Wednesday, December 17, 2008

Segmented Weights

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 Canadian.

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 out.

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 out.

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.


Anonymous said...

Typo; thrd prgrph; frst ln.


steve said...

The grammar police are about early! :-)

The larger Canadian baggage-weights are easily reconciled: Any of your regular readers knows that they will be carrying a gun(or two) skis, an axe or chainsaw and possibly a few large chunks of unidentified animal meat.

OTOH, the Americans will have a double hamburger and a hot-dog in each hand, a quart of ice-cream in the crook of one hand and a 2-litre bottle of pop in the other,-as these are to be consumed en route, they are consolidated as "passenger-weight" as opposed to"carry-on baggage"
-So, someone has a better explanation? :-)

dpierce said...

Oh, now you're just invoking stereotypes. The 2kg 2L pop bottle is nothing compared to the 70kg keg of Molson that Canadian law requires each Canadian have in his or her possession at all times.

N6349C said...

When I did my last instrument checkride, the FAA examiner was 250lbs. He told me to plan an IFR flight to KLBB (Lubbock). All his weight in the front with fuel to reach KLBB and IFR reserves put us out of the forward CG limit. I told him we could only make the flight non-stop if he sat in the back! But he didn't take umbrage and passed me anyway.

Sarah said...

Northern passengers put up with all kinds of indignities...

Southern passengers too. Being weighed would be a lot less intrusive than being patted down. Yes, that's happened to me once. I think it was the underwires.

But about w&b ... If you want to pursue the statistical approach, I think you would come up with a very conservative interpretation.

What comes to mind is... ( you're going to be sorry you brought this up ) ... 95% confidence interval would imply a maximum absolute difference from mean weight for a population. So you would have to consider the case for w&b where the seat is at min. weight or max weight, and all combinations. For 8 seats, this would be 2^8 = 256 possible CG locations. I can imagine a computer program that would crank out the worst cases, i.e. most rearward or most forward CG. Then you'd move someone fore or aft and run it again.

If it's that close, get out the scales!

Aviatrix said...

you're going to be sorry you brought this up

No I'm not. Now I have the power of hundreds of worldwide geeks to tell me about the statistics involved in that little exercise.

Sarah said...

Sigh. Yes you do. Now I need someone to fill in my hand waving over this:

95% confidence interval would imply a maximum absolute difference from mean weight for a population.

Sure it does. I think the answer is simple, but have no confidence in my answer.