All Unions start with a walking speed of 2 m/s. Every union starts at a distance of 21,600 m from the gate meaning it will take 3 hours to reach the gate if you remain at 100% HP the whole time. Once a union reaches 30% HP they cannot be slowed down any further. The minimum walking speed is 0.6 m/s.
Let’s look at how this works:
Damaging a union by 1% HP reduces their walking speed by 0.02 meters per second. When you start war this is very effective. If you drop a union 1% HP before they even travel the first meter you would add 1 minute and 49 seconds to their walking time. However as you get closer to the gate the more damage is needed to reduce their time.
For example a troop is 10,800 meters from the gate (halfway there) and has 80% health. They are walking at 1.6 m/s so it will take them 1 hour 52 minutes and 30 seconds to reach the gate. However another union attacks them and they lose 1% HP. Presuming they get attacked right at 10,800 meters their speed would then change to 1.58 m/s and it would now take 1 hour 53 minutes and 55 seconds to reach the gate. That 1% dropped them 1 minute and 25 seconds now instead of 1 minute and 49 seconds.
Keep in mind 1% is a lot of damage to do to a union instantly at any given point. Also the union’s troops continue to walk as you attack. The full animation sequence takes about 3 seconds to complete. Using the stats above dropping a union by 0.1% (much more likely to happen if you were the only one to attack right then) adds only 8 seconds to their travel time. 0.05% only adds 4 seconds. (Times based on scenario above with 10,800 distance and 80% HP). With that little change it is very easy to think your attack did not change their time since 3 of the 4 seconds added are traveled while you are watching viziers fly around.
So how do I know if my attack worked or not?
On the left side of the battle window there is a little arrow with a pull out tab of information. This tab has a breakdown of which unions troops are heading to which gate, their current HP, remaining travel time, remaining distance, and current walking speed (if it applies).
Before launching attack take a screenshot or make a note of the travel speed. Launch your attack and then compare the current speed after the attack with the current speed from before the attack.