A phrase that seems to be floating around more and more with bows these days is bow efficiency. As technology advanced over the years so have bows. Compared to bow designs from years ago they now have silky smooth draw cycles and have virtually no vibration after the shot. Their risers are light weight and rigid and are built to withstand anything the limbs and cams can throw at them. This allows for them to produce blistering speeds at the same draw weights as their predecessors. The reason for this is because of their higher efficiency and their ability to build and transfer more of their potential energy to the arrow without being lost to unnecessary vibration and noise.
As a bow goes through its draw cycle, the limbs will deflect as the axles move closer together. As this happens, they are building and storing potential energy through every inch of the draw cycle. Energy that is stored in the limbs is released during the power stroke of the bow the the tip of the arrow. The amount of energy that was transferred to the arrow from the limbs is what determines a bows efficiency.
To calculate a bow's efficiency one must have a basic understanding of a draw force curve. A draw force curve is generated by recording the bow's draw weight at each inch of a bow's draw cycle. To accomplish this a set of scales and a draw board is required. These numbers can then be plotted on a chart that will form the curve as can be seen in the picture below.
Once the curve is plotted, you will notice that everything under the curve that is highlighted red is stored potential energy. Looking at this particular draw curve, this bow gradually builds energy and is at peak weight for only about six inches of it's cycle before it drops into the valley. This bow would be a very pleasant drawing bow. However, if the bow was at peak weight longer, the angle of the front portion of the curve would be steeper. The weight would build or stack faster giving the bow a more stiff feeling draw cycle. This however, would increase the highlighted area and ultimately increase the potential energy. The same is true on the back end of the curve in the valley. By dividing the peak weight and holding weight we can determine that this bow has around 80% let off. If this bow was at 65% let off the holding weight would be around 23 pounds. This would change the angle on the back side of the curve while increasing the highlighted area and provide more energy that can be transferred to the arrow. This is why you gain speed at lower let offs.
In archery, we look at energy as foot pounds. In fact, there are a lot of game laws that are written in regards to foot pounds. So now with a basic knowledge of a draw curve we can start determining how much energy that we have available. To do this we simply add each weight at each inch of the draw cycle. In the picture above when you add all the numbers around the perimeter of the curve they come to 920. Since we measured our curve using inches of draw and pounds, our energy is in inch pounds. To convert this to foot pounds we simply convert inches into feet by dividing by 12. This gives us around 76 foot pounds of potential stored energy. This is the maximum amount of energy this bow can provide the arrow.
Now to determine this bow efficiency we need to calculate the arrow's foot pounds of energy to see how much was transferred to it. For this we need a chronograph and a calculator. When calculating ft/lbs I have always used this formula.
velocity X velocity / 450400 X arrow weight in grains = Ft/lbs.
So to put it all together we will assume this bow launched a 350 grain arrow at 287 fps. Using the above formula we can estimate that it will be producing about 64 foot pounds of energy. Since we were able to estimate that we have potentially 76 foot pounds of energy available and we can roughly estimate that around 84% of the bow's potential energy was transferred to the arrow and around 16% was lost due to noise and vibrations. So this bow has roughly an efficiency rating of 84%, which is very typical for today's bows.
As archers, there are a few things we can do to manipulate this number in our favor. Things such as shooting the correct spine arrow, an incorrect spine can absorb energy. Shooting a slightly heavier arrow will help by reducing noise. Adding weights such as speed nocks to your string will also help by keeping your string in the cam grooves better during the shot and eliminating any unnecessary string movements. These speed nocks are weight and position sensitive and can cause a bow to lose efficiency as well, that is why they need to be tuned with a chronograph. Other things like changing the strand count in a string or changing end serving diameter can help transfer more energy to the arrow from the limbs as well. Regardless, with a little basic knowledge and some tuning tools you can tweak your bow to put just a little more odds in your favor.