Bow Mechanics 2: The Return of the String

So there you are at full draw, all that stored energy literally at your fingertips (unless you’re using a thumb draw); all that’s left is to let fly. Let’s take a look at the mechanics of what happens when you release the string. As before, I shall simplify some elements of the discussion, removing some complications such as energy lost to internal friction, heat and sound. Some of what I write will therefore not be technically accurate, but the principles are sound.

What happens on releasing the string is that the stored energy drives the limbs forward until they return to brace height, at which point the string snaps taut. String and limbs suddenly stop moving but the arrow keeps going at the same speed. Factors such as the elasticity of the string may complicate this picture slightly but I shall address that in a later post. For now we will assume that at the moment the bow reaches brace height the arrow flies off at the same speed as the string was moving a moment earlier.

Once we understand this point about the way an arrow leaves the string we are in a position to understand that if we want fast arrow speed then we need fast string speed. That follows from fast limb speed. The question is therefore how to get fast limb speed.

    Dry Fire Speed

Every archer dreads the moment some non-archer asks to try pulling their bow. “OK, but don’t let go of the string!”. Lesson 1 of archery: do not dry fire your bow. Why? Put simply, if you dry fire your bow then the energy stored in the limbs has nowhere to go. It stays in the limbs, which are not built to withstand the shock.

There is one thing to know about dry firing, apart from “don’t”: it is the fastest speed at which your limbs will move. A bow drawn and released will shoot at dry fire speed (which varies with draw length for a given bow) unless it is slowed by the mass of the arrow.

    What Determines Dry Fire Speed?

A bow’s dry fire speed is determined by the bow’s construction and the amount of energy stored in it. Energy storage was covered in my last post and I shall not go over it again here.

Bow construction also has a great effect on stored energy but in addition to this it affects the dry fire speed of the limbs for a given amount of stored energy. The main factor I shall examine here is mass. Other factors have an effect but mass is the most important one.

    Limb Mass

Sir Isaac Newton showed that Force = mass x acceleration. It follows that acceleration = force/mass. In other words, for a given amount of stored energy you will get higher dry fire speed from lighter limbs than you will from heavy limbs.

The placement of the mass is also important. The bow limb can be likened to a lever. Mass at the end of the limbs requires more energy to move than mass near the handle. Studies reported in the Traditional Bowyer’s Bible show that adding 1oz to the grip section did not slow the limbs at all, whereas adding 1oz to each limb tip slowed the bow by around 7 feet per second (fps). This is roughly equivalent to shooting an otherwise identical bow that is 7lbs lighter in terms of draw weight.

Many horsebows have siyahs: rigid recurved tips. These increase stored energy (by raising early draw weight and removing stack) but if they are too massive then they will slow limb speed. We will see below that slow limb speed combined with high energy requires a heavy arrow to avoid excessive handshock. This is because of kinetic energy.

    Kinetic Energy

Kinetic energy is the term used for the energy related to movement. Its equation is KE = 1/2mv2. In other words, kinetic energy is equal to the mass of an object multiplied by the square of its velocity (speed), all divided by 2.

When a drawn bow returns to brace height it will have no stored energy. All the energy it had stored has become kinetic energy. As the string slams taut that kinetic energy has to go somewhere. It goes into vibration of the limbs, the string, the archer (handshock) and the air (noise). There is one other place it can go: the arrow.

    The Arrow

As the string travels along the power stroke we should consider the bow and arrow as a single entity whose stored energy is being converted into kinetic energy. At the end of the power stroke there is no stored energy available – it has all become kinetic energy, shared between the bow and arrow.

At the end of the power stroke the arrow leaves the string at the final speed of the string. Since the arrow has a known mass we could calculate its kinetic energy. Without needing to do this, however, we can already see that at a given speed the arrow will have more kinetic energy if it is heavier.

We have now gone from having a total kinetic energy for the bow and arrow to having an arrow with kinetic energy and a bow that has stopped moving and therefore has no kinetic energy. Nor does it have stored energy. Any kinetic energy that has not gone into the arrow becomes vibration.

    Vibration

There will always be some vibration after the arrow flies off. The string and limbs will vibrate. This is not a problem if it is kept to a relatively low level. Nor is the noise of the string twanging, which is just the vibration going into the air.

If too much energy is left in the limbs then they vibrate too much and you feel it as handshock. In extreme cases the bow can be damaged or destroyed. This is why you should not dry-fire you bow: all the stored energy ends up as vibration.

To hunters and warriors the kinetic energy of the arrow is important: it plays a major role in determining the penetration of the arrow into the target. For a sportsman trying to obtain fast arrows the kinetic energy of the arrow is of less importance, save for this basic fact: arrows that are too heavy will slow the string too much and therefore travel too slowly. Arrows that are too light will not absorb enough energy from the bow, leaving too much energy in the limbs, which will vibrate the bow and your arm.

    What Does All This Mean?

There is a balance to be drawn when selecting your bow. Static recurves (those with recurved limb tips that do not straighten as the bow is drawn) store more energy than equivalent straight bows or working recurves (those that straighten as the bow is drawn). If those recurved limb tips are too massive, however, then even the extra stored energy will not be sufficient to move the limbs quickly.

This is especially true at low-medium draw weights. High energy/high mass bows are good for shooting at heavy draw weights and for shooting heavy arrows because they store a lot of energy but they are not so good for producing really high arrow speeds with low draw weights and light arrows. There is a reason why bows like the big Mongol recurves and the English longbow were used at draw weights of 150+lbs. The English war arrows weighed up to 1/4lb!

The ideal compromise is probably a bow that has static or partially static recurves but whose recurves are of low mass. The best examples that I have seen (and I do not pretend to have seen all available bows) are Saluki bows made by Lukas Novotny. They are of low mass but maintain their recurves for high energy storage. The resultant arrow speed is phenomenal.

So there you are: your arrow is on its way. In my next post I shall look at the way arrows fly, examining arrow mass and spine and how to get them right for your bow.

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!

A Break With Tradition?

“Horseback archery is a traditional sport”. That fact is taken for granted by the majority of practitioners. It is recognised by UNESCO as being of cultural importance. We all know that horseback archery was the means by which countless waves of Steppe nomads swept over Asia and Europe, by which the Parthians and Persians fought the Romans and the great Arab conquests were achieved (at least in part). Fewer people worldwide realise that in Japan the tradition of yabusame has been practised continuously for some 800 years. I am grateful to Tanaka-san and to Tim McMillan for opening my eyes to this hidden (to me!) gem of mounted archery.

Recent discussions on Facebook have set me thinking again about the notion of a traditional sport. There are several competing philosophies in the world at the moment. The labels I have attached to them are my own and I make it clear at the outset that I do not believe any to be any better or more important than any other.

    Pure Martial Art

This is exemplified by the hundreds or thousands of practitioners of yabusame in Japan who do not compete abroad, do not compete in the Korean, Hungarian, qabaq, mogu or the other styles that we see in various countries. They simply do their own style, striving for perfection in it and treating the enterprise as an end in itself. I have not mentioned them much in what follows, simply because the pure martial artist is likely to agree, for these purposes, with the next category of person:

    Reenactment

This is the view that the ultimate question is “what did our ancestors do?”. There are few sights as impressive as a rider in full historical outfit galloping at full speed whilst loosing handmade wooden arrows from a horn and sinew bow drawing upwards of 100lbs.

    Competitive Sport

Whilst many people in this camp still enjoy and appreciate the fact that this is a traditional sport, for them the guiding principle is the sport. Fibreglass bows of a draw weight no higher than is necessary to send the arrow into the target; carbon or aluminium arrows for perfect consistency and generally functional clothing are preferred.

Of course these are extremes. Many people do not fall entirely within one category. Most fit somewhere in between but these are the three main views that horseback archery needs to cater for.

There are several areas where a balance needs to be drawn. One of the most obvious is equipment. I am thinking particularly of arrows, quivers and bows.

    Arrows

This can be simply stated: our ancestors did not have aluminium or carbon arrows. The reenactment view would therefore be that we should be using wood, bamboo or reed arrows. The sportsman would say that carbon and aluminium can be made straighter, lighter and more consistent than the traditional materials and so he would want to use them. In practice, most international competitions allow any arrow material, even if the rules technically state otherwise (in Sokcho in 2010 the rules technically stated that arrows must be bamboo. I therefore claim gold and silver on behalf of GB as I’m pretty sure we were the only ones using bamboo…)

    Quivers

At the World Championships in 2010 several Iranian competitors used “arm quivers”. These ingenious inventions consisted of clips attached to the armguard, into which the arrows were inserted. This made for vey fast reloading. Of course, such “quivers” are not historical. The martial artist and the reenactor would disapprove, even if they recognised the genius of the invention. The sportsman would applaud the innovation and adopt it if
they wanted to.

    Bows

This has been the topic of recent discussion on Facebook. Traditional horsebows do not have any form of arrow rest. They certainly do not have a cut out arrow shelf such as is found on more recent bows. The yumi, of course, has its unique length and asymmetry. It has no rest and no shelf. No horsebow, as far as I am aware, had a handle that was shaped to fit the hand in the manner of modern pistol grips. At present these innovations (pistol grips, shelves and rests) are banned under most competition rules. The reenactors would say that this is quite right. More and more sportsmen are saying that we should open our doors to a greater variety of bow designs.

Various arguments are put forward:

“Allowing other types of bow will encourage newcomers to the sport who are archers already, because they will not need to get a new bow”. This may be a good argument as far as it goes but to me it seems that it does not apply at the upper levels of the sport. By the time you are competing in international events you really ought to be able to buy a bow specifically for horseback archery.

“We don’t really know that our ancestors didn’t use these designs”. This seems to me to be a pretty poor argument, especially in relation to cut out shelves. We have lots of evidence from texts, art and archaeology, none of which suggests these design aspects. We know that handles tended to be relatively narrow. This makes it easier for the arrow to flex around the bow and means that a cut out would not be feasible (or as necessary). Admittedly a stuck on rest or a built up grip are possible. I suspect that the latter, at least, was probably used by some mounted archers. Nonetheless the burden seems to me to lie on those who say that such things are or may be historical to prove it.

“Our ancestors would have used them if they had the technology”. I have used this argument myself. I was rightly but delicately put right by a friend who pointed out that they would also have used firearms, which is no reason for us to turn our sport into mounted pistol shooting…

There is one more argument that is put forward. In my opinion it is the strongest but it is also possible the most controversial:

“We have already abandoned tradition”. It can be pointed out that we allow fibreglass bows, dacron or kevlar strings, plastic nocks on aluminium or carbon arrows with machined points, modern horse tack and personal clothing etc. We ride down a track that has been roped off and shoot at targets that are generally much closer than the enemy would have been for our ancestors. Surely, the argument goes, we have abandoned tradition already and allowing new bow designs would not take that abandonment significantly further.

It is difficult to think of a suitable answer to this point. To the pure reenactor the solution is to ban the other innovations. To the pure sportsman the solution may well be to allow all bow styles, albeit maybe creating different classes for different bow styles, as is done in regular archery. The problem only really arises for those like me who are sportsmen with a desire to preserve the tradition to some extent. Since that describes me rather well, let’s look at some of the counter arguments. (I should perhaps add at this stage that I hate the idea of different classes for different bow styles in mounted archery. At the moment men and women compete against each other using all different varieties of bow. Everybody is in the same class with no distinctions. Long may it remain so.)

It’s the look of the thing.
Carbon arrows do not look so very different from wooden arrows. You can’t tell, at a distance, whether a string is made of ancient or modern material. You could easily spot a modern bow though.
This argument does not stand up. You cannot spot, from any distance, whether somebody’s grip is a plain traditional one or a shaped pistol grip. You might be able to spot a cut out shelf but frankly if you can spot a small rest stuck on the side of a bow then you can probably tell whether the arrow is carbon or wood.
In addition, we allow bows to be made of modern materials that look modern. More than one of the Iranian team uses a bow with the word “Persian” printed in large letters down the upper limb and nobody objects to this. It looks good and advertises who they are. Clearly, then, looking ancient is not everything.

A variation on this argument is that whilst materials can vary, the design and form should be kept the same as the historical bows. While stronger than the previous version, this argument still suffers from a lack of consistency. We allow personal dress and horse tack that is not of traditional shape. We allow quivers that hold just the right number of arrows and hold them separate for easy drawing. How many ancient warriors rode to battle with only 6 arrows?
Besides which, unless you rely on the “it’s the look of the thing” approach with all its difficulties then it is difficult to see why the shape of the bow should be protected more than the materials.

They give an unfair advantage.
If everybody is allowed to use these modern designs then there is no unfairness. The advantage only arises if some people stick to using more traditionally shaped designs. That, however, is their decision. Until now I have resisted using carbon arrows out of a desire to remain more traditional. Undoubtedly my arrows were heavier than carbons and less well matched. This put me at a disadvantage but not an unfair one since I was free to go carbon. I know more than one other person, traditionalist at heart, who have abandoned traditional wooden arrows for the sake of carbon’s additional performance. I think we all felt a little sad but ultimately we want to compete.

    What Do I Think?

My opinion on this matter has changed recently and I daresay it will change further. I would love to see everybody using traditional equipment. That is unlikely to happen. That being the case I will modernise to keep up. My arrows are now carbon with plastic nocks and small silicone dots to help align the arrows in my hand. My bow has a fibreglass core and a synthetic string.

I would like to see bows remaining of traditional form, with no shelves or rests. This is largely an emotional response that I admit I cannot justify with strict logic. I have my doubts about the efficacy of rests and shelves on horseback but if somebody wants to try them then I believe they should be allowed. I just hope that nobody does.

And now a word from our sponsors…

Before I launch into my planned exploration of the mechanics of archery I want to say a few words about a great new substance I’ve discovered. It’s called sugru. Now, I don’t normally go into pushing products but this is something that I discovered by chance and that is so potentially useful that I want to get it more widely known about.

Sugru is a kind of silicone putty. You can mould it like putty but when you leave it overnight it sets into a solid silicone rubber. As it sets it will bond to just about anything, including wood, leather, metal and plastic.

An old friend of mine introduced me to sugru by giving me a small 5g pack. I put it on my bow handle and gripped into it, leaving me with a layer on the back of my bow that is shaped to my fingers for a consistent hand location. I plan to add some more to the belly side for a thicker handle, mine being on the thin side. After that I shall be adding small dots or ridges to the nocks of my arrows for ease of alignment (the nocks on my bamboo arrows have these built in but those on my carbon arrows do not).

Archery aside, this stuff has a multitude of uses, for fixing things, reinforcing them, cushioning them (you can put a little bit on each corner of an iPhone and then just throw the phone around), etc. not having horses myself I haven’t applied my mind to horse-related issues but I’m sure they’re there: uses crop up everywhere, at work, at home, in the car…

Now in fairness I will say that the good people at sugru gave me a load of it when I sent them my idea for the bow grip, so I’m not exactly unbiased. On the other hand I had every intention of buying it anyway and have been telling people about it ever since.

Don’t take my word for it. Look at http://www.sugru.com to see this stuff and then just carry on life as normal. Within hours you will start seeing little things that need fixing. Then you can thank me…

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