Trebuchet ranges vary quite a lot, from a bit under 100 meters to as far as 300-400 meters. "Siege crossbows" could have ranges of 500-1000 meters. Therefore, I think ~500 meters is a reasonable target. Today, Warwick Castle's trebuchet can hurl a 13 kg projectile 250 meters at 190 kph. If you were to redesign it to throw a lighter object - like a spoon - those numbers would increase dramatically.
Alexios I is thought to have had trebuchets, or similar weapons, and they were certainly used in the 13th century. Now, keep in mind a couple things:
- Alexios was an emperor and was fairly powerful.
- His empire was at war, and war means more funds diverted to . . . war.
- Alexios liked inventing new weapons.
Therefore, for a rich, war-like emperor, this is a more plausible scenario, especially if these trebuchets have military applications (and they do - they're trebuchets, after all).
Theoretical speed and range
I used this trebuchet calculator to get some results. Though I was limited by the calculator itself, I used the following parameters:
- Counterweight arm length: 10.5 ft (3.2 m)
- Projectile arm length: 10.5 ft (3.2 m)
- Counterweight mass: 98.5 lbs (44.7 kg)
- Projectile mass: 0.5 lbs (0.23 kg)
The resulting speed was 2381 ft/s (726 m/s), and the range was 176881 feet (53.9 km). I suspect the stresses here would be too much for the machine, so I toned things down to a counterweight mass of 49.5 lbs (22.5 kg). The result was a speed of 1182 ft/s (360 m/s) and a range of 43425 feet (13.2 km). This means you'd only need two trebuchets to travel the full 25 km distance . . . assuming that the spoon survived. Which I doubt it would. 1182 ft/s is a lot for a poor spoon.
There are some things this simulator ignores, however, and tweaking the parameters a bit leads to different results. I also considered a different trebuchet calculator that takes into account the mass and moment of inertia of the arm itself. Here are some of the parameters I used:
- Length of long and short arms: 10.5 ft (3.2 m)
- Mass of arm: 10 lbs (4.54 kg)
- Mass of counterweight: 98.5 lb (44.7 kg)
- Mass of projectile: .055 lb (24.9 g)
- Projectile diameter: 0.1 ft (3 cm)
This yielded a distance of 166 ft (50.6 m!) and an initial speed of 88 ft/s (26.8 m/s). Why? Well, it takes into account friction and the mass of the arm itself. Now, if we increase the projectile mass to 0.55 lbs (0.249 kg), we can get a distance of 232 ft (70.7 m).
As some people have suggested, these calculations might be a bit off because the calculators weren't designed to be used for throwing light, non-spherical objects like spoons! They should be more accurate if we use heavier projectiles - which could mean placing a spoon inside a more durable shell. The shell could also protect it a little during landing.
Regardless, we know that trebuchets can chuck things several hundred meters, and if you're willing to strap a spoon onto one of those projectiles, those ranges can be achieved.
theGarz pointed out that reloading and resetting a trebuchet can take a while. I agree that the distance (25 km) could be covered in a very short time; 1.5 to 2 hours is reasonable for a good runner. For the trebuchet to be an efficient mode of communication, you would need to have the turnaround time be very quick, and you'd need the accuracy to be good. Hunting in the woods for a projectile that's gone astray isn't easy. Looking for a spoon in a forest is probably worse than looking for a needle in a haystack.
It's debatable as to how much of an improvement a horse would be over 25 km; 30-50 km in a day might be a reasonable estimate for a horse's stamina unless it specifically trains for this sort of messenger work. Nonetheless, a sort of Pony Express might also be a good option - and more efficient that a trebuchet unless the trebuchet's turnaround time is short.