Bow Performance Examples

Okay.  We’ve discussed the two main components which control bow performance:  energy storage and dynamic efficiency.  Now let’s put together some real world examples and see how important bow performance really is: 

Example # 1
An archer shoots a straight-limb longbow.  He draws 60# @ 28”.  He shoots a 750-grain arrow at 140 fps.  This is based on a DE = .74 (because of the very heavy arrow) and SE/PDF = .78What weight ACS hybrid longbow would shoot the same arrow the same speed?

Answer:  First of all, a 750-grain arrow traveling 144 fps has 34.6 ft-lbs of energy.  Given that an ACS hybrid longbow has a SE/PDF at 28” of .95 and a DE of .84 (at 9 gr/#), we can back calculate the draw weight required to shoot a 750-grain arrow 144 fps.  The ACS longbow will have a dynamic efficiency of  88% given the very heavy arrow.  So an arrow with 34.6 ft-lbs of energy must be shot from an ACS that stores 34.6/.88 = 39.3 ft-lbs of energy.  Knowing that the SE/PDF (at 28”) for this particular bow is .95, we calculate that an ACS longbow drawing 39.3/.95 = 41# will shoot the same arrow the same speed.  Which can you shoot more accurately - 41# or 60#?  

Example # 2 
If this same archer, who loves straight-limb longbows so much, chose an ACS straight-limb (SL) longbow instead of the hybrid, what ACS SL draw weight would give him he same performance?

Answer:
  The ACS SL design stores essentially the same amount of energy as the conventional SL design, so SE/PDF at 28” is the same, or .78.  DE for the ACS SL with the very heavy arrow is 80% (76% + 4% due to arrow weight).  Knowing arrow velocity is 144 fps and arrow weight is 750 grains, we have to find an ACS SL bow that will deliver 34.6 ft-lbs of energy to the arrow.  34.6/.80 = 43.25 ft-lbs of stored energy.  Finally, knowing that the ACS SL has a SE/PDF at 28” of .78, we find that the archer can shoot 43.25/.78 = 55# ACS and get the same arrow performance.  As an added benefit the ACS SL design has much less perceptible hand shock than conventional straight-limb longbows due to the large reduction in limb mass. 

Example # 3
An archer shoots a a top-of-the-line recurve or hybrid longbow with conventional limbs.  His bow pulls 60# @ 28”.  He shoots a 540 grain arrow 185 fps (40.95 ft-lbs of energy) with this setup.  If he shoots the same draw weight and the same arrow from his new ACS, how much more energy will the arrow have and how much faster will the arrow go?

Answer
:  Again, an ACS has a DE of .84 at 9 grains per pound and a SE/PDF of .95 at 28”.  First, it is simple to calculate the energy transmitted into an arrow from a 60# @ 28” ACS longbow.  60#*.95*.84 = 47.9 ft-lbs.  Now putting 47.9 ft-lbs into the equation for kinetic energy and solving for arrow velocity we find that the 60# @ 28” ACS longbow will shoot the same arrow at the same draw weight 200 fps versus 185.  This represents an increase in energy of 17% (47.9-40.9)/40.9 = 17.1%   

Example # 4
The same archer above doesn’t want his arrow to go any faster.  How much lower in draw weight could he go with an ACS versus his top-of-the-line recurve and still shoot the same arrow the same speed?

Answer:
  We know from the previous example that his arrow kinetic energy is 40.95 ft-lbs.  An ACS longbow has a dynamic efficiency of .84 at 9 grains per pound an a SE/PDF of .95 at 28”.  Solving gives us:  40.95/.84 = 48.75 ft-lbs of stored energy in the ACS.  Now, dividing the stored energy by the SE/PDF yields 48.75/.95 = 51#.  So the archer could take a 51# ACS longbow and match the performance of his 60# top-of-the-line recurve.  I don’t know about you, but I sure can shoot 51# more easily than 60#! 

Example # 5

One archer draws only 26” and his hunting buddy draws 28”.   The archer with the short draw wants the same amount of energy for elk hunting as his partner.  His partner is using a top-of-the-line recurve that pulls 60# @ 28” and is shooting a 700 grain arrow (11.7 gr/#).  Because of the heavier arrow the recurve has a DE of around 78% and therefore puts 42.6 ft-lbs into the 700 grain arrow (compared with 40.95 for the 540 grain arrow).  This means that he shoots the 700 grain arrow at 181 fps.  The archer with the shorter draw length wants his ACS longbow to have the same amount of energy as his friend’s recurve and shoot the same weight arrow at the same speed.  What should his draw weight be at 26” with an ACS longbow in order to deliver the same amount of kinetic energy into his arrow as his friend’s bow?

Answer:
  From the above discussion the top-of-the-line recurve that draws 60# @ 28” will deliver 42.6 ft-lbs into an arrow weighing almost 12 grains per pound.  An ACS longbow has a dynamic efficiency of .84 at 9 grains per pound, or about .87 at about 12 grains per pound.  The ACS has a SE/PDF at 26” of  .88.  Solving for the necessary ACS draw weight at 26” yields:  42.6/.87 = 49.0 ft-lbs of stored energy.  And given a SE/PDF of .88 we can calculate that the 26” draw ACS would need to pull 49.0/.88 = 55.7# @ 26” in order to equal his friend’s top-of-the-line recurve drawing 60# @ 28”.  So an ACS drawing 56# @ 26” is equivalent to a top-of-the-line recurve drawing 60# @ 28”.  Talk about leveling the playing field!  That’s what better performance is all about. 

Summary
The examples given above reflect our actual experience testing ACS bows and other conventionally-built bows.  Many more examples could be developed, but you get the picture.  The first conclusion you can draw is that all bows are definitely not created equal.  There are huge differences between the best and worst stickbows currently being used around the world.  Which one you use is purely a matter of choice and personal preference.  Just don’t ever let anyone tell you there isn’t any difference between bows and how they perform.  
 

The  ACS is changing most of our pre-conceived notions.  It truly is an innovation in archery bow limb design that we believe will one day change the way most bows are built (when the patent runs out or through licensing agreements).   The ACS design is a concept which we can (and will) apply to every kind of bow.  Straight-limb longbows using the ACS design perform better than conventionally-built longbows of similar design.  The same is true for R/D longbows as well as for hybrids or recurves. 

We are still exploring the full extent of benefits that can be obtained using the ACS concept in various bow designs.  Want a straight-limb longbow that’s 10 fps faster with less hand shock than conventional ones? We've already built them.  Want a hybrid longbow that’s 10-15 fps faster than a typical recurve.  It exists now.  Want a recurve that’s as fast as a soft-cam compound?  It just may be possible.  Stay tuned!