Need to Know About A Characteristic of Arrow Flights

TheAzn · Post by **TheAzn** » Mon Mar 29, 2010 7:32 pm

People have always said that, in order to penetrate armor, the arrow would have to hit it straight on (without any angle).

Someone has said that the furthest range at which an arrow can hit something straight on would be half its true maximum range. However, I am not sure that this is true for a 1.5 meter high target.
People have said that, using normal hunting bows, they could shoot up to 70 - 80 meters withoug any slight change in the angle of the arrow. Since these were normal bows, I assumed that the maximum range would have been between 150 to 180 to 200 meters.

I needed a more concise estimation. Are there any equations that could help me find a specific value provided that I already have the value of the maximum range of the arrow flight?

KenH · Post by **KenH** » Mon Mar 29, 2010 8:17 pm

"People" are not always right! First, any projectile, from the fastest bullet to the slowest rock starts dropping as soon as it leaves the projector (gun, bow or hand). How fast it drops depends on the velocity imparted by the powder, string or arm.

Second, you must consider the kind of armor. Are you talking ring mail, scale mail, iron or horn reinforced leather jack, mixed plate and ring, 17th century back & breast, Gothic Tournament Armor?

Third, it's not "straight on", but rather "at right angles to the armor's surface". The actual angle of impact is a major factor of penetration. An angled hit of say 15˚ on chain/ring mail still stands probably 85-90% chance of penetration, the same hit on plate mail might ricochet off - but it might not.

Also you need to consider the arrow - it's weight, initial velocity and point type in particular. Also drag caused by shaft cross-section, point style and fletching. Bodkin points were invented as armor piercers, for example, where broadheads are not. Big fluffy feathers don't travel very far or fast compared to long thin feathers.

Another factor is impact energy - a factor of initial velocity, maximum height of the arc, and projectile weight.

Truthfully your question needs to be restated more specifically to encompass those factors.

Arrow flight, like other projectiles, is a parabolic path.

There are several on-line archery ballistics and impact calculators on line; Here are three good ones.

http://www.outdoorsden.com/archery/archbal.asp
http://home.att.net/~sajackson/ballistics.html
http://www.martindalecenter.com/Calcula ... LL-ARCHERY

jack farrell · Post by **jack farrell** » Mon Mar 29, 2010 8:25 pm

Of course if you hit the horse, the rider may fall on his face.

KenH · Post by **KenH** » Tue Mar 30, 2010 12:31 am

Brings a whole new meaning to "fall on your sword".!

TheAzn · Post by **TheAzn** » Tue Mar 30, 2010 7:06 pm

Thanks for your answers, guys. I have a few more questions.

What is and how do I find the "arrow constant"? This term can be found here:
http://www.stortford-archers.org.uk/medieval.htm

If this could help you guys, I would like to add that the value of the "arrow constant" for a 60 grams (not grains) arrow is
[.0010Newton times seconds(squared)]/ [meter(squared)]

I hope that you guys can help me.

Daniel T. · Post by **Daniel T.** » Wed Mar 31, 2010 12:01 pm

This constant is a value that describes how areodynamic the arrow is.

Look here:
http://en.wikipedia.org/wiki/Drag_equation
and here:
http://en.wikipedia.org/wiki/Drag_coefficient

TheAzn · Post by **TheAzn** » Thu Apr 01, 2010 3:55 pm

Thanks Daniel.

Final question: what's the "k" (factor to allow for the kinetic energy of the bow) and how do I find it?
For a longbow the "k" value is 0.05.