Ranged weapons

Ranged weapons - be it thrown missiles like javelins or projectiles that are propelled by a weapon - are an important part of ancient warfare and their characteristics differ markedly from that of close combat weapons. In the section about damage scaling we have already discussed how they lead to an area contact instead of a line contact between combatants (and so are potentially more damaging). In addition, before the coming of gunpowder, most weapons relied on human physical strength to acquire their destructive energy. To achieve this fully while being engaged in melee with a sword is difficult - an archer on the other hand faces no strong obstracle to applying his full strength every time he shoots. For this reason, pretty much every arrow shot in a battle is potentially dangerous, but not every sword thrust or stroke that is dealt. The combination of these two factors, combined with the fact that arrows and bolts deliver their kinetic energy to a very small area and have thus good armor-piercing characteristics, goes a long way to explain why ranged weapons are potentially capable of delivering enormous damage in a relatively short time.

Range and drag

In a frictionless world, the range of a projectile is determined by initial velocity and gravity - the initial motion must have an upward component, that decreases and becomes a downward component under the influence of gravitational acceleration, the trajectory forms a parabola that rises, reaches an arc-top and then descends and the point where the parabola intersects with the ground determines the range.

In reality, projectiles feel air drag and so the trajectory deviates from a parabola. In the velocity regime reached by man-propelled missiles, to good approximation the drag equation can be applied, which states that the drag force depends on projectile shape, frontal area and velocity squared.

Since - see above - the inital velocity of a weapon pretty much determines its range, it is generally favourable to use high-velocity projectiles despite the higher initial drag. A javelin for instance is a fairly slow and heavy weapon which has little drag effect, but its effective range is of the order of 30 m which is far below that of a longbow.

The details are complicated, but the general pattern is that:

  • dense materials have lower drag because they present less area to the air for the same mass
This is the reason Rhodian slingers were able to increase the range of their projectiles far above that of their Persian counterparts as reported by Xenophon.
  • long, narrow shapes experience less drag than bulky, fat shapes
In plain terms - arrows fly better than crossbow bolts which in turn out-perform stones. Why then were bolts used at all? The reason is that a crossbow accelerates the bold on a much smaller spatial distance than a longbow, so forces have to be correspondingly higher to reach about the same initial velocity - and the bold needs to withstand these forces, which an arrow would simply not do.

In practice, the effect of air drag is that projectiles lose part of their initial velocity throughout their flight and impact with less energy than they started with. Most of the velocity is shed during the first stage (because drag is proportional to the squared velocity), but the corresponding loss of kinetic energy which determines the damage is then about linear. The consequence is that all projectiles have more kinetic energy (and armor piercing power) at point blank range and less at maximum range, and that effect is most pronounced for irregular projectiles like stones, still significant for projectiles like arrows and lest important for slow, heavy weapons like javelins.

The simulation requires to specify the type of projectile for a unit with ranged combat capability to select the correct drag model.

Impact angle

There is a second effect that reduces the effect of a projectile at large range when armor is worn. At point-blank range, an arrow (or other projectile) hits the armor at pretty much 90 degrees and so has the shortest possible path through it before it wounds the soldier. At the end of weapons range, the projectile comes down at about a 45 degree angle. If it his the same spot of armor, that means the path it needs to push through the protective layer is about 40% larger - it is as if the soldier would wear 40% stronger armor.

That, combined with the overall loss of kinetic energy, means that arrows may penetrate for example a plate armor at point-blank range, but not at larger range (of course the same is also true for bullets fired from early guns which lose a lot more kinetic energy over distance than arrows).

The consequence for any tactics that proposes to use ranged weapons against a heavily armored unit is that the attack must be done from as close range as possible. Of course that makes it dangerous, because the unit under fire might decide to charge.

The simulation takes this effect of up-scaling armor value with range into account.

Is accuracy an issue?

Short answer - it might be.

At point-blank range, an archer can fire at an individual soldier. Certainly at over 250 m range that is not an option. Of course he doesn't have to, he just fires at the whole unit - which is large enough to be hit for sure. But that works best if the attacked unit is tightly packed - if a lose formation is under fire, many arrows would simply hit the ground and not do any damage. So the inability to target individual soldiers might imply that a volley of arrows does less damage at range.

Similarly, a longbow arrow travels with some 100 m/s initial velocity, but that means it needs three seconds to reach to the edge of its range. That doesn't much if a slow-moving unit is under fire, but it might if we're talking about cavalry - which during a charge can cover more than 30 m while the arrows fly. Thus, it would be much more tricky to actually hit the unit at extended range (arrows might simply fly over the unit and impact behind) than at point-blank range (where arrows fly straight at the charging unit and range to the impact point is not an issue).

Some of these effects are dealt with in thesimulation using heuristic formulae. The general summary of all that's been said here is that attacking with ranged weapons at the edge of their range is far less effective than attacking at short range.

Continue with Ranged weapon physics.

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