For those inquiring minds that want to know.....
In the course of re-working a stand-alone RaceLog, I started delving a little deeper into the science of predicting how weight affects performance. In the Daniels Worksheet, Without really understanding fully how it worked, I've always used JD's model (for obvious reasons), which if I remember correctly I found in his 1978 Oxygen Power publication.
The most commonly cited rule of thumb is "two seconds per pound per mile", which as far as I can determine is attributed to Tom Osler. The problem with this generalization is that the impact of weight on speed is actually based on relational percentages, rather than seconds and pounds... lose a percentage of excess weight, gain a percentage of speed. The actual seconds per mile will vary depending on both a runner's current weight and pace. All else being equal, a heavier runner will see a smaller time difference than a lighter runner, in terms of seconds. Likewise, a faster runner will see a smaller time difference compared to a slower runner.
There have been studies using various physical approaches and formulas on this topic, but the concept of "lose a percentage of excess weight, gain a percentage of speed", can be mathematically boiled down to the following formula:
Time2 = Time1*(Weight2/Weight1)^X
The exponent X sets the ratio between percent of weight and percent of time. If a 1% weight change resulted in a 1% time change, the X exponent would be 1 (or non-existent). But studies show that the ratio of weight change to time change is not 1:1. The time change is some fractional amount of the weight change.
From what I found, the Daniels model is one of the most optimistic for a given weight loss, using a power factor of 0.83. The least optimistic I found was known as the Flyer Handicap, which used a power factor of 1/3 (or 0.333), resulting in less than half of the time savings as the Daniels model. The study for this model, along with a calculator by the author of the study, used to be readily available on the Internet. Now most evidence of it is gone.
In one forum discussion I found covering this topic on here on LetsRun, there's a reference to the physics equation for energy of motion. I wouldn't have thought it would apply so aptly to running, but as demonstrated in that thread, solving that equation for two different masses can be represented by the same formula I quoted above, with an X exponent of 0.50, which just happens to fall right between Daniels and the Flyer Handicap. I just found this really interesting.
While I know, or at least I'm suppose to realize the application of weight loss to race times is not an exact science, I find it interesting to look at the numbers in the worksheet and pine over what I it says I could accomplish, if i'd just get serious about losing some weight. (currently 6'3, 200 lbs).
Given the new info I've uncovered, I'm inclined to temper my weight-based performance potential expectations a little going forward, by using the median 0.50 power factor. There may well be a new worksheet on the horizon that allows the user to enter the power factor they feel best suits them.