We know many historical sources that describe fast shooting.
But 3 of these historical sources are so detailed 
that it is possible to convert with reasonable 
certainty to time measurement:


Saracen Archery
3 arrows in 1.5 second
0.75 second per arrow

Amenhotep II
4 arrows in 2.25 seconds
0.75 second per arrow

Indian chief Hiawatha, 
10 arrows in 8 seconds
0.88 second per arrow



This is surprisingly fast, but in 2011 Lars Andersen 
proved it was possible and since a number of other archers 
have also shown it was possible.

In 2011 i proved it was actually possible to shoot 
3 arrows in 1.5 second.

Saracen Archery: an English version and exposition of a Mameluke work on archery (ca. A.D. 1368)

Here are described 3 historical tests, together they state 
what a good war archer should be able to do:
A precision test (hit the target)
A test to show that the bow is strong enough (to kill)
A test to show the archer can shoot fast enough (for use in war)

It's all together, a pretty smart test,
and easy to do for it requires only a target  and
2 sticks and a rope
Everyone at that time could easily do the test setup

Calculation:

The test says at 60 bows distance, shoot 3 arrows before you see the dust from the first arrow

There are several who have calculated and tested how long it takes an arrow to fly 60 Bows distance
The original calculation from the English translation says 1.5 second
Test  reached  corresponding time.

3 arrows in 1.5 second = 0.75 second per arrow


Possible deviations:
Some say it's 3 arrows so it's 1.5 second / 3 = 0.5 second per arrow?
But the time is from the first arrow is shot until 3 arrow is shot, so there are only 2 arrows to be reached, the first one is shot at the moment the time starts.The test does not write that the arrow flies straight to the target, the arrow could be sent in a curve up in the air, so it has longer flight time?
1:Test 2 describes the arrow flying straight.
2: An arrow from a war bow at this distance flies straight,
So there are only two options: 
straight or a very very high curve up in the air!
But if the arrow flies very high into the air, why then have a distance of 60 bows (it does not matter if the arrow is shoot directly up in the air, time is almost the same)
3: In the test it is described that you must see the dust from the first arrow,an arrow that comes upwards does not make dust when it hits, only a fast straight arrow makes dust visible at that distance.
4: If the arrow is sent high into the air then it uses 8 seconds and then there are 4 seconds for each arrow and then the purpose of the test disappears completely, because all archer can do this, there is no need to practice more.
 

In the saracen test it is described, see the dust from the first arrow. 
Only a very  fast straight arrow makes dust visible at 60 bows distance.

 

 

Amenhotep II the seventh Pharaoh of the 18th dynasty of Egypt. His reign is usually dated from 1427 to 1401 BC.

The writing of Amenhotep II, written on a stone tablet with Egyptian chariot  and the image of the 4 arrows: 

"... he came to the northern shooting range and found they had prepared for him four targets made of Asiatic copper thick as a man's palm. Twenty cubits divided between the poles. When His Majesty appeared in his Chariot like Montu with all his power, he reached for his bow and grabbed four arrows with one hand. He speeded his chariot shooting at the targets, like Montu the god. His arrow penetrated the target, cleaving it. He drew his bow again at the second target. None had ever hit a target like this, none had ever heard that a man shot an arrow a target made of copper and that it should cleave the target and fall to the ground, none but the king, strong and powerful, as Amen made him a conqueror".

Calculations:

One cubits is a known unit of a forearm and there are preserved
yardsticks about 52 cm

20 cubit is 10.4 meters

A lightweight chariot drive about 50 km / h = 50.000 meters per hour

50.000 divided by 60 x 60 gives 13.8 meters per second

 

Possible deviations:

It is assumed that you can only shoot metal plates directly,
Shots at an angle make arrows difficult to penetrate through the metal
but jump to the side instead

10.4 meters / 13.8 meters per second = 0.75 seconds per arrow


The speed of an Egyptian chariot can be slower than assumed?
We can assume that their horses were smaller than horses today so maybe the speed was only 40 Km / h

Amenhotep II was a historic Pharaoh, but also a god, so 
maybe the description is exaggerated?
It may be true, the description of shooting through thick metal plates is exaggerated, but the distance between target is possible
to perform in reality
Historical Egyptian archers must know, so if they wanted to exaggerate 
how fast Amenhotep II shot, they would have made the distance between target much much shorter so it became divine.

 

Indian chief Hiawatha, Mandan Indians

George Catlin describes in his study of the Mandan Indians
how they competed in shooting their arrows into the air in an attempt to see who can get the greatest number of arrows to fly through
the air at the same time. 
The best is said to hold 8 arrows in the air at once, before than it first reaches the ground. 
The legendary Indian chief Hiawatha was to follow the myth 
able to shoot 10 arrows.

Calculation:

Trials have shown that an imitation of a historic arrow shot from a bow
Directly upwards in the air will be in the air for about 8 seconds before landing

9/8 = 0.88 second per arrow

 

Possible deviations:
Some have discussed how long time the first arrow is in the air?
Modern bows in advanced materials and designs are very effective and shoot an arrow very far. Saxton Pope made measurements of real historical Indian bows, they were generally not nearly as effective and powerful as modern bows.

So presumably the original Indian bow will not throw the arrow 
so high in the air.
That means that the speed per arrow is likely 
to be faster than the 0.88 per arrow.

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