It’s my fault. I made a calculation error when converting metric units into Imperial units by modifying the coefficient. Now it has been corrected. Thank you for your reply.

gengzi,

I double checked my formula using a sample calculation (Pacific Yew), and it agrees with the results in the table I posted. The modulus of elasticity is a large number when expressed in psi, so make sure you have entered the correct number of zeros. You can also derive the formula for yourself from first principles if you’re not convinced it’s correct. It’s essentially an energy balance between elastic potential energy of a linear elastic spring and kinetic energy when the load is suddenly released. The model assumptions are that the chunk of the material is perfectly homogeneous, it behaves linear elastically, is loaded in uniaxial tension, and energy is converted from potential to kinetic with a 100% efficiency (i.e. no hysteresis loss), and that the material flings itself with uniform velocity. In reality these assumptions aren’t perfectly accurate. There would be some internal hysteresis loss, and the material coupon would not experience uniform tensile stress due to surface effects and grain structure imperfections. The velocity also would not be uniform, but instead more of a linear distribution from zero velocity at one end to max velocity at the end being released suddenly. I hope this helps.

Do you have any other formula to calculate this speed? I used the formula in your comment and found that it doesn’t match the result presented in your picture. Did you use another formula in your picture?

From what I can tell, design also plays a crucial role. Bow wood like Osage Orange and Yew with a high rated index can be narrower and thicker, more like classic English bows, while low rated woods need to have wider, thinner, longer designs implemented to compensate for a low index. At least that is my understanding, that you can make bows from lower scoring woods but the design needs to be modified accordingly to compensate and as such have potential with those design considerations to preform similarly to other “classic” bow woods.

There is a typo in my spreadsheet in the fling speed numbers. The SI unit for density was inadvertently left in place when I tried to replaced it the imperial pounds per cubic foot. All of the fling speed numbers are wrong. For the heavier woods, the error is small, but for the high and low density materials the errors are proportionally larger.

The correct numbers are:
Wood Species . . self-fling speed v
Yew . . . . . . . . . 141
Osage orange .. 133
Brazil wood . . .. 142
Madagascar
Rosewood . . . . . 164
Balsa . . . . . . . . . 86
S-glass . . . . . . . 586
Carbon . . . . . . . 256
C-350 Steel . . . . 197
b-C, Ti Gr 19 . . . 179
Ti Gr. 5*  . . . . . . 120
Al 7068* . . . . . . 163

The bow index, 1000*(MOR/MOE) is 10 times the strain to failure as expressed in percentages. In other words, MOR/MOE is the strain to failure. So the index is a mechanical property with the decimal point in a strange place. The reciprocal, MOE/MOR is the minimum bend radius of a 2×2″ rectangular bar, which turned out to be interesting, but no better. I tried normalizing cross sections to compare various woods to yew, looking for a constant stiffness for different woods. Taking a 1″ square cross section yew stick as a baseline I looked at the different widths and thicknesses to get the same stiffness, and compared the weights. I made lots of numbers, but no real improvement. 

I think the parameter that I was missing was speed of cast which was posted here by John 2 years ago. I will disagree with John’s use of fatigue strength for the metals. Fatigue strength is the load for 10,000,000 cycles without a failure. No one shoots that often. At worst, a bow is subject to low cycle fatigue, say a few million cycles. I added his equation to my table using metals at their yield strength, which is still much more conservative than the MOR for woods. The weirdly interesting number that dropped out was the speed of cast for a balsa wood bow, 222 fps. I think that is where you have to start looking at the toughness and other properties. It may be that the balsa bow can fire an arrow very fast, once.

I uploaded an image of my spreadsheet. The formulas are in the bottom row. The upper left corner was cell C2 and the equations are in row 16. If anyone wants to play with these, Row 16 copied and pasted look like this and these equations can be pasted into excel in the 16th row of a spreadsheet.
*yield strength input data D16 input E16 input F16 =E16/D16 =D16/1320000 =H16^0.333 =1/I16 =1/H16 =J16*F16/0.65 =F16*K16/0.65 =1/G16 =J16/G16 =68.07*E16/(D16*F16*R16)^0.5 =F16/0.65 =F16*2.54^3*1728/454

Thanks….it’s pretty wood…I run across them occasionally in GA but haven’t chopped one down yet.

Other than MOE, I’ve never been able to find any mechanical data on Gingko. It’s a fairly light wood so in general I’d guess it would rate fairly low on the list. https://www.wood-database.com/ginkgo/

Before the Europeans arrived they were so advanced that they managed the land perfectly, they actually used/use an array of advanced hunting techniques, tools and knowledge that surpass most other indigenous peoples’. This is where boomerangs came from, the kind of spears you see in aboriginal culture are more than enough. What people don’t realise is that most things in Australia that would need hunting with a bow and arrow were introduced by the European settlers, who brought guns too.
The entire way of life basically changed over just few decades, what we see is just remnants from very advanced indigenous cultures that were persecuted heavily. They actually had/have staple food sources otherwise in the form of large root tubas and other plants, so meat would always have been for nutrition moreso, nothing that big and nothing that needed anything better than a very advanced spear.
The Aborinal knowledge of the land, plants and animals and the sophistication within that is absolutely incredible, medicinal values of plants etc. I think they’d have had the bow and arrow if they needed it but the inventory of spears, slingshots and throwing tools gave them more than enough. There are some unique hunting tools that suit the environment perfectly, usually with multiple uses for travelling light.
We still don’t know what was lost through sheer ignorance and persecution, we simply don’t know quite how advanced they were but they certainly still are very sophisticated, you can just see how strong their connection is to the land if you look into it, very interesting and important culture that I’d never describe as undeveloped, I have a lot of respect for them and I think the modern World could still learn a lot from them and other indigenous people’s from around the World.

There are heaps of Australian natives listed, including river sheoak at #12, right below osage orange. I’d be blown away if it (or any other AU native) is actually any good as a bow wood though.

How do you feel now that people are building hickory bows going 170+fps at 10 grains
p/pound, and the best are doing 180/183 fps..Checkout twisted stave and some others
you are never to old too learn??.

I’m really surprised by the results, especially by the downy birch. Almost everywhere I’ve looked people tend to frown upon birch for making bows. I recently acquired a nice stave of downy birch but didn’t think much of it, wasn’t sure I’d even use it. but it turns out turns out I might have stumbled on gold which is nice cause there’s tons of it around here.