the constant problem with longbows is the manny times mentioned time and energy it takes to train a good longbowmen, as oposed to crosbowmen or musketeer
but i dont understand why concentrate on longbows, longbows were the equivalent of high calibre rifles, desined to take out heawily armoured horsemen, send arrows trough plates of steal at ower a hundred meters, using them on unarmoured napoleonic era troops would be like shooting rabbits with 12.4 calibre machinegun
there are bows, short bows, composite bows, surely the combined carpenters, metalurgists and chemists of the 1800eds could develop a cheap and effective composite bow, that, while lacking the force of the longbow, could still penetrate cloth and flesh
ewen with a range equal to the contemporary musket it could compete simply by superior volume of fire, not to mention arrows could be treated chemically to increase effect, or wrapped in cloth and oil and set on fire, or ewen have small explosive devices atached
another plus is they could shoot arrows in arc, so they could hit behind obstacles or ower friendly formations
this could be a specialised unit, trained in concentrated fire, they wouldnt even have to be specially trained in acuracy, it would be enough they send all the arrows in the same 10 meters square area
they could be affective as support for standard units
and to train someone to use a composite bow cannot take more than a couple of months, drilling people to move in formations and discipline would probbably take more time
still it seems more practical to equip a smaller unit of specially trained troops with composite bows and poison arrows to use on night raids in hit and run tactics, to take out the enemy officers and ruin moral
but it wouldnt be so strange to actually find a record of such or similar units existing, or bows being generaly used in these times, crossbows were used, as well as slings, and special units existed armed with airguns