What matters in a military context is taking a soldier out of the battle. If your arrow doesn't prevent him from fighting then it has failed.

As Dan suggested, refer to Prof Anna Crowley's appendix in 'Warbow' by Strickland & Hardy.

Nice experimental research with some mathematical modelling, albeit a small study, but concisely presented.

In a nut shell:
Heavier arrow = slower velocity at release, shorter range, more kinetic energy delivered to the target on impact.

By heavy I mean a reproduction Mary Rose arrow.
By shorter range I mean an ample 240 yards shot from a 150lb yew longbow.

The Mary Rose arrows are all heavy by any modern standards, developed through experience and knowledge of the craft. Also they are pretty standardised 'issue' arrows in short or long draw lengths, not variations of weight, spine or any other variable we might seek to address in modern archery with weaker bows.

I suspect the only important decision the archer faced was which head to draw at armoured or unarmoured targets at a given range.

History records they decided correctly.

Sorry, I probably got ahead of myself. I was suggesting the evidence presented in the appendix of 'The Great Warbow' by Strickland & Hardy helped to answer the question "Which arrow best against armour, heavy or light, etc" = Heavy.

In said appendix the suggestion is heavier arrows are slower, shorter ranged but pack a bigger punch. And by heavy I meant relative to more modern target, flight, clout arrows, my apologies. I see though that 2 of the five arrows tested were not far off the range of the Mary Rose arrows at 54 & 58g.

In 'Longbow' Robert Hardy proposed heavy arrows in the 58-73g range for armour piercing and lighter 33-42g arrows for long range work. Despite this, I do not believe we have evidence to suggest there were two different types of arrows used in this way but I will be corrected if anyone has any publication of a study of the Mary Rose arrow shafts that suggest this.

As far as I know, there are no other English examples of Medieval arrows bar the Mary Rose arrows, these from a specific context (i.e. Tudor, pinnacle of Warbow use, etc). Sadly the Westminster Abbey arrow at c.42g in its well seasoned state and without fletchings and binding remains undated: The only other pieces I have seen or know about are in too poor a condition to be useful.

And anyway, 100J quite a bit: Will need to dig around about for those out dated figures from the 50's or 60's about energy required to penetrate armour, which failed to take into account padding and the human body. They might cause a stir.

(P.S. Edited because I had to leave in a hurry before completing this first time round)

Benjamin you have me there, I don't know much about the English warbow but I know even less about Eastern archery.

And re-reading about Gancsay's and John Waller's tests against original armour and 2mm iron plate respectively with lighter than medieval longbows and arrows with case hardened heads, etc, I think I'll not risk re-reporting their findings.

And I must get a copy of Weapons of Warre.

Those arrow estimates from "weapons of warre" sound too light to me. Did they actually make reconstructions of the same dimensions and fit them with period correct arrow heads, or just go by the weight of the surviving shafts?
I seem to recall a thread on another forum where they came to the conclusion that reconstructed arrows would have been heavier than that.
The English warbow society also gives a minimum weight of 980 grains (63.5 g) for Mary Rose livery arrows despite listing poplar as a common shaft material.
http://www.theenglishwarbowsociety.com/tudor-livery-arrow_EN.html

If I recall correctly they measure them, calculate the volume, and then estimate the total arrow mass based on that plus the mass of bindings, fetching, and arrowheads. At least one author suggest the arrows may have swollen because of the water and thus the originals would weighed less than the estimates indicate. Interpretations indeed vary; Hardy considers the Mary Rose arrows thoroughly deteriorated. The English Warbow Society minimum of 63.5g strikes me as more functional than Weapons of Warre's 35-50g, but that doesn't make it necessarily correct. After all, Ascham wrote that poplar arrows were inferior but used anyway.

"With light arrows and especially light poplar arrows, English bows are woefully inferior to the composite designs favored from Turkey to Korea. While it's possible English bows were simply that bad, this makes European assessments of their archery compared with Turkish archery sheer chauvinism. . De la Broquière wrote that European arrows were stronger and European archers shot farther. "

There is more to it then that, the effective range of a bow is not just the maximum distance you can hurl an arrow. Turkish composite bows and horsebows in general are a lot lot shorter axle to axle, which makes them much less susceptible to being torqued at time of fire, less forgiving and hence less accurate. I have a horsebow and it is a complete bitch to shoot compared to my longbow. Maybe that is jsut me, but it seems to be a common opinion in the Western traditioanl archery community

Also someone who trains to shoot from horseback is probably going to spend less time practicing extreme long range shooting as that requires a high degree of stillness, even minor motions of the horse would wreck the shot

I do not know about Korean bows, though from what I have seen of modern Japenese Kyūdō it has become so stylized as to not say much about real wartime capabilities

I've also always wondered if the Mary Rose arrows weren't light because they were intended to have some kind of combustible tip, is there evidence for flaming arrows in that time period?

Here is some information on reconstructing a historically accurate, typical Mary Rose arrow.
http://warbowwales.com/#/warbow-arrows/4557916533
The weight came to 1011 grains (65.5 g) using a poplar shaft and a Tudor style arrowhead, so still quite heavy, and more along the lines of what you would expect. (A good reconstruction is obviously better than calculations.)

Joinville's horse was wounded fifteen times and continued to fight. What would have happened to the English at Crecy if they used the same arrows?

This is veering a little off the original topic, but I wanted to share.

I think I've finally figured out why the English longbow armies were so effective. The red herring here is the longbow itself. People keep wanting to see something magical there and it just isn't. It's because of tactical innovation.

The clue that tipped me off is the comment (forget all the details of who said it and when) about how 100 archers are useless but if you have 1000 then you've got something. Naively, I was thinking wouldn't 100 archers be about 10% as powerful as 1000? Actually, no. Let me explain.

The thing that a bow can do that makes it unique is that it can direct it's power over range. Captain Obvious, I know. There's this concept in military science of "mass" - meaning you need to concentrate your power to have an effect. This is why heavy infantry fights in close order. Bows can do this even better.

Let's say for the sake of argument that a longbowman can put all of his arrows in a 35m circle at 200m. That's about 1000 square meters. 100 archers firing at that target will put 1 arrow per 10 square meters per volley. Now, 1000 archers will put 1 arrow per square meter per volley. That means ~50% of the people in the formation will get hit with a least one arrow, some more, per volley. Over a period of three minutes a soldier in the target area could expect to get hit 5-10 times. Even if the arrows only caused a casualty on 5% of the hits the soldiers in that target area would be decimated. 5000 archers is even scarier. That's mass.

If that fire was directed into the center of a block of foot soldiers it can pin down the whole unit. Of course the wings could continue to advance, but could be defeated piecemeal by the opposing soldiers. It just destroys the integrity of the unit. Or you can shoot a hole in a schiltron and let your cavalry carve it up.

Of course this doesn't mean the longbow was some kind of super weapon. The English got a lot of help from the French who rode or marched right into their kill zone.

Anyway, the advantage of the longbow was that it was deployed en masse and when there are enough of them it changes the whole tactical effect - the sum is greater than the parts in this case.

Guy,

There were several chests found on the Mary Rose full of incendiary arrows - combustible material inside a package with a fuse. Even better than a run-of-the-mill flaming arrow.

Matt