Bow Mechanics – Energy Storage

It is commonly said that the most important part of horseback archery is the partnership between rider and horse. Many thousands of words have been written and typed on this point, covering the technical and spiritual sides of becoming one with the horse. I do not pretend to be a good enough horseback archer or a good enough horseman to assess whether this is true. Far better men and women than I have asserted it and I will not argue.

Without arguing against horsemanship, I want to put in a word for archery, and in particular for archery equipment. Many people could, I believe, improve their performance greatly by understanding how their equipment works and treating it properly. The bow may not be as important as the horse and it certainly doesn’t take as long to master as riding does, but it is important nonetheless, and its simplicity should make it something that everybody understands rather than something that is overlooked.

I am therefore going to write a series of posts about the mechanics of bows and arrows. I shall start with bows and how they work. After going through this I shall move on to consider arrows. I happen to believe that arrows are more important than bows but it is impossible to understand arrows until you understand bows, so I shall start there. A word of warning: this post is fairly long and fairly technical. It contains some simple pieces of advice for improving bow performance, especially at the end. It is otherwise largely of academic interest, although personally I find it fascinating to understand how such a simple tool as a stick with some string on it can propel another stick with such speed and accuracy. If you don’t care about that then this might not be the post for you.

Bows

A bow is essentially a spring: a device that stores energy as it is deformed and then converts it into kinetic energy as it springs back, propelling the arrow as it does so.

The following discussions will deal mainly with attaining high arrow speeds with a smooth release, without damaging the bow. There are, of course, many other factors that may determine which bow and arrows you use and how you set them up. These include how sturdy they are, how forgiving and, frankly, just pure personal preference of how they feel. I am not addressing those features here. These posts are just about how they work, with particular reference to the storage and release of energy.

I have made some simplifications. In my last post I dealt with relativity and fine physical details. That was a bit of fun but has no real impact on how the bow works. In this post I shall simply deal with those factors that have a real effect on the bow. This means that I am missing out some physical effects that have a minor effect on the workings of the bow. I am just going to deal with the major points.

Storing Energy

Drawing a bow transfers energy into the bending limbs of the bow in the same way as stretching a spring or elastic band. Broadly speaking, the more energy it takes to draw the bow, the more energy is stored. Not all of the energy is in fact stored but for these purposes we will assume that it is. The total stored energy is therefore the total energy required to draw the bow back to full draw. This is not the same thing as the final draw weight.

Three States of the Bow

We shall consider three states of a bow: unbraced, braced and full draw. When unbraced (i.e. there is no string on it and no force is being applied to it) we shall assume that it has 0 stored energy.

It then takes a certain amount of energy to brace (string) the bow. Once the bow has been strung it will have a certain amount of stored energy. This will be the amount of energy required to pull the bow from rest to brace height. This energy is not available to the arrow because a shot bow returns to brace height, so the energy required to go from unbraced to braced is not released when you shoot. This energy is therefore lost for the purpose of shooting. For anybody who doesn’t know, the distance from the string to the belly of the bow at brace is called the brace height. A high brace height means that the string is a long way from the belly of the bow. A low brace height means that the string is close to the belly of the bow.

The final state of the bow is full draw. This is the furthest you pull it back and generally represents the point of maximum draw weight. The energy available to propel the arrow is the energy it takes to pull from brace to full draw.

It is worth noting here that a bow does not know when it is braced and when it is being drawn. Brace is simply a position along the draw when the bow is held by the string. Imagine bracing a bow at 9”. A person with a 28” draw length will now pull the string back 19” from brace to full draw. If the same person draws the same bow but it has been braced at 6” then they will pull back 22” to full draw, passing through the former brace height. This is an important point to remember later. A bow will have an optimum brace height. Changing your brace height will affect the energy storage and arrow speed as well as the feel of the bow.

For ease of calculation, I will in these posts generally use a bow that is braced at 8” and drawn to 28”. This is a fairly high brace height but it allows me to work with a drawing distance from brace to full draw of 20”, which is useful for calculations and examples.

Changing Draw Weight and Length

For a proper understanding of bow mechanics it is important to recognise the fact that there is no such thing as “a 40lb bow”. It is simply shorthand for “a bow that draws 40lb at a certain draw length”. (In the West this draw length will generally be 28”.)

This fact is important because the draw weight of a bow changes as you draw it. At 1” of draw (from brace) it might have a draw weight of only 2lb or so but at 28” the same bow might have a draw weight of 40lb. This affects the amount of energy required to draw it and therefore the amount of energy stored and available for propelling the arrow. Contrast this with lifting a 40lb weight from the floor. When you have lifted it 1” it weighs 40lb. When you have lifted it 28” it still weighs 40lb.

Now comes a crucial step: which requires more energy, lifting the 40lb weight 20” or drawing the bow 20” to a 40lb full draw weight? Obviously lifting the weight requires more energy, because you are applying 40lb of force for the whole distance rather than applying an increasing amount of force up to a maximum of 40lb. This demonstrates a vital fact: draw weight at full draw is not everything.

Imagine if the bow had a full draw weight of 45lb. You would still expend more energy lifting the 40lb weight 20”. The early weight requires more energy than the extra bit at the end. The same is true of two bows: a 45lb bow may or may not store more energy than a 40lb bow. It all depends on something called the force/draw curve, shortened to f/d curve.

F/d Curves

Take your bow and brace it. Then draw it 2” using a bowscale and measure the draw weight at that draw. Return the bow gently to brace and make a note of the draw weight at 2”. Repeat for 4”, 6” etc, right the way up to full draw (28” for these purposes).

Now draw a line graph. The x axis plots draw length and the y axis plots draw weight. Mark your points on the graph and draw a line or curve connecting the points.

I have drawn below the f/d curves of two hypothetical bows. The blue bow draws 1lb at 2”. The draw weight increases by 2lb per 2” of draw from there to 12” (draw weight 11lb), at which point the draw weight begins to increase more rapidly, going up by 4lb, then 6, 8 and finally 11lb for the last 2”. This gives a steep curve for the last few inches. That steep curve is something you can feel as you draw the bow. It suddenly gets much harder to pull the bow back. This is known as stacking.

The second bow draws 3lb at 2” and increases in draw weight by 3lb per 2” until 12” (draw weight 18lb). From there to 18” it increases by 4lb per 2” and the final 2” of draw increase draw weight by 5lb. The line is almost straight and this would feel like a very smooth draw with no significant stacking.

Notice that the stacking bow has a draw weight at full draw of 40lb, whereas the non-stacking bow only draws 35lb at the same draw length. If you looked at these bows you would see one marked “35lb” and one marked “40lb”. As we have seen, the 40lb would stack horribly and would therefore be unpleasant to draw.

The remarkable thing is that the 35lb bow also stores more energy. Stored energy can be calculated by calculating the area under the f/d curve. This requires some slightly tricky mathematics called calculus, since the line is unlikely to be perfectly straight. We do not need to do the calculations, however, to see that the area under the red line is greater than the area under the blue line: the blue line only overtakes the red one at the very last moment and this is not enough to outweigh the fact that red has been higher for the previous 18” or so. (Note that in this graph we are looking at draw length from brace rather than total draw.)

Now think back to our thought experiment about drawing a bow and lifting a weight. The f/d curve of lifting a 40lb weight would simply be a straight line at 40lb.

As a basic rule, for two bows of the same or nearly the same weight and with the same draw length and brace height you will store more energy with high early draw weight than with low early draw weight.

It is, of course, true to say that for two bows of the same design you will store more energy with a high draw weight, just as you will also store more energy with a longer draw length, all other factors being equal.

The obvious question is how do you spot (or design?) a bow with high early draw weight and therefore high energy storage? I am not going to answer in depth, since this would require most of a book in itself. I recommend the Traditional Bowyer’s Bible volumes 1 and 4 for those who want to know more. Suffice it to say for now that it is largely a function of the shape of the bow in each of its three positions and the thicknesses and widths of the limbs at various points. As a rule of thumb, higher energy storage comes with increased recurve and more with static than working recurve. Ultimately the best advice I can give is to try any bow out before you buy it.

Draw Length

All else being equal, a longer draw will store more energy than a shorter one. The reason for this is simple: you are applying force for longer. Going back to the weight analogy, it is harder to lift a 40lb weight 24” than to lift it 20”. A longer draw can be achieved either by pulling the bow back further or by using a lower brae height – if you pull to 28” from a 6” brace then the effective draw length is 2” longer than it would be from a brace height of 8”.

Brace Height

Before I go, I have one more thing to mention. If I had to name one thing that would help the most people improve their bow’s performance with the least effort it would be brace height.

In the first place let me explain, in case anybody does not know, how you change your brace height. Put simply, you twist your bowstring. If you put more twists into it you will shorten it. This means that the bow has to be bent further to brace with that string, which raises the brace height. If you remove some twists then you lengthen the string and therefore lower the brace height.

We have just said that brace height makes a difference to energy storage. We will see in a future post that it also makes a big difference to the conversion of that energy into arrow speed. I therefore have a plea: keep your brace height consistent. Wherever I go among horseback archers I see people unstring their bows and just leave the string lying next to the bow, or put it a bag etc. The chances of keeping the same number of twists in it if you do this are very small, which means that the next time you string your bow you will have a different brace height. Your bow will store a different amount of energy and will impart a different speed to the arrow, which will therefore not hit the same place.

Prevention is simple. Keep the same number of twists in the string. Either ensure that both ends of the string are looped over the bow or, if it is going to go in a bag or otherwise away from the bow, thread the bottom string loop through the top loop and then the top one through the bottom. Pull tight and the string cannot untwist. This takes about 3s and can save you all kinds of problems.

So much for energy storage. My next post will be on the second part of the arrow speed equation – transferring the stored energy into arrow speed. This is not so technical as the storage of energy. It consists of a number of fairly simple concepts, many of which can be used to improve the performance of a given bow, making the next post of more use to somebody who owns a bow and wants to make it shoot faster.

As always, comments are welcome. Happy shooting!

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7 thoughts on “Bow Mechanics – Energy Storage

  1. Currently teaching myself horseback archery, so glad this blog was pointed out to me!! It’s fascinating, look forward to every post I read!! Thank you! 🙂

  2. Why do you recommend returning the bowstring to brace height between readings when measuring a force draw curve? Would a single prolonged draw taking measurements every inch for 20 inches yield appreciably different results from drawing 20 times incrementally increased by one inch?

    • The short answer is “maybe”. It depends on the bow. A wooden bow, for example, will lose power if drawn for a prolonged period (tests show that even holding at full draw for 3s or so will result in a slower arrow than if you just pull and release). This effect will be less marked in more modern materials. I confess I don’t know how much effect it will have in the case of a horn and sinew composite but best practice is to pull the bow to a given length, measure the draw weight and then relax the bow before repeating.

      • Right. Good to know. I have heard that about selfbows. I know that new horn bows “creak” which is probably microfibers of the sinew snapping crosslinks and shifting or sliding a bit during the draw. But I think that’s just a settling that would happen anyway during use. I have a couple of new Saluki hybrids I’m aching to get f/d curve values for. I’ll try both methods. Thanks.

      • I may be wrong, but I believe that the creak of the new hornbow is usually the cracking of tiny air pockets in the glue layers. I’m very jealous: a hornbow is on my “want” list! I would check with Lukas (maker of Saluki bows) about how long they stay drawn. My experience is of wooden bows and modern materials rather than horn/wood/sinew.

        Let me know the results!

  3. Air pockets, eh? Well that sounds plausible. Has anyone actually tested for that and shown it to be the case? It is interesting that the unstrung C shape becomes a boat shape after extensive use. That would suggest a lengthening of the backing as in a slippage of fibers but I guess air pocket collapse could do the same.
    I don’t own a hornbow but heard a new one making the creaking sound. My Salukis are hybrid bows. Novotny uses some sort of fiberglass backing and belly over a double bamboo laminate core. Various hardhoods are used for the riser and siyahs. Mine are Osage Orange and Maple respectively. They are in between the cost of his fiberglass bows and his hornbows. You can see some photos of mine (Turkish and Crimean Tatar) by googling ‘tonygt19″ and “traditional archery”. There are some other horsebows there as well..

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