Dr James Park investigates and shares a detailed summary of his latest findings
Many arrow shafts are carbon fibre composite tubes. Some carbon fibre composite arrows have an aluminium inner layer. How does this help? There are three obvious advantages provided by the aluminium layer:
- The aluminium is much stronger than the epoxy matrix used to hold the carbon fibre in place, and it provides circumferential strength to help arrows avoid splitting when hit from behind.
- Aluminium has a much higher thermal conductivity than carbon fibre composites. This helps dissipate the heat generated when an arrow hits the target, preventing the glue from melting and the points from coming out.
- The aluminium is easier to detect with metal detectors (for those who occasionally lose arrows in the grass – including me).
However, does it affect the arrows’ drift in the wind? Let’s take a closer look.
Modelling Mass, Spine, and Three-Dimensional Trajectories
I have studied the wind drift of many arrows, and the recent release by Easton of the 3.2 mm Parallel Pro arrow shafts prompted me to look further into the effects of the aluminium layer. I worked that up into a paper for the Journal of Sports Engineering and Technology (one of the journals of the Institution of Mechanical Engineers, London). You can find the journal at sagepub.com. If you search using ‘JL Park’, you should be able to find my published papers.
For this study, I created mathematically a few sets of arrows with varying thicknesses of the inner aluminium layer, ranging from 0 (none) to 18 thousandths of an inch. I used a constant internal shaft diameter of 3.2 mm and selected the outside diameter of the carbon fibre composite material to give the desired arrow spine. For all of the arrow shafts, I used a constant carbon fibre composite Young’s Modulus (that is, a constant stiffness). Taking this approach provided a very fair basis for comparing wind drifts.
Adding an inner aluminium layer means that, to retain the same arrow spine, the outer diameter has to increase slightly. However, the second moment of area (an important part of the spine calculation) increases as the fourth power of the shaft radius. That means a small increase in outer diameter makes a large difference in spine, so the required diameter increase is quite small. Aluminium is much heavier than carbon fibre composite. Consequently, we end up with a heavier arrow that has a slightly larger diameter. It is then interesting to calculate the wind drift.
Arrows have considerable aerodynamic drag, which depends on the square of the arrow speed. Consequently, there is no simple formula we can use to calculate the arrow’s trajectory. I break the arrow’s trajectory down into small steps (one-millisecond steps work well). For each step, I take the arrow’s current position, velocity, direction of travel, gravity, and drag, and I calculate the new position. I need to calculate the drag at each step due to the velocity change, doing so until the arrow reaches the target distance. I then use iteration to find the appropriate launch angle so that the arrow arrives at the correct target height.
I include wind drift in those calculations as well. The arrow tries to align itself with the resultant of its forward velocity and the wind. There is then a component of the aerodynamic drag pushing the arrow to the side. In addition, there is another component of the drift due to the arrow taking time to align itself with the airflow. I allow for both; that is, I am calculating the arrow path in three dimensions.
I calculated the wind drift for each of the modelled sets of arrows over a spine range from 340 to 900. It is shown here for spines from 500 to 600 (my paper covers the whole range). I used a bow with a peak draw force of 200 N (45 pounds) and stored energy of 81 J for this chart. In addition to my modelled arrows, I included three commonly available, high-quality arrow shafts as a comparison.
Establishing the Limits of Internal Shaft Diameters
It can be seen that the wind drift decreases as more aluminium is added. The Easton 3.2 mm Parallel Pro is very close to my model with an aluminium wall thickness of 0.006 inches (as expected). In every case, the addition of an aluminium layer led to less wind drift. Noting that wind drift decreases as the aluminium becomes thicker, where is the limit? We want the arrow shaft to retain the desirable properties of a carbon shaft, namely, not taking a set bend. If we add too much aluminium, the weaker spine shafts quickly become more like aluminium shafts rather than carbon shafts. Subjectively, if we set a limit where the aluminium contributes no more than 10% of the spine, the optimum thickness is around 0.006 to 0.008 inches (that is, about the thickness in Easton aluminium/carbon shafts).
Wind drift could also be reduced by decreasing the shaft’s internal diameter. However, that immediately leads to significant challenges with the arrow point. To minimise drag, we need to use an internally fitted point. This means we will have a sharp internal angle (a stress concentration point) where the point narrows down to the shank. Furthermore, to retain the same point mass and arrow centre of gravity, the external part of the point needs to become longer. This sets a practical limit for the minimum internal shaft diameter, below which archers can expect points to fail. Subjectively, that limit seems to be close to the 3.2 mm modelled.
Similarly, if the internal diameter is increased, the wind drift will also increase. Due to the strong dependence of the spine on the diameter, the shaft wall thickness needs to decrease as the internal diameter is increased. While this leads to lighter arrow shafts for the same spine, their higher arrow speeds make them well-suited to less windy environments, such as a field course.
In a previous article, I showed how the shaft diameter divided by the square root of the arrow’s mass serves as a good metric for an arrow’s performance in wind. In my journal paper, I compared the ratios of that metric for various arrows to their calculated wind drift ratios. There was a strong correlation, showing that the metric provides a reliable guide to an arrow’s relative performance in wind.
Overall, in every case, the addition of an internal aluminium layer leads to reduced wind drift. The Easton X10 and 3.2 mm Parallel Pro shafts are very close to optimum.
To find Dr James Park’s published academic work visit: www.journals.sagepub.com
