The historic skill of competitive distance shooting still lives on today -wherever there is room to safely practice! While some archers today have special bows made for this pursuit, many are just happy to see how far they can get their bows to shoot. A flight longbow can achieve over 300yards with the right arrow -specialised composite bows can achieve twice that distance -but these bows are of the heavier draw weights.
Special competitions have been devised specifically for the 'English' longow in the UK, using a variety of arrows with different specifications: see the 'Types of arrow' link. Turkish archers were famous for the distances they could achieve with their heavy draw weight bows.
English longbowmen were encouraged to shoot as far as possible with valuable prizes on offer:
"...and every person that shoteth at one shot XXiiii score yards of ground or above shall have for that one shot a shaft of silver of the value of XXd or XXd in money. And he that shoteth at one shot XXii of ground and above and under XXiiiiscore shall for that shot Xiid in money. And he that shoteth at one shot XX score yards of ground and above and under XXii score shall have for his one shot vIII in money..."
(Standard arrow meeting, Finsbury Field 1521)
XXiiii score = 480 yards. Even allowing for the possibility of yards being a little shorter than nowadays, this distance must have been considered (almost) achievable! A ploughman would earn around 2d to 3d for a long hard day, so a prize of ten times this wasn't a bad incentive.
Society for the Promotion of Traditional Archery