Hello Fellow Archers,
So I came up with a selfbow performance chart that can give a rough estimate for those who build selfbows. I started archery about a year and a half ago and built my own selfbows a year ago. Since I started building I was always looking for the best design that would be efficient and produce the highest FPS. Anyway I finally got my hands onto the Traditional Bowyer's Bible and have learned much since then. Definitely a good read.
Anyway, I stumbled onto a very interesting section during my reading. In TBB4, the authors hosted a competition on who can make the best selfbows. Luckily the authors provided the tabulated results along with each bow specification. The chart they provided is worth so much information since was quantitative data. Me being an engineer and like data, decided to see if I could find some sort of a trend. The rest of this post is the result of my findings.
The first thing I did was tabulated the data according to the draw weight and FPS as shown: (See first attachment)
Pretty interesting huh. There is a trend that occurs in which we can put an equation too. There are two things to note from this graph.
1.) The Y-Axis is normalized by dividing the measured speed by the draw-weight of the bow.
2.) The X-Axis is normalized by dividing the draw-weight by the draw-length minus the brace-height. The reason for this is that you don't actually draw an arrow to 28 inch if you have a 28 inch draw length. The arrow is pulled only 22 inches with the addition of 6 inch of brace-height.
Here is the final graph (See second attachment)
The final graph may look daunting but I'll explain each part. Before I explain, there are assumptions that were made in order to generate this. The assumptions are listed as follows:
1.) The arrow that the bow is shooting is will weight 10 grain per bow weight. For example, a 45# bow will shoot 450 grain arrow.
2.) The brace height (unless noted) will be 6 inches
Okay lets explain how to use this chart now.
Text written in italics will refer to my personal information for examples
In order to use this chart your bow must be a selfbow made from one piece of wood. This can either be a stave or a board bow. A thin layer of bow backing material is fine.
In addition, it is not required but recommended that your bow meets these criteria's:
1.) Have a draw weight between 30 to 70 pounds at your normal draw length
2.) The bow should weigh about 15 to 35 ounce
3.) The bow should have a minimum length of 54" and a maximum length of 76"
4.) The bow's mid-limb width should be from 0.88" to 2.5"
Example
1.) My bow pulls 42# @ 26". My brace-height is set to 6"
2.) My bow weighs 21 ounces
3.) My bow length is 64"
4.) My bow's mid-limb width is 1.5"
If your bow meets the criteria, we can proceed.
For Arrow Speed
Begin by taking your normal draw length and subtracting it from the brace height. Then divide the bow weight by this number.
Example
26" - 6" = 20"
42# / 20" = 2.1
Take your number you get and match it to the horizontal axis. In my example I look for 2.1 on the bottom axis. Once you've found your value on the horizontal axis, follow the grid-line vertically up until you reach the solid black line. From there, follow the horizontal-grid line to the left until you reach the left vertical axis and get your value
By starting at 2.1 and moving up until I reach the solid black line, I then move left to get a value of 3.3
Take this number now and multiply it by your draw weight in order to get the arrow flight speed for your bow for an arrow weighing 10 grain/drawweight.
3.3 x 42# = 138.6 FPS
My bow shooting a 420 grain arrow will achieve an arrow velocity of 138.6 FPS
For Bow Efficiency
The bow efficiency is determined as before. Find your spot on the horizontal axis. Again, mine is 2.1.
There are three dotted slanted lines which correspond to the efficiency to the bow and uses the axis to the right. The efficiency depends on both the draw length and brace height. For this graph, the three lines are determined using a fixed brace height of 6.
Find the efficiency line in which you will be using according to your normal draw length.
Since I have a 26" draw length, I will be using the middle dotted line.
Like before, trace along the vertical grid line from the horizontal axis until you reach your efficiency line. Then move directly to the right to find your bow's efficiency
From 2.1 I move up to the Efficiency@26 draw line and then move directly right. My bow efficiency is 50%.
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That's pretty much it. Pretty simple.
To recap, my bow weighing at 42# @ 26" with a 6" brace height will fire a 420gr arrow at 138.6 FPS with an efficiency of 50%. An efficiency of 50% means that 25% of the potential energy stored in my bow limbs during drawing will be converted to kinetic energy which transfers to my arrow when I release.
When using this chart please note that it is only a rough guideline that can be used to determine your bows performance. The scattering of the data is quite large so the value you get will be an average. It is recommended that you actually shoot your bow to get speed measurements which can be related to efficiency. From this chart, if your arrowspeed is actually higher than the listed value, then that means that your bow is performing above average.
When testing mine, my bow actually shot a 400 grain arrow at 135 FPS, 3 FPS slower, which means my bow is probably below average (what can I expect, it was my first working bow that I built)
Things that this chart does not include or mention
-Bow design (i.e. recurve, reflex/deflex, rounded belly, flat belly, etc.)
-Bow wood material
-String material
-String follow
-Bowyer's skill level
Designing with this chart
If you do use this chart as a basis to design your bow, you should know that there will be a trade off. There are a lot of bowyers and archers who talk about building an efficient bow that sends an arrow fast. From this graph there will be a trade off. As your bow shoots faster, it will become less efficient. And if you want a bow that shoots more efficient, it will be slower. However, there are always exception. If you have a very good knowledge about selfbows and have great designs, you may very well not fit into this chart at all. If you're still new beginner, you may fall under.
Concluding Remarks
On my quest to finding the best design I stumbled on a trend that seems to work for a general selfbow. I know that you're thinking that self/primitive bows should be natural and not be pre-designed but hey, this is part of the fun. If you have any question/comments/concerns/ or criticisms please feel free to let me know. If your want more detailed explanation on my derivations, let me know too and I'll be happy to explain.
Also, if you would like to see how your bow fits the data, feel free to post up your selfbow's specs too.
Thanks,
Archer Bunta
References
Traditional Bowyer's Bible Volume 4
"They say shoot straight as an arrow. I say curve the arrow around the corner" -Archer Bunta
