswind for a four-motored bird. So, if you are scheduling a Vmcg-limited V1 takeoff in a strong crosswind ... then you may be between a rock and a hard place.

If the speeds are limited severely by runway distances, then I guess you are stuck with it .. either you go and risk losing the aircraft with a critical failure (and, again, if you have a good sim model, the sim exercise is useful training to hammer this point home), or you delay until the wind abates.

If you are just doing a ferry flight, say, and you have a long runway, do consider increasing the speed schedules in accordance with the OM tables, to a point where the actual V1 is increased sufficiently above Vmcg-limited V1 to take account of the real world increase in Vmcg due to the actual crosswind. So long as you stick with a published speed schedule appropriate to a weight not greater than the RTOW for the runway, then you shouldn't have a problem. Certainly, if you are scheduling a Vmcg-limited V1 with an aft CG, in a strong crosswind, and you lose the upwind engine at or near to V1, then you WILL be in for an interesting ride, especially if there is much in the way of a V1 to VR split scheduled for the takeoff.

One should keep in mind that real world (as opposed to certification) Vmcg and Vmca are very CG dependent.

Just to add a minor detail to the very detailed post bu John T. above.

If the low speed V2 is being constrained by Vmca then it should be as near perfectly constant as your charts will permit, because it is being directly limited by 1.1Vmca.

if you are, instead, Vmcg limited at light weight then you should have the unexpected effect of decreasing V2 with increasing weight. This is because it is V1 which is being constrained by the Vmcg limit, and the V1-V2 difference or "speed spread" will actually be greater at lighter weights, due to the increased acceleration at those lighter weights.

As an aside, I've seen charts where V2 at min TOW was actually higher than at max TOW. That is most decidedly NOT a good thing, but it's theoretically possible if you follow the regs.

So if you look at your V2 data in detail you may e able to determine whether you are Vmca or Vmcg limited at light weight.

MFS,

Just to clear my mind on a couple of things ...


(a) if you are, instead, Vmcg limited at light weight then you should have the unexpected effect of decreasing V2 with increasing weight

I presume that you are referring to the achieved speed being above book speed here. If you mean otherwise, perhaps you could amplify the point ?


(b) I've seen charts where V2 at min TOW was actually higher than at max TOW

I've not come across this ... again, perhaps you could amplify the point ? I presume that you are referring to scheduled V2 here ?

You guys seem pretty knowledgeable on performance. Would you have a go at explaining balanced field length theory for me?

The minimum field length where an engine failure was assumed to occur at a speed such that the distance to continue the takeoff and climb to a stipulated height was equal to the distance required to stop

But somehow i guess that you knew that already, so whats the catch???

Mutt

V2 Scheduling
 

JT

I was referring to the AFM speeds. Perhaps an example would be the best way.

Assume an aircraft with TOW from 40,000lbs to 80,000lbs.
Vmca of 90kts
Vmcg of 90 kts
Vs from 80kts at 40,000lbs to 94kts at 80,000lbs.
Vmu sufficiently far below Vs that we can ignore it.

Then the 1.2Vs lower limit to V2 will be 96kts at 40,000lbs and 113kts at MTOW.

Looking at the Vmc-driven limits, the Vmca limit will be 1.1*90kts=99kts. If this were the only limit we would have a constant V2 of 99kts from 40,000lbs up to 61,000lbs or so, then increasing with stall speed up to 113kts at 80,000lbs.

But, the V1mcg limit must also be considered. Since V1 may not be less than Vef which may not be less than Vmcg (and in fact one must also add the acceleration for recognition time too), for the case shown we may have a V1 of not less than 90kts (and probably a little more, let us assume 2kts of accel, giving a V1mcg of 92kts). FAR25.107(a)

FAR25.107(e)91)(i) states that VR may not be less than V1 - assume a V1=Vr schedule.

FAR25.107(c)(2) then states that V2 may not be lower than VR "plus the speed increment attained before reaching a height of 35ft...".
We refer to this increment (at Canadair at least) as the "speed spread" and since the aircraft is often constrained by pitch rate considerations there is a finite time required. At lighter weights this means that the higher T/W accelerates the aircraft more than at heavier weights, and so the "speed spread" is greater at light weights.
One might have a situation where the speed spread was as much as 10kts, say, at the lightest weight, dropping more or less proportionally with weight.
For the numbers used here that would give a V2 at 40,000lbs of 102kts due to Vmcg limits, dropping to 97kts at MTOW say.

The combined effect of all those limits might be (apologies, I'd love to insert a sketch here, but...)

40,000lbs : V2=102kts (V1mcg limit)
45,000lbs : V2=100kts (V1mcg limit)
50,000lbs : V2=99kts (V1mcg and 1.1Vmca limits coincident)
60,000lbs : V2=99kts (1.1 Vmca limit)
61,000lbs and above : 1.2 Vs limit (from 99 to 136kts)


I haven't double checked those numbers, I will do so later - it's Saturday night!

Regarding the V2 at min being higher than at max. Yes, it was the scheduled speed - it was a consequence of unreasonably high Vmc's (both 'a' and 'g'). But it would have been very hard to respect the procedures and not get those speeds in practice. (It would also have been very bizarre)

MFS,

Thanks for that, mate ... I am now briefed ... the tale was pretty much as I had presumed. I have a Challenger AFM tucked away somewhere ... and will have a looksee when I get a few minutes to spare to dig it out of archives.

Interestingly, with a min weight takeoff's typically 15 kt V2 overrun for the 732 for instance, most people still take a bit of repetitive practice to get on top of the Vmca departure problem as the bird corkscrews itself around the runway ... sometimes I wish I could mount a video on the coaming to record the looks of horror and shock on the pilot's face during the first couple of runs ... as the aircraft rolls through the vertical .. which is about where I normally freeze the box. Seriously, though, I think that this exercise is greatly underrated and that far too many pilots never get to experience, and get on top of, the extremely critical handling of a min weight/min speed takeoff failure.

On another tack .. it is probably useful to put a little bit of explanation to any statements which are out of the ordinary for the interest of those readers who don't have the specific tech background.

I guess if you join up with Mutt and me in the sandpit ... we can style ourselves as the Three Muttsketeers ? ... ah well, I thought it was funny ...


.. anyway, Seasons Greetings to the Canadian engineering fraternity ....

we can style ourselves as the Three Muttsketeers

groan................................. :):)


Mutt.

Now I really know why several bods were upgraded to Business Class in a lightly loaded 732 until the seatbelt sign came off;)

Many thanks to the 3Ms and a happy holiday.

....Mutt, mate ... it wasn't THAT bad .....

mutt it isn't a trick question (blanced field length) just looking for a better way to explain the benefits of using it to some newbies.
Go on, indulge me.:)

JT

I shall try to be less obscure in future - although its hard to know where explanations of egg-sucking technique begin sometimes - it's easy to forget how obscure some stuff is when it's your bread and butter.

I must be hungry, that's two allusions to food in one paragraph!

I don't think you'll see too much in a Challenger AFM - I think the Vmc's are sufficiently low there that they don't affect v2 (although that's from memory, and I don't really 'know' the Challenger). it does affect some of our larger aircraft though, for sure.

Best wishes to you too for the hols - I'm sure you'll enjoy things in moderation of course.....:) groan :)

MFS, mate ... you, Mutt and I just HAVE to have a Guinness session ... the puns will fly thick and furious .....

My concern with amplification is that many of the PPRuNe fraternity use tech log as a resource ... what the specialists (in any field) take as a lemma, others might find totally confusing without some explanation to fill in the holes .... I know that I have learnt a great deal from several of the forums over the time that I have been a sandpit player .... and it is terribly frustrating if you only get half of the story ...

MaxAlt,

BFL gives a cheap and dirty quick way to get the RTOW figures done ... and, for convenience, is often referred to in documentation. By using BFL, you don't have to run as many calculations to figure the runway limit weight. It has no inherent technical advantage (Mutt might disagree as his mob use it for other reasons) other than general use and increased simplicity. On many, if not all occasions, a BFL-limited RTOW results in a slightly less than maximum RTOW for the runway and conditions on the day .... with wet or contaminated runways, or with obstacles and clearway, often the commercial needs dictate the use of an unbalanced takeoff.

Also, for many runways, the numbers may not be so critical as to warrant the additional number crunching to allow for the actual TODA, TORA, and ASDA figures.

Thanks JT, that helps a lot.

The scant info contained in some very old company documentation gave simply the following statement:

On thinking about this definition I believe it's wrong, and it leaves a lot to be explained anyhow. Do you agree with the statement?

J_T,

From an operational point of view, we dont have the time nor expertise to do AFM graph calculations prior to takeoff. We therefore use Balance Field Limits on Boeing aircraft with published weights and QRH speeds/FMC speeds, corrections for runway contamination, MEL/CDLs etc are then applied to these speeds.

On the A300 we use optimized v-speeds, while these can offer better weights, however its fun trying to explain why you get a 30 kt V1 increase for a 3,000 kgs weight increase.

Maxalt,

Balanced field length is the ideal situation where the maximum takeoff weight is possible for a given runway length.

This means that the aircraft can accelerate to Vef, suffer an engine failure and continue the takeoff reaching 35 feet by the end of the runway, or the aircraft can transition into a stopping configuration and stop by the end of the runway.

Unbalanced field length may also result from runway slope and wind corrections, and the use of clearways and stopways.

By definition a clearway doesn't have to support the weight of the aircraft, therefore if you are allowing the accelerate go portion of your takeoff to be over the clearway, you are left with an unbalanced situation. I would therefore say that the statement which you were given is incorrect.

Mutt.

The statements in italics are taken directly from Boeing documentation, which i can send to you if required.

I have to concur with Mutt, the statement to which maxalt refers misses some important points of the runway limited takeoff calculation -

(a) most runways don't have much in the way of clearway declared and, in any case, even if a lot of clearway is declared, a takeoff for a particular Type is limited in the amount of clearway which can be used due to TORR considerations - recall that at least half (US rules) the airborne distance to screen has to be over the TORA, which is normally threshold to threshold... not much point running off the end of the hard bit before getting airborne ...

(b) BFL is a simplified approach to the sums, mainly of use for typically level-ish runways without any clearway declared or where a quick, manually-derived, answer is needed and we are prepared to forgo any benefit to be derived by considering the small margin of TODA over TORA. Consider that many flight manuals provide a BFL subset of charts which is significantly easier and quicker to use than the detailed charts. In this case the declared TODA should include the stopway (typically 60m or so) or remaining strip length and the declared TORA usually is not going to be limiting (ignoring the strange climb antics of helicopters). There will be little advantage in playing with all the charts as the end result will be much the same weight.

As Mutt indicates, there is a very important advantage for an operator with lots of runways to look after in that simplified rules can be generated for flight crew use (correction data and the like) ... in my view, this is a very valid consideration and the main reason that many people emphasise the BFL approach.

The Boeing BFL quote referred to has to be read with these points in mind... if we talk about "runway", specifically, we mean "no clearway" and I suspect that the Boeing statement is looking at the barebones runway .. ie no stopway either.

But it is important that pilots realise BFL is just a constraint on the more general takeoff weight analysis and, if you need the last kilo RTOW on the day, then the generalised analysis is the better procedural way to go. As Mutt suggests, this can become quite an involved, pain in the neck, process when done manually. However, if it be simulated on the trusty PC, then it becomes a doddle ... working up the simulation is quite straightforward but takes a lot of time. When the work has been done, the production of optimised RTOW tables is quick and straightforward ...

Mutt, I presume that the 30 kt delta on the A300 relates to an obstacle limited takeoff from a long runway ? I have no background with the Type but is that a typical sort of variation ?


Now that, as so often happens, this thread is totally off the original question .... I wonder where it will head off next ?

Well then i think that its a perfect time to wish you a very Merry Christmas and to thank you for all the effort that you have put into the Tech Forum over the last year.

Mutt.

It is interesting that in all of this discussion no-one has mentioned OEI climb gradient! Remember that, essentially, V2 is the minimum speed at which a specified gross climb gradient (OEI) can be achieved (2.4% 2-engined aircraft, 2.7% 3-engined, 3.0% 4-engined). The 1.2 x Vs and 1.1 x Vmca are caps below which V2 cannot go.

A lot of the discussion above can be simplified by saying that Vr cannot be less than Vmcg. When V1 = Vr = Vmcg, V2 is the speed which is achieved at screen height following rotation at the normal rate for the aircraft type.

The case in point here, the B742, does reach this situation at light TOW, although the Boeing take-off data is a little confusing as the shaded part (low TOW) of the T/O speeds table just notes that this area is "minimum control speed limited". As there is no promulgated Vmca-1, this must be a Vmcg limiting case. As has been stated above, what actually happens to V2 will depend on the variation of Vmcg with AUW and the acceleration from Vr to screen height. However, do not try to read too deeply into the B742 table; I have never quite figured out quite what is happening! One thing to be wary of is that if your company SOP is to set the ASI bugs for departure based on V2, they will be set artificially high. In such light TOW cases it is worth calculating the approach Vref for the AUW as this is the true speed on which flap retraction should be based (ie stall margin). Therefore, if you end up with a loss of thrust and high drag after T/O, you are aware of the true min speed for flap retraction should you really need it.

With regard to Vmcg and crosswind, in the B742 you need a speed greater than Vmcg by approximately an extra 1.3KIAS per kt of crosswind in order to maintain control to the same criteria (max 30 ft displacement from centreline, max 150 lbs rudder force). Note that the B742 was originally certificated in the UK to BCARs which assumed a 7 kt crosswind, and some operators may still use these figures. Crosswind is ignored in FAR and JAR 25 on a statistical basis related to the probability levels of losing an engine in an adverse limiting crosswind!!! I agree with the above comment that the best you can do is to use the scheduled V1 for RTOW although knowledge of V1 max (ie Vstop) would help even more. Note also that Vmcg is based on aerodynamic control alone so the NWS will help for real.