Jörg Sprave and Tod Cutler got me thinking about the ‘charge assist’ mechanism for the ‘instant Legolas’ concept. After a bit of thought, I became convinced that the concept had a fundamental weakness. Here is my alternative solution.

[If you are not familiar with the background to the Instant Legolas, here is a youtube video to get you up to speed.]

In figure 1 we see the basic semi-schematic layout of the concept. Imagine looking down on the weapon from vertically above (as it would normaly be held by an archer). For the sake of clarity, I have omitted the upper limbs by taking a section through the risers just above the core of the system. This is intended to be a kinematic concept only.

In figure 1 we see the three main functional blocks of this concept:

In figure 2 we see the components of the Traveling Mechanism:

In figure 3 we see the components of the Standing Mechanism:

In figure 4 we see the components of the Nocking Bridge:

The principle stages of operation are as follows:

The thinking that brought me to this solution is as follows:

The solutions explored so far employ two basic conceptual building blocks Division of Labour’ (DoL) and ‘Transfer of Energy’ (ToE).

DoL is a great concept and has demonstrated its benefits over and over again throughout the history of human endeavour. Multiple horses can pull a carriage better than just one, a pole vaulter expends effort over a long run up to concentrate kinetic energy in their body, different specialists perform their own tasks to achieve a group goal, the great distances over which the hands of an archer must travel when operating the windlass of a crossbow, etc…. Indeed, the simple bow and arrow is in itself an excellent example of DoL. The individual fibres in the archer’s muscles do work over time to draw the bow over time to concentrate the effort in the elastic tension of the bow. (As a thought experiment, try and imagine throwing an arrow bare handed as fast as a bow can shoot it. Human muscles are too slow to generate the same levels of force in such a short time.)

ToE on the other hand, should be employed with caution. Again, the bow and arrow system is an excellent example of how it can be used beneficially. The chemical energy stored in the archer’s muscles is transferred to the elastic energy in the drawn bow. However, lurking in the background, waiting to pounce is entropy. Whenever energy is transferred from one system to another entropy always sneaks in and steals a bit of the energy. After the transfer, there is always slightly less energy available to do useful work.

Now, in the case of the Bow and Arrow, the basic system is designed for efficiency. Entropy can only make off with a very small fraction of the transferred energy and so the benefits of DoL far out weigh the costs of the ToE. However, in inefficient systems this might not be true, especially if the DoL benefits are minimal. An illustrative metaphor for this might be the ‘transporting water by filling a bucket from another bucket’ process. Instead of using a pipeline, arrange a long line of buckets. Fill the first bucket with water, then pick it up and pour it into the second bucket.Then, pick up the second bucket and pour it into the third and so on down the line. Every time the water is tipped into the next bucket, a little bit gets lost. Maybe some splashes out or not absolutely every drop leaves the previous bucket. Obviously, if the line of buckets is sufficiently long, eventually there will be no water left to transfer. Even worse, if you used bottles with ever narrower necks instead of wide open buckets, the loss of water would no doubt be even more rapid.

Obviously, this is an intuitively silly way of transferring water over long distances because, why not just simply pick up the first bucket and walk to the destination with it? This is exactly the point. Assuming that neither bucket has a leak, pouring the water from one bucket into the next offers no intrinsic value, they are both equally good at holding the water.

If we now convert the metaphoric water into real energy and the buckets into storage methods, the same principle holds true. Every transfer loses something. This loss is particularly bitter if the new storage method offers no advantage over the old one. In a simple bow and arrow system, the advantage of ToE comes from the differences in storage and power capacity. An archer, especially a very chubby one, can store an enormous amount of energy in their body compared to the maximum elastic energy possible in the bow. The archer’s body is an effective way to store and transport large quantities of energy. However, the archer can only expend that energy relatively slowly. The bow on the other hand has a very high power capacity. It can only store and release a small amount of energy, but it can do it extremely rapidly. Because the final intent is to transfer the energy to a projectile, the faster the energy can be converted the better. A high power capacity in the transfer of energy from the bow to the projectile means that the projectile will have a higher velocity as it exits the weapon.

However, in the case of the ‘assist bow’ demonstrated in the Jörg and Tod videos, there is no intrinsic advantage in transferring the energy from one elastic system to another. This is especially so at the slow speeds at which the transfer occurs. Both bows are low storage high power devices, but the high power capacity of the assist bow is never exploited. It’s a bit like using a Ferrari race car to pull a plow.

This situation is exacerbated by the way that energy is stored in an elastic system. Energy can be considered a combination of force (how hard you must push or pull) and deflection (how far that force has to move. The greater the force and / or the deflection, the greater the energy involved. However, the initial deflection of an elastic system is usually associated with a low force. When you pull on an elastic band, it starts of quite easy, only as it is stretched further and further does it get more difficult to pull. In fact, in an ideal linear elastic system (which an archer’s bow approximates very closely) the energy stored in the second half of the deflection (or draw length of the bow) is 3 times higher than in the first half! Or alternatively, the extra deflection gets ever smaller as more energy is stored.

This means that, in the case of the main and assist bow solution, the rate of deflection of the two bows during the ToE  phase (loading the main bow whilst discharging the assist bow) is continuously changing. In effect instead of the two bows moving at the same speed through this phase: the main bow should start off fast and get gradually slower; the assist bow should start off slow and gradually get faster.

As Tod briefly explains in his video, to achieve this demands some kind of variable gearing or leverage between the two bows. The cam based compound bow pulley system is certainly one way to achieve this and Tod’s own bell crank system is certainly another. However, all such systems tend to open the door just a little bit wider for our old enemy entropy to go about its nefarious deeds. Indeed, Tod’s prototype demonstrates exactly this in action. Even as the drawn weight begins to drop, it becomes necessary for Tod to jerk and tug on the string to deflect the mechanism further. The internal friction is robbing the system of any efficiency. Certainly, better bearings and rollers would improve this, but they won’t eliminate it. Some of the energy stored in the assist system is always going to merrily skip off towards the hills, hand in hand with entropy. I thought up all sorts of clever gearing mechanisms, but none of them impressed me with their intrinsic efficiency.

This chain of thought brought me to the idea that perhaps, the better solution is not to transfer the energy from the assist bow into the main bow, but to transfer it directly to the projectile. Put simply, the most efficient solution would be to draw two main bows in parallel and then discharge them simultaneously into a single projectile. With effectively double the draw weight, the high power capacity of the two bows would efficiently transfer twice as much energy into the projectile. KABBAM!

The shortcoming in this idea is clear. If all the design does is double the draw weight, then it has no advantage over a single bow with twice the stiffness. What is missing here is a method for employing DoL. Instead of drawing both bows together on the main stroke, it would be necessary to draw them one at a time. Drawing first one bow and then the second would certainly divide the labour between two independant draw strokes, but that is not the goal of the Legolas project. The idea is to utilise the currently relatively redundant forward stroke to do useful work by storing some of the archer’s muscular effort in a high power elastic system. In this way, dead strokes are eliminated and the rate of fire maximised.

So, with all this in mind, I set myself the task of designing a system that could charge one main bow on the forward stroke and a second on the draw stroke. Working out how to charge the first bow didn’t actually take long, instead of pulling on the string, I flipped the logic and simply pushed on the bow.  Keeping the nocking point of the string still and moving the bow forward charges it just as effectively as the other way around. The challenge then came in deciding what to do with the energy stored this way.

After a bit of meditation, I realised that the answer was already available within the Legolas project, ‘Encapsulation of Forces’ (EoF). Some of the designs Jörg has developed contain a latch and trigger mechanism. In these embodiments, the string is held by a mechanism so that the archer no longer has to expend any effort to keep the bow at full draw. Conceptually, this is no different to the system used for discharging a medieval crossbow, so it is a legitimate system to use. However, my epiphany came with the thought that I could perhaps employ two such latch and trigger mechanisms in parallel. One to hold the first bow string at full draw and the second to hold the second.

And that was more or less that. After a bit of shuffling of the cards, my final solution (shown at the beginning) uses a front trigger to disengage the front latch so that the first bow can travel forwards for its charging stroke then the second latch engages so that the forces in the first bow are encapsulated. Then during the draw stroke, the second bow alone is charged until the front latch re-engages to encapsulate all the forces. The weapon now has two main bows at full draw length waiting for the rear trigger to release them so they can discharge their stored energy at high power into the projectile.

What hasn’t been addressed in all of this is the design of the projectile itself. Traditionally, long bow arrows had a light weight wooden shaft. This was to minimise weight whilst creating a projectile long enough to bridge the gap between bow riser and nocking point at full draw. The instant Legolas concept makes this unnecessary by employing a guideway. This means that a much shorter projectile can be used. However, as Tod himself mentions, the rate of discharge of a longbow requires a heavier projectile. If the quarrel is too light, the bow limbs will convert too much of their elastic energy into kinetic energy in the limbs themselves. An extreme example of this is when a bow is loosed by accident without an arrow. The sudden deceleration at the end of the discharge generates such extreme forces that the bow often destroys itself.

However, in the twin discharge solution proposed here, even more energy is in flux. To avoid rapid catastrophic failure of the weapon, the projectile must be effectively twice the weight of a normal arrow. Coupled with the shorter length, this implies that the material of the projectile must be much denser. I wouldn’t be at all surprised if this system demanded fully iron quarrels. A secondary effect of this is that the projectile becomes much stiffer. This means that on impact with the target, more energy is transferred and less is lost as bending in the arrow. As a result, the instantaneous forces induced at the point of impact will be much higher. I wonder, would this weapon system finally be able to directly penetrate hardened plate steel armour?

Perhaps, Tod will give this a go, perhaps not. Either way, I had fun thinking this all through and I hope you had fun reading it. Leave a comment below with your thoughts and subscribe to my newsletter to stay up to date about the next crazy idea I have.