Longbow - the arrowstorm revisited

[Nick Harbud]

falling back on the O level Physics here but I don't think it falls to zero unless you shoot it pretty much straight up.  Assuming a still day, you've got three force vectors; shooting, drag and gravity.  You need to resolve those three to get trajectory, which should be essentially parabolic.  But don't ask me how to do that - they make computer programmes for that

Pah!  O level (or even GCSE) physics is totally inadequate for solving this problem as it takes no account of air resistance.  The maths covering this was outlined in my Slingshot article on trebuchet/bombard ballistics.  Basically one ends up with a 2^nd order non-linear differential equation that requires a numerical solution.  You are correct that there are computer programs for this sort of thing.  Indeed, in those countries where shooting the wildlife from a great distance using a high-powered rifle is considered good sport, one can use a smartphone app that takes into account not only gravity and drag, but also humidity, wind strength and coriolis effects.  However, I have it programmed into a spreadsheet using a Runge-Kutta 4^th order solution, which I reckon is generally good enough.

What was the question?  Oh yes, trajectories of arrows shot to 200m.

Using the arrow cited above, there are two trajectories where the arrow will travel 200m; 22 degrees and 63 degrees.  The flatter trajectory reaches its target in ~4.3s whereas the high trajectory missile will take ~9.8s.  The effect of the additional travel distance on final velocity is marginal.  In both scenarios the missile slows from 60m/s leaving the bow to ~45m/s at target.  The high trajectory is really high, reaching ~115m from the ground.  It will be much more affected by any wind, both because wind speed increases the further one is from the ground and also because any wind will act upon a high trajectory arrow for roughly twice as long as a flatter trajectory.

As outlined in other threads, the target will also move twice as far during the travel of the high trajectory arrow, making judgement as to where it might be somewhat trickier.  (Incidentally and slightly off-topic, the electronics in modern fire-and-forget guided anti-tank weapons try to allow for this in their targeting and are somewhat better at it than a medieval archer.)

These are major considerations in judging the effectiveness of the arrowstorm.

[Imperial Dave]

falling back on the O level Physics here but I don't think it falls to zero unless you shoot it pretty much straight up.  Assuming a still day, you've got three force vectors; shooting, drag and gravity.  You need to resolve those three to get trajectory, which should be essentially parabolic.  But don't ask me how to do that - they make computer programmes for that

Pah!  O level (or even GCSE) physics is totally inadequate for solving this problem as it takes no account of air resistance.  The maths covering this was outlined in my Slingshot article on trebuchet/bombard ballistics.  Basically one ends up with a 2^nd order non-linear differential equation that requires a numerical solution.  You are correct that there are computer programs for this sort of thing.  Indeed, in those countries where shooting the wildlife from a great distance using a high-powered rifle is considered good sport, one can use a smartphone app that takes into account not only gravity and drag, but also humidity, wind strength and coriolis effects.  However, I have it programmed into a spreadsheet using a Runge-Kutta 4^th order solution, which I reckon is generally good enough.

What was the question?  Oh yes, trajectories of arrows shot to 200m.

Using the arrow cited above, there are two trajectories where the arrow will travel 200m; 22 degrees and 63 degrees.  The flatter trajectory reaches its target in ~4.3s whereas the high trajectory missile will take ~9.8s.  The effect of the additional travel distance on final velocity is marginal.  In both scenarios the missile slows from 60m/s leaving the bow to ~45m/s at target.  The high trajectory is really high, reaching ~115m from the ground.  It will be much more affected by any wind, both because wind speed increases the further one is from the ground and also because any wind will act upon a high trajectory arrow for roughly twice as long as a flatter trajectory.

As outlined in other threads, the target will also move twice as far during the travel of the high trajectory arrow, making judgement as to where it might be somewhat trickier.  (Incidentally and slightly off-topic, the electronics in modern fire-and-forget guided anti-tank weapons try to allow for this in their targeting and are somewhat better at it than a medieval archer.)

These are major considerations in judging the effectiveness of the arrowstorm.

Impressed 

Nick, your explanation had me reaching for the strong coffee to make sure I understood it all Makes complete sense and all we need to do now is test it all out in a field! 

[Erpingham]

Pah!  O level (or even GCSE) physics is totally inadequate for solving this problem as it takes no account of air resistance.  The maths covering this was outlined in my Slingshot article on trebuchet/bombard ballistics.  Basically one ends up with a 2^nd order non-linear differential equation that requires a numerical solution. 

I'm glad it was my education and not my memory that was deemed inadequate   Thanks for that Nick.  If nothing else it shows how difficult it would be to co-ordinate the shooting of two groups, one shooting straight to the target, the other using the indirect route.  If this was done, the rear ranks at least may have been shooting at will at the estimated range, which might work on en masse by creating a beaten zone but would be low on accuracy.

[aligern]

So, does the above argument support the archers shooting on only a flat trajectory?
If so, and if we still have a problem with the length of an archer line that cannot operate more than three deep then there a couple of solutions.
One is that Phil is right and the archers shoot shallow and are perhaps six deep, but that they shoot off say 20 arrows and then interchange with the back ranks who then shoot.
I wonder how the maths of this plays out, but it would seem feasible because longbows shoot so fast.

The other is that shooting overhead is not so problematic as the redoubtable Erpingham implies. Some support for this comes from the Strategikon where the rear ranks of an infantry formation (and indeed of cavalry units) shoot overhead at advancing enemies. I think that this may be more effective than suggested in earlier posts because it is not the beaten zone that matters, but the killing zone and that is much bigger because it is nine foot high for a  mounted opponent and five foot high for a foot target.
That means that an arrow that is targeted at landing 100 yards away will hit any cavalryman for that 100 yatds, even though the beaten zone might be only from 90 to 100  yards.

I await the comments of the mathematically able!
Roy

[Erpingham]

Two points.  One to correct an impression that I have given the noble Aligern.  I don't think overhead shooting is impossible or even implausible.  What I think is difficult is co-ordinating that shooting with front ranks shooting on a flatter trajectory.  Not only do the rear ranks not see the target (or not fully) but the time to target of their shots is much longer.  Laying down a barrage across a beaten zone therefore would suggest itself for any rear rankers, and there is little need to do that by volley.   

The other on formations.  Smythe, the great longbow advocate in the later 16th century, was clear that seven or eight ranks was the deepest you should deploy longbows to be effective.  He had served with longbowmen, so his view has some weight, even if he is sometime after the era we are considering.  So, in the Sixteenth century, no one was thinking of longbows in very thin lines (except deployed in a skirmish lines before the main body)

[Patrick Waterson]

And given that the longbowmen of the late sixteenth century would have been part of a continuous tradition of 'Harry the Fift' and 'Agincourt', not to mention the Wars of the Roses, one would imagine that what served for Smythe had also served for previous generations.

The verdict of history seems to be that archers function best as a battlefield arm when grouped together in depth, as this is the configuration adopted by the effective archer nations of history (by 'effective' I mean those who conquered rather than those who were conquered).  Grouping in depth requires indirect shooting, and effective indirect shooting requires practice - plenty of it.

We are told that an Egyptian archer was required to shoot 200 shafts per day to stay in practice.  What we are not told is how many of these were shot in company with his fellows in order to familiarise everyone with trajectories, beaten zones and flight times at various ranges and enemy rates of advance.  Egyptians did not have the advantage of calculus, or of the customary Euler or more recent and precise Runge-Kutta methods of solving differential equations.  What they did have was a lot of practice - and a lot of validation on the battlefield.

The use of archery in depth was near universal in the Biblical period: the Hebrews, despite their ambidextrous Benjaminites, seem to have been the main exception, unless their armament configuration changed over time.  Despite the increasing predominance of the armoured spearman and cavalryman in the Neo-Assyrian period, the last great Biblical power, the Persian Empire, used archery in depth up to the time of its war against the Greeks in 480-460 BC.  Thereafter the picture is less clear: for centuries, the archer seems to be mainly a skirmisher, with some few bodies of formed archers playing a subsidiary role while the spear and lance and then the pilum and gladius dominate the battlefield.

Beginning with the Sassanids and the later Roman empire, massed archery on foot begins something of a limited revival, which is largely buried underfoot by the barbarian invasions (although the Byzantine use of mixed formations and its imitative Arab counterpart survive to the era of the Crusades).  It is left to the English to develop the highly effective longbow characteristically used by the Welsh into an effective system, which seems once again to use volleying, or at least shooting, indirectly in depth to cover a beaten zone.

Did the Welsh pioneer this system?  Or did the English recognise the potential of the longbow for indirect shooting, devise the system and train their own and Welsh archers in its use?

[Erpingham]

It is left to the English to develop the highly effective longbow characteristically used by the Welsh into an effective system, which seems once again to use volleying, or at least shooting, indirectly in depth to cover a beaten zone.

Did the Welsh pioneer this system?  Or did the English recognise the potential of the longbow for indirect shooting, devise the system and train their own and Welsh archers in its use?

Just checking, but do we have much info on the use of Welsh longbows en masse?  Our main stuff about Welsh longbows seems to be about short range, aimed shooting (I'm thinking Gerald of Wales in particular).  It is possible that massed archery in depth comes more continental traditions or even crusading experience (talking hypothetically here - I don't know if there is any evidence that points that way).  One might suggest a developmental process that involved an Anglo-Norman heritage that featured archery, being impressed by the Welsh and their powerful bows, having seen techniques that used massed archery elsewhere and having a flash of inspiration to put all that together.

[Patrick Waterson]

That is a thought: the man who would have been in a position to put all this together was Edward I, who had been on crusade in 1271-2, conquered Wales in 1277, 1283, 1287-8 and 1294 (the Welsh were persistent fighters) and took an army into Scotland in 1298 in which the longbow system showed as having been developed, much to the dismay of William Wallace.

Although Warwick had used archery effectively against northern Welsh rebels at Maes Moydog in 1295, Edward's first expedition into Scotland had culminated in the Battle of Dunbar (1296), which was essentially a cavalry fight.  Falkirk seems to have been the first clear use of the English system of massed longbow archery.  It seems quite possible that Edward had the system set up and ready to go at Dunbar (guessing here) but it was not used because the English cavalry managed to win unaided.  At Falkirk Wallace's schiltroms curbed the cavalry's enthusiasm and the archers got their chance.

Edward I thus remains my favoured choice as a likely deviser of the English longbow volley system, or perhaps as the adopter of a system one of his lords (Warwick??) had devised.

[Mark G]

I understood that massing longbows was a tactic developed through the Scots and 100 yes war, rather than something which emerged fully formed.
I recall something about using greater numbers to shoot off opposing crossbowmen who were massed in turn to counter this.

[Imperial Dave]

As an aside, we used to practice speed shooting and on occasion could get 6-7 shots off in a minute. That would constitute heavy repetitive volleys but the accuracy definitely suffers and the munitions run out pretty quickly too!

[Nick Harbud]

Nick, your explanation had me reaching for the strong coffee to make sure I understood it all Makes complete sense and all we need to do now is test it all out in a field! 

Well, quite a number of the re-enactors have tried this out in the field and have come to the same conclusions as the maths suggests - high trajectory fire is not as accurate as low trajectory.  Loades also notes that none of the medieval illustrations of archers show them using high trajectory in pitched battle, although they are depicted using it for siege or naval situations.  As Loades points out, this is not proof it did not happen, but it is hardly an argument in favour.  Overall, Loades believes that the poor chances of hitting anything at long range (irrespective of the trajectory chosen) means such fire would have been strictly limited in order to conserve ammunition.  The maths also supports this view.

Regarding depth and frontage of massed archers, I tend to view a deep formation as being entirely feasible, but not capable of delivering any higher density of missiles per yard of frontage than a shallower line of musketeers.  Considering first a two-deep line of musketeers.  Each musketeer requires 2 ft frontage and the second rank can fire between the shoulders of the first giving an overall density of 1 shooter per yard of frontage.  (One could increase this to 1.5 shooter/yard by having a third rank kneeling in front, but let's not explore that just yet.)

Now to work a longbow, I am informed, requires a minimum 2 yards free space to left and right.  Therefore, a single rank requires 8 ft per bowman.  However, I think it entirely feasible for second and subsequent ranks of bowmen to shoot through the considerable gaps left by the forward ranks.  With, say 4 ranks, one has a density of 0.5 shooters per yard and no one firing overhead.  What the maximum practical number of ranks might be I shall leave to others.

Of course, with this somewhat loose formation, one should probably also consider what happens when it is contacted by a charging enemy.  Do the ranks all close up?  Is it possible for individuals to dodge out of the way or otherwise evade?  Or are the archers dead meat?

[Justin Swanton]

Now to work a longbow, I am informed, requires a minimum 2 yards free space to left and right.  Therefore, a single rank requires 8 ft per bowman.

That makes sense if the archer holds his bow horizontal and parallel to the line when nocking an arrow and pulling to full draw. A longbow is about 6 feet in length. If each archer held the bow horizontal and at right angles to the line when reloading then the archers could deploy with the files about 3' apart, but there would have to be more space between one rank and the next. Total number of archers capable of low trajectory fire would probably come out at about the same.

[Imperial Dave]

re-enacting is different to real life but I don't recall having 8 feet of space around me when we fought as an archer block, more like 4-6. Of course that was firing overhead/angled trajectory mainly.

Oh and regarding closing up when faced with a charge...we didn't like being charged!!!! 

[Erpingham]

Again, turning to the sixteenth century sources, detractors felt that the longbow was a cimbersome weapon, needing considerable elbow room.  The idea in some wargames rules of close-order longbowmen is a flight of fancy.  If we take the idea of a herse of longbows being distinctive by being spaced out, this fits and would be condusive to more ranks being able to see and shoot directly. 

As to what happened when longbowmen were charged, it probably depended on who was charging.  They were vulnerable to cavalry in the open because of the speed of attack but the slower pace of an infantry attack meant that they had a good chance of stopping it closing unless it was well shielded or armoured.  It is possible they compressed their ranks to make a more solid formation but I don't think we have specific reference to it.

[Imperial Dave]

As to what happened when longbowmen were charged, it probably depended on who was charging.  They were vulnerable to cavalry in the open because of the speed of attack but the slower pace of an infantry attack meant that they had a good chance of stopping it closing unless it was well shielded or armoured.  It is possible they compressed their ranks to make a more solid formation but I don't think we have specific reference to it.

Depends on the period we are talking about but as an early medieval archer, we were armed with sword and buckler and when we were charged and stood our ground, we styed in loose formation and didn't close up. We fought as individuals in the absence of large shields and big pointy sticks!