Wednesday, October 29, 2008

Sugar Science

Finally, we know the answer to how much candy you can get in a pillowcase! From My Science Project:

The Halloween Candy Hierarchy

In designing our experiment, we wanted to account for the typical assortment of candies you might receive while trick-or-treating. Unless you live in a really upscale neighborhood, it’s not likely that you’re going to come home with a bag full of chocolate bars. Halloween candy can be roughly divided into three categories: “premium” (fun-sized candy bars), “meh” (chewy boxed candies like Milk Duds), and “bottom of the barrel” (hard candy, gumballs, Dum Dum pops). We weren’t so concerned with the quality of the candy as we were interested in its density and volume; a mini Baby Ruth bar, for example, is heavier relative to volume than a box of malt balls. For that reason, we tried to recreate a representative variety of treats, with about equal amounts (by weight) of top, middle, and lower tier candies.

As we loaded each receptacle, we mixed the candies and tossed them in by the handful, rather than just dumping in bag after bag. This was to give the pieces a natural “loft” and spatial distribution.

Keeping track of the total number of candies in each container was not as difficult as you might expect, since most bags of Halloween candy are labeled with a piece count. Since we did not verify these numbers by hand (do you really think we would take the time to count out 300 Dum Dums?) and manually counted only when bags were not explicitly labeled, the total piece count per container should be considered approximate.

Each container was filled to capacity, allowing that it could still be reasonably carried while not spilling. The containers were then weighed on a hanging spring scale. Before starting the experiment, we tested the scale using barbell plates and found it to be accurate. Prior to each container being filled, the scale was zeroed to account for the weight of the container.

I Has a Bucket

9.5 lbs - 375 pieces

We started out with a 10 quart pail, which is pretty small-time and below the aspirations of most serious trick-or-treaters. The pail held about 9.5 lbs (4.25kg) and a total of 375 pieces of candy. That might sound like a lot, but it was a mere appetizer for the feast of sugary goodness to come.

Paper or Plastic?

25 lbs - 885 pieces

Next we filled a double-bagged, regular brown paper grocery sack with candy. This was a full-sized bag, not the shorty kind. We allowed enough room at the top so the paper handles could be pulled together without straining them too much, although the bag was bulging out at the sides. Frankly, we expected the handles to give out and tear off immediately when we attempted to lift the filled bag, but they held up and remained secure as the bag hung from the scale, supporting a surprising 25 lbs (11.4kg) of candy – approximately 885 pieces. Along with pillowcases, paper grocery bags are a common means of collecting Halloween candy, and while we were impressed with its capacity, the unreliable handles are problematic. A department store shopping bag with sturdier handles might be a safer (and classier) choice.

I Has a Bigger Bucket

20 lbs - 675 pieces

Next up was a standard white 5 gallon plastic bucket. We expected the larger bucket to hold more candy than the grocery bag, but the rigidity of plastic proved to be its downfall. The bucket held only 20 lbs (9.1kg) – 5 lbs less than the bag – and about 675 pieces. Also, of all the candy collection receptacles we tested, the bucket has the disadvantage of making you look greedier, while it won’t even carry the maximum amount of candy.

Sweet Dreams Are Made of This

47.75 lbs - 1690 pieces!

On to the main event. Once we got our pillowcase filled, it looked more like Santa’s lumpy toy bag than something you would want to sleep on. With the candy straining the fabric and threatening to bust out, we had some concerns that the filled pillowcase might split at the seams or tear at the top before we could get it weighed. It held up fine, although there’s no way we could imagine dragging a sackful of candy this size around from house to house.

We allowed enough free space at the top for the bag to be grasped and picked up, then clipped the top edges of the pillowcase together in two places to simulate someone holding it with two hands, and suspended it using an iron bar. It weighed in at 47.75 lbs (21.8kg) – about the weight of a first grader – and contained approximately 1690 pieces of candy. That’s nearly twice as much as the grocery bag.

Hit the Road Jack

Now that we know how much candy a pillowcase will hold, we wanted to find out whether it was even within the realm of possibility to collect that much candy in one outing. How many doors would you have to knock on to rake in that sort of a score, and how far would you have to walk? Obviously, there are a few factors to take into account. One is the number of pieces of candy you are likely to receive at each house. Usually you get more than one piece, but some people are more generous with the treats than others, and the affluence of the neighborhood may affect this as well (though not necessarily).

Another variable is how many houses are actually giving out candy. There are always some folks who refuse to play along with the holiday, who turn off the porch lights and pretend not to be home. You’re likely to have the best luck trick-or-treating in a low traffic residential neighborhood where most homes are occupied by families, as opposed to a more cosmopolitan neighborhood where homes may be occupied by childless couples or groups of college students. As most kids instinctively know, the best hunting grounds are traditional middle-class, middle-American suburbs.

The amount of square mileage you’d have to cover also would be determined in part by the density of housing. This can vary greatly in residential areas, depending on how large the houses are, how large the lots are, and how the streets are laid out. Typically, older suburbs closer to city centers have gridlike streets and denser housing, while the loops and cul de sacs of newer housing developments lend themselves to lower density.

These Are the People in Your Neighborhood

We picked two representative but very different suburban areas to use as hypothetical examples: Campbell, California, in Silicon Valley, and St. Peters, Missouri, a suburb of St. Charles. Both are middle-class residential areas, but Campbell is older, with denser housing, while St. Peters has mostly newer developments, is more rural, and is probably a little more affluent. Using information gathered from City-Data.com, we approximated the number of houses per square mile. We counted only detached single-family homes, since these are the primary targets for trick-or-treating.

We then constructed several different scenarios, using different values for the number of candies allotted per house, and the percentage of houses distributing candy. In the worst case scenario, we figured you might have a 50% success rate (i.e., only half of the houses giving out candy) and gather an average of 2.5 pieces of candy per house. A better scenario would be a 75% success rate and 3.5 pieces of candy per house.


Get Directions to Candyland

Using images from Google Maps, we’ve illustrated how much area you would have to traverse to gather the big bag of candy, or the more moderate 5 gallon bucket of candy, under these different scenarios.

Assuming a 50% success rate and 2.5 pieces of candy per house, you would have to visit about 1352 houses to fill a pillowcase or 540 houses to fill a 5 gallon bucket. For Campbell, we've calculated the housing density at roughly 3200 houses/sq. mile. The largest yellow square represents about .42 square miles (1.08 sq. km), the area you would have to cover to get a pillowcase full of candy, while the smaller yellow square is the area required to gather a 5 gallon bucket, about .17 square miles (.44 sq. km). Under the more favorable scenario of a 75% success rate and 3.5 pieces of candy per house, you would have to visit 644 houses to fill a pillowcase or 257 houses to fill a 5 gallon bucket. The light blue squares represent the pillowcase and bucket collection areas - .2 sq. miles (.5 sq. km) and .08 sq. miles (.2 sq. km) respectively. It's hard to say exactly how long it would take to cover that much area on foot, since it would depend on how many linear miles of street you had to traverse, and how much time was spent on each trick-or-treat interaction. From a visual inspection of the map, we estimate roughly 1 linear mile (1.6 km) of street distance per every .036 square miles (.09 sq. km). Under our worst scenario, that would mean walking over 11 miles (17.7 km) for the biggest bag of candy. Including the time spent on doorsteps, you might average 2 mph (3.2 kph) and hit 3-4 houses per minute if you really hurried, which means you would have to hustle candy from dusk to midnight to make your goal.

In our Midwestern neighborhood, we're going to assume that more people are giving out candy, and giving it out by the handful, so we based our calculations on a 75% success rate and 3.5 pieces per house. However, due to the lower density of housing (about 1090 houses/sq. mile), you would have to cover a lot more area than under our worst case scenario in the more populous neighborhood - about .23 sq. miles (.6 sq. km) for the bucket, and about .6 sq. miles (1.55 sq. km) for the pillowcase. Since the numbers for housing density are based on statistical averages and do not take into account the placement of undeveloped tracts of land, in reality you would probably end up covering a lot more area, and you would need a car.

Case Closed

In conclusion, the tried and true pillowcase has proven itself to be probably the ideal receptacle for collecting and carrying Halloween candy. A heavy duty trash bag could hold more, but would be too unwieldy to handle after a certain point. We could also see using a laundry basket or a wheelbarrow, but you would get more dirty looks from homeowners and fellow trick-or-treaters.

As for the square mileage necessary, if you are truly serious about trick-or-treating, your best bet is to go to an older neighborhood where the houses are closer together and the streets are laid out in a grid. You’ll be able to get to more houses and travel from house to house in a more efficient manner. You might get better quality candy by going to a richer and newer housing development, but unless it’s very dense, you’ll reach fewer houses, and since nobody gives more than a few candies anyway, at some point you’ll experience diminishing returns.





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