Missile Accuracy: A Mystery

[Miracle]

Thanks for the detailed response.

The EDU's range setting is most likely the first case in that it restricts the range at which a unit can begin their firing animation. I've seen Naffatun throw at angles higher than 13 degrees, but only when their target is moving away from them and the Naffatun had already begun their throwing animation. In this situation their range is bounded only by the game physics; if a heavy cavalry unit traveling away at a speed of 7 m/s were targeted at exactly 40 m away by a Naffatun unit, the Naffatun could theoretically reach their maximum physical range of ~90 m if their firing animation took about 3 seconds:

firing_animation_time = 50/(415/60) - 90/30/sin(45) = 3

That means crossbowmen, who by default have a low firing angle and a long reload time, could reach artillery-like ranges if they targeted a routing fast mover.

The result is that no matter how it is implemented, height-advantaged units gain no extra range because the physics advantage is simply cut off by the EDU's lower range requirement.

I'm fairly sure the game modifies it in real-time based on some formula that involves Δy (height above datum plane). It would probably look like this:

Range = DefaultRange + (1/g)*(v*cos(θ)*sqrt((v*sin(θ))^2 + 2*g*Δy) - 0.5*sin(2*θ)*v^2)

Where θ = default firing angle at max range on flat ground against stationary target

This is assuming the soldier is firing upright.

Since soldiers on a hill will fire at a clearly positive angle when a unit reaches its range, I do not believe the EDU range is a hard-set limit. Otherwise, they would have to fire at a lower angle as you suggested.

If the game portrayed physics as well as you say, then "slope-hugging" missile units like artillery and missile cavalry could theoretically reach very long ranges. They would have to be just before the crest of a hill such that they are facing up at an angle equal to 45 - θ. The height advantage of the hill combined with a starting firing angle of 45 degrees to the horizontal should increase their range dramatically beyond the default EDU value. When you consider that the projectile comes down at an angle near or close to the vertical slope angle of the hill, this becomes a very good battlefield tactic.

[Foz]

So then the question is how do we determine if that is what is really happening? There's no good way to measure anything on the battlefield that I can think of, so we'd have to devise some way to make any difference induced by moving a unit onto a hill easily observable.

One possibility I've thought of is to examine the apparent range of the unit without firing it at anything. When a missile unit is selected, the game generally tells you whether the mouse is hovering inside its allowable range or not (IIRC green indicates in range, red out of range). Note this isn't just when attacking - even when the cursor is giving a movement icon, it changes color to indicate in and out of range. So, using a sufficiently elevated terrain feature, it should be possible to simply eyeball the effect. If height is allowing additional range in any way, such an elevated position should affect it dramatically enough to be noticed.

[zerathule]

You could use the "Fortress" skirmish map : there is a nice "cliff" from where you can shoot.

[Miracle]

Ok I've thought of a way to precisely measure any range increases due to height:

1. Deploy a missile unit diagonally away from a target on Grassy Field. Try to keep the missile unit facing its target when the battle begins.
2. Keep your cursor over the target
3. When the cursor turns green (and the firing icon appears on your missile unit), pause the game
4. Zoom your mini-map to the closest zoom level and make sure both units appear on it
5. Take a screenshot
6. Go to Paint and paste the screenshot
7. Crop the image using rectangle select and Ctrl-x/n/v, making sure to have one corner on your missile unit in the mini-map and the opposite corner on its target
8. Save the picture and open its properties
9. Use this formula to compute pixel range:
   pixel range = sqrt(imagewidth^2 + imageheight^2)
10. Repeat above steps except give your missile unit a height advantage on a different map

Here were my pixel range results using Scots Guards vs. Imperial DFK's on Grassy Plain and then on Saharan Sands (Southwest hill):

Grassy Plain: 110 pixels
Saharan Sands SW hill: 125 pixels

Note that I did not deploy the Guards on the very top of the hill.

So this provides a pretty convincing proof that height does increase horizontal range.

If we were to also assume that my physics assumptions were correct, then theoretically one could calculate the approx. height advantage in meters given initial projectile velocity and EDU range.

I also recently tested my behind-the-hill theory. It doesn't work with low-θ artillery and missile cavalry; they seem to need a clear line-of-sight. It seems to work with high-θ cavalry but gameplay-wise it's not a good idea to deploy them in this way.

[Rhedd]

Frankly, I'm stunned that there's any question about this.

Try this: Start a battle on the Carpathia map. Set up one unit of peasant archers on top of that HUGE hill just to your rear.

Give the AI one unit of peasant archers, as well.

I just did this, and I got off SEVEN full volleys while the enemy was moving (at a dead run) to a range that they could fire at. Seven.

That doesn't give any actual numbers, of course, but it shows there's no question at all that height increases range.

Try trebuchets or cannons on the same position on the same map. It's awe inspiring to watch them shoot so far.

On the subject of where the shot is calculated from, height-wise, it is assuredly calculated from the height of a soldier's firing arm. This is shown by the notes in descr_projectile.txt that explain that rocket launchers have to have limits to their spread, so that a rocket doesn't land at the feet of the crew and kill them all, while elephant rockets don't have the same problem, due to being fired from higher off the ground.

[Eng]

I believe that velocity and angle have an effect on accuracy that is why arrows cant be 100% accurate but rockets and musket shots can.
and there is no limit of range to any weapon.

[Didz]

This was all covered in detail in the tutorial for STW, height gives benefits to range and morale. Just as marching up hill increases fatigue along with rain, snow and desert.

[Foz]

Frankly, I'm stunned that there's any question about this.

Try this: Start a battle on the Carpathia map. Set up one unit of peasant archers on top of that HUGE hill just to your rear.

Give the AI one unit of peasant archers, as well.

I just did this, and I got off SEVEN full volleys while the enemy was moving (at a dead run) to a range that they could fire at. Seven.

That doesn't give any actual numbers, of course, but it shows there's no question at all that height increases range.

Try trebuchets or cannons on the same position on the same map. It's awe inspiring to watch them shoot so far.

On the subject of where the shot is calculated from, height-wise, it is assuredly calculated from the height of a soldier's firing arm. This is shown by the notes in descr_projectile.txt that explain that rocket launchers have to have limits to their spread, so that a rocket doesn't land at the feet of the crew and kill them all, while elephant rockets don't have the same problem, due to being fired from higher off the ground.

Actually, this doesn't demonstrate that the unit is allowed to fire from any further away at all, it only demonstrates that the unit climbing the hill can't fire from the same distance the one above it can, which we can easily determine through physics anyway. What you noted happens whether or not the EDU's range numbers come into play at all, and can be a direct result of the descr_projectile.txt specs for each projectile, so you can't use these results to say anything about the effect of the EDU's range numbers. OTOH what we're trying to prove is whether or not the unit is allowed to actually fire on a target further away when it is elevated above the target than it can when on the same level as the target. As you can see it is a more difficult question than the one you answered.

Miracle's test above, however, seems to have some merit to it. Really makes me wonder how the game is determining whether or not a unit can fire on another when height differences are involved.

[John_Longarrow]

Just to add to the issue, I'm playing a game as Milan right now. As such I've got LOTS of crossbows and I use them in preference to normal infantry. As such, I get to spend a lot more time keeping an eye on when targets get in range than I would otherwise. Because of that, I've noticed that my crossbows will normally start firing if on autofire BEFORE I get the green bow icon if the crossbowmen are on top of a hill. As such the conclusion I've come to is height does increase your missiles range and your archers/crossbowmen can figure this out. Its only the user interface that has a problem with this.

[Rhedd]

Actually, this doesn't demonstrate that the unit is allowed to fire from any further away at all, it only demonstrates that the unit climbing the hill can't fire from the same distance the one above it can, which we can easily determine through physics anyway. What you noted happens whether or not the EDU's range numbers come into play at all, and can be a direct result of the descr_projectile.txt specs for each projectile, so you can't use these results to say anything about the effect of the EDU's range numbers. OTOH what we're trying to prove is whether or not the unit is allowed to actually fire on a target further away when it is elevated above the target than it can when on the same level as the target. As you can see it is a more difficult question than the one you answered.

Miracle's test above, however, seems to have some merit to it. Really makes me wonder how the game is determining whether or not a unit can fire on another when height differences are involved.

Okay, okay. This is starting to make me roll my eyes, but let's add another demonstration to the one I stated above...

One unit of peasant archers (the same used before) vs one unit of any infantry with a "standard" movement rate, on Grassy Plane.

Opening fire at maximum range on flat ground, the archers get a total of five volleys before the enemy makes melee contact. Five.

So, on flat ground the peasant archer's range is sufficient to get FIVE full volleys before a target (who didn't even bother to run for three volleys) moves into MELEE range.

The same unit on high ground gets SEVEN volleys before an enemy moves into BOW range.

Empirical evidence FTW!