Bow Performance

Performance & Stored Energy

A stickbow is really nothing more than a simple spring.  When the archer pulls the string back the spring is loaded and energy is stored.   At the loose, the stored energy is transferred into the arrow, propelling it forward.  We just defined performance!  

The two most important components of a bow’s performance are how much energy is stored when the bow is drawn and how much of that stored energy goes into the arrow instead of being lost in the form of waste energy.  Let’s discuss each component a bit more.

This article will teach you about the following energy concepts:

  • Determining how much energy a bow stores.

  • Three different F/D curves for three different bow designs.

  • Common energy terminology you need to know. 

How much energy, measured in foot-pounds (ft-lbs), a bow stores is a direct function of its design.  Straight-limbed longbows store less energy than reflex/deflex (R/D) longbows.  R/D longbows generally store less energy than recurves or hybrid longbows.  In a way you can think of how much energy a particular bow stores as sort of a “storage efficiency”.  People who test lots of bows use a ratio of Stored Energy per Pound of Draw Force, or SE/PDF.  This ratio is a handy way of comparing how efficiently one bow design stores energy versus a different design.

 Determining how much energy a bow stores is fairly straightforward.  The bow’s Force/Draw (F/D) curve (draw weight per inch of draw length) must be accurately determined  (more discussion about the importance of accurate measurements comes later).  To do this accurately, a bow must be mounted into some sort of fixture that holds the bow securely.  Using an accurate scale (there’s that accurate word again!) and pulley system, the bow’s draw force is measured from brace height to full draw. 

Plotting the draw force at each inch of draw allows the person testing the bow to see what the F/D curve looks like.  The area under the F/D curve is the amount of energy stored by that particular bow.  Since many F/D curves are not straight lines, calculating the stored energy requires a point-by-point summation of the area under each data point.  To save time we use a spreadsheet program given to us by Norb Mullaney, the recognized authority of bow testing throughout the industry, to do this summation.

The attached drawing illustrates three different F/D curves for three different bow designs.  Intentionally exaggerated for illustrative purposes, the relationship of how different bow types compare with one another is correct.  Understanding the indisputable fact that a bow’s design impacts the amount of energy it stores is fundamentally important.  Take a moment to look at the following drawing. 

Before discussing each type of bow let’s define a couple of terms:

Pre-load is the term frequently used to describe a bow that stores more energy early in the draw.   Recurves and hybrid longbows typically have the most pre-load.  That’s why they store more energy than other bow designs.  The pre-load area, or F/D “hump”, is identified on the drawing.  

Stacking is another common term. A bow stacks when its draw force starts increasing rapidly.  In stickbows this typically happens out at the end of the draw.  A bow that’s increasing in draw weight 4-5 pounds per inch at the end of the draw versus one that’s increasing only 2-3 pounds per inch at the same draw point is much more uncomfortable to draw and shoot.  It’s stacking.

The F/D Curve. Take note of the shape of each bow’s F/D curve.  This is a critical factor in bow performance.  If a particular bow design stores less energy it has less energy to give to the arrow – plain and simple.  Pre-load is very important to bow performance.  It increases the amount of stored energy dramatically.  Bows that don’t have pre-load don’t have good SE/PDF. 

What this means is that all 60# bows are definitely not equal!  A straight-limbed longbow with a SE/PDF ratio of .85 (30” AMO draw) stores 51 ft-lbs of energy.  A very well-designed hybrid longbow or recurve will have a SE/PDF ratio of .98 (also at a 30” AMO draw), which means that particular 60# bow stores 58.8 ft-lbs.  An ACS hybrid stores even more – 61.2 ft-lbs.  That’s a lot of difference in stored energy!

 Just a quick word about SE/PDF measured at different draw lengths.   Long draw lengths allow lots of energy to be stored in the bow’s limbs.  Shorter draw lengths, even at the same draw weight, store less energy.  Just draw two F/D curves with the same draw weight but different draw lengths and it will become immediately obvious that the shorter draw has less area under the curve.  It has to!  Lately we have been testing quite a few bows at 24”, 26”, 28”, and 30” of draw (accuratelymeasured as per AMO standards).  A reasonable rule of thumb based on these tests is that SE/PDF goes down about 3.5% per inch of draw reduction between 30” and 26”.  Below 26” and the difference is even greater. 

So, what does this mean?  For example, let’s consider two identical recurves, one being drawn to 30” and the other one being drawn to 26”.  For purposes of this illustration the recurve being drawn to 30” has a SE/PDF ratio of .98.   The identical recurve being drawn to 26” has a SE/PDF ratio of 0.84 (.98 – 4*.035).  Furthermore, let’s assume that each bow has a draw weight of 60 pounds at their respective draw lengths.  What this shows us is that the top-of-the-line recurve drawn to 30” stores 58.8 ft-lbs of energy (.98*60#) while the same recurve drawn to 26” stores 50.4 ft-lbs (.84*60#).   It is very simple to calculate the impact this has on arrow velocity (assuming each bow’s dynamic efficiency is exactly the same)  But we’re getting ahead of ourselves.  We’ll talk more about dynamic efficiency later.

Please remember that the illustration of F/D curves for three types of bows is not absolute and 100% true for each and every bow in the world.  After having tested many different bows from many different sources we are comfortable that the illustrated relationships generally hold true.

 The following table summarizes what we have learned about how different bows store energy:


A couple of things need to be said in order to qualify the values quoted in the above table. First and most important, these are generally accurate and are based on actual measurements taken on the various types of bows. While the values are reasonable some bows will vary slightly. Secondly, an alternate way to represent the values would be to quote a range for each type of bow at each draw length. However, to do that would become needlessly burdensome. The values in the above table are reasonable, based on actual measurements taken on a variety of bows, and are therefore entirely adequate for purposes of discussing bow performance. 

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 above

This article will cover: 

  • Computing arrow kinetic energy

  • Testing with a shooting machine

  • Dynamic efficiency of various bow types

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.

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