The Armour Archive

A good friend is taking some Engineering courses this semester and has a really great project to do. He gets to build a ballista. Cool, huh? One catch. He has to document and explain all of it in real math-type calculations. In fact, he has to build it based on those calculations, not just fudge them up after the fact. He had the information on most of his materials, but there is one thing lacking.

Who knows how to calculate the torque created by the twisted ropes? This isn't a big crossbow. The arms actually have to be separately activated by the twisted ropes that hold them. His only source is a translation of some very old Greek documents, and the professor is not pleased with that as a source of information. I figured that folks here would be more likely to know than anywhere else I can think of.

Please note, I have no worries about the design or the execution. The problem is calculating the force created by the torque of the twisted ropes. He is required to calculate it (in theory) before he builds it, if I understand him correctly.

Any help y'all can give, especially if there are books that cover the subject, would be much appreciated. I really want to help my friend.

-Patrick

Torque = Force × Distance to fulcrum × sin (q)

He's have to find K, the spring constant, of the torsion skein. Which will depend on the rope material, loops in skein, lenghth of skein, and degrees of twist. The rope will strech with each use, so more twist will be needed to maintain power.

Has he looked at "Greek and Roman Artillery: Technical Treatises" by E. W. Marsden? Can you find out what his documentation is?

Suggest him/her ask in the Yahoo group SCA-Siege. There are many talented engineers there.

If they can't post, email them to me and I'll forward them to the group.

IIRC, there is little documentation for early ballista. We speculate they used trial and error to establish the "optimal" ratios between parts.

If you haven't been there, I'd suggest
http://www.stormthewalls.dhs.org/Siege/ConstructionPics.htm
Look around his site.


MJRamey

Christophe de Friselle wrote:Torque = Force × Distance to fulcrum × sin (q)

He's have to find K, the spring constant, of the torsion skein. Which will depend on the rope material, loops in skein, lenghth of skein, and degrees of twist. The rope will strech with each use, so more twist will be needed to maintain power.

I think you missed an important part. K is not a fixed value due to geometry. The skeins I have seen have a slow helix to them and are not wound like a spring. Start by looking at a 1/4 of the skein, say the top front. The ropes of the skein start in a vertical position and then a pre-load is applied. This gives them a resultant length of ((1/2 skein_height)^2+(half_skein_width*preload_angle*2*pi/360)^.5. The rope length can be similarly calculated when fully cocked. The difference in rope length can be used along with the K value for that type of rope (in that type of humidity and temperature) to develop a spring force. Remember that we are lookinig at only 1/4 of the skein and the loads are applied in vectors mostly away from the direction of motion but that a portion of each vector canceles.

The non-linear output of the skein that causes the ends to need to be so far apart so that the weapon is opperating in atleast a small nearly linear portion of the curve.

At least this is how I understand it.

There are "Simulators" for trebuchets out there that allow you to modify mass arm length and sling length. The math is often fully described. The is probably a simulator already for balista.

Wish your friend luck, it sounds like a fun project if he can keep his professor from feeling that it is to primitive a project.

Sean (wishing that this had been my senior project)

Sean Powell wrote:The non-linear output of the skein that causes the ends to need to be so far apart so that the weapon is opperating in atleast a small nearly linear portion of the curve.

If I understand what you mean by that, I think it was illustrated on an episode of Junkyard Wars" where one team was convinced to build an onager that had steel cable in the torsion bundle. The projectile was a washing machine.
It took a very strong winch to cock the throwing arm back, but when they released it, it only sprang back up to about 60 degrees. On the second try, they pre-twisted the bundle a bit more, cocked it back (with great difficulty) and yet the washing machine barely cleared the front stop bar, and it landed on the front of the onager. There was only a very small angle over which the torsion bundle exerted any torque because the steel cable had little or no stretch to it.

BTW - the other team fought (against the show's appointed "expert") to build a trebuchet instead of a giant ballista-type engine. They did build a treb, and won it hand's down.

The "Cat Mess" board is a good discussion forum to find answers about all types of siege engines, at - http://web.trebuchet.com/boards/list.ph ... _catapults but I see they're going to retire it and move the discussions to http://www.TheHurl.org