Writing by: Professor of Ballistics Jeffry Friedman at the Royal Gunnery School In conjunction Master Engineer Afried vonMarian at the College of Engineers

CHAPTER 1: War Machines Of The Empire
The War Machine of the empire are wide in varied and in tactical uses on the battlefield. The Empire and especially Royal Artillery School does not typically support generals employing the use of stone thrower or bolt thrower in their armies as such machines are archaic. The Empire has pass into the age of black powder and has made full use of that in their war machines.

This tactical document will cover all 4 of the empires main war machines, those being The Great Cannon, Mortar, Helstorm Rocket Battery, and the Helblaster. And introduce you to their tactical uses, as well as inform you of the best way to get the most out of your war machine.

As a warning to all those readers who have a firm stand against “math-hammer” or “theory-hammer” this document contains both, but does so to give concrete evidence to support the writers theories (It will not be Helblaster can kill X of these, Y of These, etc.)

CHAPTER 2A: An Overview Of The Great Cannon
The great cannon could be possibly one of the simplest yet destructive black powder device ever devised in the history of the old world. There is little that can take the impact of a great cannon and live to tell about it. This combined with its exceptional range makes it ideal for hunting large monsters, war machines, heavy cavalry, lone enemy models or even ranked heavy armored troops.

CHAPTER 2B: Fundamental Physics Of A Bouncing Cannon-Ball

After the possibility of a misfire, there are exactly 30 different paths that a bouncing cannon-ball may take. That is a cannon-ball may carry 2″, 4″, 6″, 8″ or 10″ past the initial guess range, then the cannon-ball may stick in the ground, or bounce 2″, 4″, 6″, 8″ or 10″. (5 initial possibilities x 6 secondary possibilities each = 30)

The possibility of a misfire is 1 in 6 or 16.66%. That leaves 83.33% for the 30 paths, thus each there is a 2.777777% chance that the cannonball will travel on any given path. (83.33 / 30 = 2.77)

So the way to maximize your chance to hit a unit is to maximize the number of paths that carry the cannon-ball into/thru the unit.

The above diagram shows all the possible paths the cannon-ball take. The green dot represents the initial guess range. The blue dots are the points after the first artillery dice is rolled. The red dots are the points after the second artillery dice (or bounce) is rolled. (Note: it is possible for a cannon-ball to land on a blue dot then bounce to a blue dot. The red dots just show the extend to which a cannon-ball CAN bounce)

CHAPTER 2C: Great Cannon Tactica
Now it is obvious to the common man that a great cannon crew should aim just short of their intended target. But what is not obvious is how short. You should always guess 10″ in front of the back of your target; this will always maximize the number of paths going thru the unit.

For a 50mm deep unit a perfect guess of 10″ in front of the back would net in a 41.66% chance of a hit. For a 100mm deep unit a perfect guess of 10″ in front of the back would net 52.77 % chance of hitting the unit.

The great cannon is an awesome weapon, but cannon be of much use if it cannon hit its intended target, as such it is suggested by many commanders to take them in a pair and place one on ether side of the battlefield to eliminate things they can not hit.

CHAPTER 3A: An Overview Of The Mortar
The second mainstay war machine of the empire is the mortar. Only slightly trailing the great-cannon in number of battles participated in. For thousands of years the great cannon/mortar combo has slain countless enemies of the empire.

As written in the previous chapter the great cannon excels at shooting larger targets such as war machines, chariots and monsters. Where the great cannon is less useful is where the mortar picks up, and that is shooting at large blocks of lightly armored infantry. But because the mortar is launched high into the air it is more lightly to effected by wind, weather and other conditions then a cannon ball is. As such it is best used against the center of a lightly armored battle line, where it can lay waist no matter what direction the winds take it.

CHAPTER 3B: Fundamental Physics Of A Drifting Mortar
First imagine that you have 2 targets sitting on the table top. The two targets are circular with 1″ diameter and are sitting 12″ apart. In the diagram above they are shown as the red dots. A mortar shot lands between them with the center 2″ from one and 10″ from the other. The center of the template is the green dot.

Scenario #1
The artillery dice roll is 10″, you now have a chance to hit target “A”. You must also scatter within the 23 degree blue arc to get a fully covered hit. The chance of scattering within that 23 degrees is 6.38% (23/360*100)

Scenario #2
The artillery dice roll is 2″, you now have a chance to get a hit on target “B” and now just need to scatter within the 120 degree red arc to get a fully covered hit. The chance of scattering within that 120 degrees is 33.33% (120/360*100)

As you can see, even though the targets were the same size, and you scattered the correct distance in each scenario, you are still 5 times more likely to get a full hit on target “B” then “A”. The mortar is a most fickle device because a long roll on the scatter or a short/long guess greatly reduces your chances to hit.

CHAPTER 3C: Mortar Tatica
If it is a calm day, and your scatter dice rolls are hits, or you roll low on the distance traveled then the mortar can be of great use. But if there is a decent wind or adverse conditions such as long scatters the mortar will not be off much use. There however is no real art to shooting the mortar, you want to guess the distance correct & land the mortar dead on in the center of the unit.

The mortar has the same chance of a misfire as the cannon. (16.66%) If you look at diagram “A” you see 25 men ranked up on 20mm x 20mm bases. Note that with a dead on guess, you still only retain a 35.74% chance of landing the mortar shot within the unit, which is only just over double your chance of a misfire. Diagram “B” shows 20 men ranked up on 25mm x 25mm bases. With a dead on guess against this unit you have a 37.28% chance of landing the shot within the unit.

As discussed in the “Fundamental Physics of a Drifting Mortar” the mortar is a fickle device and in the hands of a commander who is not good at guessing ranges it is terribly inaccurate. Diagram “C” shows the same 20 men ranked up as in Diagram “B” but this time the mortar crew commander has guess the range short by 4 inches. See how the chance of the shot landing within the unit drops from.37.28% to 3.35%. For what is a reduced effectiveness by over a factor of 10. It is for this reason many commanders take mortars in pairs.

CHAPTER 3D: Mortar And Multiple Units
As you not up till now this tatica has not discussed shooting the mortar at troops bunched together. As noted earlier the mortars best use is against a battle line of lightly armored troops. This tatic is still highly encouraged as it helps compensate for the randomness of where the mortar shot will land. However it is not as good as many people have been lead to believe.

If you look at Diagram “D” you see the same unit as Diagram “A” however now there are 2 identical units, one on each side of it with 2″ in-between. Imagine this being 75 night goblins piled in together, what make for a prime target for a mortar. As in diagram “A” The chances to land the shot in the center unit are the same a reasonable 35.74%, however the chance that the shot will drift directly into ether one of the outside units is a meager 3.85%.

CHAPTER 4A: An Overview Of The The Helstorm Rocket Battery
The Helstorm rocket battery is a wholly remarkable new invention to come out of the college of engineers. At the time of its first trials it was disregarded as too random and too experimental by most empire generals to be used. However it has proved itself on the battle field by filling a niche roll that none of the other empire war machines fill. That is attacking heavy armored blocks of troops at great range.

CHAPTER 4B: Fundamental Physics Of Rocketry
The rocket battery is unique as it is the only war machine in the old world that behaves the way it does. If first acts as a cannon, then as a mortar. This adds high degree of randomness, as the shot could feasibly scatter 20″ forward of the guess range or 8″ backwards. It is so random in fact that a shot from the rocket battery could indeed drift and get a full hit any soldier within a 4.79 square foot area. This represents 20% (or 1/5th) of a standard 4 foot by 6 foot table.

To determine the accuracy of the rocket battery look at the diagram above. The solid dot represent the initial guess, the clear circles represent the distance the shot travels after the first artillery dice. The colored circle represents all the places in which the shot could scatter too. The colors of the circles are important for each 6″ of red line that passes thru a target it adds about 1.06% to the chance of hit. For orange it is .53%, yellow is .35%, green is .27%, and blue is .21%.

So if you were to have 18″ of red lines, 12″ of orange lines and 6″ of yellow lines passing thru a target it would yield a 4.60% chance to hit.(((1.06*3)+(.53*2)+(.35*1))). Now this percentage is relatively low, the bulk of the rockets accuracy comes from a hit roll on the scatter dice. Each clear circle that falls within the target area adds 5.56% to the chance to hit. So continuing with the scenario above, if a target has 2 clear circles within it, as well as all the lines listed above it has a 15.72 chance of being hit. (5.56 + 5.56 + 4.60)

So what one should attempt to do is first maximize the number or clear dots, then red lines, then orange lines, then yellow lines, then green lines, and finally blue lines. Once you do this you come to the determination that to get the most out of your rocket battery your guess range should be 5″ short of the center of your intended target. Guessing 6″ short would get you a greater chance of partial hits, but guessing 5″ short gets you a greater chance of full hits & landing the shot in the unit.

The rocket battery has the same chance of a misfire as the cannon & mortar. (16.66%) If you look at diagram “A” you see the same 25 men ranked up on 20mm x 20mm bases as in diagram “A” of the mortar. Note that with a good guess at 5″ short, you maximize your number of clear circles as well as a lot of red & yellow lines, you still only retain a 16.2% chance of landing the rockets within the unit. This is relatively inaccurate compared to the mortars 35.7% chance on the same unit. However the chance of getting at least one full hit is still a respectable 35.5% when put beside the mortars 43.6%.

Diagram “B” shows the same unit as in Diagram “B” of the mortar sections, 20 men ranked up on 25mm x 25mm bases. You can see the rocket batter improved to 18.6% chance of landing the shot within the unit and 36.0% of getting at least one full hit. Compare this too the 37.3% chance of a direct hit and 45% chance of getting at least one full when a shot fired at the same unit with a mortar.

CHAPTER 4C: Helstorm Rocket Battery Tatica
Despite the inaccuracy the rocket battery its high strength and ability to kill heavily armored infantry make it fill a roll that the mortar does not excel at. Another benefit of the helstorm is that it does not take up one of the much competed for “special” slots.

The helstorm is that it is much more forgiving to bad guessing then the mortar is. As you can see in diagram “C” even when a shot is under guessed by 4 inches, your chance of landing the shot dead in the unit only drops from 18.6% to 16.4%. Where as a guess that is 4″ short with the mortar could drop your chance to land the shot in the unit from 37.28% to 3.35%.

When firing at a unit dead on from ahead as seen in diagrams “A” and “B” you want to guess your distance short by 5″. However in an effort to maximize your effectiveness if you are shooting at a unit or target that is longer then 4″ (or 100mm) then you should attempt to guess 6″ short. Diagram “D” shows that because you are shooting at an angle the target is deeper then 4″ now, so you should guess 6″ short. As Diagram “D” shows you can achieve up to a 22.8% chance of getting a shot to land in the unit and a 42.4% chance of getting at least one full hit. This comes very close to the mortar’s 45.1% chance of getting at least one full hit on the same size unit. As such it is a very useful tactic to shoot at units not dead on, but at an angle.

When shooting the rocket battery at a battle line of troops it is negligibly better then the mortar at hitting units on the sides. In Diagram “E” you can see the same set up as in diagram “D” of the mortar section. Note that the mortars have a 3.85% chance the shot scatter into ether side unit, this number improves to 4.05% with the rocket battery.

CHAPTER 5A: An Overview Of The Helblaster Volley Gun
The Helblaster is quite a unique war machine when compared to the three other employed by the empire generals. Where as the other three war machines are more offensive weapons, the helblaster acts more as a defensive weapon or an area denial tool for few enemies would want to walk into the face of up to 30 ST 5 shots.

CHAPTER 5B: Statistical Lifespan Of A Helblaster
First a note on “Math-hammer” the below formulas doesn’t take into account if you only fire your helblaster twice, or it gets destroyed by fliers, or you have to spend 2 turns moving it onto a hill. It is impossible to make a formula to take every battlefield condition into account. The below is based on the following assumption “You will fire the helblaster every turn for 6 turns, if it is possible (not being un-jammed from the previous turn, or is already destroyed)”

The first misconception about the helblaster that needs to be cleared up is its reliability. Many people believe that the helblaster has a 1 in 6 chance of blowing up a turn. This would be their logic of (1/6 chance of misfire * 2/6 chance of misfire destroying it * 3 decks)*100 = 16.66%.

If you carry this 16.66% * 6 (turns in a game) you reach 100% chance the helblaster will not survive being fired for 6 turns.

However this is slightly flawed. This would be the case if you were forced to roll all 3 dice regardless of what happened on the first two, or roll all 3 at the same time. But in reality you are not guaranteed that you will get to roll the 2nd or 3rd dice. For example the heblaster my jam on the first deck and you would not be able to roll the other 2 dice. So if someone were to inquire about what the chance of the helblaster blowing itself up on the third deck, you would have to find the likelihood of getting to roll the 3rd artillery dice first.

The true formula for how likely It is to explode in a given turn is:

((Chance to roll First artillery dice * 1/6 chance of misfire * 2/6 chance of misfire destroying it) + (Chance to roll Second artillery dice * 1/6 chance of misfire * 2/6 chance of misfire destroying i)) + (Chance to roll Third artillery dice * 1/6 chance of misfire * 2/6 chance of misfire destroying it)) = Total chance of being destroyed in a turn.

OR
((1.00 * (1/6) * (2/6)) + (0.8611 * (1/6) * (2/6)) + (0.6952 * (1/6) * (2/6)))*100 = 14.20%

Farther more if you carry on with the example of firing the helblaster for 6 turns during a game, the formula is NOT: (6 *14.20%) = 85.2% chance it will blow up.

The correct formula would be.

((Chance of getting to shoot in first turn * 14.20%) +
(Chance of getting to shoot in Second turn * 14.20%) +
(Chance of getting to shoot in Third turn * 14.20%) +
(Chance of getting to shoot in Fourth turn * 14.20%) +
(Chance of getting to shoot in Fifth turn * 14.20%) +
(Chance of getting to shoot in Sixth turn * 14.20%)) =
% Chance the helblaster will destroy itself during a 6 turn game

OR

(1.00 * 0.142) + (0.7160 * 0.142) + (0.6546 * 0.142) +
(0.5704* 0.142) + (0.5013 * 0.142) + (0.4399 * 0.142) = 55.13%

So the helblaster in 6 turns of shooting has a 55.13% chance of being destroyed by itself. Now what the formula above is saying is not “Your helblaster is less likely to blow up on turn 6 then turn 1″, what it is saying “You are less likely to get to have a helblaster around to blow up on turn 6 then turn 1″.

To Sum up, there is about a 14% chance it will blow up on any given one turn, and about a 55% chance it will blow itself up if fired as much as possible for 6 turns. At a 55% chance of destroying itself the helblaster will be destroy itself somewhere about 2 to 3 out of every 5 games.

CHAPTER 5C: Statistical Effectiveness of the Helblaster
A note on the “Math-hammer” in this section, I’m not going to waist ether the readers or my time calculating how many chaos warriors, or skinks, or this, or that the helblaster would kill in a shooting phase, as this is relatively elementary. As well as most warhammer players already know what a helblaster will do to certain units. However below is the formula for calculating kills.

Shots * chance to hit * chance to wound * chance to fail save = kills.

However, I am going to calculate the number of shots you could expect out of your helblaster, as this is slightly more elaborate. The numbers below take every possibly of dice rolls into account. Even the .0021% chance you will roll 3 misfires & 3 duds in one turn.

Below you can see a pair of charts; these charts show the percent chance the helblaster will pump out that many shots in a given turn. The “0″ include all forms of deck #1 jams & non-ka-boom explosions from the misfire chart. The charts show the same data, just in two different forms.

Just to reiterate these charts include EVERYTHING that could happen to your helblaster and its net resulting number of shots.

As you can see the chart on the left is divided into thirds, this is roughly the statistical chance of getting those number of shots. To explain there is about a 32% chance of getting 20 or more shots, a 37% chance of getting 12-18 shots, and a 31% chance of getting 10 shots or less.

Two things to note are that you should average somewhere between 16 and 18 shots a turn. Also that the chance of 30 shots is greater then that of 28 or 26, this is mainly because of the “deck 1, misfire, ka-boom” roll

CHAPTER 5D: Helblaster Simulation
To reinforce what was laid out above and to gain some new insight into how the helblaster operates I devised a relatively simple excel spreadsheet that used visual basic to simulate a game.

The program operates under the following assumptions
-Games last 6 turns.
-The player will fire the helblaster every turn if possible.
-There are no enemies, just targets, so the only thing to kill the helblaster is itself.

Based on these three assumptions, I ran 10 sets of 500 games each for a total of 5000 games. This isn’t enough to get an exact average, but it should be more then enough to get a good idea of how the helblaster operates for our purposes. Please note I know this doesn’t simulate an “actual” game, but as stated in the previous section, to try to include variables for terrain and the likes would be near impossible and a waist of time.

I also understand that a helblaster could blow up in the first turn of 5 games in a row, or it could not blow up in 7 strait games. These numbers below are Averages over a long period of games. So use these numbers to give you an idea of what SHOULD happen (mathematically) if the following assumptions up above were made.

The results are that after 5,000 games, making up for a total 30,000 turns.
-The helblaster was alive and on the table for 22,104 turns
-Of which 16.909 turns it actually produced shots.
-Over 5,000 games it produced 277,602 shots.
-It blew itself up 2782 times.

This Means
-It averaged 4.42 turns alive per game.
-Of which it had 3.38 turns it actually produced shots per game
-Producing 16.39 shots per turn it was shooting
-Producing 55.41 shots per game
-It destroyed itself in 55.64% of the games.

From the simulation you can see that the helblaster blew itself up in 55% of the games, this number matches closely with the statistics from the section above. Also the 16.4 shots per turn is in line with what we would expect after the statistics that were also discussed up above.

The one new thing that the simulation points out that had not been discussed in this tatica yet, was that over a large quantity of games, the helblaster should live on average 4.4 turns a game (if not destroyed by the enemy).

CHAPTER 5E: Helblaster Tatica
As everyone knows the helblaster took a little bit of a hit with the new empire book. It no longer stands as the “Unit Killer” it once was. In the old book it was look on as many players as something that was “near mandatory” for leaving something that could be so good at home was folly.

With the new empire book out it’s a much less attractive choice, and the only thing that keeps it still being viable is that the empire has such few rare units to chose from.

As stated in the introduction the helblaster has been mainly used by many generals as an area denial tool. If you want to keep your enemy away from one area of the board, a helblaster near that area will make him think twice, as such it could easily be used for flank or war machine protection detail.

Other generals used its small size to fit it in-between parent units in the middle of their battle line. Here it was relatively well protected & could not as easily be avoided. It also offered a considerable amount of black powder to your battle line with minimal frontage.

Some people have suggested using two helblasters in a battery to help with the randomness and downgrading it took with the new book. Also one might try deploying it near some outriders as they can fill similar rolls.

Both the helblaster and outriders are “mover or fire”, have a360 degree line of sight, 24″ range, high number of shots, and are similar in points cost. Sense the new book, the helblaster has lost some its psychological effect on enemy generals. The potential of walking into 30 Strength 5 and 4 shots with just some fair dice rolling is something that most enemy units will avoid.

The Helblaster/outrider combo also takes up not a lot of space, and can jump out forward in turn 1 to get a better vantage point, and from here they create a 24″ radius buffer zone around them.

Some have said that taking an engineer with the helblaster is a good idea. This is all within the eye of the general. As this can be not to terribly expensive it may be a decent idea. However the helblaster is no less prone to blowing up and now takes up a hero slot as well.

CHAPTER 6: A Summation Of War Machine Tactics
(AKA: War Machines For Dummies)
This final chapter has been added at the suggestion of “Rufas The Eccentric” as to sort of some up everything quickly with no real math or explanations involved as they are all written out at length above. So this is a quick Pros/Cons/Tatics/Instructions.

Great Cannon
-Prime Targets = large monsters, other war machines, heavy cavalry & lone enemy models.
-Can be taken in pairs to decrease area on board that the enemy can hide in.
-You should guess 10″ short of the back of the target.

Mortar
-Prime Targets = large weak, lightly armored blocks of infantry.
-Can be taken in pairs to help with randomness
-High scatter & bad guess reduces chance to hit incredibly.
-As an example of its intolerrance for bat guessing – Under or over guessing by 4″ can decrease the effectiveness by a factor of 10.

Helstorm Rocket Battery
-Prime Targets = Tough, heavy/med armored bocks of infantry
-Does not take up special slot
-Much more forgiving then the mortar to bad guessing
-Larger “Danger: Watch out for falling explosives” area
-Can be Taken in pairs to help with randomness
-If the target is less then 100mm (4″ deep) guess 5″ short
-If the target is more then 100mm (4″ deep) guess 6″ short.

Helblaster Volley Gun.
-Prime Targets = Knights, fliers, monsters, or really anything else.
-Does not take up special slot
-Could be taken in pairs or with outrider to help with randomness
-Could be taken with Engineer to improve BS
-Good at covering flanks/other war machines
-14.2% chance of blowing itself up in a given turn
-55% chance of blowing itself up in a 6 turn game, if fired every turn its able & not killed by the enemy
-It will produce on average 16.39 shots per turn