[UltraTech] Rockets/Missiles

[DemiBenson]

While trying to reverse-engineer the UT rockets (pages 144-146) to build some mini-missiles, I ran into some discrepancies - some in prices, some in performance.

To start with, I made a table of warhead cost and weight for the standard sizes (15, 25, 40, 64, 100 mm). The three in the middle are already statted out in grenades, but the 15mm and 100mm are not. But looking for a relationship between the spherical volume of the warhead and the weight, the numbers fit very closely to

Warhead weight in pounds = Volume in mm^3 / 125,000

but rounded to nice values.

So I applied that to the 15mm and 100mm warheads and get

	Size	Weight
Micro	15	0.014
Thimble	25	0.06
Mini	40	0.25
Hand	64	1
Satchel	100	4

The 100mm satchel charge lines up nicely with cost of the TML warhead being 4 times that of the IML, confirming that it weighs 4 times as much.


Missile Costs
But, you'll notice that the actual cost of the 64mm missile warhead and 64mm grenade are off by a factor of 4. Odd, since it makes a mininuke missile cheaper than a mininuke grenade or mortar round even though the former includes a long-range delivery system. I'll assume that the warhead costs listed on page 145 are solid slugs which are extra cheap, and for real warheads the cost should match that of grenades - $40/pound.

The next cost discrepancy is in rocket costs - gyrocs appear to be $50/pound (the warhead is a negligible $0.50), the TML rocket is roughly $20/pound of motor weight, and the IML is $100/pound of motor weight. I can understand gyrocs being expensive because they're cutting-edge miniaturization. I find it odd that the hypersonic TML is much cheaper than the slightly-supersonic IML.

Missile Performance
Thankfully we have stats for gyrocs, and we can quickly determine that the payload ratio of a gyroc is almost exactly the same as that of the TML (gyroc: 0.14; TML: 0.16). Apparently the TL9 weapon designers have a standardized multi-purpose payload delivery rocket that they just scale up or down. If both the top-end and bottom-end missiles have the same payload ratio, it's reasonable that all the ones in the middle do too.

However, the IML's payload ratio is an astonishing 0.5 (1 pound warhead with a 1 pound engine). For a supersonic missile with an 8 second endurance... I'll be kind and merely say "This stretches belief".
Since we're on the topic, the gyroc's stated speed and range (1900 yps and 1900 yards) works out to hypersonic velocities, which again stretches belief for such a small missile.

Fixing Gyrocs
In order to make gyrocs less ridiculous, I went back to the source material - the Gyrojet weapons of the 1960s. Despite notoriously poor production quality, gyrojet rockets could attain 380 m/s (415 yps, transonic speed) at burnout, which occurred 20 m distance from the barrel. Working out all those numbers, that gives us ~360 g acceleration for 0.1 seconds. If we assume TL9 is standardized to be roughly subsonic (400 yps, and assume shape is designed to reduce sonic boom), and run the numbers through the 3rd edition Vehicles missile formula, it comes out to an endurance of 0.11 seconds! Clearly, TL9 gyrocs are a stable, useful version of the TL7 gyrojet.

This still doesn't explain the egregious range of gyrocs, though. The wikipedia gyrojet article claims the flare version could be shot 500m straight up, and since burnout was within 20m, and speed at burnout was ~380 m/s, obviously the rest of the distance was ballistic (and took more than 1 second to get there). Missile performance should probably incorporate glide-after-burnout in the stats.

Standardizing Missiles
Before we can figure out the rest of the hypothetical missiles, we need to figure out what to do with the 64mm IML. There are quite a few things wrong with the stats as-is: payload ratio is far off from the expected range; engine cost/pound doesn't seem to line up with any of the others; the launcher is bizarrely heavy (twice the weight of the rocket, when even a modern M72 LAW has a 66mm 4 pound missile in a 1.1 or 1.5 pound launcher); and even assuming a glide-phase, the IML's endurance is too high (8 seconds vs the 5 seconds for a faster, heavier TML that would naturally have a longer glide).

To fix this, I set three parameters:

1. Payload ratio for all missiles is roughly 0.15.
2. Most mini-missiles will be subsonic or low transonic; anti-vehicle missiles will be supersonic.
3. Max range assumes a glide-phase.

And all the stats just fall into place:

		Warhead	Total	Engine	Payload
	Size	Wt	Wt	Wt	Ratio	Speed	Max	Endurance
Micro	15	0.014	0.1	0.086	0.1400	400	65	0.11
Finger	25	0.06	0.4	0.34	0.1500	400	250	0.43
Mini	40	0.25	1.6	1.35	0.1563	400	1000	1.71
IML	64	1	6.5	5.5	0.1538	500	4000	5.52
TML	100	4	25	21	0.1600	2000	10000	2.94

Since the payload ratio is roughly the same everywhere, the WPS ("Total Wt" above) also follows that nice, easy-to-game 4x progression as the warhead weights do. Launchers will follow a similar pattern.

For max range, I calculated a straight-up "powered interval" and added a glide-phase factor based on size/caliber to account for smaller rockets having proportionally more drag. It's actually too late at night to come up with a really good formula for the length of the glide-phase, consider these numbers as place-holders. When you compare these rockets to the conventional guns statted on pages 137-138, the rockets look terrible despite having higher peak speeds and higher down-range weight even after engine burnout. On top of that, even unguided rockets could have active aerodynamics to keep a flatter trajectory. I suspect Mr Pulver has a better formula for projectile drag than I have.

In this system, gyrocs get screwed... but with stats similar to the real-world gyrojet, it unsurprisingly has a range similar to the real-world one, too.
The IML ends up weighing a lot more (and will cost more), but that's to be expected for a supersonic missile capable of shooting down fighter aircraft.
Speaking of costs, what should the cost structure be? To keep it in line with grenades and the TML, rockets should cost $20/pound for the engines (halved at TL10+), and $40/pound for the warheads.

What good are mini-missiles? For the most part, militaries will stick to their guns, but rockets will have some specialist uses: Smaller ones are subsonic, so may be difficult for the target to even notice he's under attack (a US officer in Vietnam shot off his gyrojet in the middle of a military base, and no one noticed). All the launchers are cheap and light-weight, suitable for putting in a shoulder servo mount or as concealed single-shot weapons.