500 fps wrote: Very small! 0.08 ft/lbs.

If you have a very good chronograph that is capable of discretely detecting a 0.1 ft/sec change in speed then for your experiment the smallest amount of energy change you can detect is therefore only 0.05 ft/lbs. The difference in your measuremts is only 0.08. The question is whether or not your accuracy can justify your conclusion.

If, for example, you want to conclude a measurement result of 10 inches is really shorter than a measurement result of 11 inches how precise must you be with the measurement. Clearly it must be less than +/- 1/2". If your chronograph has discrete increments of 0.1 ft/sec then under the best of circumstances you can not determine if one energy measurement is greater than the other unless the differece is greater than 0.05 x 2 or 0.1 ft/lbs. Again that would be under the best of circumstances. Normally, meaurements are not considered acceptable unless the discrete limit is at least 1 order of magnitude smaller than the minimum amount needed to draw the conclusion. In other words in the 10" smaller or larger than the 11" measurement you would need discrete measurement increments of +/- 1/2" = 1/10 = 0.1" In terms of your experiment then you would need increments of +/- 0.04" = 0.08/10 = 0.008 ft/lbs. In order to get discrete energy measurements of 0.008 ft/lbs you need discrete velocity measurements of 0.016 ft/sec.

I should add that errors in the measurement of arrow mass will compound the problem.