kimwoodward.org

You've probably heard it before, take in less calories than you expend and you will loose weight.  We can use our knowledge of how many calories that it takes to maintain our current weight without gaining or loosing to make something of this statement.  By simply taking in less calories than that maintenance value in a day we will be able to loose weight.  Right about now you are probably thinking, "but I don't know how many calories that I need to do that."  Fortunately, there is some simple math that can be used to figure out the calorie count and to figure out based on calorie deficit, how much can be lost.  I like to call that Diet Math.  The idea is based upon the use of BMR calculations with Harris Benedict Equation multipliers.  The BMR is the Basal Metabolic Rate and represents the number of calories that are required to maintain your current weight.  The calculation is related to your weight, your height, and your age.  The original study for this metabolic calculation was titled, "A BIOMETRIC STUDY OF HUMAN BASAL METABOLISM" by J. ARTHUR HARRIS and FRANCIS G. BENEDICT which was written in October 1918.  The article can be found here.  In the study, Harris and Benedict make the statement that "The heat production of the individual in a state of complete muscular repose 12-14 hours after the last meal, i.e., in the postabsorptive condition, has been called the basal metabolism."  From the article, the following equations can be derived.

Basal metabolism as defined in this article define energy expenditure during a state of rest, not exactly something that we do all the time.  Calories are a figure of energy expenditure or intake.  In fact, just the act of getting out of bed, walking across the room, driving a car, etc. will expend even more energy.  That is wherethe Harris Benedict Equation values come into play.  The Harris Benedict values relate to the amount of exercise, or lack of, that you undergo on a normal basis.  The values are based on averages but are pretty good as indicators of the values.  The following table lists the Harris Benedict values:

Gee that's nice Kim, so what can I do with this information?  Ok, lets use me as an example.  When I started on this little diet loss adventure I weighed 284.2 pounds.  That weight was actually down from an all time high of 289.0 three months earlier.  I am male, stand 6 foot one inch and am 58 years old.  My BMR at the start was:

66 + (6.23 x 284.2) + (12.7 x 73) - (6.76 x 58) = 66 + 1770.566 + 927.1 - 392.08 = 2371.586

Now I go to the gym for a moderate workout (walk on treadmill, stationary bike, or lift weights) between 3 and 5 times a week (I used to go about 10 times a week but I figured out that I needed a life more).  Therefore my Harris Benedict value is 1.55.  So the number of calories that I need to maintain my weight is 2371.586 x 1.55 = 3,675.9583 calories. 

That's a lot, and I was gaining weight at the time I started.  That equates to a lot of trips to KFC, McDonalds, and Taco Bell which are all near where I work.  I was eating out every lunch meal during the week.  My wife was trying her hardest to cook good healthy meals but I was gobbling down much more than I needed.  Here is what I am talking about.  Let's say that I was eating Breakfast and Lunch at McDonalds which I normally did.  I would have a couple of Breakfast Burritos (2 x 300 cals) plus a Sausage Biscuit (410 cals) and a Fruit Yogurt Parfait (160 cals) all from the dollar menu.  Total: 1170 cals.  Next we have Lunch, typically I would have a Mickey Ds Sweet Tea (230 cals), maybe two double cheeseburgers (2 x 460), a side salad with ranch dressing (190 cals), and two apple pies (2 x 250 cals).  Total: 1840 cals.  Oh yea, I might have some snacks in between breakfast and lunch and lunch and dinner.  I am trying to watch my weight so I use the 100 cal packs of almonds.  Total: 200 cals.  But that is not enough because I generally have 5 cups of coffee during the day, each with cream and sugar (5 x 70 cals).  Total: 350 cals.  Now I've got to deal with dinner which is pretty healthy and lets just say that it is somewhere around 550 cals.  Now if you were keeping track you know that I have consumed around 4110 cals.

Since the value of 4110 is above the 3676 calories that I need to maintain my weight at the same value.  Since there are 3500 cals in a pound, we can figure out how much weight I will have gained in a day, gorging myself on the meals mentioned above.  (4110 - 3676) divided by 3500 = 0.124 pounds per day.  That may not seem like much but it is a gain and over 5 days I would have put on a little more than half a pound.  Multiply that by 52 weeks and I have now gained ... well you get the picture.  Better to go the other direction.  In fact, when Diet to Go came along with a pre-packaged deal of 1600 cals per day on the average, my eyes lit up.  Wanna know why? Well do the math: (3676 - 1600) divided by 3500 = 0.593 pounds per day.  Now that is a caloric deficit so my weight will be going down by that much per day.  Is that amount of weight loss really true?  Well my activity has varied by quite a bit since I started the diet on November 3, 2009.  My weight loss graph indicates that something at least is going on.

But what about that time honored adage from the health community that says you shouldn't loose more than one pound a week?  We have answered the question of how much weight you can loose in a point in time.  With me it seems that I am violating the one pound a week rule.  Yea, okay, but I need to get down to a usable weight as soon as I can because of health reasons.  Besides, I have been seeing my doctor and getting a physical and the numbers look incredibly good.  I feel better and I am getting my waistline to go down to a level that does not show that I will be having problems with health issues in the future.

The next question to tackle is how to predict when we will hit a certain weight if we "stick to the program".  Note that if you fall off the wagon from time to time it just means that you have a caloric increase.  That means that you will gain a little, if the number of calories you take in during the day is above the amount of calories that you require to maintain a constant weight.  If your overall progress is calorie deficits then by definition you will loose weight.  My graph seems to be spectacular in the weight loss department, but that is only because I have a huge caloric deficit compared to my overall weight.  As you loose, don't forget that your weight is constantly changing.  For sake of argument lets assume that it is always in a downward direction.  The closer you come to a zero difference between the number of calories for constant weight and what you are consuming, the more the curve levels out.  For my weight, 1600 calories is sufficiently far enough away that my curve is almost linear.

What I have done to predict my weight loss is to graph my weight loss against time.  In that graph, when I reach the last measured point, I use a moderate activity based loss curve as the optimistic weight loss and a sedentary activity based loss curve as the pessimistic weight loss.  For any given goal weight along the y axis, that weight will intersect both the optimistic weight loss and pessimistic weight loss.  The dates corresponding to those intersection points reflect the optimistic and pessimistic dates for when I think that I will achieve the goal weight.  For me, I am looking at 10%, 15%, 20%, 25%, and final goal weights.  This gives me a chance to work on getting to a specific goal.  When I reach that goal, I can now feel just that more confident that I will reach the next goal.  Then I make the next goal the line on the chart to figure out new dates.  My weight loss graph shows just that.

Since the weight is constantly changing, and each calculation is based upon your current weight, the curves change continuously and it becomes harder to predict from a simple calculation just when you will achieve a goal weight.  However, we can simplify the calculation if we assume a linear curve (not that far off) and deal with number of days.  Here is an example of the calculation based upon my weight from this morning, 252.4 pounds (after almost 10 weeks on DTG).  Optimistic: (1.55 x (66 + ( 6.23 x weight in pounds ) + ( 12.7 x height in inches ) - ( 6.76 x age in year)) - 1600) / 3500 and Pessimistic: 1.2 x  (66 + ( 6.23 x weight in pounds ) + ( 12.7 x height in inches ) - ( 6.76 x age in year)) - 1600) / 3500.  These equations are in pounds lost per day.  We can divide the number of pounds to be lost with the results of these equations to get a figure for the number of days to go before we see the goal weight.  In my case, if my current weight is 252.4 and I wish to get to 241.6 (15% from my initial weight when I started).  Then my pessimistic value (based on sedentary) would be 37.5 days and my optimistic value (based on moderate activity) would be 21.4 days.  From this date of 1/9/2010 it looks like I should see my goal somewhere around the first week or so of February.

From simple analytic geometry, we can use an y = mx + b linear formula to solve for the number of days that we would be able to achieve the goal weight.  The formulas assuming a moderate activity are:  

number of days (pess) = (cur_weight - goal_weight) x 3500 / (1.2 x (66 + ( 6.23 x cur_weight ) + ( 12.7 x height ) - ( 6.76 x age)) - 1600)

number of days (opt) = (cur_weight - goal_weight) x 3500 / (1.55 x (66 + ( 6.23 x cur_weight ) + ( 12.7 x height ) - ( 6.76 x age)) - 1600)

This equation gives the number of days from the current date measurement to get to the goal_weight. 

The equations for women are similar:

number of days (pess) = (cur_weight - goal_weight) x 3500 / (1.2 x (655 + ( 4.34 x cur_weight ) + ( 4.7 x height ) - ( 4.68 x age)) - 1600)

number of days (opt) = (cur_weight - goal_weight) x 3500 / (1.55 x (655 + ( 4.34 x cur_weight ) + ( 4.7 x height ) - ( 4.68 x age)) - 1600)

Note that the cur_weight and goal_weight are in pounds, height is in inches, and age is in years.