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Bow and crossbow -- power and accuracy compared

Crossbows get a bad press, particularly in the UK. In fact, many people would be reluctant to classify crossbow shooting as a martial art at all. There is a popular perception that the crossbow is trivially easy to shoot, and to shoot accurately. There is an even more popular perception, largely put about by newspapers, that the crossbow is `deadly', `lethal', `vicious', and so on. No doubt a crossbow can be all these things, as can an ordinary bow, or even a power drill. On-line auction sites such as eBay won't carry advertisements for crossbows, although they usually will for bows. In fact, crimes involving knives outnumber crimes involving crossbows by several orders of magnitude, but crossbows are not really any harder to obtain than knives (in fact, you can legally buy a crossbow if you're 17 years old, but not a knife, for which the minimum age is 18).

In fact, my contention in this article will be that, comparing like with like so far as is possible, a crossbow is less powerful, and hardly more accurate than an archery bow.

In the interests of comparing like with like, I will be considering a modern recurve bow, with a draw weight in the region of 40lbs, and a modern sport crossbow, with a draw weight of around 150lb. Of course, compound bows offer certain advantages over recurve bows, but so do compound crossbows over recurve crossbows, so this does not change the comparative situation. For military use crossbows were made with draws of over a thousand pounds. These, of course, would not have been hand-held, and are really in a class of their own. In the interests of fairness I will be considering bows and crossbows priced in the £200 region. Of course, it is possible to spend more (or less) on either a bow or a crossbow and, again, this does not affect the comparison much.

Principles

Both bow and crossbow propel a projectile by converting potential energy stored in the bow into kinetic energy in the projectile (arrow or bolt). There is no other source of energy, so the ultimate determinant of power, and of arrow velocity, is the energy it takes to draw the bow. But a heavier draw does not necessarily equate to a higher power or a greater velocity, as we shall see.

Modern recurve bows are typically made of a composite of glass fibre, carbon fibre, and other plastic materials. The bow part of the crossbow -- the prod -- is usually made the same, although metal prods do exist. Traditionally both would have been made of wood. Strings are typically made of synthetic materials such a Dacron; traditionally these would have been gut or linen for bows, and perhaps wire for heavy crossbows.

A traditional bow is held at full draw by the archer's finger strength. Not only does it require training to be able to hold the bow drawn, but the release of the arrow from the fingertips imparts a small lateral motion to the arrow, for which the archer must compensate whilst aiming. A crossbow, however, holds the string drawn by a trigger mechanism. This has three advantages: the weapon can be held ready to shoot for an extended period of time; no muscular strength is required to hold at draw whilst aiming (which can therefore take longer); and the string is not deflected by finger motion on release. All these factors contribute, in principle, to the greater accuracy of the crossbow.

Power and arrow velocity

For military purposes, an arrow that is carrying more kinetic energy when it hits the target will, all other things being equal, hit the target harder, and penetrate the target more deeply (if it penetrates at all), and is therefore to be preferred over one that is propelled less fast. For target sport purposes, velocity is more important than kinetic energy (although these factors are related, of course). So long as the arrow doesn't bounce out of the target, it doesn't matter how hard it hits, or how far it penetrates. If the arrow flies fast, it will droop less over its path and be less affected by wind. Both these factors make aiming easier and more consistent.

For hunting (not legal in the UK) the requirements fall somewhere between military and target sport applications.

Given a bow that can store a certain amount of energy at full draw, the energy can be used to propel a light arrow faster, or a heavy arrow more slowly. The actual kinetic energy will be the same in either case. However, air resistance increases rapidly with velocity so, even for target shooting, it is ineffective to shoot a very light arrow -- it will lose energy to friction very quickly, and slow down. This wasted energy serves no useful purpose at all. All this means that increasing the draw weight of the bow does mean that the arrow will fly faster, but the increase in velocity is not in proportion to the increase in draw weight. There will be a point at which increasing the draw does not significantly increase the arrow velocity, for a given size and weight of arrow.

This limitation applies both to bow and crossbow, but the bow has further limitations on draw that do not apply to the crossbow. The problem is that a bow is subject to the effect that is incorrectly called `archer's paradox' -- the fact that the motion of the string, when the shot is loosed, is not along the axis of the arrow. For a right-handed archer the string will pull the tail of the arrow to the right on loose, which will deflect the arrow path to the left. The arrow needs to have a certain stiffness (`spine') to compensate for this effect, and this spine increases with increasing draw. In practice, therefore, if we increase the draw weight of the bow it is necessary to use a heavier arrow to get the requisite spine, and this means that the arrow will fly slower.

Now, as mentioned before, for military applications this increased arrow weight is not particularly important. What is important is the kinetic energy transferred to the arrow and, all other things being equal, this depends on the draw weight. In fact, a heavier arrow will retain more kinetic energy along its path to the target than a light one would from the same bow, because it will be travelling slower and therefore lose less energy to air resistance. Therefore, for military applications, both bow and crossbow typically had as heavy a draw as the bowyer could make. This is why military longbows typically had draws over 100lbs, and crossbows over 300lb -- much heavier than this and the weapon becomes very difficult to make, and very difficult to shoot even if it can be made.

For target sport, however, the situation is rather different. Remember that in this case we want to maximize arrow velocity, not kinetic energy. There is therefore an advantage to creating a bow with a lower draw, for two reasons. First, it is simply easier to shoot if you don't have shoulders like Popeye's. Second, it can shoot a lighter arrow (and therefore shoot it with higher velocity) because the arrow can have a lower spine. Modern target bows rarely have draws of more than 40lbs -- there is simply no point.

But a crossbow is not really affected by arrow spine, because the string moves predominantly along the axis of the arrow when loosed (that is, it is `centre shot'). This means that the benefit of increasing draw weight is not offset be increasing arrow size and weight, until the point at which air resistance becomes significant. Consequently crossbows with draws of 200lbs are still relatively common, although it is difficult to make a reliable recurve crossbow with such a high draw, because of manufacturing problems. Most recurve crossbows have weights 100lb-150lb, and there are advantages in going for the heaviest you can draw without hurting yourself.

So let's get to the, um..., point. A modern recurve bow will typically have a draw of about 40lbs, a crossbow 100-150lbs. This means that the crossbow is about three times more `powerful', right? Wrong.

It's wrong because, despite the increased draw weight, the crossbow actually stores much less energy, because its prod is much shorter than a bow, and the draw length consequently shorter. Energy is proportional to force multiplied by distance -- and the force required to draw a crossbow only reaches its peak at the last inch or so of draw.

It turns out, if you do the maths, that a 150lb crossbow at full draw is only storing about one third to one half the energy of a 40lb bow. For both military and hunting purposes, therefore, a bow is therefore much more effective, in terms of hitting the target hard, than a crossbow, when both are at the limits of what can reasonably be manufactured and used. The crossbow will typially shoot its projectile somewhat faster than a bow -- typically 200-220 feet per second, as compared to 180-200 feet per second. But that's because the crossbow bolt only weighs about a third as much as the arrow, not because the crossbow is more `powerful'.

This all means that, despite what you may read in the Daily Mail a modern recurve bow of the type that is used in the Olympic games is a much more fearsome weapon than the kind of crossbow you are likely to be able to buy from a mail-order supplier.

Accuracy

There are good reasons, in principle, why a crossbow ought to offer better accuracy than a bow. First, inconsistencies in the finger release are eliminated. Second, the draw is of uniform length, even if the archer is not particularly skilled. Third, a crossbow can have a two-point sight, even a telescopic sight. It is very difficult to fit a two-point sight to a bow, quite apart from the fact that they are banned in most competitions.

But again, the reality is more complicated. Let's consider the putative advantages one by one, and see if they are really are as important as it first appears.

Release inconsistencies. A major source of inaccuracy when shooting a bow is moving the nock end of the arrow with the fingers when releasing the string. The nock end doesn't have to move very much, from one shot to the next, for there to be a large scatter on the target.

The crossbow does not suffer from this problem. It does have a problem, however, which the bow does not have, and which has a similar effect on accuracy. The crossbow is fired by means of a trigger, the mechanism attached to which must hold the draw weight of the prod. The trigger pull pressure on a typical 150lb crossbow is likely to be around 10lbs (much higher on cheap models). This is one area where a top-of-the-range crossbow will win out over a budget one, but even the best crossbows have trigger pulls of at least 3lb. Try pulling 3lb (let alone 10lb) wih one finger while keeping the butt end of the crossbow perfectly still. It takes practice, not to mention strong finger muscles.

Consistent draw length. Crossbows do offer a consistent draw length, and therefore a consistent bolt velocity. However, modern recurve bows can be fitted with clickers and similar devices, to regularise the draw. So this advantage isn't all that it might first appear.

Two-point sight. Potentially this is a great advantage. It takes a lot of practice to shoot a bow with only a single-point sight (or no sight at all in the case of most longbow matches). Having a two-point means that the aim can be relatively accurate even if the archer's posture and draw are not entirely consistent from shot to shot.

But even here things are not quite what they seem. The distance between the two sight points is relatively short -- perhaps twelve inches or so. The crossbow can be out of alignment with respect to the target by quite a long way before the sight picture changes very much. More to the point, both the front and rear sights are much closer to the eye than the front sight is on a bow. In fact, many archers extend their front sights to increase the eye-to-sight distance.

In short, the sighting and release mechanisms of the crossbow allow reasonable accuracy to be achieved with a relatively small amount of practice, compared to a bow. But a modern bow in the hands of an expert will shoot more accurately than a crossbow in those of a beginner; and it's not obvious to me that an expert crossbow shooter will out-shoot an expert archer, particularly at fixed-distance target shooting.

In my own experience -- and I've been shooting both bows and crossbows for more than twenty years -- I shoot somewhat more accurately at fixed distances with a recurve bow than a crossbow, and much more accurately than either with a compound bow. However, this probably doesn't mean all that much because (1) I practice with a bow much more frequently than a crossbow and (2) I spent a lot more money on my bows. However, I practice most with the traditional longbow, and shoot least accurately with it. But that's not really unexpected.

The bow/crossbow comparison is somewhat harder to make for unmarked field archery (and, presumably, hunting). In this case, the shooter must estimate the distance to the target and compensate for it in aiming, taking into account the slope of the ground and the height of the target. Bows that are not centre-shot work least well in this kind of environment, because the effect of `archer's paradox' is distance-dependent. Crossbows do not experience archer's paradox, so their sights do not need to be adjusted in the horizontal plane for range. They do need to be adjusted for windage (i.e., cross winds) in the horizontal plane and in the vertical plane for range. But because the projectile velocity is a bit faster than that of a bow, both windage and range vary less with distance. My experience is that I can shoot in the range 15-40 yards with a crossbow without needing to adjust sights. By that I mean that, within that range, the variation in arrow placement with distance is less than the variation that results from my natural shot-to-shot inconsistency. If I were a better crossbow shooter, and had a better crossbow, I would probably need to pay more attention to my sights.

Ergonomics

Neither a bow nor a crossbow can be considered a concealed weapon: both are physically large, and somewhat unwieldy. However, in field shooting, a crossbow can be shot from dense foliage and scrub, something that is difficult for all but the shortest bows. A crossbow can be shot from a kneeling or even prone position if this provides a better line to the target. Taking these factors into account, along with the slightly improved accuracy where target distance is unknown, one might surmise that a crossbow would be a slightly more effective hunting weapon than a bow.

For battlefield applications, the crossbow has the disadvantage of being comparatively slow to reload. Most heavy crossbows are fitted with a cocking lever, but some require to be wound up with a handle, or some sort of pulley arrangement. Even with a cocking lever it takes about ten seconds to fire each shot. I find that with a longbow I can fire perhaps three-four times that fast.

I understand that crossbows were sometimes used in war by snipers and assassins. I can understand the appeal of a crossbow in such situations -- it can be fired from hidden or confined spaces, and can be held in the cocked position for an extended period of time.

And the winner is...

If I were a medieval lord looking to raise an army, and had to choose between equipping my soldiers with longbows or crossbows, it would be a close call. Longbows are inexpensive and quick to make, require little maintenance, can throw a heavy arrow very hard, and are quick to reload. However, they require considerable physical strength as well as skill to shoot properly. Training longbow archers is a long-term proposition.

Crossbows, on the other hand, are relatively easy to learn to shoot well enough for battlefield use. They require little physical strength, particularly if fitted with cocking winches, and can be used at close quarters if necessary. But they offer a relatively low rate of fire, and are difficult to make with the very high draw weights needed to offer comparable power to a longbow.

For hunting, I would expect the crossbow to offer a significant advantage over a longbow, and a modest advantage over a modern bow, in terms of accuracy and ergonomics. This advantage would be least prominent where proponents of both weapons are highly skilled. Both bow and crossbow can readily be made powerful enough for hunting purposes.

For target shooting, I would expect a highly skilled recurve archer to outshoot a highly skilled crossbow archer, but I imagine it would be a close contest. The less skilled the competitors, the more the crossbow would have the advantge.

Anybody can be a mediocre crossbow archer. It typically takes 10-20 hours instruction and practice for a person to learn to shoot a recurve bow well enough to be getting most of the arrows on the boss at 20 metres. One can achieve the same accuracy with a crossbow in about ten minutes.

But to shoot a crossbow well -- well enough to achieve scores as high as a decent recurve archer -- is not easy. It's a skill -- whether it is an art is more open to debate.