After yesterdays excursion into armor and material properties, with a small side of kinetic energy, today I will explain how you can calculate how much kinetic energy your bow will transfer into an arrow.
For this thread there are, once again some terms I will use, that you need to understand:
Potential energy is the energy stored in an object, due to its position, tension in itself, etc.
Draw weight is the amount of force required to draw a bow to its complete draw length.
So lets put some numbers on our example, that you can see above. Lets assume the draw lenght (black line) was around 30". The actual draw distance could be 24", and as the draw weight, we are going to assume 120 lbs.
With this we come to the calculation:
24 x 120 / 2 = 1440
But wait we have 1440 inch pounds, whatever abomination of a unit that might be ;) , so lets convert that to something more commonly used.
1440 / 12 = 120
Now we have foot pounds, which is a bit more common, but I'd prefer Joule.
120 x 1.35 = 162
So the energy we are putting into the bow is around 160 Joules, but how much of that is actually going to be put into the arrow?
Well, here comes the part, where I sadly have to disappoint you ... it depends on your bow how much of that energy is transfered to the arrow as kinetic energy.
We will have to multiply our potential energy with the efficiency of this transfer, which really can be very low at 0.3 but could also concievably be as high as 0.95. For medieval warbows we can estimate it to be closely around 0.7 though.
So our arrow has a kinetic energy of ~ 0.7 x 162 = 113.4 Joule
A little side note ... one inch more draw length adds about 5 times more energy than one pound more draw weight, but while draw weight is 'capped' by the material, draw length is mostly limited by your arm length.
The next topic will most likely be either mail armour or momentum and projectiles ...
If you think (or know) that some of the estimates that lead me to this conclusions are wrong, please let me know.
I'll just state it here once again: I don't expect archery in Elyria to work exactly this way, but I hope this little write-up will help some people understand how archery works.
Back to the collection thread