The below cited flight safety story contains a reference to an ATSB report, about which I have a comment. The story alleges that the report cites an incorrect weight and balance calculation as the problem. They say, “This meant that the captain had to apply a significant amount of back pressure [to the yoke] at takeoff, running the risk of the aircraft’s tail hitting the runway. The report states that he was also forced to exceed the calculated takeoff safety speed. In my opinion this is an incorrect observation, could yield a report that could confuse flight crew members and therefore not serve the Safety Purpose.
In my opinion, flight crew should be given this report. When planning a takeoff, a procedure to overcome errors in weight and balance calculations should be briefed, planned and discussed. There is never a reason for flight crew to apply an increase in back pressure of the yoke during take off above the normal level. If the aircraft weighs more than the amount listed on the weight and balance forms, the aircraft will still fly just fine, albeit at a higher speed. All a flight crew member has to do is reference the Take Off Aircraft Data for higher weights. Most often the increase in take off speeds is within 10-15 knots even for a gross error.
In this case the aircraft actually weighed less than the weight and balance form (W&B) stated. A tail heavy acft is like an aircraft with part of its forward weight missing. Just add that missing weight to the current weight on the W&B, move up to a new higher theoretical take off weight. Remember that take off occurs at the take off attitude and angle of attack (AoA-TO). The take off speed goes up and down in proportion to the weight when the acft is in balance.
The ATSB report leaves us with the impression that the correct procedure is to pull back on the yoke and thus raise the nose of the acft above the take off attitude and AoA. Doing so would result in a tail scrape or tail strike. But in fact raising the nose above the take off attitude, even at the correct speed for weight would cause a tail strike. The correct procedure is to set the take off attitude and let the acft lift off on the wings as the wings generate lift equal to or greater than the actual weight. So the error here is that there are several take off attitudes, a range of take off angles of attacks or a series of yoke back pressures or nose attitudes. In fact, there is only one. The ATSB should consider amending their report to serve the Safety Purpose. 
http://time.com/3266087/qantas-takeoff-children-weight-atsb-group-movement-advice/
A Check-in Error Caused Takeoff Problems for Qantas Flight (Time, Sept. 4)
Airline employees incorrectly registered 87 children as adult passengers, creating an imbalance in the aircraft’s weight distribution
A Perth-bound Qantas flight from Canberra had a close call earlier this year, with the pilot having to make a risky last-minute adjustment to get the aircraft off the ground.
A report released Wednesday by the Australian Transport Safety Bureau (ATSB) said that a problem was caused because a group of school children on the Boeing 737 had been checked in as adults and assigned the standard adult weight of 87 kg.
The children – comprising more than half of the flight’s 150 passengers – were all seated in the back of the aircraft, resulting in it becoming nose-heavy. This meant that the captain had to apply a significant amount of back pressure at takeoff, running the risk of the aircraft’s tail hitting the runway. The report states that he was also forced to exceed the calculated takeoff safety speed.
The rest of the flight went off without a hitch, but it was a tense few moments for the pilots. The ATSB later found that the final load sheet overstated the aircraft weight by 3.5 to 5 tons.
Qantas told the ATSB that it has issued a notification to check-in staff, reminding them to ensure that children are registered as children in the airline’s systems.
http://goo.gl/ZywORT
Safety Forecast 