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Topic: What's The Deal With 747-8 Tail Tanks?
Username: KC135Hydraulics
Posted 2013-01-02 14:01:44 and read 8253 times.

I've been reading some things about a "deactivated" tail fuel tank on the new 747. What's the deal with that? Is the tank installed but not used? If so, what's the deal with that? Obviously the -400 can operate with that tank so why can't the -800?

Thanks Brahs!

Topic: What's The Deal With 747-8 Tail Tanks?
Username: Roseflyer
Posted 2013-01-02 15:48:47 and read 8093 times.

They found a problem with flutter during flight testing that is only present when there is fuel in the tank. Basically the structural load with fuel in the tank made the airplane susceptible to flutter in a very specific part of the flight regimen. Since they have to flutter test the airplane and prove to the FAA that the airplane will not have any conditions that are unacceptable, the solution was to lock out the tank until they fixed it.

The 747-8 has basically a new wing and is stretched. The structural changes were significant. A very small change can result in increased susceptibility to flutter because small changes in structural stiffness or weight, can change the vibration spectrum.

http://www.flightglobal.com/news/art...-tanks-on-flutter-concerns-367148/

Topic: What's The Deal With 747-8 Tail Tanks?
Username: Viscount724
Posted 2013-01-02 18:34:03 and read 7983 times.

Article in last week's Aviation Week mentioning the 747-8 tail fuel tank issue.
http://www.aviationweek.com/Article....d_12_21_2012_p03-01-531189.xml&p=1

Excerpt:

The 747-8 passenger model’s 3,300 gal. tailplane fuel tank was de-activated before the first aircraft entered service after analysis indicated that, under certain fuel load circumstances, the tail tank could induce flutter.

Re-activation of the tail fuel tank will provide added range and improve the aircraft’s performance, says Lufthansa’s Boje. The extra weight of the fuel in the aft of the aircraft can be used to assist in trimming the 747-8 to lower cruise drag. The 747-8’s fuselage extension “tends to be nose heavy so we might gain performance,” he adds.

Lufthansa also plans to ask Boeing to study minor software changes to the fuel transfer system which would extend the length of time the fuel remains in the aft tank, which would increase the trim benefit.

Topic: What's The Deal With 747-8 Tail Tanks?
Username: tdscanuck
Posted 2013-01-02 19:17:53 and read 7943 times.

Quoting KC135Hydraulics (Thread starter):
Is the tank installed but not used?

Yes. However, the "tail tank" isn't really a tank in the separate sense, it's just sealant on the existing horizontal stabilizer torque box (much like the main tanks). All 747's carry the structure for that tank, the only difference is if the sealant/plumbing/pumps are present or not.

Tom.

Topic: What's The Deal With 747-8 Tail Tanks?
Username: LH707330
Posted 2013-01-02 20:51:22 and read 7886 times.

Quoting Viscount724 (Reply 2):
The extra weight of the fuel in the aft of the aircraft can be used to assist in trimming the 747-8 to lower cruise drag. The 747-8’s fuselage extension “tends to be nose heavy so we might gain performance,” he adds.

Why then did they stretch the aft end so much less than the nose? Didn't the redone wing also have an aft-loaded lift profile?

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: Max Q
Posted 2013-01-02 23:18:21 and read 7815 times.

Quoting LH707330 (Reply 4):

Why then did they stretch the aft end so much less than the nose? Didn't the redone wing also have an aft-loaded lift profile?

Tail clearance on take off and landing perhaps.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: wilco737
Posted 2013-01-02 23:53:24 and read 7797 times.

The tail tank isn't used a lot anyways, so at the moment LH is fine that they cannot use the tail tank. Usually we only need the tail tank on our long flights to EZE and sometimes GRU or HKG-FRA if it is a long flight. I think I have seen fuel in the tail tank 3-4 times in 2 years of flying 744.
The fuel from the tail tank is used first, so the CG moves forward at the beginning of the flight. Well, during take off the tail tank fuel pumps are off, during climb out the EICAS message asks us to switch the tail tank pumps on so that the fuel can be used.
If Boeing can make it possible that this fuel can stay longer in the tail tank, then it would save fuel as the aft CG would be better for the cruise performance.
The MD11 pumped the fuel into the tail tank during climb out and kept the CG as aft as possible (within limits of course) and shortly prior descent it started to pump it forward into the other tanks. That saved fuel.
The 744/748 uses the tail fuel first, so there is maybe more potential to reduce the fuel comsumption of the -8i. I am sure Boeing is looking into it.

wilco737
  

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: CARST
Posted 2013-01-03 06:26:36 and read 7612 times.

Quoting wilco737 (Reply 6):

Assuming Boeing would have already found a solution to the flutter problem, couldn't you just switch the tail-tank fuel pumps off until a very late segment of your flight? Do you have to comply with the EICAS message asking you to switch on the pumps?

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: 747classic
Posted 2013-01-03 06:39:35 and read 7608 times.

Quoting Roseflyer (Reply 1):
They found a problem with flutter during flight testing that is only present when there is fuel in the tank. Basically the structural load with fuel in the tank made the airplane susceptible to flutter in a very specific part of the flight regimen.

Boeing first discovered the problem already in the summer of 2011 and AFAIK not during flight testing.

Engineering computer models were run to simulate the failure of a specific wing mounting strut, one of several redundant components that hold the outboard engines on the wings. For safety reasons, such a potential failure must be proved not to threaten flight safety if it occurs.

The computer analysis revealed that if that engine mounting strut were to fail, then extra weight (tail tank more than 15% full) at the rear of the aircraft would cause wing flutter. (the 748 has a heavily modified wing platform and greater length compared to the 744, causing a different flutter behaviour)

Boeing said this specific engine mounting strut has never actually failed on any previous 747 model nor in flight tests of the 747-8.

"This is something we found during analysis, not test,"

See : http://seattletimes.com/html/busines...echnology/2017283893_boeing20.html

Here are the highlights :

- The 747-8I was certified in December 2011 without the additional 3,300-gal. tail tank fuel capacity because Boeing could not show full compliance with FAA requirements that no structural flutter be present in the airframe after any single failure condition.
- The specific case concerned potential flutter in the event of a failure of the R3 under-wing, mid-spar strut-to-wing fitting, which is one of six connecting the outboard engines to the wing.
- The specific load condition assumes also the full weight of the 3,300 gal. in the tail tank as well as a lot of weight forward.
- Boeing became aware of the situation earlier in 2011 and, because there was no likely impact foreseen to any of the initial customers until at least 2013/2014, made the fix part of its longer-term development schedule.
- The tail tank is not currently required for passenger operations by launch customer Lufthansa. In a nominal 467-seat configuration, with the tank full, the 747-8 exceeds weight limits if it is operated at more than a 60% load factor.
- Because the first 747-8I/BBJ (with a relative low payload) is not expected to be active before the end of 2013 the tail tank will not be required before 2014.
- Boeing is at the moment studying several options, ranging from routine checks to minor structural modifications, to reactivate the closed-out tail fuel tank For this purpose RC021 will be used as a test aircraft.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: wilco737
Posted 2013-01-03 07:59:42 and read 7543 times.

Quoting CARST (Reply 7):
Assuming Boeing would have already found a solution to the flutter problem, couldn't you just switch the tail-tank fuel pumps off until a very late segment of your flight? Do you have to comply with the EICAS message asking you to switch on the pumps?

For sure not. It is an EICAS message which cannot be ignored. There is a QRH procedure for it and it clearly states: "switch on STAB fuel pump" or something similar.
The airplane is not certified for that kind of operation. The CG calculation states that the fuel has to be used first. Maybe that would be possible, but that would be out of my knowledge about the flight envelope and CG limitations as this is not standard procedure.

wilco737
  

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: ferpe
Posted 2013-01-03 11:48:10 and read 7398 times.

To those who know, why is Boeing not using the 744 and 748 stab tank as a CG trim device, Airbus implemented this system from the Concorde project on the 310 and the 340/330 IIRC. It would certianly make sense for the 748, IIRC the lenghtening of the fuselage is mainly in front of the wing.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: KC135Hydraulics
Posted 2013-01-03 12:11:31 and read 7364 times.

Thanks everyone for the great information, this has definitely answered all my questions!

Another question: On aircraft which use the horizonstal stab to hold fuel, (747, MD-11, etc) what sort of fitting(s) are used to plumb that tank to the rest of the aircraft? Is it some sort of swivel fitting that allows the stab to rotate up and down for trim?

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: Stitch
Posted 2013-01-03 12:54:26 and read 7333 times.

Quoting ferpe (Reply 10):
To those who know, why is Boeing not using the 744 and 748 stab tank as a CG trim device...It would certianly make sense for the 748, IIRC the lenghtening of the fuselage is mainly in front of the wing.

LH has said they want to use the tail tank on the 747-8 for CG trim, so I would expect it will be made available (it might be one of the factors impacting how quickly Boeing can implement the fix).

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: tdscanuck
Posted 2013-01-03 13:58:30 and read 7290 times.

Quoting ferpe (Reply 10):
To those who know, why is Boeing not using the 744 and 748 stab tank as a CG trim device

No current production Boeing aircraft does fore/aft in-flight fuel transfer and I don't see them about to change. The 737/757/767/777 can't even to side-to-side transfer in flight (the 787 can). Although you can get drag benefits by manipulating the CG, you pay for it in a big bump is system complexity (mostly in the failure modes analysis and testing). This is part of the reason why the Airbus fuel systems are usually considerably more complicated...it is also more capable...in the market, they appear to be at parity on total cost of ownership.

Quoting Stitch (Reply 12):
LH has said they want to use the tail tank on the 747-8 for CG trim

I think they're just doing that as a one-shot deal though, not active trim management throughout the flight. Once you burn the CWT down to the right point, you go to tail tank until it's gone.

Tom.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: CARST
Posted 2013-01-04 00:09:31 and read 7063 times.

Quoting wilco737 (Reply 9):
For sure not. It is an EICAS message which cannot be ignored. There is a QRH procedure for it and it clearly states: "switch on STAB fuel pump" or something similar.
The airplane is not certified for that kind of operation. The CG calculation states that the fuel has to be used first. Maybe that would be possible, but that would be out of my knowledge about the flight envelope and CG limitations as this is not standard procedure.
Quoting Stitch (Reply 12):
LH has said they want to use the tail tank on the 747-8 for CG trim
Quoting tdscanuck (Reply 13):

I think they're just doing that as a one-shot deal though, not active trim management throughout the flight. Once you burn the CWT down to the right point, you go to tail tank until it's gone.

Replying to all the things said above: While working on a fix for the tail tank flutter issue, wouldn't it be possible for Boeing to modify the system in a way that the fuel in the tail tank gets used at a later stage of flight? I assume that this could be done just by reprogramming the system so the EICAS message appears later in flight to switch on the stab fuel pump. That way Boeing could use the tail fuel tank to improve the CG in flight without the need for a complicated Airbus system to shuffle fuel around. Possible or not? Easy or not?

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: wilco737
Posted 2013-01-04 00:37:51 and read 7056 times.

Quoting CARST (Reply 14):
Possible or not?

I am sure it is possible and the software can be edited.

Quoting CARST (Reply 14):
Easy or not?

Easy? Doubtful that it will be done in a short period. I guess it needs flight testing for the flight envelope and the CG limits at what point you have to use the tail fuel.
I am sure Boeing is working on it as it would save fuel for sure.

wilco737
  

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: 747classic
Posted 2013-01-04 02:03:24 and read 7039 times.

With the present stabiliser fuel transfer system on the 744 and the 748 it is not possible to transfer the fuel in a later phase of the flight. The system is only used during ultra long flights, with a relative low payload.

"The prime reason stabiliser fuel is burned fairly early in long range flight - before most of the centre wing tank fuel or virtually any of the wing tanks fuel – is because of concerns about the aircraft CG following a failure of the stabiliser tank transfer/jettison pumps and a consequent inability to use any of the (now trapped) stabiliser fuel.

If we keep the stabiliser tank fuel to the end of our long flight, when we have no fuel in the centre tank and little fuel in the wing tanks, and at that point we discovered that both the transfer/jettison pumps had failed leaving fuel trapped in the stabiliser tank, then, with little or no fuel in the centre or wing tanks, the CG would be far too far aft for the aircraft to land safely, and there would be very little we could do about it.

So, to guard against this problem, if there is to be a failure of both transfer/jettison pumps, we need to know about it early in the flight, so that we can land whilst we still have sufficient fuel in the centre and wing tanks to keep the CG forward of the aft limit for landing ".

For more details, see reply 2 from Bellerophon (also active at A-net) at http://www.pprune.org/tech-log/262046-747-fuel-question.html

IMHO, only after a total re-design of the tail fuel transfer system a CG control system could be added.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: CARST
Posted 2013-01-04 04:41:49 and read 6982 times.

Quoting 747classic (Reply 16):
If we keep the stabiliser tank fuel to the end of our long flight, when we have no fuel in the centre tank and little fuel in the wing tanks, and at that point we discovered that both the transfer/jettison pumps had failed leaving fuel trapped in the stabiliser tank, then, with little or no fuel in the centre or wing tanks, the CG would be far too far aft for the aircraft to land safely, and there would be very little we could do about it.

But the system could be modified, so that the fuel in the stabilizer gets used at a later stage of the flight. Not at the end, when it could result in a problem, but lets say after 70% of the flight. There will always be an alternate airport on the remaining 30% if the stab fuel pump is not working. That would at least result in an advantage regarding the CG trim for the first 70% of the flight.

And the explanation by Bellerophon was covering the older 747 models only. So with the more nose-heavy 747-8 that could have changed, too. At least that is what I am thinking, correct me if I am wrong.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: tdscanuck
Posted 2013-01-04 06:49:22 and read 6930 times.

Quoting CARST (Reply 14):
While working on a fix for the tail tank flutter issue, wouldn't it be possible for Boeing to modify the system in a way that the fuel in the tail tank gets used at a later stage of flight?

Possible, yes, but not without a significant redesign of the fuel system and a lot of testing.

Quoting CARST (Reply 14):
I assume that this could be done just by reprogramming the system so the EICAS message appears later in flight to switch on the stab fuel pump. That way Boeing could use the tail fuel tank to improve the CG in flight without the need for a complicated Airbus system to shuffle fuel around. Possible or not? Easy or not?

It's not that simple. The failure modes are the problem. You either need to "prove" that you'll never get stab fuel trapped in a situation where it will push you outside the CG envelope (which would need a fuel system redesign to increase redundancy), alter the CG envelope (*major* operational impact and testing burden), or couple the fuel system into other airplane systems so it responds dynamically to real weight/CG in real-time (major fuel system redesign). You'd also have to rerun a lot of fatigue analysis and flutter since you've now altered the assumption that center fuel is used first.

Quoting CARST (Reply 17):
But the system could be modified, so that the fuel in the stabilizer gets used at a later stage of the flight. Not at the end, when it could result in a problem, but lets say after 70% of the flight. There will always be an alternate airport on the remaining 30% if the stab fuel pump is not working.

Not all flight profiles have an adequate alternate at the right points, and you'd still need to couple in to the weight/CG in real time (which introduces a bunch of new failure modes).

Quoting CARST (Reply 17):
So with the more nose-heavy 747-8 that could have changed, too. At least that is what I am thinking, correct me if I am wrong.

You still need to deal with the worst case aft-CG situation. Having a more forward natural CG reduced the number of times that you might be at aft-CG but it doesn't make that part of the envelope go away.

Tom.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: 747classic
Posted 2013-01-04 09:22:28 and read 6881 times.

Quoting tdscanuck (Reply 18):

Fully correct,

It will be highly unlikely that the present 748 fuel system could be adapted (and certified !), to include a form of (limited) CG control, without a major redesign of the entire fuel system.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: KC135Hydraulics
Posted 2013-01-04 12:12:32 and read 6808 times.

How is it then that the MD-11 is able to move fuel around to the tail tank and back for CG purposes, but this is too complex/costly for Boeing to impliment? Surely McDonnell Douglas didn't expend a massive amount of energy to make this a reality, so why can't Boeing do it? Seems fishy to me! This is decades-old technology.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: tdscanuck
Posted 2013-01-04 12:33:34 and read 6804 times.

Quoting KC135Hydraulics (Reply 20):
How is it then that the MD-11 is able to move fuel around to the tail tank and back for CG purposes

Because the MD-11 had huge range problems and MD were willing to do "whatever it took" (once they realized how deep they were in) to correct it. If Boeing needed to do active CG control to make contractual guarantees on the 747-8 you'd probably see it...but the plane makes guarantees without it.

Quoting KC135Hydraulics (Reply 20):
but this is too complex/costly for Boeing to impliment?

It's a trade. The MD-11 didn't make guarantees even after the scramble to regain range. The 747-8 meets spec so it doesn't pay off to implement.

Quoting KC135Hydraulics (Reply 20):
Surely McDonnell Douglas didn't expend a massive amount of energy to make this a reality

It depends on your definition of "massive" but it wasn't trivial. MD-11 also has a different fuel system architecture (trijet) which may have had some impact on how easy it was to implement.

Quoting KC135Hydraulics (Reply 20):
so why can't Boeing do it? Seems fishy to me! This is decades-old technology.

They can do it, there's just not a good enough reason to do it. This is almost always why any particular change/technology isn't implemented. You can apply the same line of argument to ask why Boeing didn't put FBW into the 737.

Tom.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: ferpe
Posted 2013-01-04 15:43:38 and read 6734 times.

Quoting tdscanuck (Reply 21):
They can do it, there's just not a good enough reason to do it.

I think part of that is how big is the upside of that trade, ie how much will you gain from running the 748 CG more optimal then today? 100nm on design range (8000) or 200?

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: kanban
Posted 2013-01-04 20:31:12 and read 6653 times.

Tom, from the comments it appears that there is no capability to dump the fuel from the stab tanks... is that correct?

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: wilco737
Posted 2013-01-05 03:41:35 and read 6567 times.

Quoting kanban (Reply 23):
Tom, from the comments it appears that there is no capability to dump the fuel from the stab tanks... is that correct?

Not directly, but if fuel jettison is done and you switch on the stabilizer fuel pumps to on, then the fuel is transferred to the center tanks and then it can be dumped.

wilco737
  

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: 747classic
Posted 2013-01-05 05:42:15 and read 6730 times.

Here is a system diagram of the 747- 400 fuel system.

This system is almost identical for the 747-8, only the individual tank quantities differ and the 744 reserve 2 and 3 fuel tanks are renamed at the 748 in reserve 1 and 4 an drained in main 1 and 4 i.s.o. main 2 and 3.

744 fuel system.



Clearly visible :

If a dual failure hits the tail fuel transfer system ( both transfer/jettison pumps fail or 2 parallel installed transfer jettison vlv's failed closed.) all tail fuel is trapped and cannot be transferred to the CWT or jettisoned anymore.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: kanban
Posted 2013-01-05 11:48:19 and read 6524 times.

Quoting 747classic (Reply 25):
If a dual failure hits the tail fuel transfer system ( both transfer/jettison pumps fail or 2 parallel installed transfer jettison vlv's failed closed.) all tail fuel is trapped and cannot be transferred to the CWT or jettisoned anymore.

Thanks.. that is what I thoughtI I was reading... it almost implies that a jettison pump and ducting to the immediate exterior would have safety benefits... providing the APU did not ignite the jettisoned fuel.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: francoflier
Posted 2013-01-05 12:58:03 and read 6564 times.

I've always wondered why Boeing never designed a simple emergency stab fuel tranfer system. Basically just an electrically operated valve, on an emergency electrical bus for redundancy, that would allow the fuel to gravity flow down to the center tank. That might have been anoug to allow flight with fuel in the stab tank for longer.

It would take a while I suppose, maybe around 1 or 2 hours.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: ferpe
Posted 2013-01-06 03:13:36 and read 6336 times.

Quoting francoflier (Reply 27):
I've always wondered why Boeing never designed a simple emergency stab fuel tranfer system

As I understand it the tail tank is used very very seldom today, when used you fuel the tank at the stab. For it to be a CG trim device you need to use it on most flights, thus fueling at the stab for each flight might become unpractical, you would need a fuel transfer system so you could pump wing tank fuel up there and back. A lot more complication then what is there today as a last hour of flight bump.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: rwessel
Posted 2013-01-06 04:28:05 and read 6302 times.

Quoting ferpe (Reply 28):
As I understand it the tail tank is used very very seldom today, when used you fuel the tank at the stab.

I'm pretty sure the 747 just pumps fuel to the tail tank from the normal single point refueling receptacles. That would seem to be borne out by the diagram a few posts up.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: francoflier
Posted 2013-01-06 04:28:30 and read 6311 times.

744 operators across the pacific use it a lot more than your average European user...

I've seen it used on most Westbound flights from the West coast myself.
And it would not be a CG control system, just a simple system that allows you to keep it back there longer to help the horizontal stab pushing down a little longer. Just a fuel is kept in the outboard wing tanks as long as possible to help with structural relief.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: tdscanuck
Posted 2013-01-06 05:56:32 and read 6282 times.

Quoting francoflier (Reply 30):
And it would not be a CG control system, just a simple system that allows you to keep it back there longer to help the horizontal stab pushing down a little longer. Just a fuel is kept in the outboard wing tanks as long as possible to help with structural relief.

The issue is that, although the functional implementation is simple, the failure modes are not.

Tom.

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: KC135Hydraulics
Posted 2013-01-06 13:10:34 and read 6178 times.

Back to the MD-11, how did McDonnell Douglas address fuel trapped in the tail in the event of a failure? What happens on an MD-11 if fuel is trapped in the stab?

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: tdscanuck
Posted 2013-01-06 15:37:52 and read 6129 times.

Quoting KC135Hydraulics (Reply 32):
Back to the MD-11, how did McDonnell Douglas address fuel trapped in the tail in the event of a failure?

I do not know what they did, but three possible lines of attack would be:
1) Have redundant everything, so no single failure could trap the stab fuel, then show that the probability of any compound failure was sufficiently low for the severity of the problem.
2) Show that the aircraft had adequate pitch authority in the event of worst case trapped stab fuel
3) Clip the weight/CG envelope to restore the conditions of 2) above

Tom

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: wilco737
Posted 2013-01-06 18:01:43 and read 6085 times.

Quoting KC135Hydraulics (Reply 32):
Back to the MD-11, how did McDonnell Douglas address fuel trapped in the tail in the event of a failure? What happens on an MD-11 if fuel is trapped in the stab?

The MD11 has a one fuel pump which leads directly from the tail tank to the tail mounted engine (eng #2). So if the fuel is trapped the tail tank fuel will be used only for that engine.

wilco737
  

Topic: RE: What's The Deal With 747-8 Tail Tanks?
Username: KC135Hydraulics
Posted 2013-01-06 19:10:59 and read 6026 times.

Thanks again, everyone. All my questions have been answered in depth.


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