Understanding Dynamic Efficiency

The other very important variable in understanding a bow’s performance is its dynamic efficiency (DE).  DE for any particular bow is the ratio of the kinetic energy of the arrow after it leaves the bow divided by the stored energy, which was explained previously. 

Arrow kinetic energy is determined by accurately measuring the speed of an arrow by use of a chronograph.  The formula for arrow kinetic energy (in ft-lbs) is shown below:

KE (ft-lbs) = (arrow weight in grains)(arrow velocity in fps squared)/450,240

Note that the arrow weight in grains must be accurately measured, also.

The only way to accurately measure how quickly a bow shoots an arrow is to use a shooting machine
.  A seemingly infinite number of variables are introduced when human hands hold the bow and draw the bow and release the string.  Two people shooting the same bow with the same arrow and supposedly drawing it to the same draw length each time can EASILY see speed numbers that are 10 fps or more apart.  Any data not collected with a shooting machine is probably worthless for bow comparisons.  Sorry, but there it is.

Using a shooting machine which holds the bow in exactly the same way each time and which draws the bow string the exact same distance each time and which releases the bow string exactly the same each time results in arrow speed readings which vary less than 1fps of each other.  Time after time after time.  That kind of accuracy is impossible to achieve by hand.  Any time someone provides you with bow performance numbers not obtained with a shooting machine, and preferably by an independent third party using a shooting machine, you should take the numbers with a large grain of salt.

Dynamic efficiency, just like SE/PDF, is a function of bow design.   Many variables affect a bow’s dynamic efficiency, but the largest single factor that we’ve been able to find is the weight of the bow limb.  Consider two top-fuel dragsters that are exactly identical in every way (horsepower, etc.) except one weighs 5000 pounds and the other one weighs 2000 pounds.  Which one do you think will be quicker to the quarter mile pole?  I don’t know about you, but my money would be on the lighter dragster!

Earlier we said a stickbow was nothing more than a simple spring.  For stickbows that have heavy limbs, a larger portion of the energy stored (SE/PDF) will be wasted in accelerating the dead mass of the limbs forward back to brace height upon the loose.  If you can store the same amount of energy while reducing the mass of the bow’s limbs then more of that stored energy HAS to go into the arrow where it belongs.  

That’s what the ACS design does.  By using a proprietary and patented cross-sectional design (U.S. Patent No. 6,718,962), we are able to build limbs that are much stronger and stiffer.  That enables us to use much less material in the limb resulting in limbs that weigh between one-third and one-half as much as conventionally-constructed bow limbs.  The ACS patent covers a wide range of shapes - convex, concave, hollow, triangular - just about any shape you can imagine.  The concept of using cross-sectional geometries that do not have straight back and belly surfaces that are parallel to one another is what has been patented.  By varying the cross-sectional geometry we can make the limb stiffer where it does the most good without having to make it heavier.  

In one of the bow tests recently done for us by Norb Mullaney he comments:  “The high levels of dynamic efficiency are especially notable, ranging from 80.74 percent with a 360-grain arrow to 88.09 percent with a 700-grain arrow.  These are the highest values of dynamic efficiency I have ever found for a longbow or a recurve.”  Norb, as most people know, is the most widely recognized bow tester in the nation.  His technical bow tests have been published for almost three decades in Bowhunting World magazine.   

Anyone in the industry who wants a bow tested by someone who is known to be impartial, unbiased, accurate, and thorough calls on Norb.  Needless to say, he has tested LOTS of bows through the years.  For him to identify the ACS as having the highest dynamic efficiency of any bow he has ever tested validates the benefits of the ACS design.

Dynamic efficiency of any bow varies with arrow weight.  A heavier arrow absorbs more of the stored energy than a lighter arrow.  The quotation from Norb, above, notes dynamic efficiencies ranging from just over 80% to 88% as arrow weights went from 360 grains to 700 grains.  The measured DE of all bows will be higher with heavier arrows than with lighter arrows.  But the fact remains that given the same amount of stored energy the more efficient bow will cast any arrow faster than a bow with lower efficiency.

To compare the dynamic efficiency of one bow type to another it is necessary to measure arrow speeds based on some consistent arrow weight.  For purposes of this discussion the numbers quoted in the following table are all measured from bow tests in which each bow was shot with an arrow that weighed 9 grains per pound of draw.  Using the range quoted above by Norb it is reasonable to conclude that each type of bow’s dynamic efficiency will vary as much as plus or minus 4% from the 9 grains per pound number as arrow weight goes up or down.

As previously mentioned, dynamic efficiency varies from one type of bow to another.  The following table provides reasonable numbers for various types of bows at arrow weights of 9, 11, and 13 grains per pound.


One other interesting thing to note about dynamic efficiency:  it varies very little between 26” to 30” of draw.  Generally no more than 1% has been observed.  Therefore, as long as consistent arrow weights are used (X grains per pound of draw) for each draw length, the dynamic efficiency for any particular bow doesn’t change much.

The same qualifications need to be offered for the above table as were stated for the SE/PDF table.  The numbers in the above table for the non-ACS bows are based on various observations and bow tests, and are representative of that class of bow but not of any particular bow.   Again, for the purpose of discussing performance differences between bows the above numbers are representative and therefore entirely adequate for drawing general conclusions.