In the mock-up below, clay and cardboard make the limb irons visible to judge.  This model  is meant to represent a hardened and tempered, single, unified piece of 4140.  With these dimensions it is still about 3/4 lb lighter than the previous design.

The hook on the end of the high tensile steel strapping is essential to prevent the whole limb being cast bodily out of the machine.    This same force will also serve to wedge the limb deeper into the tapered bottom face of the rectangular socket.   Our actual socket will probably need more taper than is shown here.   Also, it might be a good idea to put some strategically located lightning holes in the socket.

The  lame looking mock-up seen below,  shows the limb tip and a the way I intend to capture the bowstring to stop it flying off the machine whenever it is fired.  The white electrical tape is looped around the bowstring and is meant to represent a stout piece of webbing that will be lashed to the end of the limb.

When the designer is ready, the design will appear.

3 Responses to “Doing the ironing.”

  1. Pat B says:

    Yes, I like that one much better. The limb is attacking edge-on, instead of flat-on. Far better in terms of withstanding big forces. And I like the taper too. That’ll do a lot to trim down the weight, and weight counts for more the further out you are from the bundles. The result will actually be somewhat better than a ratio of the gross weights of the old and new limbs would suggest.

    As for the metalwork, I like it too, with reservations. If you do go past 90 deg during cocking, the limb will be jammed tight into a tapering socket by the pulling action, which is good. But that does leave it vulnerable to movement in the opposite direction. During the early stages of cocking the limb is being pushed towards the cylinder, not pulled away from it. Can you take precautions against that?

  2. Nick says:

    The curved shoulder on the wood just before it enters the socket will lock against the bundle. Also there will be an epoxy soaked dacron whipping binding the heel of the limb to the strapping. Keep in mind that it is the inertia of the limbs moving forward at the end of the power stroke that serves to continually push the limb forward. Granted there may be some forces in the opposite direction, but in terms of migration, everything tends to move forward. At least, that is what our empirical experience suggests so far.

    Good point though. Thanks for the concern. Nick.

  3. Pat B says:

    Okay, now I think about it, the angle between bowstring and limb will not deviate much from 90 deg for most of the first quarter turn of the cocking action, so the forces pushing the limb back into the bundles are not that great. You’re probably safe enough.

    I also like the sharpened edges I see there. More aerodynamic.

    While on the subject of the limb, I’ll try to explain what I meant in a recent email by an object’s effective weight. The actual scientific term is “moment of inertia”. It’s a combination of mass and distance. But for our purposes the term “effective weight” is more expressive.

    Imagine you lay a 10 ft plank over a brick, with equal lengths on either side. You place a 10 lb weight on one end and push down on the other end with your foot. You’ll need 10 lb force to lift it (imagining that the plank itself weighs nothing). Then reposition the plank so you have 2ft length on your side and the weight has 8 ft. The weight now has a “mechanical advantage” of 4:1 against you, so you’ll need to push with 40 lb of force to lift it. In other words, as far as your foot is concerned, the weight appears to be 4 times as big as it actually is. That’s what I mean by “effective weight”.

    Lifting heavy weights slowly using a lever means taking the mechanical advantage on your side – the long end for you, the short end for the weight, as in a jemmy or tyre lever. That way your force will be amplifed according to the ratio of the lengths. If you make it 10:1, you need only 10 lb of force to lift 100 lb.

    But when your objective is to move light weights quickly, a mechanical advantage is not what you want. The more speed rises, the more it becomes a disadvantage. Because what you gain in force amplification you lose in velocity de-amplification. In the previous example, the weight will move only 1/10 as fast as your foot. So, with light weights that have to move at speed, it’s desirable to reverse that situation, and give away as much mechanical advantage as you can afford. Let’s say it’s a 1 lb rock that you want to propel upwards. If you invert the plank lengths, so it’s now 1:10, you’ll need a 10 lb force just to counterbalance the missile, and more than that to accelerate it, but the payback is that the missile will be moving 10 times as fast as your foot. Or, to put it another way, multiplying the missile’s effective weight by 10 is the price you’ve had to pay to multiply its relative velocity by the same factor.

    How much that higher effective weight affects the final result depends on how much force you have available. The velocity ratio remains true, whatever happens – it’s 10:1 – but the absolute velocity depends on how much the amplified weight slows down your foot. Because a heavier weight is harder to accelerate, obviously. And there is a limit. If the ratio is high enough, you might not be able to move it at all.

    Of course, what complicates things is that the plank DOESN’T weigh nothing. In giving away length to the other side, you’re increasing the effective weight of the lever, which has no payback. It’s an unavoidably bad bargain whose only effect is to increase the total loading. So while it’s desirable to increase the effective weight of the missile in return for higher velocity ratios, it’s also desirable to minimise the effective weights of the mechanical parts that are propelling it.

    If we turn now to your limb. Imagine there is no bowstring or missile to complicate things. Just the limb to be accelerated on its own. I’m guessing the dimensions. Let’s say it’s 24″ long. The axis of rotation passes through the centre of the limb between the bundles. One of the bundles is pressing against the limb at a distance of 4″ from the axis. Where is the load? Well, when an object is not focussed on a single point, but is spread over a length, then for purposes of calculation in physics you take the centre of gravity as the point. With your old arms, which were of uniform cross-section all the way along, the c.o.g would be right in the middle, one foot from the axis. If it weighs 9 lb, it’s as if you had a weightless rod of 12″ with a 9 lb weight stuck on the end. With the propelling force 4″ out from the axis and the load 12″ out, the load has a mechanical advantage of 3:1 over the bundle. Or, to put it another way, the effort needed to accelerate it is such that it seems to weigh 27 lbs.

    Since that amplified weight does nothing to our benefit, how can we reduce it? One way is a lighter arm. Maybe a lighter material, like aluminium. Another way is to re-shape the arm so that the c.o.g. is closer to the axis, and therefore “weighs” less. And that is exactly what you’ve achieved with the tapered arm. Now, instead of being half way along the length, the c.o.g. is maybe 2/5 of the way along. Even if its actual weight is the same as the old arm, it’s still “lighter”. But you say its actual weight is a few pounds less? Better still.

    What I’m saying is that the savings with the new arm are bigger than they appear to be. It might take a few disasters to get the taper right. But if the limb breaks, the important thing is to note where it breaks. If it’s near the axis, the taper wasn’t responsible. It would have broken anyway. If it’s near the tip, the taper is the culprit, and it means you need a new arm with a bit less taper.

    There’s more to be said on this. My feeling at the moment is that the system is using too much energy accelerating its own moving parts, and not enough accelerating the missile. You might be able to do something about that.

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