More than anything else i think the paper goes to show that in the case of two machines having equal power upon release but varying drawlengths, the one with the longer draw or acceleration pathway, will always have the greater velocity unless the basic laws of physics have changed. This can be proved with two latex rubber bands of varying thickness who acceleration pathways are indentical.
In this instance, all the movement in lineor and parralel. There is no horizontal or secondary direction to provide acceleration. Thus, no deviance. The final outcome would be the same. A Thinner latex tube (slingshot) with a final pull of say 20lbs will have to have a longer stretch or elongation to reach that draw weight than a thicker heavier matertial. The thicker one will have less draw length, than the thinner one at the same draw weight.
Accelerating the same mass with the smaller tubing over a greater distance would have a greater velocity than the short thicker one with less of a draw. On youtube, there is a slingshot builder JoergS who has a slingshot channel. A video of his "hi-tech" slingshot with pulleys goes to show this quite well I think. He uses the pulleys to change the distance of the pull, but overall draw weight remains the same. The result is an approximate 20% increase in velocity. I will see if I can pull it up and post the link. Hang on...
Here it is.
http://www.youtube.com/watch?v=DO_Meq0Hiac - from the comment section regarding pull weight, draw length and velcity as measured by his chrony: "The Chrony shows a speed increase by about 15-20% at the same draw? weight. I can get about 90 m/s max speed, with smaller bullets. It is still too cold for record shots, under 10 degrees centigrade. Rubber needs warm temperatures for best performance."
So you see, in my mind the experiments are somewhat inconclusive.
With the sliingshot there is only one directional acceration force acting, which I call a vertical or paralell movement. Ballistas, and most bows have two components to the acceleration factor. The is the forward movement of the limbs (vertical), and a sideways movement (horizontal).
Each of these movements contribute to the end velocity.
A perfectly balanced ballasta system will have a true 50/50 horizontal vertical make up. Increase one component over the other and the net velcity changes. More horizontal movement will result in faster velocities. More vertical than horizontal will produce less than optimal results.
Paralell limb tech has made its way into sports and hunting equipment over the past few years, resulting in an ever increasing average velocity as the tech. catches up. It really matters very little whether the limbs actually face forward or backward, as long as it is paralel limb tech, as there is a limit to much draw one can actually use with the current accepted designs.
JoergS and I got into a pretty debate on a forum, where I had claimed higher velocities than what he could achieve with a regular slingshot design in my compounding slingshots thread on slingshot forum. So Joerg set out to make his own compounding slingshot forays. You guys are not the only ones I constantly challenge. Im not prejudised. I manage to piss off or insult everyone LOL.
Of course, you know my torsion assisted compounding slingshot (inswinger of course) would be much faster than JoergS machine on the video.
While Kooi and Marsden might argued an elasticated string would only detract from attainable velocities, I would challenge that as well. You must remember how I got started with inswingers. I took a simple slingshot as a starting point, analylized where energy was wasted and creating the most effecient design in utilizing the available energy was the singular goal.
I ended up with a slingshot with the same inswinging limb arrangement as the Hatra, a stage one and most basic inswinger design.
Over the next 10-12 years it began to morph into something else on its own.Simply by addressing ineffeciencies of the current design, and continually improving.
The entire rotation cycle of the inswinger can be likened to a car or truck transmission with the rotation being degrees of rotation (engine rpm), but instead of the gears changing throughout the acceleration process, the amount (ratio) of string draw measured in inches or centimetres per degree of arm rotation constantly changes. Actually with the Hatra design, it is the number of degrees the arm moves to produce an inch of draw. It constantly changes through out the draw, and upon release. In the rest postion at 12 oclock, there is virtually no vertical component left. (
Only horizontal. Any further movement past that 12 oclock position is actually a negative vertical movment,meaning the arms have now reversed their direction having passed the apogee. This may in fact add another acceleration factor (parametric resonance?) into the equation, but I am not sure. At worst, it cancels out some of the effect of the additional horizontal movement by an equal percentage of the negative vertical movement in relation to the continuing horizontal movement.)
(In any case the lever changes direction which simple science tells us causes an object to undergo further acceleration. You experience with your bicycle every day. This is just another juicy tidbit adding another small percentage of velocity gain, and right at the end of the stroke as well helping to create a flatter accel. curve. The extra 15 degrees is important. 20-25 works well, on up to about 35 max. From there on out too much neg vertical movement to offset horizontal gains. Huge untapped potential there, but I do not expect nor want Nick to completely rebuild everthing! He just finished the new Kam LOL Were he to add another 30 degrees instead of just 15, you would be tapping that chrony yet once again.)
It is the same with an outswinger, the amount of degrees to produce one inch of draw is radically different. So which is the most effecient?
In the basic Hatra config. the horizontal component is exactly twice that of the vertical. It is definitely not so with the outswinger. When you add pulleys and increase the amount of draw length in the Hatra, the effect is doubled according to the mechanical advantage you assign to it.
When you increase the amount of horizontal movement by adding an additional 15-20 degrees of movement to the Orsova design, you end up with a discrepency in performance between the two. Clearly the Hatra with only 105 total degrees of movement is at a disadvantage in range and velocity not only as the Orsova now has a greater usable rotational range. Using only 105 degrees of rotation in the new Orsova limb position (design) does not take the limbs past the point where they begin to move away from each other, as would the Hatra at 105. Because of this, the horizontal and vertical (dynamics) have also changed - the string has more movement per degree of rotation of the arms. It has been assigned more velocity potential.
From here, it is merely a matter of using the correct mass as a projectile to extract max. performance from the design. So in the end, using the older design palitone with less rotation than the offset springs offering up to 65 degrees, doesnt really matter in my way of thinking. The testing itself is flawed. The calculations may be correctly done, but it still does not conclusively prove the Hatra's superiourity as a design improvment.
I may be wrong because the math is all Greek to me (pun intended LOL), it may have calculations dealing with the differences and rate of change throughout the entire loading and release cycle - I just dont know. Only the methodology seemed to be not right, and the change in dynamics may not have been taken into account at all because of the complexity they would add to the calculations.
yikes, I think I even confuse myself with all that gobblety gook. So despite whatever our good college and friend in arms Mr. Hart says, here is what Nicks Firefly has to say about the entire affair:
The final sixth shot of the day, seen on the far right, is noticeably more deformed than the first five. This is because its velocity was boosted up to 270 fps by another major change that was introduced into the limb set up. I removed the bronze hardstops from the curved stanchion, and that allowed the limbs to rotate an extra 15 degrees past the usual 90 degree position they have always had relative to the string. This allowed for a longer string and a longer draw before a 4800lb draw weight was achieved. That represents a 50 fps increase basically for free. One may wonder why this 270 fps is remarkable, given that 285 fps was achieved the other day with the limbs in their normal 90 degree at rest position. Probably the pretensioning in the bundles was much higher the other day and that pretty well overwhelms any efficiencies that might be apparent from other factors. (Stupid me didn’t record the draw weight from then because the dynanometer was not zeroed properly , so now there’s no way to know for sure) Today’s testing was done with a deliberate attempt to keep the pretensioning of the bundles consistent throughout the experiment. Not maxed out, just consistent. That being the case, it really does seem that having the limbs rotate past 90 degrees boosts the velocity quite a bit."
Anyways, if you think JoergS slingshot rocks, add some inswinging levers to it properly proportioned. The same pull that loads the latex powerband on the Sprave slingshot, also loads an additional amount of energy which is then stored in the spring, effectively doubling it upon release. When you add in the horizontal movement (additional accel. component) AND the amount of extra stored energy in the spring to the total stored in the latex powerband, no way can JoergS design begin to come close. The laws of physics dont change on my say so.
Thats my story and Im stickin to it. At least for now LOL.