How Many?
Friday, December 18, 2009 at 12:01PM At my daytime job, we're in the process of training end users for their fancy new Microsoft Dynamics AX system. This is not a simple change, as most factory workers have been at their job since they graduated high school, and their working world is defined by the monotonous task they perform in their defined space every day. I'm the guy that points out that operating the same way for more than 10 years is insane, takes their money, then develops and implements a new system, which can take anywhere from 6 months to 3 years. And then some.
Everyone handles transition differently, and one factor of that is how old their legacy system is. Upgrading folks from a mouse-less green screen system to anything remotely current is quite difficult--mouse training is required in addition to software training. As crazy as it seems, millions of dollars of transactions are still performed on these prehistoric systems.
Luckily for me, I don't have to really talk to people that much, since I'm the techie in the background making everything work. That doesn't mean I don't have sympathy for the users. I do my part, by buying--out of pocket--fried dough. That way, when people don't want to train, I can tell them their two choices are being replaced, or sitting down and eating a donut--proof that all people love donuts.
The local donut shop by my current client believes that bigger is always better. The result is that many of their filled donuts and cinnamon buns have over a 6'' diameter. It didn't take long to notice that users preferred more normal sized donuts. After a few days in, I purchased donut holes in addition to the regular fare. These didn't last long at the office.
After a brief investigation, I found out that many people figured that the conversion of donut holes to a whole donut was 8:1. If this notion encourages sleep at night, then I'm fine with it--but I don't believe it to be true.
To begin with discovering the truth, here are my considerations for volume and caloric calculations. There will be no mass calculations.
- Converting from a yeast donut hole to yeast donut only.
- Ratio of [frying] oil to dough is higher for a donut hole.
- Ratio of frosting to dough is higher for a donut hole.
- A donut is three donut holes wide, so I will use the donut hole (dh) as a [length] unit of measure.
- Even though calories are based on Dunkin Donut nutritional information, the ratio should be constant.
First, let's compare volumes. There will be a small margin of error given that the donut hole is a sphere, and am calculating the donut as if it were a perfect 'washer'. The volume of a washer is pi times the radius squared times the height of the larger disc, subtracted by the same of the smaller disc, or simply pi(rout2 - rin2)h. This means the volume of a normal glazed yeast donut is 2pi, or about 6.28319 dh3. The volume of a donut hole, calculated via 4/3*pi*radius3, is .17pi or .523599 dh3. With a slight margin of error, this implies that there are 12 donut holes in a donut by volume--which is nonsense, even if we took two off the total to account for the top and bottom curvature of the donut. Regardless, given the differing frosting and oil ratios, volume isn't the best way to calculate the conversion.
Easiest way to sort out this mess, and in terms of guilt, is by nutrition. There are 220 calories in a glazed yeast donut. 50 calories in in a glazed yeast donut hole. 4.4 donut holes per donut. Done.
Calculus, Donut, Washer Method in Food 
Reader Comments (4)
Not too shabby, but a donut is technically a torus: http://en.wikipedia.org/wiki/Torus
Slightly diff volume calculation.
And yeah, calories would probably be the most logical choice here too. Nice work broheim!
Counterpoint--If we're doing volume, should air be included? The shape of the donut changes during the frying process, and the amount of non-dough substances. It came to me in the shower the other day, that before frying, the dough is a giant rolled out sheet, that is then stamped out. At this point in the game, height is constant, and there are no curves, since all sides are perfectly flat from being rolled out. Given height is a constant (we'll say of 1), you could do a simple pi r squared to compare.
I like your logic... GREG PS I nominated you for a Homie at The Kitchn so get over there and vote for yourself and your other fav blogs http://homies.apartmenttherapy.com/2009/category/home-cooking
Oh my...my Dash'ing Stash, you lost me at 8:1...I feel if people worry about stuff like that, then they should not be eating them. I only buy two chocolate glazed at Dunkin Doughnuts once or every other month, and that is it. You amaze me though...I am afraid I did not do well in science, and I scath by in culinary math, by eye only :) Merry Christmas my friend!!!