Neither prediction is doing very well (the blue and red curves). The yellow curve is a fit to the equation w(t) = aebt + 130, and I only fit the equation to the last two points, because I think the first measurement is inflated relative to my current diet. If I include the first point and leave the asymptote unknown, Mathematica chokes! I used 130 instead because that is the number from the red curve and it seem reasonable. More data will always help!
Saturday, August 30, 2014
Week #2: 303.2 lbs (37.2%)
Down 6.8 lbs for week 2! I don't think its really valid, though, as I worked on the house yesterday and am pretty dehydrated. But I'll take it anyways!
Saturday, August 23, 2014
Week #1: 310.0 lbs (37.4%)
One week down! I lost 11.4 lbs this week and 2.5% body fat, but I'm sure more than half of that was water. So much for the Mifflin St Jeor equation! A few years ago I found another equation that said I would burn about 12 kcal per lb, so if I add my walking to that (and use today's weight as the "initial" condition) I get another function that I think is more reasonable, and that I expect to trend well going forward:
So, according to Mifflin St Jeor, I should lose only 2.0 lbs this week, but the new equation predicts 4.6 lbs, which sounds more realistic to me! I'll keep an eye on these curves, as well as a regression fit, into the next few weeks.
w(t) = 130.229 + 184.468e–0.0257947t, where t is in weeks.If I plot this equation, the Mifflin St Jeor equation, and the data points, I get:
Saturday, August 16, 2014
Week #0: 321.4 lbs (39.9%)
It seems that everyone nowadays is blogging about and posting their weight loss progress (or lack thereof) on Facebook and Twitter. I think this is great for accountability purposes! The problem I have always had when attempting to lose weight was the periodic cheating, and that the only one who knew I was cheating was me. I need someone to yell at me when I screw up!
Since I am an engineer by training and at heart, I am taking a very logical and mathematical approach to all of this. My goal weight is 220 lbs. For my height, 6 ft 4 in, that is the upper bound of my ideal weight range, and my actual body fat percentage should be in the normal range at that weight. (Doctors tend to follow the government's advice and use BMI to tell if you're overweight. BMI is only intended as an approximation to body fat percentage, so if you have a scale that can measure body fat, that is a better estimate anyways. My BMI at 220 lbs will be 26.8, which is still considered overweight, but I expect my body fat percentage at 220 lbs will be around 22%, which is considered healthy.)
As I am an engineer, I would like to define a strict regimen for diet and exercise (a.k.a., a procedure!) that I can use to project my progress. This will consist of the following menu each day:
I will also be trying to stay well hydrated by drinking 1 fl oz of water for every kg of body weight. I am including coffee, milk, tea, and orange juice in this "water," and I will be updating the daily quantity weekly. The first week will then include 74 additional ounces of water each day.
Since I am an engineer by training and at heart, I am taking a very logical and mathematical approach to all of this. My goal weight is 220 lbs. For my height, 6 ft 4 in, that is the upper bound of my ideal weight range, and my actual body fat percentage should be in the normal range at that weight. (Doctors tend to follow the government's advice and use BMI to tell if you're overweight. BMI is only intended as an approximation to body fat percentage, so if you have a scale that can measure body fat, that is a better estimate anyways. My BMI at 220 lbs will be 26.8, which is still considered overweight, but I expect my body fat percentage at 220 lbs will be around 22%, which is considered healthy.)
As I am an engineer, I would like to define a strict regimen for diet and exercise (a.k.a., a procedure!) that I can use to project my progress. This will consist of the following menu each day:
- Breakfast (570 kcal):
- 53 g Kashi GoLean Crunch cereal (200 kcal)
- 1 cup whole milk (150 kcal)
- 1 cup orange juice (110 kcal)
- 1 medium banana (105 kcal)
- 2 cups coffee (5 kcal)
- Lunch (364 kcal):
- 2 slices Freihofer's double fiber bread (200 kcal)
- 1 Tbsp spicy brown mustard (15 kcal)
- 65 g Inspirations deli turkey (77 kcal)
- 1 can V-8 juice (72 kcal)
- Snack (165 kcal):
- 12 fl oz hot tea (4 kcal)
- 1 tsp honey (21 kcal)
- 1 Kashi Peanut Peanut Butter bar (140 kcal)
- Dinner (607 kcal):
- 1 SmartOnes frozen meal (282 kcal)
- 16 fl oz whole milk (300 kcal)
- 12 fl oz herbal tea (4 kcal)
- 1 tsp honey (21 kcal)
My total daily caloric intake will be 1706 kcal, on average.
For the loss term, I will use the Basal Metabolic Rate computed using the Mifflin St Jeor equation: 10w + 6.25h – 5a + s, where w is weight in kg, h is height in cm, a is age in years, and s is +5 for males and –161 for females. This equation gives the number of calories burned per day with no additional exercise. For my specs, this will be (4.55w + 1036.5) kcal/day, where w is weight in lbs.
I will also commit to walking at lunch each work day. On the weekends, Ashley and I are working on the house, which is a different kind of exercise. A moderate walking pace is 3.3 METs, where 1 MET is the equivalent of burning 1 kcal per hour per kg of body weight. That means my daily walk burns 0.8w kcal/day, where w is weight in lbs. This makes my total loss term (5.35w + 1036.5) kcal/day.
Now I have enough to form a differential equation for my weight (production – loss):
dw/dt = 1706 – [5.35w(t) + 1036.5] = 669.5 – 5.35w(t) kcal/dayWhat I really care about is lbs per day, not calories per day. One pound of human fat tissue contains approximately 3,555 calories, so assuming the weight loss is all fat (which I hope it is!), we can rewrite the equation as:
dw/dt = 1.318 – 0.01053w(t) lbs/weekSo, in my first week, I should lose about 2.07 lbs! If we solve this equation for w(t), we find:
w(t) = 125.166 + 196.234e–0.01053t lbsThis means I should expect to hit 220 lbs in about 69 weeks, or 1 year, 4 months! That's a lot of dieting! I hope my assumptions are wrong!
I will also be trying to stay well hydrated by drinking 1 fl oz of water for every kg of body weight. I am including coffee, milk, tea, and orange juice in this "water," and I will be updating the daily quantity weekly. The first week will then include 74 additional ounces of water each day.
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