I'm just wondering where is the sweet spot, if there is one, between arrow weight and speed.....
Yes there is a sweet spot. But, that "sweet spot" is different for each individuals' set-up. It's been my observation in 30+ years of bowhunting that too many compound bow hunters are missing their sweet spot by trying to to shoot the fastest arrow, the largest diameter broadhead possible, or both. And by doing so, they are sacrificing precious energy and momentum necessary for good penetration. Given the choice between speed and penetration, I will take better penetration every time.
It's no crime to want to shoot the fastest, flattest arrow possible. Yet, a fast, flat arrow is relatively ineffective with an arrow build that doesn't have the ability to provide good penetration. The challenge is that these goals are dependent on multiple components including draw weight, draw length, foc %, total arrow weight, and broadhead design. You could even factor in the arrow shaft diameter and single-bevel broadheads if you want to get super-technical. And, that is just the beginning of the overall equation to achieve your particular sweet spot. It's also been my observation that bow hunters shooting the lower poundages with shorter draw lengths are those that need the benefits of a heavier, higher foc arrow and efficient broadhead design the most. Yet ironically, this is the group that tries to gain arrow speed at the cost of total arrow weight and therefore penetration. As an example, a bow hunter shooting 55lbs. of draw weight at a 26" draw length shooting a total arrow weight of 500-650 grains at a 18% or greater foc, would achieve much more penetration at 220 fps than they would from a 375 grain arrow at 280 fps.
Now, the compromise for these hunters shooting lower poundages and shorter draw lengths is that they have to be more decisive in their shot selection given the species itself, the demeanor of the species at the time of the shot, and of course the distance because of any particular species' ability to jump the string. Another extremely significant factor in regard to string jumping that is rarely discussed is how much noise the bow makes at the shot. A dead silent bow is just as if not more important than arrow speed in my experiences. A bow that sounds like a .22 rifle at the release of the arrow is going to cause that animal to load an bolt every time, and if the animal is already on alert, you can probably cut that reaction time in half.
There have been numerous field experiments done in regard to arrow speed and an animal's ability to duck the shot at various distances. Interestingly, many of these video experiments seem to show that there is little to no discernible advantage to a super fast arrow speed inside 20 yards. In other words, an impala can jump the string on a 300 fps bow just about as easily as they could on a 220 fps set-up at 20 yards or less. The faster arrow only displays its advantage on greater distances outside of 20 yards. The takeaway from this is that there are just some shot situations that you should not take given the limitations of your set-up.
In summary, my definition of the "sweet spot" would be a set-up with an arrow I could shoot accurately with the most total arrow weight and foc that I could get away with and still maintain a relatively flat trajectory at a reasonable speed. I realize that a "flat trajectory" and a "reasonable speed" are subjective terms to each individual's set-up. For me, shooting 70lbs. at a 29" draw, with a 320 fps IBO, I like to shoot an arrow with a total weight between 475-525 grains and expect to get about 265-280 fps. With a quality, heavy-duty, fixed blade broadhead, I can expect to get excellent penetration on most any North American big game species and any African plainsgame on up to an eland.
@lpace Bottom line is that I think you are right in the wheelhouse with your 450 grain arrow at 16% foc assuming you are shooting a set-up somewhere in the 65lb./ 28" or higher range? I think with the impala you just got a bit unlucky... To that I would say welcome to the club