Well here’s a guy who’s obviously pleased with himself.    Click for Vid., 20110203114847

From Marsden’s treatise, “Greek and Roman Artillery” , we copy the following translation from the ancient Latin regarding the “Lightning” arrow firer.  This description from the fourth century is by that renowned scholar Mr. “Anonymous”.  (Curious how he keeps popping up through out all recorded history.)   Anyway,  here is what he has to say about an original machine that he had apparently witnessed in operation:

“It has been discovered by practical experience that this type of ballista, essential for the defense of fortifications, is superior to any others in velocity and power.  When an iron arch has been fitted above the stock, along which the arrow is projected, a powerful sinew rope is drawn back by means of an iron hook and, when released,  it propels the arrow with tremendous force at the enemy.  The size of the actual machine does not allow this rope to be pulled back by the manual exertion of the soldiers;  but two men, one to each of two wheels, draw the rope to the rear by pressing against the spokes in a rearward direction,  since mechanical force has been obtained to match the enormity of the task.   A roller- device now elevates and now depresses the machine, as may be necessary, in order to direct its missiles higher or lower.  This remarkably clever demonstration, a combination of so many different components, is directed by the control of one man only at his leisure, so to speak  —  control confined simply to loading the missile ready for projection; this is apparently to avoid the consequence that if a crowd of fellows was engaged in manning it, the ingenuity of the device would be reduced.  A missile projected from this engine, comprising so many important and clever devices, travels so much further that it has even the momentum to fly across the width of the Danube, a river noted for its size;  it is called the Lightning ballista and,  by its name, gives evidence of the effect of its powers.”

There are some interesting parallels between Firefly and the Lightning ballista as described by “Anonymous”.   The Fourth Century AD when this passage was written and the location mentioned along the Danube are both consistent with the Orsova find that Firefly is based upon.  Likewise, the potential for one man to aim and fire a machine like this is clearly demonstrated in the video at the beginning of this post.  The “roller-device”  that Anonymous describes to elevate and depress the machine is particularly interesting at this point in our project as I am about to complete the counterstay and prop upon which any elevation adjusting mechanism would likely bear.   In his footnotes,  Marsden comments that he took this “roller-device” to be the universal joint seen on the top of the stand, but this hardly seems compelling given that the universal joint had been in use on these types of machine for more than 700 years prior to this description, and would hardly provoke comment as something new and ingenious by the time the fourth century rolled around.   Also, the exact wording of “now elevates and now depresses” would seem to indicate that the “roller-device” causes the machine to elevate or depress, and not merely allow those functions to occur as is the case with a universal joint.  Now clearly these are all nit-picky little points, and whatever it was that Mr. “A” had in mind could easily be lost in translation; all that aside,   there is another factor that my own experience with these machines suggests is vital for accurate shooting.

We first need to understand that there are two basic styles of aiming and firing a machine like this.  They are: (1) shooting in an unsupported offhand manner as shown in the preceding video, and (2) shooting with a rest in a more deliberate and precise manner such as a sniper might use.  In this latter role, the prop and counterstay are used to form a solid rest while aiming and firing.  With the prop in place,  side to side adjustments are easily accomplished by slewing the machine right or left because the prop has wide latitude to move in those directions.  Aiming the machine up or down is a bit more problematic.  Gross adjustments can be made by sliding the prop up or down the angled counterstay,  but for the final hair splitting refinements this is hardly ideal.  Typically I have used wedges to slip in and out to make the precise vertical adjustments,  and that system can work quite well once you get used to it.  However,  it would be much smoother and faster to simply rotate an eccentric roller and have the machine elevate or depress a few fractions of a degree.     I believe that the  importance of such a “roller-device” cannot be underestimated once you actually get down to trying to make those impossible shots.

Perhaps I’d better put my current design for the prop and counterstay on hold,  and see what can be done to incorporate an eccentric roller controlled by a hand lever of some kind.

It seems like it’s time to break out my very special thinking cap and have a little vino to help lubricate the process.

10 Responses to “Mr. Anonymous and the Lightning arrow firer.”

  1. Captn Harpoon says:

    When you combine gravity with a a set of rollers/pulleyd placed forwards would work well enough with a lever.

    If Firefly were forward heavy. A rope attached to front going up and around a set of rollers/pulleys to a lever is about as simple as one could get.

    On a four foot lever attaching the other end of the rope about a foot from the lever axle (hooking over pegs for adjustment?)

    Use the lever or winch lever to elevate it, the lever locking into a slot (or ratcheting). To lower, disengage winch lever, and let gravity lower it.

    You only need to apply power one way. You would need to set the pivot point rearwardly so the front could use the weight to lower it an lock into place.

    With a perfectly balanced system, the projectile might be able to provide the weight needed to lower it.

    I need a new tin foil cap for really serious thinking…

  2. Captn Harpoon says:

    I completely forgot to tell ya Firefly looks frikkin awesome! The very first glance gave me an impression that she should be indeed be looking to the Heavens.

    A small telescope mounted on top somehow, might give ya a better look at potential targets LOL!

    PS. crosshairs added to the telescope would help with ranging haha.

    This blog is starting to be a real page turner….look forward as always to next posting.

  3. Captn Harpoon says:

    Now I got ya. Fine adjustment for pinpoint accuracy as opposed to just ranging. Nice simple design. How about left to right movement for windage?

    Any new harpoons in the making? I have wondering what sort of damage could be done to half inch boilerplate with hardened tips, all metal shaft (full metal jacket haha).

    NOt authentic perhaps but might be some kinda fun.Heres a nice vid for ya to think about: http://www.youtube.com/watch?v=QfDoQwIAaXg&NR=1

  4. Pat B says:

    I’ve read your blog all the way through. Bits of social observation mixed with engineering – it’s like reading The Wheelwright’s Shop. Great stuff.

    Back in April 2009 one of your posts – “It’s got to. Right?” – has you writing a little memo to yourself deducing that there must be an increase in missile speed in the second half of the action. You seemed a little unsure of your own logic, which makes me think that you have a good intuitive grasp of the physics involved, but lack the theoretical background. So I thought I’d fill you in on some of it.

    Over the last few days I’ve worked on a formula showing the velocity of the missile relative to the arm-tip for a machine with arms that are half the width between the cylinders. That roughly corresponds to the one you have built, at least as far as I can tell from the photos.

    In the following table the figures in the left column are the angles through which the arm passes during the release. It starts with a full 135 degrees of cock (-45). the “0” line is where the arm-tips pass directly between the cylinders. And 90 deg is where the arms finish, with the string taut.

    -45 0.50 Arms cocked to 135 degrees
    -30 0.80
    -15 0.96
    0 1.00 Arms facing directly inwards
    15 0.97
    30 0.93
    45 0.92
    60 1.00 Missile now passing between cylinders
    75 1.33
    90 indet

    The figures on the right show the velocity of the missile relative to the arm. At the start it’s only going half as fast as the arm-tip. It reaches equal speed at 0 degree. Then it slows down slightly and doesn’t get back up to equal speed until the arm is at 60 deg, with only 30 deg left to go. And even at 75 deg it’s only 33% faster. The “indet” at 90 deg stands for “indeterminately large”. In theory, with the angle between the two halves of the string vanishing to 0 as it tautens, the velocity ratio becomes infinite. In practice it isn’t, of course. The further you go towards that extreme the more unreliable the figures become. But it’s still pretty big.

    I did a breakdown of the last 15 deg, going in 5 deg jumps:

    75 1.33
    80 1.62
    85 2.31
    90 indet

    Still not impressive, with the missile going at less than 3 times the arm-tip speed with only 5 deg of turn left. So a finer breakdown is needed, between 85 and 90:

    85 2.31
    86 2.59
    87 3.02
    88 3.72
    89 5.30
    90 indet

    And then a breakdown of 89-90:

    89 5.30
    89.3 6.35
    89.6 8.43
    89.9 16.91
    90.0 indet

    Well, I could go on all night, getting finer and finer divisions. But at this point I just took that 89.9 and started adding 9s:

    89.9 16.91
    89.99 53.52
    89.999 169.26
    89.9999 535.24

    Well, those are Mickey Mouse figures, of course. I’m speculating that your arm-tip might be going at 50 fps at that point, in which case the missile velocity is 535×50 fps. You wish! The reason the figures become unreliable as the extreme condition gets closer is that physical anomalies become magnified to the same degree as the velocity. The amount of “give” in the fibres of the string, the wind resistance of the string, the weight of the string, a slight misalignment of the arms…. all these things, which make no difference during the rest of the action, become huge factors in the last few degrees. And, not least, there is the inertia of the missile, which is its resistance to acceleration. At that point it has huge leverage over the springs. If your missile weighs 1 lb and the velocity ratio is 100:1 at that point, as far as the arms are concerned, they’re trying to pull an object weighing 100 lbs. There’s a good chance that your arm is actually slowing down at that point, as a result of this magnified back-force.

    Even so, what should be clear is that most of your final velocity is gathered during the last 5 degrees of movement. Just thought you’d like to know. Keep up the good work. I’ll certainly be following it with interest.

  5. Captn Harpoon says:

    Hey Pat B,

    Nice work! Finally someone who can help with the math. Buried somewhere in a page comment is a chart I did exploring the relationship between arm length to spring centre to spring centre. Dynamics change drastically as the ratio changes. This is where Nick must go if he wants to increase velocity potential further.

    I have been trying to get NIck to shorten the limbs an appropriate amount but he is unconvinced still. Unable to do that he is willing to extend rotation of the arms by aprox. 15 degrees for a 22% net gain in velocity (at partial power). The gain should even be higher with full rotation, possibly as high as 30%.

    Please post some numbers where the arm length is 1/3 the spring centre distance. This is a point very close to the machines natural balance. That should be enough to get NIck up to 500fps, and allow him full rotation needed to max performance capabilities.

    I suspect however that once past the 90 degree point your calculations might become a little too complex (amount of work needed).

    I’d like to point you in the direction of a paper by V.G Hart and M.J Lewis entitled “Hatra Ballista: a secret weapon of the past?”

    The paper was written to compare the performance of the outswinger ballista to the inswinger. The numbers you post are in line with a graph he did with the angular velocity of the arm in radians, and velocity of missile in m/sec.

    Part of the testing Nick will do hopefully will be able to defeat the math. It has been my arguement with him that advancing the rotation changes the velocity potential (increase) while he insists it is only because we have also increased the draw length.

    Since Nick has NOT changed the draw length of Firefly, it is expected that Mr. Harts math may have failed him. Should Nick decide to use other means to further increase the amount of rotation possible, another 5 degrees taking it up to 20 extra degrees will again boost potentials.

    Going much past 20 degrees from normal 90 degree rest position serves to introduce a somewhat disagreeable instability, where any imbalance in forces between the two springs will be magnified and act upon the machine. The 15 degrees he has managed to get by removing brass inserts from stanchions should be plenty while providing a good safety margin.

    I am heavily into advanced inswinger design, as is Nick. I dont think NIck would mind if I invited you to visit my blog where I also experiment with hand held ballistas, passing on some of what I learn with the ballista community here and on RAT. Goog Warhammer1 Ballista blog.

    I need some help with optimizing parbolic curvatures (rotational movement on a moving axis) utilizing Kepplars second law to induce (centripedal?parametric??)acceleration.

    I am attempting to design/build an N-levered catapult capable of near supersonic projectile velocities based on an HOnors thesis I came across while researching ballistas and seige-weaponry. Perhaps an exercise in futility, but along the way I have come up with some really great innovations and ideas.


  6. Pat B says:

    I’ll have to re-work the equation for shorter arms. If I get time over the next couple of days, I’ll get onto it. But I’m not optimistic. Starting from a 90 deg angle, I would expect your shorter-arm design to show better velocity-ratios during the first half, simply because the angle of the string is more open. After that, I don’t know. But it’s worth doing, because Nick will want to consider arm-lengths when building a new pair. We’ll see what the figures tell us.

    As for letting the arm go beyond the 12 o’clock position, I think the maths professor was probably mistaken in thinking that the extra draw-length would be responsible for any improvement. With outswingers, draw length is really neither here nor there. Most of the draw-length in Nick’s machine is unproductive in terms of accelerating the bolt. Outswingers benefit much more from extra draw-length. The advantage with inswingers is up at the front near take-off time. A longer string has more velocity potential when it tautens than a short one. That’s why the English longbow is long. But if you want a longer string, just put your axles further apart.

    As for your “supersonic” machine, what weight of missile did you have in mind?

  7. Pat B says:

    Here are the figures I’ve calculated for the shorter arms, 2/3 the original length, set alongside those for the longer ones that I posted two days ago. I’ve trimmed the figures from my last post to cover just 90 degrees of turn.

    —– ——– ——–
    00 …. 1.00…. 1.00 (Arms facing directly inwards)
    15 …. 0.97…. 1.06
    30 …. 0.93…. 1.10
    45 …. 0.92…. 1.15
    60 …. 1.00…. 1.27
    75 …. 1.33…. 1.68
    90 indet

    Then a breakdown of the last 15 deg, going in 5 deg jumps:

    75 …. 1.33…. 1.68
    80 …. 1.62…. 2.04
    85 …. 2.31…. 2.88
    90 indet

    Then a breakdown of the last 5 degrees, in 1-degree jumps:

    85 …. 2.31 …. 2.88
    86 …. 2.59 …. 3.23
    87 …. 3.02 …. 3.73
    88 …. 3.72 …. 4.59
    89 …. 5.30 …. 6.51
    90 indet

    Finally, I started with 89.0 and just started adding 9s.:

    89.9000 ….. 16.91 ….. 20.71
    89.9900 ….. 53.52 ….. 65.55
    89.9990 …. 169.26 …. 207.30
    89.9999 …. 535.24 …. 655.55
    90 indet

    As I expected, the shorter arms start off with a superior velocity ratio. But, surprisingly they hold it throughout. I actually expected the figures to converge towards the end. So a good result for the shorter arm.

    However, these figures disguise a crucial fact. They are not absolute velocities, but velocity ratios. They just tell us how many times faster the missile is moving than the arm-tip. They don’t tell us how fast the arm-tip is moving, they don’t tell us whether it is accelerating or decelerating, and they don’t tell us whether the tip of the shorter arm is faster or slower than the tip of the longer arm at any point.

    If you have two levers, one twice the length of the other, and they have the same angular velocity – i.e. they execute 90 deg of turn in the same time – the tip of the longer arm will be going twice as fast as the tip of the shorter. In practice, the shorter arm will have a higher angular velocity because it has a higher mechanical advantage against the loading, but if its tip is to travel as fast as the tip of the longer arm, its angular velocity must be twice as big. That is, it must do its quarter-turn in half the time. I doubt very much that it would. It might do so for the first few degrees, while velocities are still relatively low, but as they increase I’d expect the longer arm to start catching up. The best analogy is two cars starting in first and second gears. While speeds are low, the former will have the advantage and will accelerate into the lead. But as speeds rise, the advantage swings the other way. Eventually the second car will catch and overtake the first.

    Of course, in real-life mechanics all kinds of imponderables arise to confound theories – the weights of moving parts, the friction in the system, the inertia in the limbs and levers, and the only way to know is to put it to the test. If Nick is thinking of trying shorter levers, I wouldn’t attempt to dissuade him. But my intuition tells me that the longer arms will win the contest.

  8. Captn Harpoon says:

    Well, I cant argue with math too much but if you check an entry entitled “the little experiment” Nick moved the rope down about three inches and shot. There was a slight or negligible loss in fps two or three fps, but the big diff was that the machine was also pulling an extra half pound or more of extra weight up front on each arm.

    Bet if you were to whack that rather heavy limb tip off by three inches and lose a half to full lb of wood (and steel?), the laws of physics and formulas take over, resulting in an increased speed due to a lot less mass to accelerate.

    I have suggested the string positioning be changed so that it goes over the end of the limb and no wood out front.
    If you do re check the entry, look at the amount of wood and steel in front of the string with the shorter postioning.

    The extra weight on each arm has got to be about the same as the arrow.

    I’d be willing to sacriface two or three fps in order to hurl two three times the normal arrow/projectile weight.
    Over distance (range shooting) the heavier arrow will retain more of its velocity.

    I have a habit of cheating math I believe LOL. That and a boatload of testing. Currently Im testing my zero point energy system where the string is under no tension at all at rest when using the extra rotation past 12 oclock position. I leave just enough tension so that the string does not come off the pulleys at rest and string is all but slack.

    I say the shorter limbs are the way to go for increased performance, the heavier projectile capacity outweighing the speed factor in importance, and will still bet the shorter limbs will be faster by 3-5%. The extra rotation really makes a diff. if you get to use it.

    BTW, I have compounding models, thus the pulley(s). The inswinger design seems to really like a heavier load IMHO. 300 – 330 is plenty fast, but NIck is after speed.

    Like you and the rest of the folks who follow Nicks work, I am looking forward to the testing.

  9. Captn Harpoon says:

    BTW I forgot. Shorter arms do not have a higher mechanical advantage on loading the machine, it has a higher mechanical advantage upon firing the machine.

    This makes a big diff. in the upper end of the power stroke where it does the most good according to the amount of degrees of rotation needed to produce one inch of draw and where the most acceleration takes place.

    The most inescapable fact is that more rotation is equal to more available energy. In any case, the 22% increase in velocity is enough to hit 400fps anyhow, which is Nicks goal(for now).

    I have no idea what a full draw would do, perhaps another 5% increase…

  10. Sarah says:

    Loved the video, Daddy-o.


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