# How to measure projectile speed in Antiquity and Medieval times?

We currently know the formula behind projectile energy: E=(m*v^2)/2 according to which speed is more important than weight hence why gunpowder weapon was more effective vs armor. How could people measure the projectile speed in up to 10m/s increments in a time frame from Ancient Rome(transition era) to Late Medieval?

• Have a range with marked distances and count the time the project takes to hit these distances. Commented Jun 24, 2017 at 12:58
• With the praise the writers of the era gave to slingers that threw stones as large as a mina (more than a pound) I doubt they realized speed is more important. Commented Jun 24, 2017 at 13:52
• @AlbertoYagos that's because a sling can provide so much projectile speed that after a certain point a projectile mass or its' properties(ie specialized lead projectiles instead of stones) are the only thing you can increase. Commented Jun 24, 2017 at 15:07
• Did they know the constant of gravity? If they knew the constant of gravity, they could simply do the math by measuring how far the projectile fell relative to when it was shot and where it landed relative from where it was shot. No need to keep track of time, all they'd have to do is shoot parallel to the ground.
– Aify
Commented Jun 24, 2017 at 20:44
• Actually, they wouldn't even need to know the value of gravity, they'd just have to find out the height at which the projectile takes 1 second to fall to the ground when dropped. Then shoot parallel to flat ground, and measure how far it went.
– Aify
Commented Jun 24, 2017 at 20:45

The tried-and-true low-technology method of measuring the initial speed of a projectile is the ballistic pendulum. Basically, the projectile is fired into a heavy pendulum; the pendulum will raise to a height which depends on the speed of the projectile; see the Wikipedia article for details. The ballistic pendulum was invented in the 18th century by Benjamin Robins; before that one could only measure average speed by measuring the distance travelled by the projectile and the time it took to reach the target.

On the other hand, before the late 16th century (which is well into Renaissance territory) there was no particular reason to attempt to measure the initial speed of a projectile accurately. Ancient and medieval physics had purely qualitative theories of dynamics; the only parts of mechanics which had actual numerical formulas were statics and kinematics; with no quantitative theory of dynamics no particular use could be made of the knowledge that a specific projectile was shot with 266 or 276 meters / second.

• This one seems to do the trick. Although to measure the speed you need to first calculate the formula in order to do so you need to know at least two other formulas beforehand))) Apperently it would be easier if they'd just stick with the projectile energy represented by the swing the pendulum gives and mesure overall properties by this instead of draw weight and whatnot. Eventually they'll discover that projectiles of different weight produce different amount of force and that the graph is not entirely linear which in turn will lead them to the concept of speed. Commented Jun 24, 2017 at 15:10
• I'm pretty sure they'd already have the concept of speed. Edit, maybe? Commented Jun 24, 2017 at 16:56
• @NickDzink: They knew what speed was, and velocity, and acceleration. As I said, kinematics was quantitative since the antiquity. Bu what would it have helped them do if they knew the initial speed accurately? There was no quantitative concept of kinetic energy until well into the 17th century. Nobody does accurate measurements for the fun of it. Commented Jun 24, 2017 at 17:09
• @AlexP - Please read the last sentence of Nick Dzink's comment. If he meant exactly what he wrote, you should argue with him instead. Commented Jun 24, 2017 at 17:12

+1 to the Ballistic pendulum idea. Here is a method requiring less mathematical insight, and is more of a brute force method. We actually use a variant of this method in many tests of speed on computers today.

The idea is to measure a large number of events, back to back. Say I am firing arrows; I can line up 20 archers with the instruction that when I say "GO", the first archer fires an arrow; the next has drawn his bow but does not fire until he sees the first arrow land, the third waits for the second arrow to land, and so on. The entire operation of all 20 arrows being fired and landed is timed, by however they may time such things. I'd suggest ticks of something like a metronome or weight-driven clock, or the amount of time it takes a ball to roll down a spiral chute (move it to the top the moment it rolls into your hand at the bottom), or any other standard that measures a consistent amount of time; within 1% or so. Say it is measured in 'tocks'.

Next: Measure the distance of all arrows fired; and add them up. That can be done with any standard measuring stick. Divide that distance by the total tocks, and you have the average distance traveled per tock for the arrow.

The error is minor; expert archers (or slingers) will release their missiles within about 1/10th of a second after seeing the previous hit the ground. The timing is likewise going to be very consistent; even with the spiral chute, the time it takes a practiced ball catcher to move the ball will be so consistent it just becomes part of the timing and varies by less than 1/20th of a second.

This approach probably does not work for gunpowder weapons; but for things in the Roman era, trebuchets, slings, arrows, spears, etc that are too fast to count time accurately, but slow enough to watch, this aggregate measurement approach will work.