Arrow Spine: Determining Factors

Now that we have established what spine does, you need to know how to change it. The following factors affect the spine of arrows:

    Shaft Stiffness (Spine)

There are far too many possible jokes for me to bother making any.

Fairly obviously, the most important factor in determining how much an arrow bends is how bendy the arrow shaft is. This will be determined by the material and the thickness of the shaft. The bendiness of the shaft is generally referred to as its spine, but it is important to remember that it is not the whole story. I tend to think of the bendiness of the shaft as “arrow spine” or “static spine”, as opposed to “dynamic spine”, to which we are coming.

Arrow spine is measured in pounds of draw weight but I hope that by now you realise that draw weight is not the only factor. If you have not grasped this point, you might like to read my earlier posts on bow mechanics. Arrow shafts are sold by spine weight, usually in bands of about 5lbs. For wooden shafts you will simply see a box labelled “35-40” or similar. Carbon and aluminium shafts have a slightly odd system of coding, unique to the type of shaft, which tells you the wall thickness, diameter and mass per inch, as well as shaft spine. There are tables, known as spine charts or spine tables that will help you to find the right shaft.

For a given shaft spine, however, you can make the arrow more or less stiff by adjusting the following factors. They all affect how much the arrow flexes when subjected to the force of the bow’s shot. This is sometimes called dynamic spine (i.e. spine when moving).

    Length

Longer arrows are more flexible. Take a long stick and waggle it. Then snap off a 6″ section and try to waggle that. See?

In addition, a longer arrow should denote a longer draw length (you should not have a large amount of arrow sticking out in front of the bow at full draw) and longer draw length means more stored energy and, all else being equal, more force on the arrow, resulting in more bend.

Having said that you should not have a lot of arrow sticking forward, there is nothing wrong with a couple of inches. Leaving the arrows a bit long may therefore be used to lower the spine of the arrow.

    Point Mass

Heavier points make at arrows bend more. When the bow first applies force to the back of the arrow it will bend the shaft until enough force travels up to the point to move the point which, being heavier, needs more force to move. The heavier the point, the harder it is to move and so the more the shaft bends before it moves the point. Put another way, take a stick and waggle it, then attach a weight to the end and waggle again. See?

    Brace Height

Lower brace heights increase the length of the power stroke, thereby increasing the amount of energy available for pushing the arrow. This makes it bend more. Take that stick again and waggle it. Now waggle it harder. See? The same applies to string mass: it changes the force applied to the arrow.

    Overall Adjustment

It is possible, by means of changing length and point mass and brace height, to change the dynamic spine of an arrow quite considerably. Don’t.

Changing your point mass or arrow length affects arrow mass as well as spine. Point mass will also affect something called FOC, which is the proportion of arrow mass that is in front of the middle of the shaft’s length. This affects flight characteristics. Changing your brace height will change the energy available to the arrow and can produce handshock, poor arrow flight and so on.

What you should do is brace your bow at the correct height as recommended by the bowyer, then select the correct arrow spine. Get your arrows about 4″ too long. This gives you a decent starting point for bareshaft tuning, which is what we shall cover next time. Point weight, arrow length, brace height and string mass should be thought of as things you have to keep constant in order to maintain consistent spine once you have found it. In selecting and tuning your arrows in the first place, they are for fine adjustments, not major changes.

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Arrow Spine and the Archer’s Paradox

We have come at last to arrow spine and the archer’s paradox. Let us examine the paradox first.

    The Archer’s Paradox

This is a much misunderstood phrase. The “paradox” is that if an archer wants to hit a target then the one thing he should not do is line up the arrow with the target. This was noted in the days before centreshot bows and mechanical releases, which minimise the archer’s paradox. As usual, I shall ignore such matters and assume a regular horsebow.

It is easiest, while I explain the paradox, if you imagine holding a bow vertically with an arrow nocked (or even get your bow out and try it). If you hold your bow so that the string and the handle line up with the target then before you draw the bow back the arrow sticks out to one side. It cannot point at the target because the handle is in the way. When you draw the bow this effect becomes less marked, simply because the nock is moving further from the handle and the point is moving closer to it. The angle is still there, however. If the string is released and returns to brace height then a perfectly rigid arrow would not be propelled directly towards the target.

    Spine

The reason we can hit the target is that arrows are not perfectly rigid. They flex when force is applied. They actually flex quite a lot. If you get the chance, I recommend looking on YouTube for high speed footage of the archer’s paradox. Beiter have some excellent clips.

The fine detail is not terribly important, but basically what happens is that as you release, the string does not go in a straight line to brace height. It rolls off the tip of your fingers/thumb, which has the effect of moving the arrow’s nock end laterally away from the bow (this is easy to visualise if you think about the release). The string is also moving forwards and the effect is to bend the arrow and propel it forwards. The string is now moving on slight angle because it is returning to brace but has been moved to the side on release. This, together with the fact that arrows don’t like being bent, causes the arrow to flex back the other way as it is driven forwards. On release it will continue to flex as it flies, although various factors will help it to straighten out more quickly, notably drag at the nock end caused by the fletchings.

This is where the magic of spine becomes really useful: if we select our arrows to bend exactly the right amount on release then it will bend around the bow’s handle and fly directly at the target.

The next couple of articles will be about spine. The first will deal with the factors that affect spine and the one after it will be on how to test and adjust spine.

One important point before I move on to those topics, however, is that the most important thing is that all your arrows should match. They should be of the same mass and the same spine. That way at least you can shoot one and know where the others will go. If your arrows are of different mass and spine then you cannot know where to aim because you cannot know how each arrow will act. It is better to have all your arrows slightly wrong than some right and some wrong. How close they have to be to each other is a matter of personal tolerance. Personally, I ensure that all of my arrows are within 5gn of each other in mass and within 5lbs of each other in spine.

Next time, we shall look at the various factors that impact on the spine of an arrow.

Arrow Speed and Mass

I am now going to turn my attention to the arrow.  In this post I shall look at some of the the physics of the arrow’s flight.  In my next post I shall look in more detail at how to select your arrows and tune your equipment for the best arrow flight.

The Need For Speed

I spent a lot of time talking about how a bow achieves high arrow speed.  Why is this so desirable?  There are two reasons.  The main reason given in standard archery is flat trajectory.

Once an arrow leaves the bow it is influenced by only two forces: gravity and air resistance, also called drag.  We shall look at drag in a moment but first let’s consider gravity (and here you can be thankful that we are ignoring Einstein, because gravity in Einstein’s theory is really weird).

Galileo’s Arrow

Gravity is, for these purposes, a force that pulls all objects towards the ground.  Since it is a force it should have the effect of accelerating objects in line with Newton’s law F=ma (force = mass x acceleration).  We should therefore expect the acceleration due to gravity to be equal to the force divided by the arrow’s mass.  This is wrong because the strength of gravity on the arrow is proportionate to the mass of the Earth and the mass of the arrow.  For any given object, therefore, the effect of mass in resisting the force is exactly cancelled out by the effect of the same mass in generating the gravitational force in the first place.  This is a long way of saying that acceleration due to gravity is not affected by the mass of the arrow.  This was first demonstrated by Galileo Galilei.  He did it by rolling balls of different masses down inclined slopes.  Alas he did not drop things from the Leaning Tower of Pisa.

As an aside, this point was beautifully demonstrated by Apollo 15 astronaut David Scott in 1971.  He dropped a hammer and a feather on the moon and they hit the surface together.  The only reason this doesn’t happen on Earth is because of air resistance.  I am going to ignore air resistance when discussing gravity.  This will make no practical difference.

An arrow will fall to the ground at a fixed rate.  As well as not being affected by mass, the rate of descent is not affected by horizontal speed.  An arrow shot horizontally that misses the target (probably one of mine) will hit the ground at the same moment as an arrow that is simply dropped (I’ve done that as well).  The longer an arrow takes to reach the target, therefore, the more it will lose height on its way and hence the more you will have to aim high to hit the target.

The way to avoid having to aim high is clearly to get the arrow to the target quickly, and this means shooting it at a high speed.  The higher the arrow speed, the less you will have to aim high.  This, incidentally, is the origin of the phrase “point blank range”, which simply means a range at which you do not have to aim high to allow for gravity.  The faster the arrow/bullet/cannonball is travelling, the further point blank range is.

That is the reason given by regular archers for having high arrow speeds.  Of course, regular archers are a bunch of sissies who stand still while they shoot.  Those of us who are shooting from the back of a running horse have an extra reason for wanting high arrow speeds: you don’t have to aim off as much to allow for the speed of the horse either, for analogous reasons.

Air Resistance Is Such A Drag

Sorry, couldn’t resist.  I shall use the term drag because it is quicker.  It refers to the way that air slows things down.  I mentioned that it is why a feather falls more slowly than a hammer on Earth but not on the moon (where there is no air).  We are here ignoring vertical drag and looking only at the drag that slows the arrow’s forward speed.  I am also going to ignore the effect of the fletchings.  This is because you can put any size fletching on any size and mass arrow, so it is not so important to arrow selection.  All else being equal, use small fletchings to get high arrow speeds.

Drag has some relatively complicated physics associated with it and, since we all know that I hate complicated physics, I shall simplify it.  The first point is that drag is higher on things with a large cross section.  In archery terms, this means that a thick arrow has more drag than a thin arrow.  If all else is equal, go for a thinner rather than a thicker arrow.  Note that “if all else is equal” does not mean that you should compromise on getting the correct arrow mass and spine.  They are more important than the width of the arrow.

The other main factor that will affect the drag force on your arrow is its speed.  The faster something is going, the greater the force of drag.  Think about air as being like water: you can swirl your hand lazily through the water in a bath or pool but if you try a sudden fast hand movement through the water then you will feel the water resistance increase immediately.  Air is the same.

Now, drag is a force and like all forces it obeys F=ma.  A given amount of drag will have a greater effect on a lighter than a heavier (more massive) arrow.

Speed, Mass and Deceleration

The last two paragraphs show that a heavier, slower arrow will maintain its speed through the air more than a lighter, faster arrow will.  This is a major concern for hunters, because it affects the kinetic energy at impact, which will affect penetration.  For the same reason, the different deceleration rates would have concerned our warrior forebears.  We are not concerned with kinetic energy: we only need enough to penetrate a foam target.  We want the arrow to reach the target as quickly as possible and stick in.  This means that speed is everything.

If the deceleration rates vary, however, then isn’t there a risk that the light arrow, despite starting out quicker than the heavy one, will still end up reaching the target later because of the difference in drag?  Should we consider sacrificing speed for mass?

The short answer is no.  In the kind of situations we will encounter, studies suggest that the heavier arrow will not catch up with the lighter one, provided that each has been shot from the same bow, to which each arrow is properly matched.

If you have a bow with much greater energy storage then maybe your heavier arrow will catch my lighter one from my faster bow that stores less energy but for a given bow the increase in arrow mass will be matched by a decrease in arrow speed that outweighs in terms of time taken to hit the target.

Maximum Dry Fire Mass

I touched on this is an earlier post.  As you decrease arrow mass you will reach a point where arrow speeds do not increase any further.  This is the maximum dry fire mass.  Flight archers, in their quest for maximum distance, will often have arrows at this mass.  There is no point in going lighter because you will not increase your speed but you will increase the effect of drag.  Outside of flight shooting you will want to be heavier than maximum dry fire mass anyway, to save yourself and your bow from excess vibration energy.

How Heavy Should My Arrows Be?

This is the all-important question and like all such questions there is no easy answer.  It will depend on your bow, your string, draw length, fletchings and a host of other things.  There is, however, a generalised rule of thumb.  Archers sometimes measure arrow mass in terms of grains per pound of draw weight (gpp).  As we know, draw weight is not the whole story but it is a decent approximation of energy storage and speed.

Hunters will often use arrows of 12-15gpp.  They like to have heavy arrows for greater punch at the target.  Flight shooters may well be using arrows around 5gpp or lighter.  Either extreme is probably not a good idea for a competitive mounted archer.

Ideally you should consult your bowyer and experiment with various weights within the bowyer’s suggested range.  As a general rule, however, you should probably be aiming at somewhere around 7-10gpp.  That should give you a nice speed without damaging the bow or your arm.

ALWAYS CONSULT YOUR BOWYERIF YOU BREAK YOUR BOW THROUGH USING ARROWS THAT ARE TOO LIGHT FOR IT THEN THAT IS YOUR PROBLEM, NOT MINE!

And on that cheery, note, I shall leave you and start on my next article: arrow spine.  As always, please do comment – it makes me feel loved!

What Else Can Einstein Tell Us About Horseback Archery?

Ce article est a propos de le theorie de la relativite.  Ce n’a pas de utilite pratique, mais si tu le comprends en Anglais, Fred, je serais tres impressionne!

This article is about arrow speed really.  It’s just not going to help you to improve yours.  I promise I’ll get there!  Speaking of getting places…

Where Are You Going?

As I type this I am sitting on a chair in my kitchen.  I may think of myself as not moving.  This would be quite spectacularly wrong: the Earth is rotating at about 1000mph.  It is also orbiting the sun at about 66,000mph.  The solar system orbits the centre of the galaxy at nearly 500,000mph.  Our galaxy is approaching the constellation Hydra at a speed of about 1.3 million mph.  If there is one thing I am definitely doing, it is moving.  (Since I am in the UK, I am also on a tectonic plate that is moving away from North America at about 1” per year.  I shall not make any political quips whatsoever.)

The point of all this, apart from being generally awesome facts, is that everything and everybody is moving.  This is the basis of the theory of relativity: since everybody is moving you can treat any given thing as being stationary and everything else as moving relative to it.

When I flew to the USA this summer I basically sat in my seat for a several hours while America got closer.  From my point of view the Earth moved beneath my seat.  An observer on the ground would say I flew 5,000 miles.  An observer on the sun, however, might say that owing to the rotation of the Earth, I stayed pretty much still while America travelled to me and the Earth moved in space as well, which neither I nor the ground-based observer would see.  We see the sun moving through the sky, but in a different way from the way that an observer in the middle of the galaxy would see it, and so on.

All motion is relative and we are all free to consider ourselves as standing still while everything else moves around us (except for things that do not move relative to us, such as me and the aeroplane).  This is sensible in and of itself but it gets weird fairly soon…

Relativity and Mogu

Imagine a mogu match.  For those who don’t know, this involves one person towing a cloth-covered wicker ball while one or more others chase him and try to shoot the ball with blunt arrows dipped in ink.  It’s brilliant fun and quite spectacularly dangerous.

Your friend is towing the ball and you are 10m behind it, both of you riding at 10m/s. You shoot an arrow at 50m/s directly in front of you (at the mogu ball, but let’s ignore up and down).  You observe the arrow’s flight from your horse and I observe it from my seat in the stands.

From my point of view you are moving at 10m/s and your arrow at 60m/s (50m/s from the bow and 10m/s from the speed of the horse.  From your point of view, you and the ball can be thought of as both standing still while the world moves.  You therefore see the arrow as travelling 10m.  It takes 1/5s (10m @ 50m/s).  I, on the other hand, see the arrow travel the 10m between you but as far as I can see it has also travelled another 2m because you and the ball are moving as well.  I therefore observe the arrow travel 12m at 60m/s.  Like you, I see it taking 1/5s.

Arrows of Light

Now imagine that you shoot an arrow made of light, which necessarily travels at c: the speed of light.  This is roughly 300,000,000 m/s.  One of the weirdest things about physics is this: everyone observes the same speed for light, regardless of your motion relative to the source of the light.  We will both observe the light arrow travelling at speed c.

Now rerun the mogu game.  You still see the arrow travel the 10m between you and the ball.  I still see it travel slightly further because the whole scene is moving past me.  This is disturbing because we both see the same speed of the light arrow but I see it travel further than you do.

Speed = distance / time.  Therefore time = distance / speed.  Since we both see the same speed but since I see it travel further than you do, I must see it take more time to hit the ball (you hit!  Well done!).  The speed of light is constant; time is not.

The faster you and the ball are travelling, the further the light arrow will seem to travel from my viewpoint, and therefore the slower I see time running for you and the ball.  This is called time dilation: the faster you move, the slower time passes for you as seen by somebody else.   This is very odd indeed but it is a real effect that can be measured in the real world.  It is not to do with light, it is just easiest to explain using light.  It affects all objects at all speeds.  But at everyday speeds it is a really small effect.

What’s Your Draw Length?

Let’s leave mogu for a nice simple Korean or Hungarian track.  We will agree on the moment that you pass the start and finish lines.  We will also agree on our relative movement, although we may disagree as to who is moving.  We will disagree on the time you take to travel the distance (or the distance takes to travel past you), because of time dilation.  If we agree about the speed but disagree about the time then we must disagree about the distance (speed = distance / time, so distance = speed x time).  This is the phenomenon of length contraction.  Things in motion relative to you get shorter from your point of view.  Since you consider yourself to be sitting still and the track to be moving, the track gets fractionally shorter for you.  This is why you can travel it in 10s of your time but still take slightly longer form my point of view: from my standpoint the track has not contracted so you have travelled further.

Conversely, as I sit in the stands (why do we sit in stands?  Shouldn’t they be called sits?) the track is stationary for me but you are moving.  You become slightly shorter in the direction of your travel.  The same is true of anything else that is moving relative to me.  This includes your arrows (real arrows now, not arrows of light).  When somebody asks you how long your arrows are, the correct answer is to ask them whether they mean before or after you release it, since an arrow shot at 180fps will be shorter by about 0.000000000000015m, which is about the length of a proton.  And no matter how consistent you think your draw length is, it is shorter when you are riding than when you are standing still.  Just not by much.

The Judge’s Decision is Final

The net result of all this is that if you measure yourself completing a 90m track in 9s then sufficiently accurate timing gates would record your time as 9.0000000000000005s.  The difference, 5 femtoseconds, is about one hundred-million-millionth of the time it takes you to blink.  In other words, it is an inconceivably small difference.  But it is really there.

All competitors are reminded that scores are awarded on the basis of the time shown by the timing gates and that we only go to two decimal places…

Bow Mechanics 3: String Theory

Yes, I know I said that the next post would be about arrows but you shouldn’t believe everything you read online.  I want to deal briefly with strings before moving on to arrows.

First and most importantly, you must check with your bowyer before you change your string.  Use of an unsuitable string can break your bow beyond repair.  Be warned!

There are many different kinds of string.  In particular, there are various string materials and two main ways of turning the threads into a bow string.  I am not going to go into much depth but I want to discuss two main features of strings that can affect performance: stretch and mass.

String Stretch

You might think that a nice elastic (stretchy) string would give some extra pace to the arrow.  You’d be wrong.  If you use an elastic string then at the end of the power stroke it doesn’t stop dead, leaving the arrow to fly off.  Instead, the string slows down as it stretches.  By the time the arrow flies off it has lost some of its speed.

Studies in fact show that the various modern materials are unlikely to differ enough in their stretch to make a significant difference to arrow speed.  Materials such as B50, Dacron, FastFlight etc have different elasticity but they are close enough that the difference in arrow speed from stretch will be no more than 1 or 2 feet per second (fps).  This is about the same as increasing your draw weight by 1 or 2 pounds.

The way the string is put together will also affect stretch.  There are two basic methods of making a string: Flemish splice (also known as laid in) and endless loop.  You don’t need to know the technical differences but it is worth knowing which you have.  As a general rule, Flemish splice strings have slightly more stretch to them.  Endless loops have higher performance: they don’t stretch as much and they can be made identical more easily than Flemish strings (allowing you to maintain performance the same with spare strings).  The Flemish splice string will also “creep” more.  This means that once the bow is braced the string will stretch so that it becomes slightly longer.  This, of course, lowers your brace height over time, making consistency harder to achieve.

So why would anyone choose a more elastic string than necessary?  Because they are more forgiving on the bow.  At the moment that the string snaps taut there is an awful lot of force going through the tips of the limbs where the string attaches.  If there is no ‘give’ in the string then weaker tips will break at this point.  This is the main reason why you should check with your bowyer before using a new type of string.  In particular, bows made from traditional materials such as horn, wood and sinew may well not be able to cope with modern low-stretch strings.

String Mass

String mass generally has a greater impact on performance than stretch.  A high-performance string material such as FastFlight or Dyneema weighs much less than something like Dacron (which is what most “off-the-shelf” strings are made of).  To take an example, I have in front of me two strings.  One is a Dacron string that weighs (including the serving) 151gn.  The other is FastFlight and weighs 63gn.

So what?  Well, the string, like the arrow, is a mass that needs to be driven forwards by the bow’s stored energy.  The heavier the string, the slower the arrow will be.  According the Traditional Bowyer’s Bible, Vol.1 (which admittedly deals primarily with straight limbed wooden bows), a 20gn increase in string mass will slow the arrow by roughly 1fps for a bow of around 50lbs draw weight.  The effect is greater on lighter bows (because a greater percentage of the stored energy is needed to move the string).

This assumes that the added string mass is evenly spread.  Mass added to the centre of the string has about 3 times the effect (as does mass added to the arrow, but we’ll come to that in a later post).  Those little brass nocking points clamped to your string weigh 5gn each.  If you have two of them on your string and are shooting a relatively light bow then you could be losing about 2fps just from them.

All this may not seem very much but there are good reasons to get it right.  One is that the string is the cheapest way to gain arrow speed.  Bows and arrows are expensive but a decent string is not.  If you can reduce your string mass by 100gn (which you could easily do if your current string is one of the big heavy horrors that you sometimes find) and replace your brass nocking points with a dental floss wrap or similar then you can make considerable gains in arrow speed.  Further gains can be made with your arrows, to which I shall turn next.

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!