Einstein’s Horsebow

Every archer knows that a bow’s draw weight increases as you pull it back (I am ignoring compound bows, with their pulleys and cams. I advise everybody else to ignore them as well). Perhaps my favourite fact of all time is that as you pull the string back you also increase the physical mass of the bow.

As every schoolboy once knew (I feel really old…), Albert Einstein proved in 1905 that the energy of an object at rest is equal to its mass multiplied by the speed of light squared. In mathematical notation, this is written as E=mc2, the most famous equation in history, known even to people who have no idea what it means. Since the speed of light, c, stays the same (roughly 300,000,000 metres/second), any increase in energy must lead to an increase in mass.

A bow is a device for storing energy and then releasing it suddenly into an arrow. As you draw a bow it stores the energy that goes into drawing it (some of the energy, anyway). This means that a bow at full draw has more energy than a bow that is braced. Since energy equals mass x a constant (c2), a drawn bow has a greater mass than an undrawn one. As you pull your bow, you make it heavier.

Of course, you don’t notice this effect. That’s because if E=mc2 then m=E/c2. No matter how strong you are, the energy you put into your bow is tiny compared to c2 (90,000,000,000,000,000). The increase in mass when you pull back an average draw weight horsebow is about the same as adding a single bacterium to the bow. That’s about a millionth of a grain of sand.

This is of no relevance whatsoever to the practical workings of bows and arrow, which is what I am going to write about next, but it is a fantastic fact.

And no, Einstein did not have a horsebow.

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:


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.


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…)


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.


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…


Under Pressure

    Pressure Events?

The grading system originally involved a system of “pressure events”. This rule has now been removed because it was found to be too complicated. I have to say that I liked that rule, so I shall tell you a little bit about it. The essence was that to get HA3 and above you had to have shot some of your scores under pressure.

My original plan was to require actual competition scores. This would have been impractical in some places, notably the USA, since there are not enough competitions available. We therefore said that pressure events could be shot either at competitions or at special “pressure grading events”. These would produce pressure by the simple means of reducing the frequency with which you could attempt them: if you don’t shoot a good enough score at that event then you will have to wait for a month before trying again.

I had two reasons for wanting to implement this. First, I think it important that people be able to perform under pressure (I am hopeless at all sports under pressure). This is a competitive sport (and for those who view it more as a traditional event than a competitive one, remember that our forefathers were under a lot of pressure as they rode into battle!).

Second, it helps to level the playing field between those who have horses and those who do not. Let’s say that you need 4 scores of 60pts for a particular grade. If my average score is about 50pts then I might manage 60pts every now and again but if I only shoot once per month then I probably won’t get 4 scores of 60pts. You, on the other hand, might have horses and shoot every day. Your average might be 45pts but if you are shooting 20 times each month then you will probably reach 60pts 4 times. This is the law of averages in action. You may not be as good as I am but you will get a higher grade. Of course you are likely to become better than me pretty quickly with all the training but you should not get the higher grade until you are genuinely better rather than just giving luck more opportunities.

Pressure events were to be events that could only be shot once per month or in competitions. This would have reduced the advantage given by the opportunity to shoot more often. It would also test the ability to shoot under pressure because the archer would know that if they didn’t make the grade this time then they have to wait a month.

Extensive testing in the USA revealed two things:
many people found the rules about pressure events confusing;
people feel that they are under pressure as soon as they start to keep track of the score.

We therefore decided to remove the section abut pressure. Grades may be obtained at any venue so long as you shoot according to the rules, keeping times and scores, and you may submit one score per style per day.

In the long term I would like to see the pressure system introduced. That is probably some years away, however. Imagine a world in which there were enough competitions everywhere in the world to allow us all to enter as many as we want. For this we need the sport to grow. I hope that this grading system will help that to happen.

Grading System

The BHAA committee has now passed a resolution to implement the grading system that was conceived at Bow Camp 2012 and subsequently developed by Darran Wardle in the US together with me and Claire (with valuable help from others, notably Trey Schlichting, Roberta Beene and Beesh Frischman, who have been testing the system). Pin badges to be awarded for reaching each grade are in the final stages of production.

The details of the grading system, including the rules and tables, can be found on the MA3 website: http://mountedarchery.org. Click on the “Competitions” button on the menu bar. They will soon be available on the BHAA website but I am going to summarise the system, with some explanation. First though, why did we want a grading system and how did we want it to look?

    Why Have a Grading System?

We came to this project with different ideas. There were two main reasons given for wanting a system. One was the reason many sports have such a grading system (we took a lot of ideas from target archery and from shooting): to give people a marker of how well they are progressing and how far they have to go, as well as giving encouragement to keep working at improvement, especially to those just starting out.

The other reason, largely put forward by the Americans rather than the British, was the ability to allow those of similar abilities to compete against each other at competitions. My chances of beating Kassai Lajos are pretty slim (except in the Jordanian Style: beating him in that is possibly my proudest moment ūüôā ). If the competition has a category for those below a certain grade then I can compete with a decent chance of winning something.


The grading system, we all agreed, should test ability, which should include consistency. Having one good day should not suddenly give you a grade far above your ability. For one thing, this would leave you competing against people graded higher than you in future, which is what we were trying to avoid. We wanted the grades to reflect the scores you are capable of shooting consistently, not the highest score you have ever shot.
On the other hand, not everybody can shoot very often. We therefore decided that higher grades should require more scores to give a better indication of your true ability.
In the same vein, those who are new to the sport are not expected to master all the various disciplines. Those at the top are. We therefore require the higher grades to be able to shoot more different styles of event than the lower grades.
Finally, the higher grades obviously require higher scores than the lower grades. As a person advances through the grades they therefore need to shoot more different styles (Korean, Hungarian, qabaq),

    Student Grades

We have split the grades into two basic types: Student (S) and Horseback Archer (HA). The S grades are supposed to be an introduction to the sport. It is shot using the Korean event, which is generally easier than Hungarian for beginners. The big difference is in relation to speed. The allocated time is more generous than in regular Korean competition (16s over 90m rather than 14s). Points are lost for going too slowly but there are no points awarded for speed. This is a deliberate decision intended to encourage newcomers to the sport to learn to shoot accurately. Speed can come later but there is a danger that new students would simply ride a fast horse and rely on the fact that they only need one or two hits plus the speed bonus to get the grade. We were keen to avoid this.

    Horseback Archer Grades

There are 8 HA grades. The requirements get tougher as you move up through the grades. The full details are posted on the BHAA and MA3 websites, but I shall summarise them here. Regular rules are used throughout.
Obviously higher grades require higher scores. They also require more scores: HA1 and HA2 require 2 Korean and 2 Hungarian scores at the required level; HA3 and HA4 require 3 of each plus a qabaq; HA5 and HA6 require 3 of each plus 2 qabaq; HA7 and HA8 require 4 Korean, 4 Hungarian and 2 qabaq. We require consistency as well as high scores!


Not all competitions will be run according to these rules. We are not trying to take over the world and we are perfectly happy to allow gradings to be achieved at competitions using a wide variety of rules, so long as it is possible to translate the scores fairly. The targets need to be at least as far away as they are under our rules but things like bonus points for hits and speed can be calculated afterwards if you know your times and your individual arrow scores.

As ever, please do comment or email with any thoughts you may have. The grading system is now running in Britain and the USA and is being considered by others in various countries. If you would like more details then please get in touch.

Letting Go of the Korean Target

I love the Korean target face.  I think it adds to the flamboyance and style that makes our sport so different from standing 70m from a target and shooting endless identical arrows at a boring circular target.

Unfortunately, much of the world is not set up for the Korean target.  We were very lucky that WHAF, in their ongoing kindness and support, sent us some beautiful targets ready for our national championships last year.  We had bosses of the correct size and everything went well.  Many people do not have ready access to big square target bosses, even if WHAF were to send faces to everybody who wanted them.  In particular, we were informed by our American friends that almost all bosses over there are circular and either 80cm or 120cm (the two most common sizes for FITA archery targets).  Pythagoras told us many centuries ago that the corner of a 90cm Korean target face is some 63.6cm from the centre, whereas the edge of a 120cm boss is only 60cm from the centre.

This caused us some difficulty when establishing a grading system.  Clearly for a system to have any meaning you had to be comparing like with like.  If one person has a bigger target than another then how do you compare their scores?  We needed to have either everybody using the same scores or a way of comparing scores on different targets accurately and fairly.

The general feeling was that in America, and possibly many other places, use of the Korean target face would restrict the number of people able to use the system we were trying to establish.  We had to allow people to use the ubiquitous FITA target faces.

My feeling was that this was not a major problem.  It should not be beyond the wit of man to devise a system of converting zones 1-5 in a square of known edge length to zones 1-5 in a circle of known diameter.  It should simply be a matter of working out how much bigger the square is than the circle.  Each zone should decrease proportionately since they are marked by a given fraction of the edge/diameter.

As it turns out, this cannot be done after all.  The Korean target faces do not have zones of equal edge length.  Measuring from the centre towards one edge, the 5 zone is 12cm, 4 and 3 are 7cm each and 2 and 1 are 9cm each.  A direct comparison is beyond my abilities.

I am still pondering ways to get around this problem nothing in the whole system has caused me more mental turmoil than abandoning the Korean target face.  If anyone can think of a mathematical model that will allow a direct comparison then please get in touch.  In the alternative I intend to keep a close eye on scores shot under each system in the hope of working out a rough (but as accurate as possible) conversion based on a mixture of geometry and statistics.  I will not give up those wonderful targets without a fight!

The Need For Speed

    Speed and Accuracy

Having explained in my last post why we felt the need for a unified and agreed set of rules, at least for some events and as a basis for change, let me now look, in a series of posts, at some of the areas where controversy may arise from our rules.

The most obvious area where opinion has been divided so far has been in relation to the awarding of points for riding fast. This has been an area of constant change over the past couple of years.

I think it is agreed by most people that just awarding one point for every second under the time favours speed over accuracy. Most efforts to correct this have revolved around awarding extra points for hitting multiple targets. This favours riding quickly but still being able to nock and shoot quickly enough. It does not favour accuracy in terms of hitting the middle of the target over hitting the edge. This can lead to some odd situations.

At the Al Faris competition in Jordan there were 10 bonus points for hitting all 5 targets on the Korean serial shot. This means that where two people each hit the first 4 targets the fifth target becomes disproportionately important. If one person just clips the line and another just misses it then that fraction of a cm is worth 11 points (1 for the arrow score plus 10 bonus points). The more bonus points are available the more this issue grows. Award fewer bonus points and you don’t balance it properly against speed.

We did not disagree fundamentally with the awarding of points for hitting all targets (we do exactly that in our rules) but we have kept the bonus points rather lower, so that a rider gains 3 points for hitting 3 targets in a row during the Korean serial shot event and 5 for hitting all 5 targets. There was some support for awarding bonus points for hitting both targets on the double shot but ultimately we decided against this.

Bonus points are only one way in which we have tried to balance speed and accuracy. We have taken an additional step: limiting the points available for speed.

Under our rules points are awarded for going under the allotted time but only up to a maximum of 10m/s. This means that there are no points available for going faster than 9s over 90m, 15s over 150m, 18s over 180m and so on. Riders are free to go faster but gain no more points for doing so.

By way of example, the allotted time for a 90m Korean run under our rules is 14s. Going slower than this loses you points. A rider doing 90m in 14s scores his arrow score. 12s scores arrow score +2 and so on. A rider doing 90m in 9s or faster than 9s scores arrows +5.

    Why This Rule?

There are really two parts to this rule. One is why limit points for speed and the other is why 9s.

The idea of limiting the score was introduced partly to balance the sport and partly to discourage excessively fast riding. Not everybody agreed about the second part. I shall not give details of who thought what but some felt, for safety and horse welfare reasons, that the rule should actually penalise faster speeds (i.e. you lose points for going faster) and others felt that you should be able to gain as many points as you can for speed. This was a compromise provision.

Other ideas included using a target with 10 scoring zones (or just doubling the arrow scores) to encourage more accurate shooting and a suggestion that has been made by a number of people: the score for the run should be the arrow score divided by the time. The second was felt to be complicated and the first was felt to favour accuracy too far over speed. The group opted for the limiting of points for speed.

The combination of limiting speed points and awarding fewer bonus points for hitting all targets has one further effect: really accurate shooting is rewarded. There is now no substitute for hitting the middle of the target. If you can do it quickly and repeatedly then so much the better, but there is less chance of being outscored by somebody who only just hits the target but does so on a faster horse.

    Why 10m/s?

So why that particular speed? There was some disagreement. Some wanted something slower, say 12s over 90m. Others wanted to go faster, maybe 6 or 7s. 9s over 90m was a compromise that has one very obvious advantage: it works out as 10m/s. this makes it easy to be consistent between different events and distances. Divide the distance in metres by 10 and that is the number of seconds beyond which you get no more points. It was, basically, a practical compromise. As it happens we feel that it works well in practice as well.

We opted to make this rule apply to all events, including the Hungarian. Although this event is not usually the subject of experimentation in the way that Korean is, we felt that consistency was important. In addition it is currently possible to do relatively well, especially at lower levels of competition, by riding the course quickly and just loosing a single arrow. Riding the 90m in 7s and scoring a single point with the arrow gives a respectable score of 60 points over the 6 runs. This does not seem to us to be the spirit of the Hungarian event and limiting the number of speed points to 7 per run (for covering the 90m in 9s or faster) limits the extent to which this tactic will work.

Coupled with a minimum target distance of 7m and bonus points for hitting 3 in a row or all 5 targets in the Korean serial shot, we feel that this rule encourages riding at a decent but not excessive speed whilst shooting quickly and accurately. It is not perfect, and never could be because people have different opinions on these matters. I believe that it is a pretty good compromise between the various views and produces a fair balance between horse speed, nocking speed and accuracy.