How do airlines handle uncertainty in passenger weight for weight and balance calculations?

Question

When commercial airlines calculate the mass and distribution of passenger load, in the cases where they do not weigh the passengers directly, they use standard weight measures which have been approved by the appropriate aviation authority.

The standard weights can be broken down by passenger type (adult/child), by sex (male/female) and by other factors such as season or business/economy class. To obtain these figures a survey is carried out at an airport and appropriate measures are taken to ensure the sample is representative.

The result is a single value that represents the standard weight for a male/female/child/etc. Whilst the standard weight may have a minimal bias (i.e. a small deviation from the population mean), it does not represent the variance of the observed passenger weights. That is if the sample mean is 90kg with a std deviation of 10, the there is a ~15% chance that a passenger has a weight more than 100kg (assuming normal distribution, for the purpose of this example).

Given that airline operators have to be extremely careful and conservative with their weight management how do they account for this uncertainty in their calculations? Using the example above, if there were a flight with 100 passengers each >100kg, there would be an underestimation of mass by over 1 tonne (relatively small in comparison to total loaded aircraft mass, but still a large figure in itself).

Are accommodations for this variation incorporated into the standard passenger weight (say use mean + x std. dev.) or does this get included in the operational limits that the airline set for their max weight allowances in their various forms, for example reduced Max Zero Fuel Weight (MZFW) or Max Take Off Weight (MTOW)?

Edit: This is a slightly different question to a similar one about how a commercial aircraft has its mass determined. The focus here is more specific in looking at how the standard passenger weights are calculated and what are the assumptions around using that data.

Answer 1

They don't handle that uncertainty.

Safety is always the prominent factor in the aviation industry. That said, measurements need only to be "accurate enough" for the purpose of safety. Being off by small amount would not compromise safety.

Furthermore, the atmospheric condition is always different; it is so dynamic and cannot be precisely measured. As long as the measurement is accurate enough, the aircraft will fly.

Theoretically, you could argue that there's a chance:

• calculated weight is already at MTOW
• every passenger happens to weight way above average
• they all bought a lot of souvenir at the airport shops
• density altitude was extraordinary high
• a 10 knots tailwind was present at takeoff

and the aircraft overrun the runway during its takeoff roll. However, such a chance is so small that we accept our current method as it is and expect the aircraft to tolerate that uncertainly within its designed safety factors.

Such believe was found to be wrong when a small aircraft crashed on takeoff in 2003. Regulations were then modified so that on a small enough aircraft, the actual weight of each passenger (plus luggage) must be used, rather than using a standard weight for estimation.

Answer 2

Not only does the FAA define standard passenger weights they have a lengthy AC describing how you should calculate loading. You can find that AC here.

4. What should an operator consider while reading this AC?

a. Accurately calculating an aircraft’s weight and CG before flight is essential to comply with the certification limits established for the aircraft. These limits include both weight and CG limits. By complying with these limits and operating under the procedures established by the manufacturer, an operator is able to meet the weight and balance requirements specified in the aircraft flight manual (AFM). Typically, an operator calculates takeoff weight by adding the operational empty weight (OEW) of the aircraft, the weight of the passenger, cargo payload, and the weight of fuel. The objective is to calculate the takeoff weight and CG of an aircraft as accurately as possible.

b. When using average weights for passengers and bags, the operator must be vigilant to ensure that the weight and balance control program reflects the reality of aircraft loading. The FAA will periodically review the guidance in this AC and update this AC if average weights of the traveling public should change or if regulatory requirements for carry-on bags or personal items should change. Ultimately, the operator is responsible for determining if the procedures described in this AC are appropriate for use in its type of operation.

You may be particularly interested in CHAPTER 2. METHODS TO DETERMINE THE WEIGHT OF PASSENGERS AND BAGS

The opening of the chapter pretty much covers that deviations may happen

200. What should an operator consider when choosing the appropriate method?

a. For many years, operators of transport category aircraft have used average weights for passengers and bags to calculate an aircraft’s weight and balance, in accordance with standards and recommended practices. This method eliminates many potential sources of error associated with accounting for a large number of relatively light weights. However, differences between the actual weight of passengers and bags and the average weight of passengers and bags can occur when using average weights.

b. Statistical probability dictates that the smaller the sample size (i.e., cabin size), the more the average of the sample will deviate from the average of the larger universe. Because of this, the use of standard average passenger weights in weight and balance programs for small and medium cabin aircraft should be examined in greater detail.

c. The next four sections describe four methods available to operators to determine passenger and bag weight. They are standard average weights in Section 2; average weights based on survey results in Section 3; segmented weights in Section 4; and actual weights in Section 5. An operator should review the following discussion and consult Table 2-1 to determine which method or methods are appropriate to its type of operation.

I will refrain from quoting the rest of the document but its worth a read on covers the topic well, it should answer the main body of this question.

Also of interest may be the FAA handbook on weight and balance.

From an operations stand point there are things to consider as well. First off airplanes have a CG range, not a single CG point. This range does in fact have some room to play with. The airlines only need to be within this range for TO/LD. Check out the FAA handbook for more on CG ranges. In theory the airline can (and does on occasion) move people around, although my understanding is that this happens more so in smaller commercial planes. When I fly the Archer or Warrior I typically fly you better believe all my passengers are stepping on a scale before the flight!

Some planes may have ways to mitigate this to an extent. Depending on airframes the fuel loading can be distributed differently among the tanks but you still must be with in limits for TO/LD of course. Any large plane that may also be carrying cargo (for shipping reasons not the baggage its self) may have some ability to rearrange the pallets to keep the CG within limits but this again depends on the situation.

-- EDIT (in response to CG range question in the comments below)--

As for how the planes are designed to handle this there is a CG range. This varies from plane to plane and some have bigger ranges than others. A full break down on how that works could be the subject of its own question here. Generally speaking there is a Max Takeoff weight that must fall with in a CG envelope. Here is the CG envelope for a Piper Warrior

(source)

The charts for airliners have bigger numbers and some more boxes but its easier to describe the issue with a chart like this. As you can see at max gross weight you have 6 inches of CG play. While this may not seem like a lot its more than enough to play with when loading the plane. This leaves room to have passengers of different weights in different seats etc. For the sake of a complete answer it should be noted that these ranges are just the tested limits of the airframe if your CG falls out of these ranges the plane may still fly however it will exhibit different behaviors (high/lower cruise speed, easier entry to a stall or tougher exit etc.). There have been various accidents in history that happened as the result of a massive CG shift in flight, there is some debate as to the role that the over loading of AF4590 (the Concorde that crashed) played in the accident. You should be able to find similar CG range charts for most modern airliners out there if you want more specific ranges.