COMMUNITY - FORUMS - GENERAL DISCUSSION
On bows and potential energy

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


The truth is born in argument

8/18/2017 5:42:30 PM #1

Interesting, the math might be a little off since especially for self bows or composite bows the draw weight is not constant throughout the draw length, but that means a fairly complicated differential equation, your numbers are good enough for rough estimation purposes I think.

Though, unlike a bullet, the energy transfer of an arrow isn't what does most of the damage, penetration is key, you're poking/cutting a hole rather than causing massive impact trauma like a bullet, and that's more dependent on momentum and having the right tip on your arrow to get through the armor that your opponent is wearing.


8/18/2017 6:02:28 PM #2

For self bows and composite bows the draw weight is nearly constant. You are thinking of compound bows.

I will make a thread about momentum sometime soon though, so worry not, what you are alluding to will be mentioned.


The truth is born in argument

8/19/2017 5:23:02 PM #3

If I am understanding your charts correctly, and please correct me if I an misunderstanding. A Yoru bow will always out power a Kypiq bow because of draw strength, but a Yoru would be better served by a long bow of the appropriate size; while the Kypiq would be better served by a composite recurve.

Would this be reasonable simple conclusion?


8/19/2017 5:33:06 PM #4

A yoru bow will always be many times stronger than a Kypiq bow, because of draw weight and draw length. The differences between recurve bows and self bows aren't that huge in comparison.

But yeah, I don't know how accurately the chart portrays the average self bow, or recurve bow, so I'd actually say they are probably equal, with the differences we are seeing here being caused by the differences between the individual bows, rather than the bows design.


The truth is born in argument

8/19/2017 7:40:21 PM #5

Posted By Giasrhen at 10:23 AM - Sat Aug 19 2017

If I am understanding your charts correctly, and please correct me if I an misunderstanding. A Yoru bow will always out power a Kypiq bow because of draw strength, but a Yoru would be better served by a long bow of the appropriate size; while the Kypiq would be better served by a composite recurve.

Would this be reasonable simple conclusion?

I think another possible conclusion is that Kypiq are not well served by any traditional bows because of their naturally short draw length. Possible alternatives would be crossbows (possibly mechanically wound) and blowguns (which were actually quite popular with woodland Native Americans).

8/19/2017 7:51:27 PM #6

Don't forget slings


8/19/2017 7:59:25 PM #7

might want to check that, it's about pygmy hunter's bow.

you can also give them Gastraphetes


8/19/2017 8:03:36 PM #8

Slings suck ... maybe that should be the next topic.


The truth is born in argument

8/19/2017 8:09:46 PM #9

yep next subject should be "slings, atlatl, and the aklys; why we quit throwing our own feces."


8/19/2017 9:54:58 PM #10

Posted By markof at 12:59 PM - Sat Aug 19 2017

might want to check that, it's about pygmy hunter's bow.

you can also give them Gastraphetes

Not saying that no one ever used a small bow, but if you need to penetrate any sort of armor and not just an animal hide, you'll need more draw length or weight (or both) than a Kypiq is likely to provide.

8/19/2017 9:59:33 PM #11

Posted By Dekul at 12:42 PM - Fri Aug 18 2017

Interesting, the math might be a little off since especially for self bows or composite bows the draw weight is not constant throughout the draw length, but that means a fairly complicated differential equation, your numbers are good enough for rough estimation purposes I think.

Though, unlike a bullet, the energy transfer of an arrow isn't what does most of the damage, penetration is key, you're poking/cutting a hole rather than causing massive impact trauma like a bullet, and that's more dependent on momentum and having the right tip on your arrow to get through the armor that your opponent is wearing.

Most bullets impact with a fraction of the raw force that a bow, or even a bare handed punch delivers. They do however cause rending cavitation bubbles in your liquidy flesh, rupturing veins and arteries without direct contact. Think of a bullet passing through as causing AOE bleed damage.


I'm a forester. A man who takes trees that are all different and cuts them into boards that are all the same / Seeds that are all the same, and grows them into trees that are all different.

8/19/2017 10:08:29 PM #12

Firearms easily reach 10 times the KE of a bow.

A while ago there was a discussion on the official CoE Discord involving slings and a .44.

Slings ended up being calculated to be at around 40 Joule, the .44 on the other hand was at around 1400 Joule.


The truth is born in argument

8/19/2017 11:19:03 PM #13

Posted By MatthewDKiefer at 2:59 PM - Sat Aug 19 2017

Most bullets impact with a fraction of the raw force that a bow, or even a bare handed punch delivers.

Having seen a few people get shot during my past military service, I assume that you are referring to how one can be shot and hardly notice? The force of a bullet is certainly greater than a bow or punch, but bullets are also really good at penetration.

They do however cause rending cavitation bubbles in your liquidy flesh, rupturing veins and arteries without direct contact. Think of a bullet passing through as causing AOE bleed damage.

Cavitation bubbles can happen due to passage of a bullet, but they are not particularly lethal by themselves. You're talking about hydrostatic shock here, which seems to have rare but decent supporting evidence as a wounding mechanism. This is the idea that a bullet (or other shock to your body) can produce wounds, such as ruptured blood vessels in the brain, at great distances from the initial injury. Here is the foundational report in this field.

Some bullets, like the 5.56mm/.223 NATO are very light and fast. They are designed with a center of gravity that increases the likelihood that they will tumble and thereby deposit more of their energy in flesh rather than over penetrating and zipping off into the distance. This is a whole different topic, though.

8/20/2017 8:51:28 AM #14

Posted By Huntsmaster at 11:54 PM - Sat Aug 19 2017

Posted By markof at 12:59 PM - Sat Aug 19 2017

might want to check that, it's about pygmy hunter's bow.

you can also give them Gastraphetes

Not saying that no one ever used a small bow, but if you need to penetrate any sort of armor and not just an animal hide, you'll need more draw length or weight (or both) than a Kypiq is likely to provide.

I agree, i was reacting to your post with the blowgun and crossbow, my bad i should have quoted you, sorry.

Just like they say in the text about the Pygmy, they do not use their bows on large prey, for those they use spears.

AS Kypiq value life, it make sens that they'll keep lethal weapons as a last ressort, only in time of war or against feral/evil ennemies, using most of the time non lethal weapons, like poison/drug delivery system, blowgun seems the less lethal here, bollas, nets....


8/25/2017 9:33:14 AM #15

And this, friends, is why the Kypiq will never use bows in war, and the Yoru will be siege engines.