Actually 40 lbs of force acting on a 40 lb arrow will accelerate it horizontally at 32.16 ft/sec/sec and if by some miracle you could construct a bow that was capable of handeling both a 400 grain and a 40 lb arrow, all things being equal the 40 pound arrow would be propelled more efficiently than the 400 grain arrow.
Are you an engineer because you sound like an engineer. A lot of knowledge on paper but no common sense. So let me clarify this since I am not as smart as you think you are. Are you saying that oh let's say my wife's bow set at 40 lbs and a 25 inch draw is capable of launching a 40 lb arrow 32.16 ft? Do you thing it is capable of launching a 400 gr arrow? I realize this is an excercise in futility because you aren't going to admit that you are wrong so we will both just have to settle for knowing that you are
PS I didn't say 40 lbs of force I said a 40 lb draw
You have so exagerated the system that you are inadvertanly changing other factors and aren't compairing apples to apples. Your distorted scenario actually compares a 40 lb bow acting on a 400 grain arrow vs a 0 pound bow acting on a 40 pound arrow. When you stay in the realm of realistic conditions and only change the mass of the arrow, the more mass the more KE and the less mass the less KE. There is no getting around it!
The point was meant to be exagerated to emphasize the fact that there is infact a point a in which it will become less efficient. Several guys here have posted tests they have done verifying it. You might like to throw out mathemetical calculations that make your feel intelectually superior but at the end of the day that's why people roll their eyes when they here the word "engineer". That's because most of you guys don't have any common sense. You think there is a formula that can explain every real world situation and quite frankly there just isn't. I know that's the world you feel comfortable in but there just isn't a calculation for every real world phenomenon. I have done the testing myself but I didn't keep the data and I don't currently have the means of testing but maybe someone will jump in with some results they have verified for themselves though you have shown a propensity in the past for disregarding verified data that doesn't fall into line with your previously stated opinion.[&:]