MINIMUM zero fuel weight
 

Could anybody explain the relevance of the MINIMUM zero fuel weight??

It can impact things like VMC (which gets worse at lighter weights) or gust loading cases (where the accelerations seen by the structure are higher at lighter weights, since the same airload is applied to a lighter aircraft)

Strictly, one could say that these cases are actually at "minimum flight weight" not minimum zero fuel weight, but there's a pretty close relationship between the two, and if one were being conservative one could assume that min ZFW was the minumum flight weight.

Hi!

And in case you weren't allowed to bank 5º to the operative engine side during the VMC certification tests, would the weight still affect VMC?

Thanks

Zero Fuel Weight has no bearing on VMC.

Yes, to some extent (because there would be a different alpha at different weights for the same speed - in fact, you might find that the heavy weight/high AoA case was more critical.

But the TRADITIONAL impact of weight on VMC would be eliminated.

Directly, this is technically correct. (As my post states)

But minimum flight weight has a powerful effect on VMC.

And the lowest possible value for minimum flight weight is clearly the minimum zero fuel weight case.

Therefore zero fuel weight is an indirect constraint on VMC, and if you don't want to have to worry about minimum payloads and minimum fuel loads, and just take a simple and conservative approach, you could simply state "minimum flight weight = min zero fuel weight" in which case MZFW would be a direct driver to VMC.

Could you explain me more deeply how AoA affects VMC assuming the bank angle is zero?

Sorry for asking so much but I find Aerodynamics really interesting!

Thank you

Sure.

Simplifying the VMC trim problem, we have to generate enough yawing moment with the rudder to counter the yawing moment generated by one good engine and one dead engine (on a twin)

Suppose the Cn(dr)max is the maximum yawing moment coefficient we can generate from the rudder, then the maximum rudder yawing moment at a given speed is:

Cn-rudder = 1/2 * rho * V^2 * S * c * Cn(dr)max

and if the asymmetric thrust T has a moment arm x, then for exact balance we get:

1/2 * rho * V^2 * S * c * Cn(dr)max = T * x

Now, if you really simplify things, you ignore the fact that T is actually a function of speed, V. You also assume that Cn(dr)max is a fixed, known, value. Which means it's quite simple to solve for speed once you know all the other values, by simple algebra.

Where angle-of-attack comes into play is our assumption that Cn(dr)max is fixed - it isn't. If an aircraft is at low angles of attack, in most cases the fin will be in quite undisturbed flow, and the rudder will be aerodynamically effective.

take the same aircraft to an angle of attack near the stall, and the flow coming off the top of the fuselage may be blanking (washing over) much of the fin; this causes a loss in directional stability (which in this case isn't important) and also a loss of rudder effectiveness.

This may mean that a light aircraft can trim single-engine-out at a given speed, but a heavier aircraft at the same speed may not be able to. Usually the weight component effect (for the 5 deg bank case) overpowers this effect, but it may not be insignificant for some aircraft. I think I saw an Airbus paper presented at some conference or another where they went into some detail about the alpha effect, because it was significant for one of their aircraft.

Stay patient; a cure is expected any day now for this condition. ;)

To put it simple, VMC is a function of current aircraft's gross weight, thrust available from operating engine, aircraft CG and bank angle into the good engine.

The 757, 737, and 777, as well as twin airbuses have minimum approach and takeoff speeds that may be flown, which take into consideration of VMC.

VMC - in terms of the certified number - has NOTHING to do with your current weight or cg, or your specific engine conditions, or the bank angle. It is a certification "line in the sand" derived to specific - and artificial - conditions which is then used as a constraint to the scheduled speeds of an aircraft.

The actual minimum speed at which a given aircraft can be controlled is dependent upon the terms you suggest (and others) but that isn't "VMC"

It sure does. Take a normally asperated engine. At 10,000' that engine produces about 2/3 rated thrust. Therefore VMC will be lower at that altitude. Take a heavy aircraft at 10,000'. It is possible that the aircraft will stall before reaching its VMC. Thats the way its always worked.

I don't think you're understanding my point.

The actual thrust available on a given plane is not relevant to the calculation of VMC.

What matters is the thrust levels which were defined for certification - which can indeed be a function of altitude (and temperature too) - but those may be either above OR BELOW the thrust you have on any given day, on any given aircraft.

Many thanks for the answer! Really interesting! And in addition to the loss of rudder effectiveness at high AoA the heavier aircraft would require more thrust for a given speed, so this would also increase VMC, wouldn't it?

It's really incredible how 5º can change everythig!!!

No. VMC is demonstrated and calculated for a defined thrust level; whether the aircraft NEEDS that much thrust for level flight, or any other purpose isn't an issue.

What would happen in a test/demonstration is that you'd set the thrust per the test definition, then adjust climb/dive angle to maintain the target speed. Since VMC is usually tested at light weights, you can end up in quite a nose-high attitude trying to hold the speed constant. (To the extent that the so-called "dynamic VMCA" demonstration actually allows a relaxation of the demonstration conditions, to avoid having to go to dangerously high attitudes)

Ok, roger. Thank you! :ok:

Huh?
 

A minimum in-flight weight I can understand (many models of the B707 had this restriction) but exactly how could a minimum ZFW affect Vmc?

You gotta have fuel for Vmc to be of any consideration.
Now, on all aircraft that I have flown (transport and otherwise), there has been no mention of any sort of a minimum ZFW, nor is one necessary, so far as I can see...unless you leave bits behind.:rolleyes:

Minimum flight weight I believe I understand. Is this the lowest weight for which certificated performance data have been developed? Perhaps due to flight control effectiveness or other considerations related to the lower performance speeds associated with lower weights. The minimum flight weight for the aircraft I currently fly is about 90% of it's BOW, so was probably only an issue when it was ferried from the factory to the completion center for outfitting. Or if it were converted to a freighter.

I have never before heard of a "minimum zero fuel weight" limitation. Without any wish to oversimplify, I must still ask whether it is possible that this limitation may be applied for the same reason as a "maximum zero fuel weight" limitation, but in the opposite sense? Could there be a structural reason for this limitation as there is with Max ZFW? Suppose full wing fuel were assumed with too little weight in the fuselage between the wings. Might the structures require a minimum weight be carried in the fuselage with wings full in much the same way that a maximum weight to be carried in the fuselage is established with zero fuel?

Comments?

Best regards,

Westhawk

Maybe it only relates to the parameters used for certification testing, that is to say weights below a certain figure were never used so that weight then becomes the lower limit. As we know most Boeing A/C use FL200 as the maximum flap operating height, I can only guess that the aerodynamics were never investigated at higher levels , so that became a certification limit.
As flight test programmes are expensive and time consuming to carry out, the manufacturer would normally only try to provide a certification envelope that covers 99.9% of normal airline ops requirements.

vmc
 

hello every one,

first you have vmcg(v min control ground) & vmca(v min control airborne).
the difference, except the obvious ground/airborne factor is : vmcg considers tire friction(NOT nosewheel steering) & vmca considers 5° bank towards the live engine to counteract with the lateral liftvector component the opposite yaw of the operating engine. altitude hold capability is not a factor. only directional rudder control/effectiveness is considered.

there is a physical(scientific) relationship between aircraft weight-takeoff speeds & takeoff distances: the lower the weights, the lower the t/o speeds & t/o distances & vice versa.

for uncontaminated rwy's & at very low weights the t/o speeds bump on the vmcg(function of airtemp & press altitude= density alt.). so FM states: you can still reduce the weight, but not the t/o speeds & related t/o distances.

the lowest zerofuel weight =simplified: basic weight + 2 crew +bags= dow,dry operating weight, this gives also the most aft zfw cg position & lowest arm for rudder effectiveness & highest vmcg/a.
of course, in order to fly it is advisable to add some fuel to the equation which will bring the t/o cg forward & improve directional control, with lower vmcg/a.

on contaminated rwy's you have to consider 3 factors:
1) sometimes large weight reductions cfr rwy contaminants
2) v1(mcg) limit weights
3) take the lowerweight of 1) or 2)
4) v1 adjustement(reduction) for actual weight, not below v1mcg

a last consideration: regulations stipulate config/thrustoutput of critical engine/weight parameters for vmc demonstrations.
vmca can only be demonsrated if above stall speed.( a job best left to the test pilots)
4 engine aircraft have a 2 engine out vmcland.

Because, at the limit, minimum in-flight weight cannot be less than minimum zero fuel weight.

So, if I certify using minZFW as my VMC min weight, I have conservatively covered the minimum flight weight case.

And minZFW is easier to control than minimum in-flight weight - if I weigh the empty aircraft I can usually quite easily show that I'm above the minZFW, without even worrying about crew etc. Since it's impossible to remove weight by loading the aircraft, that aircraft just automatically met any in-flight minima required.