Before electronics, was there a method for judging distance in archery?
What methods were used historically? How were combat archers trained to judge distances?
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I'm a horse archer; we use instinctive archery – there are no range finders, just a bow, a string an arrow and an archer. After a few thousand shots at various ranges, your body just knows how to aim – I'm not even conscious of doing it. Eventually you're able to hit a target from the back of galloping horse reliably (I'm not saying I'm there yet, but I'm working towards it).
It can take me a couple of rounds to sight in when I change distance; the club normally shoots at 10 m, but the range where I go is more convenient at 20 m. When I switch to the longer distance my arrows are low until I correct. I suspect that would vanish if I were to practice more often, but I also suspect that historical archers shot some ranging shots before combat started, and probably used other archers as reference to adjust range.
Not sure I can express this clearly, but when I think about aiming, my aiming declines – it really is instinctual. Trying to control the process leads to error. Archery is about perfect form – about this arrow. One teacher I heard express it as "build a connection between yourself and the target and let the arrow trace that connection."
I overheard one of the instructors mentioning that it was common for historical archers to loose 300 shafts a day; when I'm doing my best I'll loose 144/day 3 days a week. For me this is a hobby/stress relief. For them it was life and death.
The cited reference is only the first one that popped up in my search. You can check for related terms such as traditional archery. I occasionally practice with some longbow archers from the Society for Creative Anachronism; they don't use range finders either, but they have a slightly different technique for managing range. I'm not a longbow archer, so please take my summary with a grain of salt – I've heard them instructing their students to line up the shot then tilt their bodies above the waist to manage the distance. (You can't do that atop a horse for reasons of balance, so I've never tried.) @Pieter Geerkens points out that Joe Gibbs demonstrates this in his videos.
You might want to check out your local chapter of Horse Archers USA or Mounted Archers of the America, the SCA, or other related disciplines. I believe there is also an active traditional bowhunting community – I see their magazines occasionally, and they may have more information.
Aside: someone attempted an edit and I wanted to clarify. An archer *looses* a shaft. Sometimes I lose shafts, but only rarely indoors. When we lose a shaft outdoors we have to search very hard because we don't want a horse to step on the arrow. Sometimes people talk about "firing" arrows, but the term "fire" is related to gunpowder. Some people care. But "loose" is the correct word in this context.
In combat, the purpose of an archer was not to land aimed shots on specific targets. It was to put large amounts of pointy wood-and-steel in the air, in the general direction of a block of enemy troops. When the block of enemy troops is tens of metres deep and hundreds of metres wide, aiming is largely irrelevant. For long range shots where an enemy is running over uneven ground, it's basically impossible to predict movement anyway within the arrow's flight time.
In this, archery is more similar to Olympic javelin or hammer throwing. What matters most is the distance at which you can engage the enemy with your ranged weapons, and the rate of fire you can achieve. The more shots you can land in the enemy's ranks, the fewer enemy your footmen have to fight. So long as your arrows are landing somewhere within the enemy ranks, you're good. Bonus points if (as at the Battle of Crecy) you outrange your opponents' archers enough that you can shoot them with virtual impunity.
Ranging wouldn't have been as important as it is today. The importance of ranging comes from the "first shot" advantage - being able to drop your projectiles onto your chosen target first time accurately (whether that is from a sniper rifle or an artillery piece) is important in modern warfare because most conflicts are decided by who gets the first hit in successfully. Add to this that modern weapons are also exponentially more expensive than those of ages past (a single "smart" missile often comes in at several thousand pounds these days), and thus such smart weapons need to be able to hit first time, every time which is where the reliance on ranging and other ballistic factors come into play.
Medieval weaponry doesn't have the accuracy of modern weaponry. Long bows and the like relied less on individual accuracy of the bowmen and more on massed concentration of fire on the target area. Medieval armies were also large compared to modern engagements and thus the element of surprise was lessened, if not non-existant.
During sieges, for example, you had the time to estimate ranges using given landmarks - siege weapons were often built where they were to be employed and thus there was plenty of time to send scouts to get ranges. Not to mention such sieges often lasted weeks and thus the first few shots from any siege weapon would have been ranging shots at best - the defenders were unlikely to be able to move either.
With just a little practice, most people can learn to judge distance fairly accurately. Even in modern times, use of a rangefinder is situational. In hunting with a modern sight, it is important to know the range of a shot. Yet it can also be inconvenient to break out and use an electronic rangefinder.
3D shoots are a type of archery contest intended to simulate actual hunting conditions. Typically, rangefinders are not allowed. What I have seen many people do in practicing for 3D shoots, is to judge distance without a rangefinder and shoot. Then use an electronic rangefinder after the shot to check on their accuracy. With only a few weeks of practice doing this, a person can usually become accurate at estimating distance to within a few yards. That is as accurate as needed for archery.
As others have mentioned, knowing exact distance may have been less important in the past. However, I've talked to people on construction sites and in other cases where they were able to accurately describe distance prior to measuring. This was not an uncommon skill for people to have prior to rangefinders and modern measurement, if those people were in a trade that required it.
To the extent that understanding range was important to historical archers, I am confident that many of them would have had the same kind of sense of distance that these construction workers and 3d shoot participants demonstrate.
Fortunately you can use recent history to answer your question. Until very recently, Bradley fighting vehicles (and others) did not have a range finders. Range were based upon the estimation of the commander and gunner. Modern day snipers are trained to judge range without the use of electronics.
I'd dispute that range estimation was not important in antiquity ballistics. Ammunition cost time, labor, and probably money. Even finding appropriate sized rocks for catapults (and their ilk) would be labor intensive and dangerous. Firing the various instruments caused wear. How would a commander react if some of his missile weapons broke with no meaningful effect on the enemy? This could be somewhat mitigated by test shots, say one archer files an arrow and the rest of the archer uses that to judge the range.
The best way to judge range is to construct a range card. Walk the battlefield measure the ranges, note any depressions that could offer the enemy cover. In the movie Kingdom of Heaven this is what they are doing for the defense of Jerusalem, marking ranges with painted rocks. The limited catapult shots had to count. Range cards are typically limited to deliberate defenses, but ranges could also be stepped out if employing spies when on the attack. In the movie The Green Berets a person dressed as a allied soldier is caught measuring (by pace count) to a VC desired target.
Failing that, one method that worked for me, was dividing the distance. It is easy to calculate the distance of a football field, and then estimate the number of those a target is away from you. So about 10 football fields would be about 1000 yards or meters. With archers, we are talking much shorter distances so it was easier to be more precise.
There are a whole series of you tube videos on range estimation and many of the techniques would be available to gunners from antiquity. Videos on using the reticle method, would not be applicable. Note that light and the color of the targets have an impact on range estimation and leads to the skill of the "gunner".