When I blogged about how to
calculate the loaded weight of an airplane, lots of folks pitched in with other
related issues, like how much a planeload of passengers really weigh. At my current job,
I work with the same people for weeks at a time, and if I'm going to pick up someone new,
the people I'm with can tell me, often with mirthful laughter, how much I should allow
for the weight of their colleagues. So I always use actual weights or my own best
estimates based on looking at people and lifting cargo.
I linked already to the recently revised Canadian standard
weights for males, females, children and infants, and reader Christopher linked to a Transport Canada document proposing new changes to weight and balance
practices for small airplanes.
The report describes the limitations of applying standard weights to small aircraft
weight and balance calculations.
Companies will naturally try to maximize the load to optimize the service and remain
competitive with other companies. This means that, on any given day, many flights operate
at close to maximum gross weight on paper when, in fact, some of these flights are
operating above maximum gross weight.
Statistical probability dictates that the smaller the sample 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 when transporting 9 or less
passengers does not provide an acceptable level of confidence for ensuring compliance
with aircraft weight limitations.
The TC document points out that the law requires the operator to ensure not that the
airplane is within limits on paper, but that No person shall operate an
aircraft unless, during every phase of the flight, the load restrictions, weight and
centre of gravity of the aircraft conform to the limitations specified in the aircraft
flight manual. It suggests two solutions, using actual passenger weights and
something called segmented weights.
The situation it describes is absolutely true. Pilots do the weight and balance
according to standard passenger weights and not according to the size of the actual
passengers. When you fly a charter in an eight-passenger airplane, you're generally
flying a group of related people. People in a family share eating habits and genetics, so
if one is heavy, you typically have a group of eight heavy people. The northern diet is
heavy on pop and potato chips, and thus the northern resident is heavier than the average
Using actual passenger weights is already an option, and some operators already use
it. Northern passengers put up with all kinds of indignities, and I didn't see anything
to indicate that the culture of thinness was ingrained to the point that people would be
grievously offended by a weigh in before boarding. One problem is that the passengers
don't usually show up in time for the pilot to do the calculations between when they
arrive and when they board. A smart pilot precalculates the weight and balance for the
whole day, before she sees a single passenger. So what is this segmented weights, thing?
I've never heard of it before. It looks like statistics. I have some mathematics training
including one pathetically easy statistics course, so I should be able to figure this
It's like I'm returning to the original purpose of the blog: learning things!
This concept involves adding a portion of the standard deviation to an average weight in
order to increase the confidence that the actual weight of a passenger and carry-on
baggage will not exceed the resultant, increased weight value called segmented weight.
For a large sample, like two hundred people on a large jet, chances are good that the
pounds carried on board by people who weigh more than population average will be balanced
by pounds not carried on by people who weigh under that average. But as the number of
people boarding decreases, so does the probability that their average will be
significantly different than the population average. So as the number of people boarding
decreases, you need to add a fudge factor to hedge against the possibility of having a
load of biggies throw off your W&B. As the seating capacity goes down, the fudge factor
per passenger goes up.
People with more statistics training than I have have worked out a table and state
that if I use the row appropriate to the seating capacity of my airplane and the column
appropriate to the male/female ratio, I will have a "95-percent confidence level and a
1-percent tolerable error." That apparently means "good enough for the government." This
all assumes that the current standard passenger weights do accurately reflect the
overall average weight of that portion of the public who travel on airplanes, weighted by
their frequency of travel.
The chart has a bit of a problem for someone doing row-by-row seating. Lets say I have
an eight passenger airplane, full in the summer, with two guys in the back, a man and a
woman in the next row, two women in the next and two guys up front. That's five guys and
three women, a 62/38 M/F split, so I guess I'll use the 60/40 column. Therefore according
to the Canadian summer chart, I count my eight people at 215 each, for a total passenger
weight of 1720 lbs. That works fine for the weight, but how am I supposed to do the
row-by-row balance? My best guess is that I should use the figure of 192 lbs for the
women and 231 lbs for the men, because those are the figures I'd use per passenger if the
load were all female or all male respectively. That would give me a total of 1731 lbs in
the final W&B. So can I put on that extra eleven pounds of fuel or not?
Okay, maybe it's because I rounded the 62% to 60%. If the load were half men and half
women, the average would be 211, for a total weight of 1688. Four women at 192 lbs plus
four men at 231 lbs adds up to 1692. That's only four pounds off, but what is the pilot
supposed to do with those four extra pounds in the paperwork? You have to do the math row
by row, because you may have to swap men and women back to front to get the CofG to work
I don't think these new weights will change the amount of weight on a typical charter
flight. If the pilot would have flown with the load under the old rules but it comes out
as overweight using the new rules, the pilot will either take fuel out of the paperwork,
but not out of the plane; or they'll officially use "actual weights" and pilots can be
really bad carnival weight guessers.
Meanwhile examining the tables closely tells me some interesting things. We're told
that Transport Canada allowed eight pounds for summer clothing in determining passenger
weights from the health survey weights, but they advise pilots to add ten pounds to
volunteered weights. That means that Transport Canada assumes the average Canadian
passenger lies about his or her weight by taking off two pounds.
Comparing the FAA and Transport Canada tables, we see heavier passenger weights in the
former table in each category. I thought the difference might be carry-on rules but they
actually mask a greater difference, because the American table includes only six pounds
per person for carry-on baggage while the Canadian table includes thirteen pounds of
carry-on bags per passenger. Both tables are recently updated. It's not a clothing
difference either, because I'm comparing summer weight to summer weight. Canadians add
six pounds for winter and Americans add five. Conclusion: Americans weigh more than
Canadians, but Canadians have heavier parkas and boots.
Also: airplane missing in the Bermuda Triangle.