Autarch - sieges
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enDomains at War Designer’s Notes: Historical Reference Points
http://autarch.co/blog/domains-war-designer%E2%80%99s-notes-historical-reference-points
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p><span style="font-size: 13px;">While designing </span><em style="font-size: 13px;">Domains at War, </em><span style="font-size: 13px;">I frequently tested my game mechanics against available real-world examples. Nowhere was this more challenging than in the area of siege warfare, which is akin to the PhD level of ancient warfare. Below are a few of the historical reference points I relied on in assessing whether the construction and siege mechanics had a reasonable level of versimilitude.</span></p><p><strong><span style="font-size: 13px;">Siege of Alesia</span></strong></p><p>During the Siege of Alesia, Caesar is recorded as constructing 18 kilometers of circumvallation in three weeks. How would this herculean accomplishment be described in <em>Domains at War</em>?</p><p>18 kilometers is approximately 60,000 feet, so the circumvallations would cost 60,000gp. Caesar’s force consisted of 12 legions totaling 50,000 men. Roman legions were renowned for their expertise in siege warfare, so let’s assume each legion had one siege engineer in its ranks. That gives Caesar the capability to conduct 12 construction projects. Assume that each siege engineer was assigned 1/12<sup>th</sup> of the circumvallation (5,000’) and 2,500 men. (Caesar wisely retains the other 20,000 men as guards and pickets.)</p><p>Each construction project would have a labor cost of (60,000gp / 12) 5,000gp. Assuming entirely unskilled labor, each construction project’s work force would have a construction rate of (2,500 x 0.1gp/day) 250gp per day. Each line of the circumvallation would have taken (5,000gp / 250gp) 20 days to complete. That’s right around the historical time frame of 3 weeks.</p><p><strong><span style="font-size: 13px;">Siege of Constantinople</span></strong></p><p>At the time of the siege of Constantinople, the great city had 20 kilometers of walls. Five and a half kilometers were land walls, while the remaining 14.5 kilometers were sea walls. Constantinople had, for centuries, been the largest city in the world, with a population as high as 800,000 at its peak. This indicates a very high urban value – 2,500,000 gp or more. <em>Domains at War </em>suggests that a settlement has 1 shp per 8gp of value, and 1 point of unit capacity per 1,000 shp. If Constantinople had an urban value of 2,500,000gp, it had about 312,500 shp and 312 points of unit capacity.</p><p>Encircling a settlement requires 250’ of circumvallation per point of unit capacity. Therefore the lines of circumvallation required would be (312 x 250’) 78,000 feet. 78,000 feet equals 23.7 kilometers. That this is a reasonable circumvallation around Constantinople can be seen by finding the radius of circular 20-kilometer walls (3,184 meters), adding the range of artillery fire (500 meters), and then recalculating the circumference (23,135 meters, or 23.1 kilometers). The circumvallations would surround the city, just outside of artillery range.</p><p>However, around 72% of Constantinople’s walls are adjacent to the sea. These would be blockaded by ship rather than circumvallation. Each two points of unit capacity requires one ship in the blockade. Therefore (312 / 2 x 72%) 112 ships would have been required to blockade Constantinople. Historical reports indicate that the Ottomans had between 100 to 430 ships, with the most recent modern estimate setting their number at 126. <em>Domains at War </em>would say 126 ships is too few, because Constantinople’s defenders had 26 ships, and the number of defending ships is subtracted from the number of blockading ships. The Ottomans should have had (112 + 26) 138 ships to fully blockade the great city. That 126 ships was, historically, insufficient to blockade the city is evidenced by the fact that friendly ships actually sailed into Constantinople on two occasions during the siege (20<sup>th</sup> April and 27<sup>th</sup> May). </p><p>Constantinople fell swiftly, as sieges go, taking only a month and a half to be captured. However, the actual fall was caused by an assault, not bombardment. The Ottomans, despite firing on the walls with massive cannons for weeks, were not able to inflict much damage that the Byzantines couldn’t repair.</p><p>With a unit capacity of 312, Constantinople could have been defended by 30,000 men or more. Historically, however, Constantinople was only defended by 7,000 men – perhaps 100 units. Historically, the Byzantine troops were insufficient to garrison the entire walls of the city, and only the outermost walls were manned. The Ottoman forces numbered at least 80,000 (800 units). The Ottomans therefore had a 700-unit advantage.</p><p>Comparing Constantinople’s 312,000 shp with the Ottoman’s unit advantage of 700 on the Duration of Siege table, the table predicts that the Ottomans should capture the city in about 54 days (17 days base duration x a duration modifier 3 for being a penninsula). Historically, the siege lasted from April 6 to May 29 1453, or 54 days.</p><p><strong><span style="font-size: 13px;">Siege of Tyre</span></strong></p><p>The siege of Tyre, conducted by Alexander the Great, is among the most famous of antiquity. Tyre was an island-city with approximately 1.5 miles of curtain walls, some of which stood as much as 150’ tall. It had a population of over 50,000 citizens, making it a Class II city with a minimum stronghold value of 625,000gp. In <em>Domains at War, </em>a stronghold worth 625,000gp would have 78,000 structural hit points and a unit capacity of 78 units (7,800 men). According to the historian Quintus Curtius Rufus, Tyre lost 6,000 fighting men in the city and 2,000 men on the beach, for a total of 8,000. This is quite close to our estimate.</p><p>Since Tyre was an island, encircling it required a huge fleet. <em>Domains at War </em>would say Tyre required (78 x ½) 39 ships to be encircled. However, Tyre was also protected by a navy of its own, described as great in number. This would increase the number of ships required to blockade Tyre. Historically, Alexander the Great ultimately increased his fleet to 223 ships during the siege.</p><p>In the course of the siege, Alexander constructed a great causeway (siege ramp) from the mainland to Tyre, a breathtaking project that took thousands of men seven months to complete. From archeology and ancient history, we know that Alexander’s causeway was about 2,500’ long, 200’ wide, and 5’ deep (the water was shallow due to a natural sandbar running from the mainland to Tyre). The causeway thus had a volume of about 2,500,000 cubic feet. In <em>ACKS, </em>an earthen rampart with a volume of 15,000 cubic feet costs 2,500gp. By this bottom-up calculation we can conclude Alexander’s causeway would have cost about (2,500,000 / 15,000 x 2,500gp) 416,666gp. For simplicity, let’s call it 420,000gp. Since Alexander’s siege took about 7 months (210 days), we can calculate that he had a daily construction rate of (420,000gp / 210 days) 2,000gp per day. Presumably the causeway was divided into 4 construction projects, each with 3,000 men constructing 500gp per day. That would accord with historical references to thousands of men working on the project.</p><p><strong style="font-size: 13px;">Construction of Warwolf</strong></p><p>Historically, King Edward Longshanks built the mighty trebuchet Warwolf in 3 months using 5 master carpenters and 49 other laborers. How woudl this be described in <em>Domains at War? </em>We represent it as a construction project to build a heavy trebuchet (2,500gp) under the supervision of a siege engineer. Assume Edward's work force consists of 5 master carpenters, 10 journeymen, 20 apprentices, and 15 skilled laborers - 50 workers, a little short of the historical number 54. The work crew has a construction rate of [(5 x 5gp/day) + (15 x 0.2gp.day)] or 28gp per day. After (2,500 / 28) 89 days, a little under three months, the work crew finishes construction of the trebuchet.</p><p> </p></div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/file-categories/domains-war" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Domains at War</a></div><div class="field-item odd"><a href="/file-categories/dw" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">D@W</a></div><div class="field-item even"><a href="/file-categories/campaigns" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">campaigns</a></div><div class="field-item odd"><a href="/file-categories/sieges" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">sieges</a></div><div class="field-item even"><a href="/file-categories/construction" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">construction</a></div><div class="field-item odd"><a href="/file-categories/alexander-great" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">alexander the great</a></div><div class="field-item even"><a href="/file-categories/julius-caesar" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">julius caesar</a></div><div class="field-item odd"><a href="/file-categories/warwolf" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">warwolf</a></div></div></div>Tue, 30 Apr 2013 14:33:06 +0000Alex2652 at http://autarch.cohttp://autarch.co/blog/domains-war-designer%E2%80%99s-notes-historical-reference-points#commentsDomains at War Designer's Notes #2: Sieges
http://autarch.co/blog/domains-war-designers-notes-2-sieges
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even" property="content:encoded"><p><span style="font-size: 13px;">The mechanics of siege warfare, both at the battle and campaign level, presented the most challenging part of the design of </span><em style="font-size: 13px;">Domains at War</em><span style="font-size: 13px;">. Pitched battles are glorious in their simplicity; sieges revel in complexity. Artillery, arson, assault, location, mining, supplies, treachery – all play their part.</span></p><h6>Artillery</h6><p>The artillery presented in <em>Domains at War </em>are modeled after the very best stone-throwing weapons ever constructed. Nevertheless, the actual destruction of an enemy stronghold by stone-throwing weapons is a slow and painstaking affair in <em>D@W</em>, just as it was in history. Ancient artillery were very useful for shattering wooden ramparts and forcing castle defenders to take cover, but to actually breach stone walls required ceaseless bombardment over long periods of time. Most shots bounced off the stone, dealing little damage. As many as one thousand shots may have struck the same wall before the 10’ thickness of a curtain wall was breached. Each artillery piece was kept firing around the clock for days on end. At the siege of Lisbon in 1147, the crusader’s trebuchets fired 250 shots per hour for ten hours straight, a record-setting rate of fire!</p><p>Still, despite the impressive rates of fire, it will take days and weeks, and not minutes or hours, to breach a stronghold’s walls. This may be frustrating to gamers whose expectations for sieges are set by <strong>disintegrate</strong> spells. Some of you will doubtless wish to “buff up” artillery in <em>Domains at War </em>to achieve a more exciting pace in sieges. Before doing so, it’s worthwhile to ask yourself how much military utility you want strongholds to have in your setting. When gunpowder altered the balance of power in favor of artillery, the castle and the walled city soon became antiquated. Likewise, if you make artillery more powerful, there will be much less value in building castles and walled cities in your campaign world.</p><p>The damage values themselves were calculated based on the kinetic energy generated by the artillery. Kinetic energy is calculated with the formula <em>k=1/2mv<sup>2</sup></em>, where <em>k </em>is energy in joules, <em>m</em> is mass in kilograms and <em>v</em> is velocity in meters per second. I had historical evidence for the mass of stone thrown by the various weapons, and velocity I approximated with <em>v=(gd)<sup>½ </sup></em>, where <em>v </em>is velocity in meters per second, <em>g</em> is gravity (9.8m/s<sup>2</sup>) and <em>d</em> is the weapon’s maximum range. This provided a range of kinetic energy from 4,009 joules for a heavy ballista to 200,455 joules for a heavy trebuchet. An artillery weapon’s damage (average hit points) is approximately <em>k/4.6a</em>, where <em>a </em>is the area of effect in square feet. Thus, a heavy trebuchet (200,455 joules and a 20’ radius area of effect) deals (200,455/4.6 x 1,256) 34.7 damage on average, or 10d6. A heavy ballista (4,009 joules and a 5’ radius area of effect) deals (4,009/4.6 x 78.5) 11.1 damage on average – rounded to 3d6 (10.5). </p><p>You can use these formulas to create your own stone-throwing artillery of exotic sizes and strengths.</p><h6>Strongholds</h6><p>Because of the mechanics of unit capacity during assaults, having a large stronghold has both benefits and drawbacks in <em>Domains at War</em>. This is a feature, not a design error! Large strongholds can be defended with much larger garrisons, and take much longer to batter down with siege weapons. However, large strongholds have longer walls, require more troops to man them, and can be assaulted by larger forces simultaneously. A sprawling, under-manned castle may fall to an assault more easily than a small, heavily garrisoned fortress.</p><p>The actual unit capacity of each fortified structure was calculated by summing the number of 120-troop units that could man the perimeter and the number that could garrison the interior. The number of units that can man the perimeter is equal to the perimeter length (in feet) divided by 60’. The number of units that can garrison the interior is equal to the equal to combined the square footage of all floors divided by 2400 square feet. (Remember that a unit occupies an area 60’ long and 40’ deep).</p><p>If your campaign features new or unique fortified structures, you can use this formula to derive the number of units they can hold.</p><h6>Structural Hit Points</h6><p>The structural hit points in <em>ACKS </em>and <em>Domains at War </em>were calculated based on the assumption that heavier structures can absorb more punishment. Each structure generally has around 1 shp per ton of weight of external walls. Particularly well-built structures might have 2 shp per ton.</p><p>To work up shp for a structure the rules don’t cover, simply calculate the volume, in cubic feet, of all external walls. Treat each cubic foot of wood as weighing 64lb, and each cubic foot of stone as weighing 160lb. (This is an approximation, but it is based on the real-world densities of oak and granite.) Divide the result by 2,000 to convert it into tons, and this will give you a reasonable value for the structure’s structural hit points.</p><p>Since a structure’s cost is largely determined by its size, you can quickly estimate a structure’s shp from its cost. In general, wooden structures have 1 shp per 80gp of cost, while stone structures have 1 shp per 8gp of cost. There is, again, some variance based on complexity (complex structures cost more gp and have fewer shp) but at the scale of a stronghold this shortcut should be correct to within +/- 15%. This correlation allows <em>Domains at War: Campaigns </em>to use stronghold value as a shortcut to derive all manner of stronghold characteristics.</p><p>The above mechanics will also work for ships, substituting “hull” for “wall,” of course. </p></div></div></div><div class="field field-name-field-tags field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/file-categories/acks" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">ACKS</a></div><div class="field-item odd"><a href="/file-categories/dw" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">D@W</a></div><div class="field-item even"><a href="/file-categories/domains-war" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Domains at War</a></div><div class="field-item odd"><a href="/file-categories/alexander-macris" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Alexander Macris</a></div><div class="field-item even"><a href="/file-categories/sieges" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">sieges</a></div><div class="field-item odd"><a href="/file-categories/math" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">math</a></div><div class="field-item even"><a href="/file-categories/designers-notes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">designer's notes</a></div></div></div>Mon, 22 Apr 2013 15:48:56 +0000Alex2633 at http://autarch.cohttp://autarch.co/blog/domains-war-designers-notes-2-sieges#comments