A literary and scientific approach to goal weight


As I mentioned in my previous post, if you want to start a diet and exercise plan, you should first decide what your goal weight is, and how long you want to take to get to it. These can be moving targets: I first decided on a goal weight of 180 lbs (from my starting point of 205 lbs); when I got to it without too much trouble, I decided to shoot for 170, then 160, and eventually settled on a final goal weight of 155 lbs. I also decided that I wanted to lose about 1 pound per week, meaning that in an ideal world it would take a hair over a year to achieve the goal. This being the real world, it took more like one and a half years, but I got there eventually. Why it took longer, and how I measured my weight loss accurately, are two things for upcoming columns. For right now, let’s talk about why I ultimately chose 155 lbs for my goal weight.

The choice was based on a combination of scientific methodology and literary research. Literary first: I’m a connossieur of old science fiction stories. If you read old space operas from the 1930’s through the 1950’s, you come across purple prose like this:

Biff Harrison stretched himself up to the full height of his loose-jointed, 6’2” frame. Determination lit up his steely gray eyes. “What do the Centaurian’s want?”, he demanded through clenched teeth, his 185 pounds of hard muscle straining against the force field that held him and Dolores prisoner.

            Dolores cast her eyes demurely downwards: “Don’t make me say such awful things!” she responded in a doleful voice, her cheeks blushing a deep red…

You read similar sorts of things in modern romance novels. The heroes almost universally stand between 6’ and 6’ 4” tall, and weigh between 180 and 185 pounds. Picking the middle of the range, let’s say that our canonical romance/spacce opera hero stands 6’ 2” (1.88 m) and weighs 182 lbs (83 kg). Height varies with weight: shorter people tend to weigh less than taller ones simply by virtue of being shorter. But by how much?

Well, I stand 5’ 10” (1.78 m) tall. Should my weight be in proportion to my height? No, not at all. This is one of Galileo’s great contributions to science, referred to sometimes as the Galilean square-cube law. Weight is proportional to the mass of an object:  mass is proportional to volume times mean density. The mean density of most people is pretty similar, about the same as the density of water. Because of this, my weight should be proportional to my volume.

People are complicated shapes, so let’s consider a simple one. A cube with side length 1 meter has a volume of (1) cubed = 1 cubic meter. A cube with side length 2 meters has a volume of (2) cubed = 8 cubic meters. If the weight of the first cube is 100 pounds, the weight of the second will be 800 pounds because the volume is 8 times higher. (I know I’m mixing English and metric units here – sorry!)

Ideally speaking, then, since the cube of 1.88 is 6.64, and the cube of 1.78 is 5.6, if I want to look like the archetypal romance novel hero, the ratio of my weight to his should be in the proportion of 5.6 to 6.64. This is about 85%, and 85% of 182 pounds is 154 pounds. Voila!  I won’t claim that I look exactly like a scaled-down romance novel hero, but my proportions are decent, especially if you squint a little.

There are other ways of considering this. Galileo pointed out that the weight is supported by the cross-sectional area of the bones, which presumably are proportional to the total body area, i.e., to the square of the height rather than the cube. If I want to have the same “bone cross-section loading” as a romance novel hero, I should make weight proportional to surface area, or height squared, implying an ideal weight of 163 lbs. Indeed, this idea leads to the concept of the Body-Mass index, which is weight (in kilos) divided by height squared (in square meters). The healthy range for BMI is something like 20-25 range for adults, although there is dispute over the proper use of this metric. Under these considerations, the BMI of our typical romance hero is 23.4, whereas my BMI is 22, both in the ”healthy” range.  Either way, the implication is that for adult males of “average” height and build, body weight should change by about 7 lbs per inch of height, or about 4% per inch.


The Physics Diet


Happy holidays and post-holidays!


This is an “and more” post to help people combat post-holiday funk and guilt about over-eating and drinking during the season.   Many people have New Year’s resolutions which involve losing weight, either weight gained over the holidays or because they feel the general need for weight loss. I’m writing this post and a few others to give some practical advice for those in need, and to look at the science (physics, particularly) of dieting and weight loss. This is going to be the first in three or four posts on the general subjects of dieting, exercise and weight loss, including a literary and philosophical discussion of one’s ideal weight.

I feel that I can write with some authority on this. Between April 2012 and April 2013, I lost 50 lbs, going from an initial weight of 205 lbs to a final weight of 155 lbs. More to the point, I have kept my weight at this level since then. I’ve included a graph of my weight on this blog.  (The blue dots are the actual weight, and the red dots from straight line fits to the data to figure out how fast I was losing weight.  Each dot is my average weight for that particular week – week zero was when I started.)  The shape of the curve is pretty interesting in itself, and I’ll come back to that point in a later post. Other details: I am 5’9” (178 cm) tall, which implies a Body Mass Index of about 23 at my current weight. This is well within the region considered healthy. I have a 32” waist (down from 40”), meaning a waist-height ratio between 0.4 and 0.5, again generally considered to be in the healthy region.  All of my vital stats (blood pressure, trigliceride levels, cholesterol levels, blood sugar, and heart rate) improved when I lost this weight, so I think I can safely say that I am in better health now than when I started.

Before I begin discussing weight loss methods, there are two points I want to make:

  • If you decide to lose weight, please talk to your doctor first and discuss different options, how fast you should lose weight, and what your goal weight should be. The methods I describe here should work for anyone in reasonable health to begin with, but are not good for everyone.
  • There are many fad diets and exercise plans out there. What I am describing are techniques for losing weight rather than a detailed specific plan. In particular, for reasons I will discuss in a later post, I am not going to specify particular foods one should or shouldn’t eat to lose weight.

These techniques are straightforward. This doesn’t mean they are easy! I don’t know why, but there are very few things worth doing in this world which are easy. They are also discussed in varying different forms in other places on the web and elsewhere. What I am discussing uses the same basic underlying ideas as other plans which range from very complicated (The Hacker’s Diet) to the very simple (such as a plan discussed by Tom Murphy). It is also similar to commercial plans such as WeightWatchers. Any and all of these work if you follow them, so don’t just read what I’m saying. In point of fact, the approach I took when I wanted to lose weight was to gather up as much information as possible from different sources and evaluate them. I considered WeightWatchers, but because I am a poor professor and a cheap bastard, I decided to formulate my own plan. (One later post will include instructions on how to effectively exercise at home without paying any money for equipment or a gym membership.)

So: here is the big plan for losing weight. It involves three parts, each equally important:

  1. Exercise more than you currently do;
  2. Eat less than you currently do;
  3. Weigh yourself every day and record the weight, but make plans based on weekly averages of your weight.

Here’s an easy way to remember this: sweat, starve and scribble. (Don’t really starve yourself, of course…) A few points regarding this:

  • Some people are going to read this and think,”well, duh — this is obvious!” Well, maybe, but there are a lot of fad diets or exercise routines out there which attempt to circumvent these rules. IMHO, they may work for the short term, but are probably unsustainable. What I am writing about is sustainable, and based on real science, at least as best I understand it.
  • The type of exercise doesn’t matter much as long as it is hard, aerobic exercise. I started out doing 45 minutes on an exercise bike, three times per week, which seemed like a reasonable way for me to begin. I’ve ramped up the duration, frequency and intensity since then, but again I will discuss this in a later post. I’ve also added other aerobic exercises which don’t require a machine (again, to be discussed in a later post.) Pushups, situps and other types of conditioning exercises won’t work for losing weight, although they’re good for other things.
  • The eating less part is more difficult, as it is pretty hard to count calories accurately. As a rule of thumb, try to go to bed slightly hungry (Not starving! Not with a belly crying out to be filled!) Slightly hungry seems to be a good measure for most people if you want to lose weight.
  • Keeping accurate records of your weight is as important as the other two aspects of the plan! Try to use the same scale each time at the same time of day (just after waking for me), and if possible, weigh yourself nude. (Clothing adds anywhere from about 1 to 5 pounds to your weight.) Some people use their computers or apps for their smartphones; I write my weight in a Monthly Planner book, but use an Excel spreadsheet program to calculate averages.
  • Plan for the long term. Don’t try to lose too much weight too quickly. My doctor and I decided that losing between half a pound to a pound per week was healthy, so that’s what I attempted (and largely succeeded at.) Again, discuss this with a doctor before beginning!

In the next several posts I am going to go into detail on how to do this. The next post will introduce the “master equation” for dieting, and discuss its implications.

Dieting in a Flash


I’m pretty happy with the new TV show “The Flash” – it just keeps on giving to someone like me, who likes to look for the science in fiction. In my last post I made a rough estimate of the Flash’s speed, and in last week’s episode they confirmed that it was in the right ballpark. There’s a throwaway line between Barry Allen, the Flash, and his mentor/father figure, Detective Joe West. The captain says that he’s used to runners doing a mile in 4 minutes, not in 4 seconds. Barry looks a bit sheepish and tells him, “More like three seconds.” This is about one-third of my estimate of about 1 mile every second, but mine was a pretty darn crude one so I don’t feel too bad. A mile every three seconds is 1800 feet per second, or about 540 meters per second. Because he’s going a bit slower than I estimated, all of my calculations in the last entry are off by factors of about 5-10, but the general conclusions still stand. In particular, he’s traveling at Mach 1.5, so as people watch him go by, he should generate a sonic boom.

The episode gave me a new topic to consider: his diet. In the episode, he kept on having dizzy spells, nearly fainting at one point. His science support team ultimately realized that moving that fast took a lot of energy – he needs to eat a lot to support his running habit. There’s some banter on the show about redoing the calculations based on eating cheeseburgers instead of pizza, or some such (I think the line was “It’s a whole new set of equations!”, but I can’t swear to it.) So: how much more should he be eating?

The energy expenditure rate by the average adult male is about 2,000 Cal per day, which is the same as 100 Watts – we’re all relatively bright light bulbs, energetically speaking. Now, people move around with an average speed of some 3 miles per hour, give or take, which is about the same as 1.3 meters per second. The Flash moves 400 times faster than this, so he’s expending energy at a much higher rate.

Accodring to biophysics textbooks, the energy expenditure for running generally scales proportionally to the speed. (This has to be taken with a big grain of salt, because there is, of course, no data for running 1.5 times the speed of sound.) So when he is running, if we believe this model, he is expending at least 400 times more energy than normal. The issue is complicated, because the energy needs could be much higher: running costs for these sorts of models are based on the energy expenditures of moving the body itself, ignoring external factors like air drag. It could be tens of millions of times higher, if one believes a simplistic model based on air resistance.

To give him the benefit of the doubt, let’s say it’s only a thousand times higher. Well, he doesn’t run all of the time: he’s a sprinter rather than a marathon runner. If he’s only moving at such high speeds for 1% of the time, his total metabolic rate will only be some ten times higher than the average human being, meaning he needs to eat some 20,000 Cal per day to do this.

Getting rid of this excess heat won’t be easy. The human body is only about 20% efficient in turning food energy into useful work. The other 80% goes out as heat. He’s got to get rid of some 800 Watts of heat! (This isn’t only when he’s running – remember, his top energy expenditure rates will be a thousand times higher than normal.) Instead of being a bright light bulb, he’s an iron. This is equivalent to doing very heavy exercise on a stationary bike, all of the time.  Sweat should continually be pouring off his skin, making his attempts to impress Iris problematic, at best.  He’s also going to dehydrate pretty quickly.

This is the conservative estimate for his metabolic rate; another way to look at it is to think about the power consumption rate of a supersonic transport like the late, great Concorde SST, which flew at about the same speed he runs at. The Concorde’s engines had an amazing 200 megawatt power consumption rate. (It flew higher than subsonic passenger aircraft to reduce drag.) It carried about 100 passengers, so maybe we should estimate the energy requirements for the Flash as perhaps 1% of the energy requirements for the SST, meaning 2 megawatts whenever he’s running. If this estimate is the correct one, even if he only runs around for about 1% of the time, he’s still going to run through food at a rate about 200 times that of the average human, and have to dispose of excess heat at about the same rate as a small car’s engine. Hot stuff!