Here’s a couple of interesting questions:

  1. What is a refeed?
  2. What are the types of refeeds?
  3. Do I need to refeed?
  4. When do I need to do a refeed?

A refeed is eating more calories. I am going to not talk about the various types of refeeds since some of them involve adding carbohydrates.

The stated purpose of refeeds is to rebalance hormones, ie, “avoid Metabolic Adaptation”. From the page Why Diets Fail – How to use Refeeds & Calorie Cycling to Avoid Metabolic Adaptations!

The Energy Gap: Describing the decrease in your calorie expenditure (how many calories you burn) by going into energy saving mode and the increase in hunger hormones (ghrelin).

Metabolic Adaptations & Adaptive Thermogenesis: The process in which your bodies metabolism, thyroid and key anabolic hormones such as testosterone, IGF-1 and estrogen take a nose dive.

So, what makes a person go into energy saving mode?

Eating at a large caloric deficit can cause a person’s metabolism to drop. My contention is that the only time this is an issue is if you eat at a too much of a deficit where your body fat can’t sustain your loss. This happens in two cases; where the body fat is very low – like a bodybuilder cutting for a physique contest, and where the caloric deficit is larger than the amount of fat your body can mobilize to cover the dietary shortfall.

Both of these involve some pretty simple calculators. First, determine your body fat in lbs. The US Navy Calculator is one way to do this. Then multiply that number by 31 cals/day/lb. This gives you the maximum caloric deficit that your body can provide for from fat stores. Note this is for a sedentary person.

So if you are 200 lbs and the Navy Bodyfat calculator says you have 50 lbs of fat, then you have 50 times 31 = 1550 calories available from your body fat. Note this is a theoretical maximum. The actual may be somewhat less than that amount.

Next calculate your Total Energy Expenditure. For a 200 lb guy that’s probably somewhere around 2600 calories a day. There are plenty of calculators which can show these numbers. In this example, the person expends 2600 calories a day and 1550 can come from body fat so they must eat at least 2600-1550 = 1050 calories a day. Anything less and their metabolism will drop.

It’s a similar situation but much more dire with less body fat. Someone who weights 175 lbs with 10% body fat only has 17.5 lbs of body fat or  542 calories a day available from body fat. They can’t eat at more of a deficit and keep their metabolism firing at that rate.

What should you do to monitor your own metabolism?

Turns out there’s a really easy way to monitor your metabolism. For every 10% drop in metabolism the body temperature drops 1 degree C.


Christmas Status Letter


Holidays provide time to reflect on the past year. It’s long overdue to circle back to the purpose of this BLOG. I started this journey of hacking my Type 2 Diabetes almost 18 months ago. In that time, I fixed my Diabetes and so much more.

No More Insulin or Medications

I am on ZERO medications. No diabetes medications. No hypertension medications. I still use a CPAP machine since I am afraid of quitting the machine.

Weight Loss

I have lost over 100 lbs. My starting weight was around 285 and it was 178 this morning. I’ve been in maintenance for a month now and my weight has stayed steady. I wish I had charted better in the beginning.

Added Exercise

After I lost most of my weight (around 80 lbs) I added exercise. I have been doing CrossFit for about four months now. I can lift weights that match the girl’s weights. I usually finish the Workout of the Day (WOD) last but I do finish – even the hard ones. I workout five days a week. The typical CrossFit workout is less than one hour. I take rest days Thursday and Sunday.

Blood Sugar Control

My blood sugar after working out last night was 65 (US units) which is really good. I most often see numbers in the mid 80s. My last HbA1C was taken this summer (before CrossFit) and it was 5.8 (which is at the bottom end of the prediabetes range).

My Macros

My diet consists largely of chicken, nuts and broccoli.

Chicken is a good Protein and different cuts provide different amounts of fat. Kim Chee (from Walmart refrigerated veggie section) is a good probiotic (good for stomach biome). Broccoli is a good veggie and easy to heat in a microwave bag. Finally, nuts fill in the fat numbers in a healthy way.

My Macros

My daily macros are:

My current macros are 1800 calories with 125g of Protein, 20g of Carbohydrates and 136g of Fat. Protein is a minimum. Carbs are a maximum. Fat fills up the remaining calories to meet the limit. If I go over on Protein I will go under on Fat to match. In percentages of daily calories this is 27% Protein, 5% Carbohydrates, and 68% fat.


Here is what I take daily.

Breaking Stalls

I had a long stall this year which lasted for maybe six months. I did some extended fasts which helped a little bit. I then tripped across the idea of doing Protein Sparing Modified Fasting. That broke the fast and gave me a way to make progress with the last 25 lbs that I needed to lose.

My Goals

My goals have shifted over the past 18 months. They started with hacking my Diabetes. I wanted to get off Insulin. That took two weeks.

Since then I have worked at improving my Insulin Sensitivity. For me, the main tool was Intermittent Fasting (IF). One thing that interferes with this is getting in enough Protein. I have added a Protein meal at lunch time. This hasn’t hurt my Blood Sugar numbers.

Another way of improving Insulin Sensitivity is High Intensity Training. I do CrossFit. Training with increasingly heavier weights and intensity will improve Insulin Sensitivity. I hope to keep up this training and there are plenty of goals to reach. I got my first box jump and pullup in the past month.


Bible Fasting

Some verses to ponder on fasting:


Est 4:16

Go, gather together all the Jews that are present in Shushan, and fast ye for me, and neither eat nor drink three days, night or day: I also and my maidens will fast likewise


2Ch 20:3

And Jehoshaphat feared, and set himself to seek the LORD, and proclaimed a fast throughout all Judah.


Mar 2:20

But the days will come, when the bridegroom shall be taken away from them, and then shall they fast in those days.


Joel 2:12
Therefore also now, saith the LORD, turn ye even to me with all your heart, and with fasting, and with weeping, and with mourning:


Act 27:33

And while the day was coming on, Paul besought them all to take meat, saying, This day is the fourteenth day that ye have tarried and continued fasting, having taken nothing.


Protein Sparing Modified Fast (PSMF)

There’s a lot of scientific data concerning Protein Sparing Modified Fasts (PSMF).

Here’s one article (Nitrogen Metabolism and Insulin Requirements in Obese Diabetic Adults on a Protein-Sparing Modified Fast), ).

When this fast was applied to seven obese adult-onset diabetics who were receiving 30–100 units of insulin per day, insulin could be discontinued after 0–19 days (mean, 6.5). In the three patients who had extensive nitrogen-balance studies, balance could be maintained chronically by 1.3 gm. protein per kilogram IBW, despite the gross caloric inadequacy of the diet. The PSMF was tolerated well in an outpatient setting after the initial insulin-withdrawal phase had occurred in the hospital. Significant improvements in blood pressure, lipid abnormalities, parameters of carbohydrate metabolism, and cardiorespiratory, symptoms were associated with weight loss and/or the PSMF. For diabetics with some endogenous insulin reserve, the PSMF offers significant advantages for weight reduction, including preservation of lean body mass (as reflected in nitrogen balance) and withdrawal of exogenous insulin.

Another paper (Multidisciplinary treatment of obesity with a protein-sparing modified fast: results in 668 outpatients. A Palgi, J L Read, I Greenberg, M A Hoefer, B R Bistrian, and G L Blackburn – Full Text) showed excellent results. Here’s the abstract:

Six hundred sixty-eight obese outpatients, 71 per cent (+/- 34) in excess of ideal weight, were enrolled in a multidisciplinary weight control program. The major components of the program included nutrition, education, behavior modification, and exercise. Rapid weight loss was accomplished using a very low calorie (less than 800 kcal) ketogenic diet. Patients adhered to the protein sparing modified fast (PSMF) for 17 +/- 12 weeks and averaged 9 +/- 17 weeks in a refeeding/maintenance program. Mean weight loss was 47 +/- 29 lb (21 +/- 13 kg) at the point of minimum weight and 41 +/- 29 lb (19 +/- 13 kg) at the end of the maintenance period. Systolic and diastolic blood pressure and serum triglycerides fell significantly in men and women. Success in weight loss was greatest in the heaviest patients, those who adhered the longest to the PSMF, and those who stayed the longest in the maintenance program.


How Much Glycogen Stores in Low Carb?

It’s often claimed that Glycogen stores are reduced in Low Carb diets. I wondered by just how much and there’s a paper out there which has specific numbers in it (Scandinavian Journal of Clinical and Laboratory Investigation Volume 32, 1973 – Issue 4. Pages 325-330. Liver Glycogen in Man –- the Effect of Total Starvation or a Carbohydrate-Poor Diet Followed by Carbohydrate Refeeding. Depts. of Gastroenterology and Clinical Chemistry, L. Hson Nilsson & E. Hultman, S:t Eriks Sjukhus, Stockholm, Sweden & E. Hultman).

Liver glycogen content was determined in specimens obtained by repeated percutaneous biopsies during starvation and under various dietary conditions in 19 human subjects. During rest and following an overnight fast, there was a decrease in liver glycogen content by a mean of 0.30 mmol glucosyl units per kg wet liver tissue per min during a further 4 hours’ starvation. Prolonged starvation or carbohydrate-poor normocaloric diet decreased the liver glycogen from a mean of 232 to 24–55 mmol glucosyl units per kg within 24 hours. During an additional period of up to 9 days on the carbohydrate-poor diet the liver glycogen remained at a low level. Refeeding with a carbohydrate-rich diet gave a rapid increase of the liver glycogen to supernormal values, 424–624 mmol glucosyl units per kg wet liver tissue.

Wow! That’s a pretty dramatic drop in liver glycogen in just 24 hours.

Glycogen Refill

Maybe even more amazing is the very fast refill to 2x-3x the “normal” levels. That goes a long way to explaining weight gain when leaving the Low Carb diet.

As a reference on the liver (Clinical Methods: The History, Physical, and Laboratory Examinations. 3rd edition.Chapter 94 Evaluation of the Size, Shape, and Consistency of the Liver. Douglas C. Wolf.)

The liver weighs 1200 to 1400 g in the adult woman and 1400 to 1500 g in the adult man.

According to this article:

Liver glycogen provides about 400 calories or 100 grams of glycogen

If there’s 3-4 grams of water with every gram of glycogen that’s a total of 400-500 grams that are lost with reduction in glycogen. That’s less than 1 lb but a significant portion of a typical liver size (around 1/3 of the size).


How Much Muscle is there in a Person?

Bayesian Bodybuilding (How can you gain muscle while losing fat & more) cites an interesting study of muscle composition (Am J Clin Nutr. 1982 Jul;36(1):131-42. Biochemical composition of muscle in normal and semistarved human subjects: relevance to anthropometric measurements. Heymsfield SB, Stevens V, Noel R, McManus C, Smith J, Nixon D.). In this paper they dissected dead bodies to determine their body composition. Of particular interest was the Protein composition and water during semi-starvation.


Yang – Part 1 – What is Lost During a Diet or Fast?

There was an interesting study done back in the mid 1970’s. The study may not be possible today since there may now be ethical issues about starving people. We seem to have a fear of fasting that fails to take into account our human history of long fasts and famines.


The six subjects in the study were each given one of three different diets for ten days each. Over the course of the thirty days they ate either a ketogenic diet, a mix fat/carbohydrate diet, or they were fasted.
This is a pretty unique study since it provides the opportunity to see what effects fasting has vs other means of weight loss. Perhaps most interestingly is that they looked at what was lost during each of the three diets. Here’s the results of the losses from each in table form (with percentage of the total weight loss):
Diet/Intervention Weight Loss Water Loss Fat Loss Protein Loss
Ketogenic Diet 466 g/day 61.20% 35.00% 3.80%
Mixed diet 278 g/day 37.10% 59.50% 3.40%
Fasting 751 g/day 60.90% 32.40% 6.70%
Here is the same data in grams per day:
Weight Loss Water Loss Fat Loss Protein Loss
Ketogenic Diet 466.6 g/day 285.6 163.3 17.7
Mixed diet 277.9 g/day 103.1 165.4 9.4
Fasting 750.7 g/day 457.2 243.2 50.3

Ketogenic vs Mixed Diet

Once again the Ketogenic diet is shown to be more effective at weight loss than a mixed diet. However, the different is almost entirely made up of a much larger water loss on the keto diet than on the mixed diet. Looking at the grams per day of fat loss (the only thing that really matters in weight loss) the keto diet and the mixed diet are almost identical. Protein losses were equivalent on both the Keto and Mixed diets so there’s not much of an advantage to either. In the case of Keto vs Mixed it might just come down to which diet is easier to comply with and Keto wins that hands down for most people.

Fasting vs Ketogenic Diet

The results here show that a person can lose more weight fasting than they can even with either a ketogenic or a mixed diet. After all, they are eating nothing while fasting. Fasting produced almost three times the weight loss of the mixed diet. And when it comes to fat loss, fasting also wins hands down with a 1/3 greater amount of fat lost.

However, protein losses while fasting are almost twice those of the ketogenic diet on a percentage basis. The loss of 50g of Protein a day is almost two ounces of protein per day. That could be a significant amount for someone and is not a great preservation of Lean Body Mass.

The answer here may be found in the subjects themselves. They were six grossly obese males. The mean weight was 140 kg (308 lbs). They were great subjects for fasting since they had more than enough fat mass to support a ten day fast.

Fasting was slightly better about not having as much water loss as the Keto diet but Fasting was not as effective for weight loss as a percentage of weight lost.

What Does This Study Say About Fasting?

  1. Fasting produces the quickest weight loss of any of these three methods.
  2. Over 60% of the weight lost during a fast was water weight. This was the same for the Ketogenic diet. A mixed diet with carbohydrates is better at holding onto water. Much, it not all, of water weight is quickly regained after leaving the any diet.
  3. Fasting does not spare Protein as well as the Ketogenic diet. In fact, it is about twice as bad at preserving Protein.


Another Bone to Pick with Dr Fung

Another point I disagree with Dr. Fung is on the subject of Electrolytes. Dr Fung’s book, The Complete Guide to Fasting, leads many people to think that they don’t need electrolytes while doing Extended Fasting. They reach that conclusion from soundbites like the chapter heading:

Electrolytes Remain Stable (TCGtF, p 49)


Prolonged studies of fasting have shown no evidence of electrolyte imbalances…

This is led many to conclude that they don’t need to be concerned about electrolytes during extended fasting.

This is further exacerbated by Dr Fung being a clinician, IE, Dr Fung runs a weight loss clinic. He has thousands of patients and if he says that electrolytes are not needed then they are not needed… Or so the logic goes.

However, there are many others in the keto community who will tell you that they got into serious trouble by ignoring electrolytes. In particular, they had to end fasts due to electrolyte levels being way too low and some have ended up in the ER getting electrolytes via IV bags.

Looking at What Fung Actually Says

Fung’s book has different messages on electrolytes depending upon the fasting length.

p.48-49 During short-term fasts, salt depletion is not a concern.

p. 49 During prolonged fasting (more than a week) the kidneys are able to reabsorb and retain most of the salt needed by the body. However, some salt supplementation may be required.

People seem to miss the second part (on Extended Fasting).

There very little guidance on supplementation in the book, but several examples are found in the book (p. 240):

If you experience dizziness during your fast, most likely, you’re becoming dehydrated. Preventing this requires both salt [ed: Sodium and Chloride are two electrolytes] and water.

The same advice is given for headaches on the same page.

Also (p 241):

Muscle Cramps
Low magnesium, which is particularly common in diabetics, can cause muscle cramps. You may take over-the-counter magnesium supplement.

Facts Keep Getting in the Way

I have a serious concern with Dr. Fung’s method when it comes to Extended Fasts and the evidence against needing electrolytes. On p 50, Dr. Fung has Figure 1.4 which states in the legend:

Figure 1.4 Electrolytes remain stable during extended fasting

The book shows charts for Chloride, Potassium and Sodium.

But what is missing from these charts? What is in the charts themselves? And, who is the subject of the charts?

The charts are from the Guiness Book record holder for longest extended fast, Angus Barbieri. I have written about Angus’ fast. His fast was medically covered in this study (Stewart, Features of a successful therapeutic fast of 382 days’ duration).

Angus was a big man

There are some significant things of note. Angus was 456 lbs at the start of his fast. To use his extreme situation as evidence that electrolyte supplements are not needed during an extended fast is sketchy at best since he had so much available substrate to draw from during his fast.

Missing Data?

Further, Dr Fung omits in his book Angus’ Magnesium (Mg) levels which were published in the study and did show him with low Mg levels for much of the fast. The Normal range is clearly marked and the points are below that line. This is the figure from the study itself.

As you can see Angus’ Magnesium levels did drop during his fast very quickly and were on the low range of normal for almost the entire fast.

Fung doubles down with the statement (p 228):

While monitoring the world-record-breaking 382 day fast, researchers measured the magnesium content within the cells, which remained firmly in the normal range.

Dr Fung does go on to note (p 229) something ignored by many:

Nevertheless, we often supplement patients with magnesium to be on the safe side.

Did Angus Get Supplements?

The study also clearly notes that Angus was given supplements for the entire duration of his fast:

During the 382 days of his fast, vitamin supplements were given daily as ‘Multivite’ (BDH), vitamin C and yeast for the first 10 months and as ‘Paladac’ (Parke Davis), for the last 3 months.

I am not sure if the formula for Multivite has changed between the mid 1960’s and today, but the current formula is:

As you can see, Angus was actually given Magnesium, Potassium, Calcium and Phosphorus during his fast in the form of a supplement. Not in high dosage but not ZERO either.

Did Angus Receive Other Electrolytes?

The most serious issue with respect to Dr Fung’s claims about Angus’ fast however, is the study indicates that Angus actually did receive additional electrolytes during the fast.

From Day 93 to Day 162 only, he [sic: Angus] was given potassium supplements (two effervescent potassium tablets BPC supplying 13 mEq daily) and from Day 345 to Day 355 only he was given sodium supplements (2.5 g sodium chloride daily).

Here’s the chart from Dr Fung’s book which clearly shows Angus’ Potassium levels dropping below normal to the point where he was given potassium supplements (day 93 in the study). They went up to normal after Angus was given the Mg supplements and even after he discontinued the supplements.


Angus Barbieri is an example where electrolyte supplementation was required which is the exact opposite of what Dr Fung says in his book. Angus Barbieri was not only given Potassium when his levels fell, he was also given Sodium Chloride for another portion of his fast. He also had a daily vitamin which contained these elements.

Angus Barbieri was medically monitored and tested during his extended fasts. The doctors could tell when to supplement and when it was unnecessary.

It is a serious mistake to use Angus Barbieri as evidence that electrolyte supplementation doesn’t need to be done in Extended Fasting. Fung’s book on this subject is sloppy and ignores the evidence in the study. It sends a mixed message in the practical advice section later in the book from what it sent in the earlier part of the book.


I Keep Running into Fung-damentalists

I am a huge fan of Dr. Jason Fung. You can see throughout this BLOG how Dr Fung’s video on Diabetes and Intermittent Fasting turned my life around. But I also keep running into people who misunderstand Dr Fung’s words in his book and lectures.

An Extended Fast is not Short Fast

One of the ways that people frequently misunderstand Dr Fung is to take what Fung said about Short Term Fasts (3-4 days) and make it apply to longer (Extended) fasts (5+ days).

The study Dr Fung quotes on this point was (Zauner, Resting energy expenditure in short-term starvation is increased as a result of an increase in serum norepinephrine).

With any study it is important to know at least a few things:

  • Who were the participants? Are they like me?
  • How long was the study for?
  • What type of study was it?
  • What special conditions were there for the study?

In the case of this study the participants were:

Eleven healthy, lean volunteers (7 women and 4 men) participated in the study.

The study only lasted four days.

The first measurement was made after an overnight fast [started at 2100 the previous day (day 1)]. Further measurements were undertaken 36 h (day 2), 60 h (day 3), and 84 h (day 4) after the beginning of starvation. All volunteers entered the metabolic unit at 0700.
So, quoting the study to say that it is applicable to an Extended Fast it not justified based on the study. And that is not what Dr Fung has said. And if someone specifically asked Fung if the study warrants drawing conclusions about metabolism on longer fasts I seriously doubt he would say it does.
The study was done on an outpatient basis to mimic real life except the the study did limit sporting activity. Also, if you were told to limit yourself to only “necessary activities” would you do less? I’d skip doing the laundry for four days, etc.
The study was performed on an outpatient basis to keep subjects under normal living conditions. However, the subjects were instructed to perform only necessary physical activities (ie, to avoid sports).

What Did Fung Actually Write?

On several pages of Dr Fung’s book, he writes that Fasting does not lower metabolism. For instance:

In fact, metabolism revs up, not down, during fasting (The Complete Guide to Fasting, p 73).

And here:

And, studies show that after a four day fast, resting Energy Expenditure increased by 12-percent. Rather than slowing the metabolism, fasting revs it up. (TCGTF, p 49).

 As I have showed above the context of what Fung is writing is about a fast which lasted only four days. Further, Fung includes the data from the study in the chart (TCGTF, p 74).


Dr. Fung is talking about a short (four day fast). It is a mistake to extrapolate from a four day fast to a much longer fast.

The chart actually shows a decline in metabolism (the red line in the figure above) from day three to day 4 (45.3 to 44.3).

The reason that the body gets that energy burst at the start of any fast is explained in the study:

Our results indicate that an increase in serum norepinephrine concentration rather than a decrease in serum insulin concentration initiated by the decline in blood glucose concentration may be the primary initial signal of metabolic changes during early starvation.
This is a short term effect until ketone levels rise a few days into the fast and are able to provide energy at that point.
And to be fair to those who misunderstand him, Dr. Fung has not made this any easier due to the expansive language he uses. When he says “metabolism ramps up during fasting” in this context he means intermittent and short fasts. To take what Dr Fung says specifically about short term fasts and extrapolate it to Extended Fasts is not warranted either from the evidence from the study nor from Dr Fung’s own words.

Protein Sparing Modified Fast Calculator

I put together the previous formulas into one single webpage, the Protein Sparing Modified Fast Calculator. I’ve put my own current numbers into the calculator. Just hit the “Calculate” button to see my numbers. Feel free to try it out with your own numbers and see if it helps you figure out any of this. I don’t see the numbers you enter nor are they stored in any database. All of the calculations are done on your phone web browser or Internet browser (Firefox and Chrome works but Internet Explorer doesn’t).

If you find any errors, please let me know. I tried it with my own numbers and they make sense but I didn’t have a woman’s secret numbers to check.

Here’s a decent introduction to the Protein Sparing Modified Fast (PSMF). I only take exception to one point which is the question of how long you can do a PSMF. They say you can’t do it for an extended period of time. If you continually re-calculate your numbers you should be able to fine tune for maintenance levels. This calculator makes that re-calculation relatively easy. Here’s the results I got for my numbers.

Your Scale and Metabolism Numbers

Current Weight: 199.8 lbs
Goal Weight: 171.3 lbs
Lbs from Goal Weight at start: 28.5 lbs
Body Fat at start: 25.4%, 50.8 lbs
Lean Body Mass (LBM): 149.0 lbs
Basal Metabolic Rate (BMR): 1818.0 cal/day
Initial Total Daily Energy Expenditure (TDEE): 2500 cal/day
Initial Maximum Fat Loss on Protein Sparing Modified Fast: 0.45 lbs of body fat per day


Protein Sparing Modified Fast (PSMF) Dietary Macros (per day)

It is very important on the PSMF that you eat at least the macros listed here. If you go below these numbers you risk lowering your metabolism and you actually can’t lose body fat any faster. Attempting to be just above the numbers is OK.

Protein: 119.2 g (476.8 cals)
Carbs: 20 g (80 cals)
Fat: 40.9 g (367.7 cals)
Your total Dietary Calories are 924.4 cals for maximum fat loss.

If you consume 216 g (1943 calories) of fat you will stay at your current weight.At your goal weight you will be able to consume 119.2 grams of Protein, 20 grams of Carbs, and 176.3 grams of Fat.


Can You Fast?

One important question to ask when considering extended fasting is whether or not you have sufficient body fat to fast.

You currently use 2500 cal/day. You have 1575 calories per day available from your body fat for maintenance. You have less calories available from body fat than your daily requirements and may not be able to fast. If you fast, your body may drop your base metabolism, energy expenditures or may consume protein stores. You will be -924 calories short per day

The thermic effect of food contributes somewhere from 5-20% of your current TDEE number so if you are fasting that can reduce your TDEE. Reducing your TDEE by 10% would result in you using 2250 calories per day. Calculating in a 10% Thermic Effect of food still leaves you in a caloric deficit during fasting. The Protein Sparing Modified fast solves this issue by providing the calories needed for the deficit.

How Much Muscle Can You Gain?

The Maximum Lean Body Mass that you can carry on your frame is 186.5 lbs at your goal of: 15.0% Body Fat. That would be a weight of 214.5 lbs.


Use this information at your own risk and with the advice of your medical professional. We are not doctors nor do we pretend to be one on the Internet. We do not take responsibility for errors in these calculations. We do not guarantee that these numbers will work for people at the extremes of the ranges. If you discover an error in calculation, please let us know through email: keto at land-boards dot com.