Understanding Stored Energy

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 (accurately measured 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.  And secondly, an alternate way to represent the values would be to quote a range for each type of bow at each draw length.  But 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.