There was a discussion today on Archery Talk that inspired me to write this post. This discussion began about people theorizing which company would be the first to put out a 400 fps bow to IBO specifications. It soon morphed into a discussion about whether or not 400 fps could even be obtained. If you know me at all, you would know that I cannot resist a discussion about archery and physics. Something in my blood makes this literally impossible for me to avoid.
Rather than reading and enjoying the thread, or even just posting a few passing comments, I was moved to break out Mathcad. Here are the results of the calculations showing what the theoretical speed limit is for a perfect bow:
Now to explain all the assumptions. This simple calculation shows that a perfect bow in a perfect world set at 30″, 70 lbs, a 5″ brace height and shooting a 350 grain arrow could reach 418fps. However, this assumes that there is no friction, no vibration, no sound, no heat, no anything produced at the shot except 100% energy transference from the bow (PE) into the arrow (KE). It also assumes that the bow starts to draw immediately at 70 lbs, remains at 70 lbs the entire draw length and has zero let-off. Doesn’t sound like much of a fun bow to draw back! The flip side is that after the arrow leaves the string, the shooter would feel absolutely nothing except the weight of the bow in their hand.
Of course we all know that this scenario is not only unlikely, but also impossible. Add in a bit of a ramp to get the bow to 70 lbs peak weight, let-off to make it possible to hold and aim, vibration/sound/heat/etc. throughout the bow on the shot and the speed drops right down to where we are today, around the 360 fps mark.
Is it possible to increases today’s speed within the IBO specifications and if so how? Yes, it is very possible and the “how” can happen either of two ways: make the act of drawing the bow store more energy (quicker ramp to peak draw weight, shorter valley, less let-off) or increase the efficiency of the bow. Many of today’s bows are pushing and even surpassing 85% efficiency; more gains can be made in reducing bearing friction in the cams, more efficient cam design, taking vibration out of the shot and putting that energy in arrow, etc. Manufacturers will continue to make strides this way and continue to see some speed increase.
But will archers submit to putting more energy into the bow with their muscles and put up with a “harsher” draw? How stiff of a draw will be usable and practical? Some “speed freaks” will put up with anything if it gets more fps on the chronograph while other archers want a “smooth” draw that is easy to pull and forgiving to shoot. It will be up to the bow designers to find the designs that people are willing to spend their hard earned dollars on.
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{ 5 comments… read them below or add one }
as a physics major what you are saying makes absolute sense I only hope that the general public who is not fully familiar with the nomenclature will understand if they desire to
after almost a year has not one person commented on cody”s comment
it is realy basic it doesnt take a physics to figure that.
What’s the point in faster and faster? I mean bows have been killing deer and other big game for thousands of years. My last bow shot at around 260fps and it killed 6 deer with no issues. I would rather have accuracy than speed, even if I rainbowed arrows I would be happy with a tight group. Guess I’m not a speed freak!
Human nature is to attempt to improve on everything. With archery, “improvement” is mostly measured by speed right now. While I do like speed, I’d rather have accuracy. Years ago speed meant a rough shooting bow, now you can have both with many of the bows out there.
While I agree on ibo speed max the question of absolute max speed is not catered for in this explanation. Surely if we are referring to absolute maximum speed obtainable we should consider much more than current tech and bow design.. For example compressed air or hydraulic assisted bow draw should enable massive draw strength say 2000 lb. Gas assisted auto leveling arrows, or rocket assist for speed increase. What about 2 stage arrows? Transfer all energy to 30% of the arrow. With nano tech turbine or ramjet motors we might be talking about whether or not mach 2 can be achieved with a bow fired projectile in a couple of years. That is if we are talking about absolute max speed with no constraints.