Projectile Velocity vs. Range Table

[Red Harvest]

The projectile velocity determines the maximum possible range of a unit firing at a target. It is also determines how flat or curved the trajectory is for a given range. This is not the same as the range found in the units file. In all cases, the theoretical range is greater than the range allowed for targeting. However, when a unit is moving away it can still be hit beyond the "targeting range." For various reasons, some of you might want to modify velocities to reduce this excess range (which can be quite substantial.)

The RTW projectile calcs seem to adhere to the basic vacuum trajectory model from physics. With that in mind, for same elevation missile unit to target, the following velocities can produce the following maximum ranges at a 45 degree firing angle. I have marked ones currently used by the program in bold for comparison.

Velocity____Max Range
(m/s)______(m)

15_________23
20_________41
25_________64 Used for Pila range of 35, heads range 40
30_________92 Used for Javelins with range of 50
35________125
40________163
45________207
48________235 Used for Arrows with range of 120 or 170
50________255
55________309
60________367 Used for Slingers with range of 80 stone or 120 bullets, plus ballista, onagers
65________431
70________500
80________653
90________827 Scorpions with range of 250

Note: flaming ammo gets the same velocity as non-flaming at the moment (very questionable in the case of arrows.)

[Benny Moore]

This is very interesting! So there is a realistic physics simulation behind this, and it's only the targeting range that's screwed up? Or am I not getting this?

[CBR]

So max range is about velocity^2/10


Qvintvs: Range is not really screwed up. That some missile weapons has higher velocity, then they need, is just to make some trajectories more flat than others. It was the same in STW/MTW really.


CBR

[Puzz3D]

Archers in STW/MTW used a trajectory much closer to 45 degrees at their open fire range than they do in RTW. The argument put forth by LongJohn for this high trajectory at something much less than the realistic maximum range was that it helped simulate a larger scale battle. I believe that movement speed, fatigue rate, range, reload rate and combat speed should all be selected according to a consistent scale which allows the battles to play out in a somewhat realistic fashion. This was done more rigorously in STW/MTW than in RTW. You can see the lack of consistent time scale in RTW when units move rapidly to engage in combat and then go into a kind of slow motion when the individual men are fighing.

[Benny Moore]

What I mean by screwed up is the sort of thing he just described. Most units have far too little range, and the proportions are all screwed up as well. Ballistas should fire the farthest, then scorpions, and then onagers and archers should just about tie. Slingers should be fairly close to the archers.

[CBR]

Well yes RTW generally is screwed up But I think the higher velocity is needed when units can move so fast as they do and that would mean trajectory is more flat than STW/MTW


CBR

[Red Harvest]

Yes, I would not describe it as screwed up, either. There is some excess range because of the velocity, resulting in a flatter trajectory. For example CA wanted a flat trajectory for slingers, so they gave them a velocity that achieved this. It does seem to have some important consequences for pila and javelins that are worth "tightening up" a bit if you don't want to see them shooting much farther than their nominal range at withdrawing troops. And as I said, it gives you a way to limit flaming arrows without eliminating them altogether.

Another part of this is that "effective range" would be less than "maximum range." It is a judgement call as to where the line should be drawn. I'm sure graphics (aesthetics) and movement speeds factored in as well. I have created new projectile names for shorter range arrows and such and given them lower velocities proportional to the longer range arrows.

I have confirmed some of the shorter ranges to within a few meters in the game, so I think what I have posted is accurate. If you find something is way out of line, please post it here so that any erroneous info can be purged/corrected.

CBR, yes, you have it. The simplified "ideal case/vacuum" range equation is:

Range (meters) = velocity squared * sin (2 * firing angle) / gravity

Where: velocity is in meters/sec, gravity is 9.80 m/sec^2

[Puzz3D]

The vacuum physics is a problem because projectiles don't loose energy, and thus have the same lethality at maxumum range as they do a 0 meters. Since you don't have realistic ballistics, a compromise has to be made between close range effectiveness and long range effectiveness with the result that projectiles are too effective at long range and not effective enough at short range. This makes it very difficult to balance ranged weapons in Total War games.

I think CBR is refering to the fact that archers don't lead their targets, so they wouldn't be able to hit fast moving targets if the arrow didn't have high velocity.

The physics model for projectiles sounds great when you first think about it, but I wonder if a look up table with various factors determining kills per volley wouldn't have worked better.

[Red Harvest]

The simplification for vacuum trajectory is OK, because I see nothing to indicate that the RTW velocity is used to calculate hitting power anyway (strike angle, projectile mass/aerodynamic cross section/or ballistic coefficient, and some sort of penetrating index for the round would be needed.) What is more likely needed is a more generic loss of efficacy with increasing range. There are a lot of factors besides just drag that are going to reduce the arrow's killing potential at range: less perpendicular striking angle (very important for armour), wobbly flight, even the most modest breeze, targeting errors, individual archer skill, moving targets, target having more time to take defensive measures (a big factor this last one.) As range increases, accuracy should fall several fold.

Range effects could be done as you say with look up tables. For example: take the base missile attack or chance of a "hit" or lethality and attenuate for range so that it is one fourth as effective at 85-100% of effective range, half as effective at 70-85%, three fourths at 50-70%. (These are just placeholders.)

Archers/etc. seem to lead their targets somewhat, because it is very hard to make them miss by moving, and long range shots are nearly as accurate as short range when targets are walking toward them.

As an aside: Kern's book, Ancient Siege Warfare suggests that the Assyrian besiegers took archery effective range to be quite short, 60 meters or even less. Granted this was in the ~800 BC time frame, and these were less developed compound bows than later Scythian/Parthian weapons. However, people shooting down from a wall 10 to 20 meters tall have some advantages. The Assyrians seem to have used scale armour and mobile shields extensively to protect their assault teams, so the short range might be a reflection of effective countermeasures

[Marcus Maxentius]

Sorry, I failed Physics in high school, but are the distances listed in the RTW folder and on stratcommander.com the max ranges or effective ranges?

[Red Harvest]

Sorry, I failed Physics in high school, but are the distances listed in the RTW folder and on stratcommander.com the max ranges or effective ranges?

It is their max targeting range--a quasi-effective range. They seem to be able to shoot farther at enemies who enter the targeting range and pull away. This excess distance is limited by the max range that the projectile can achieve with the given velocity (the "max range" in the table, the one calculated from physics.) So once a target is acquired the unit starts its firing sequence and seems to be still be able to hit targets that have since left the range listed for the unit in the stats file, but only by so much. And it usually can only fire one volley this way, since the targeting won't be allowed if they remain out of range after that volley.