Sunday, December 30, 2012

Samurai Battles Project Update

Another Ashigaru spear unit passes off the painting table.  This unit carries the next clan's heraldry showing two white circles on a cornflower blue field.



I set about fielding clans in groups (brigades) of six units (1 x Samurai foot, 1 x Samurai horse, 2 x Ashigaru missile, 2 x Ashigaru shock).   An order of battle dug from Jan2010 Miniature Wargames for Shizgatake, however, listed most of the brigades as having nine units each.  Perhaps, I should increase the brigade strength to nine vs six units?  Should levy missile and shock troops be added into this mix?  

I am in the process of creating card decks to duplicate the Dragon and Fortune & Honor cards present in Samurai Battles.  While a bit tedious making each card, the result is quite satisfactory when affixed to a regular playing card.  These homemade cards are much more durable than the stock card decks sold with Samurai Battles.  The card information is printed out on Avery Sticker Project paper and then trimmed to size.  A sample of the cards both in uncut sheet and finished card is illustrated below.




Friday, December 28, 2012

18mm 1799 Napoleon in Italy

As a change of pace from the last two months painting that focused primarily on samurai and 1859 projects, I switched gears and the last of my Russian Napoleonic AB stock fell under the paint brush.  From the remnants of the Russians, three battalions could be mustered: two musketeer battalions and one combined grenadier battalion.

The two musketeer battalions are fielded as the Yaroslavl Musketeer Regiment with the contribution of the Yaroslavl grenadier companies towards the combined grenadier battalion. 



The combined grenadier battalion is composed of grenadier companies from Yaroslavl Musketeer Regiment and the Astrakhan Grenadier Regiment.  Keep in mind that during this early period, Russian grenadier regiments wore the short mitre for the fusiliers while the grenadiers wore the tall mitre.  That reminds me that I need to order Russian fusiliers now to field the two fusilier battalions of Astrakhan Grenadier Regiment.



Notice that the combined grenadier battalion maintains distinctive facings and mitre backs for each of the two contributing parent regiments.

Monday, December 24, 2012

Samurai Battles: Games and Painting

Jake brought his 6mm Samurai Battles Travel Edition to Spokane for an afternoon of Samurai Battles before the Christmas holiday.  Details of his 6mm travel set can be found at Dartfrog's Adventures in 6mm.  Jake's game pieces are even better looking in person.  His river tiles are really well executed and tempt me to do something similar for my own game map. 

We played three games to conclusion on Sunday.  Two games of 4th Kawanakajima: Attack Against Takeda Command Tent with both getting a chance to play the aggressor and attacking Takeda command and one game of 4th Kawanakajima: Ford of Amenomiya.

In Game 1 of 4th Kawanakajima: Attack Against Takeda Command Tent, I commanded Red and Jake took Yellow.

Yellow began by attacking on Red right followed by counterattacks  by Red.  Casualties were heavy on both sides.

Red prevailed in the center-right and then advanced up the center as Yellow left collapsed.

In desperation, Yellow launched an attack with his cavalry to try to rebalance the game.  Red units that had fallen back from early casualties were hit in this cavalry charge. Two Red foot units were eliminated but it was too little too late.  Red was victorious. 



In Game 2, we replayed the Game 1 scenario but switched sides.  This time I commanded Yellow.  Jake wasted no time in putting Yellow command tent under pressure and the command tent soon fell to Red.  Not able to recover, Yellow managed to destroy a few Red units before losing the battle 6-4.

In the final and longest game of the afternoon, Red harassed Yellow as he slowly advanced upon the fords.  Yellow took a pounding from missile troops before finally closing to contact.  First, the far left ford fell to Yellow and then pressure and clashes increased over the central ford.  In the end, Red cavalry was destroyed and Yellow held all three fords in an overwhelming victory. 
In an attempt to put down every threat across the entire board, Red used his cavalry as a mobile fire brigade.  Once it was clear that the left ford was permanently lost, Red shifted his cavalry to the center and launched a series of desperate attacks across the ford.


Jake has soloed the Game 3 scenario several times and all attempts to win as Red fell short.  This result was no exception.  Next time, I would like to give this scenario a try as Red and see how I might fare.  Another fun afternoon on the field of battle with Samurai Battles.  With the addition of Honor tokens and the Dragon card deck, no two game likely will play out exactly the same.  For those minimaxers, every turn presents tough choices.

Maintaining the Samurai Battles theme, two more 15mm units mustered off the painting table this week.

One unit of ashigaru with sword:

One unit of dismounted samurai:
I now have six units in this army consisting of four Ashigaru and two Samurai units.  The Ashigaru have two missile units (one bow, one arquebus) and two shock (one spear, one sword).  The samurai units are made up of one foot and one horse.

My plan is to field another six units having the same troop mix but this time the banners will be distinguishable from these first six.  

Saturday, December 22, 2012

15mm Second War of Italian Independence Project

Progress continues on the 1859 project.  Between work on Samurai and 1859 projects in November and December, not much else has reached the painting table.

Four units have been added to the project in December.  The units include:
  • Four squadrons of the Austrian 1st Civalart Uhlan Regiment
  
  • One battalion of the 8th Bersaglieri Battalion

  • One battalion of the 5th Bersaglieri Battalion


  • One battalion of the 1st Cacciatore del Alpi Regiment

The uhlans and Bersaglieri are Mirliton figures and the Cacciatore are Battle Honors Zouaves.  With no figures available for the Garibaldini, an alternative was needed.  I figured an ACW chasseur would come close to matching the Cacciatore but I found no such figure.  Given that hole in most ACW ranges, I opted to use a Zouave from Battle Honors with a paint conversion.  Some sources suggest that the Cacciatore wore a dark blue cap and tunic in 1859 and my notes show the standard blue-gray greatcoat was also worn in the field.  What fun would that be to field more figures that appear as line?  Of course, I opted to paint Garibaldi redshirts in their more famous red shirts!  While the San Martino OB shows no Cacciatore present, it was a pleasant diversion from painting the blue-gray of the Italian greatcoat and the Austrian white.  I have enough figures in the Battle Honors pack to field two more battalions.  The uhlans are lacking their lance pennons as are all of my painted Mirliton cavalry.  I need to make an effort to create pennons for all lance-armed cavalry.  Perhaps, over the winter break from work?

One more order went out to Mirliton to restock artillery and crew for both Austria and Sardinia.  I'll be adding 8 Sardinian and 6 Austrian guns.  Also included in the order are 12 Austrian dragoons and one pack each of command personalities.  Order will likely arrive in about three weeks from Italy.

Friday, December 21, 2012

Musketry Effectiveness on the Early Nineteenth Century Battlefield - Part 3



Battle of Maida in 28mm

Simulation I: Firing Begins at 300 Yards
Input Parameters for Simulation: Table 2
Exceptions: None. 

As a baseline scenario, the defender will begin firing upon the advancing attacker at 300 yards and continue firing until either the attacker is destroyed or the attacker reaches the defender. The distance of 300 yards was selected since officers rarely advocated beginning volley fire beyond this range. Simulation using the input parameters listed in Table 2 with 10,000 trials yielded the following results in Table 3: Simulation I Summary Statistics
Table 3: Simulation I Summary Statistics 

With the defender commencing volley fire at 300 yards, in no case was the attacker destroyed before reaching the defender. At the 50th percentile, the defender fired 7 volleys into the oncoming attacker inflicting about 50 casualties. In half of the trials, the defender was firing a volley roughly every 30 seconds with, on average, 14 misfires per volley. For the defenders, smoke reduced visibility by roughly 50%. Distribution graphs for select simulation results follow.






Simulation II: Firing Begins at 100 Yards
Input Parameters for Simulation: Table 2
Exceptions: Distance At First Volley = 100 yards. 

For Simulation II, the initial volley was delivered at 100 yards rather than at 300 yards. All input parameters remain as in Simulation I with this exception. Simulation with 10,000 trials yielded the results in Table 4: Simulation II Summary Statistics

Table 4: Simulation II Summary Statistics 

With the defender withholding fire until the attacker approaches within 100 yards, simulation produced no trial where the attacker was completely eliminated in the advance. The casualties, on average were higher in Simulation II even though firing began much later and the number of volleys delivered was less than half the number of volleys delivered in Simulation I. Again, the defender managed to sustain a fire rate of one volley every 30 seconds but in the simulation, only two or three volleys were fired before contact. At the 50th percentile, the defender's three volleys produced about 62 casualties. These 62 casualties equate to a 24% increase in casualties over Simulation I. In one-half of the trials, smoke reduced visibility 38% rather than the near 50% from the baseline simulation.

Examining the casualties per volley data more closely reveals that Simulation I requires five volleys before exceeding the average number of casualties produced by the initial volley in Simulation II. Distribution graphs for select simulation results follow.








Simulation III: First Volley Distance – Sensitivity Analysis 
Input Parameters for Simulation: Table 2 
Exceptions: Distance At First Volley varies between 50-300 yards. 

To study the sensitivity of the defender's ability to inflict casualties, the distance of the initial (first) volley was varied. In Simulation III, the initial volley distances were parameterized to take on values of between 50 and 300 yards at 25 yard increments. All input parameters remain as in Simulation I with this exception. Simulation with 10,000 trials at each initial volley range yielded the 50th and 90th percentile results as show in Figure 14: Attacker Casualties by First Volley Distance

Figure 14: Attacker Casualties By First Volley Distance 

The results of Simulation III clearly illustrate that an optimal firing doctrine can be identified. From Figure 14, if the defender begins firing too soon, the accumulation of smoke and misfires decrease the overall casualty rates. Casualties levels at both the 50th and 90th percentile demonstrate a marked drop in total casualties when firing begins beyond 225 yards.

If the first volley is withheld until the attacker is within 100 yards, fewer casualties are inflicted upon the attacker. Given the assumptions of this study, simulation results identify that the first volley should be delivered between 125-200 yards to maximize casualties. This analysis is supported by Clausewitz who placed the effective range of musketry at 150-200 yards.(1) 

Simulation IV: Battle of Maida

Input Parameters for Simulation: Table 2 
Exceptions: Distance At First Volley 100 yards. 
Number of Firing Muskets = 730 
Number of Attackers = 1680 

The final simulation examines results from the Battle of Maida in 1806 as a validation of the Musketry Effectiveness Model. The Battle of Maida was fought between the British and French in southern Italy between two relatively small forces. Of interest to the simulation is the crucial portion of the battle pitting the attack of the French 1st Legere Regiment (1,680 men) against Kempt's British Light Infantry battalion (730 men). Kempt's Light Infantry were supported by two British four-pound cannons. As the French advanced, they came under fire from the British guns at about 650 yards. This artillery fire was maintained until the Light Infantry fired its first volley as the French reached about 100 yards distance. During the artillery bombardment, French casualties could be expected to total 200-220 men.(2) 

At 100 yards, Kempt opened fire delivering a withering volley. As the French continued, Kempt delivered a second volley at close range. The second volley caused the French to break-off their attack and retreat. As the French broke, Kempt's Light Infantry charged the now panic-stricken 1st Legere. In the ensuing pursuit, British claim inflicting an additional 300 casualties.(3) British estimates suggest that the 1st Legere may have suffered as many as 900 casualties in the attack. The French claim far fewer. If the 200 casualties from artillery fire and the 300 casualties in pursuit are subtracted from the British claim of 900 French casualties then roughly 400 casualties were sustained due to musket fire. Simulation IV takes the parameters from this action to validate the model.

Results of Simulation IV show that on average about 450 casualties can be expected as illustrated in Figure 15: Attacker Casualties Maida – Freitag II Curve



Figure 15: Attacker Casualties Maida – Freitag II Curve 

The 400 French musket casualties derived from anecdotal accounts represent roughly the 30th percentile of casualties simulated by the model. While the model produces a mean casualty count greater than the reported 400 musket casualties, the simulation results contain casualty-counts for more than the two volleys reportedly delivered by Kempt. Still, the simulation can produce historical results. Figure 16: Number of Volleys – Freitag II Curve illustrates the average number of volleys fired in the Maida simulation.




From these four simulations, three conclusions can be inferred. One, an attacker is not likely to be destroyed by musketry fire when advancing upon an enemy that is of equal size. Two, the distance at which a defender chooses to begin firing upon an advancing attacker matters. And, three, the modeled, Musketry Effectiveness Curves produce historically plausible results. 

Battlefield smoke, musket misfires, rates of volley fire, and confusion on the battlefield, all contribute to the assertion that the first volley was the most deadly when delivered at medium range and should be withheld until the most opportune moment. While this empirical study points toward optimal battlefield doctrine, historical and anecdotal evidence shows that maintaining the discipline necessary to withhold fire until the most advantageous moment was difficult at best and impossible at worst.

Psychology on the battlefield likely played an important (and difficult to quantify) role to maintaining this discipline. Several of the intangible factors that increase the difficulty of choosing the optimal moment to begin firing not included in this analysis are: Training and experience of the defenders, leadership of the officers, the ability to execute the firing routine under chaotic conditions, and the anxiety and tension of watching an attacker bear down on the defender's position.



Lights skirmish in scrub
Footnotes:

  1. Muir, p. 81. 
  2. Hopton, The Battle of Maida 1806, Fifteen Minutes of Glory, p. 133. 
  3. Hopton, p. 122.


Select Bibliography:
Hopton, Richard, The Battle of Maida 1806, Fifteen Minutes of Glory, Leo Cooper, South Yorkshire, 2002.
Muir, Rory, Tactics and the Experience of Battle in the Age of Napoleon, Yale University Press, London, 1998.
Nafziger, G.F., A Guide to Napoleonic Warfare, Privately published.
Nosworthy, Brent, Battle Tactics of Napoleon and His Enemies, Constable, London, 1995.
Rothenberg, Gunter E., The Art of Warfare in the Age of Napoleon, Indian University Press, Bloomington, 1980.

Thursday, December 20, 2012

Musketry Effectiveness on the Early Nineteenth Century Battlefield - Part 2

The model developed for this simulation extends Nafziger's analysis and adds stochastic processes to aid in quantifying the interaction of variables not considered by Nafziger. The model will concentrate on the impact of a company of 100 British infantry in two ranks firing musket volleys into an equal number of French infantry attacking across open ground in three ranks. To provide context for the analysis, consider the sequence of events depicted in the model. 

As the attacker advances on the defender's position, the defender will open fire delivering an initial volley. Some muskets will misfire during the volley and a cloud of smoke will erupt from the weapons, enveloping the defenders and obscuring their view. If the distance between the attacker and defender is great, few casualties will be inflicted. The defender continues the advance while filling in gaps in the line caused by those casualties. While the attacker steadily advances, the defender reloads and prepares for a second volley. Those muskets misfiring in the first volley will attempt to be made operable in time for the second volley. Likely still shrouded in smoke, the defender fires a second volley into the attackers but at a closer range. The defender experiences additional misfires and lingering battlefield smoke reduces the accuracy of the second volley. More attackers fall but continue the advance. This process continues until either the attacker contacts the defender or the defender is eliminated.

To provide visual context to the model, Figure 3:Simulation Process Flow illustrates the relationships between the component processes.
Figure 3: Simulation Process Flow

To initialize the model, a selection of process input parameters is chosen. These process input parameters are detailed in Table 2: Input Parameters for Simulation.
Table 2: Input Parameters for Simulation

The Musketry Effectiveness Model is comprised of a number of sequential processes. These component processes in order of execution are:

  1. Number of Muskets Active, Pre-Volley – the count of muskets operational after the prior volley. If this is the first volley in the simulation then the parameter is set to Number of Muskets initial value.
  2. Number of Inactive Muskets, Pre-Volley – the cumulative total number of muskets that have misfired up to the current volley that have not been repaired.
  3. Musket Repair Process – the number of muskets that have been made serviceable prior to the next volley. This process follows a uniform distribution with a minimum repair count of zero and a maximum repair count of (Total Number of Inactive Muskets) x (Repair Rate Multiplier). The Repair Rate is modified by Repair Rate Multiplier to prevent a 100% repair rate in one simulation cycle.
  4. Muskets Active for Volley – the number of muskets that are capable of firing in the next volley. This is the sum of (1) and (3).
  5. Minutes Since Prior Volley – the total elapsed times in minutes from the firing of the previous volley to the current volley. Time between volleys follows a Beta distribution since the musketry fire rates are bounded by a minimum and maximum fire rate.
  6. Smoke Visibility Factor Pre-Volley – represents the smoke generated (or accumulated) from the previous (or prior) volley(s) minus the percentage of smoke dissipated due to elapsed time. The percentage computed reduces the musketry effectiveness due to obscuring the sight of the defenders to their target.
  7. Attacker Distance from Defender – the distance in yards that the attacker is separated from defender at the time of volley. For the French, this march rate equals 90 yards per minute.
  8. Volley Fired? - if this computed distance is zero then no volley is fired since the attacker will have reached the defender.
  9. Misfire Rate – probability that a musket will misfire. Follows a triangular distribution. Anecdotally, the musket misfire rate averaged 15% to 20%.(1)(2) Others have claimed that a musket will likely misfire in 1 of 6 volleys. Given that, the likeliest misfire rate is 15% with the minimum and maximum values increasing monotonically with each successive volley.
  10. Number of Muskets Misfires – the total number of muskets misfiring this volley (rounded up) based on the misfire rate computed in (9).
  11. Base Casualty Factor – the casualty rate based on the Musketry Effectiveness curve (Beta distribution) cross-referenced to the attacker's distance from the defender.
  12. Adjusted Casualty Factor – adjusts the Base Casualty Factor by Minimum Extreme distribution and the probability of hitting the same target more than once.
  13. Casualties Sustained – computed as the product of the Number of Muskets Active and Adjusted Casualty Factor. The number of casualties in one volley cannot exceed the number of original attacker divided by the number of ranks.
  14. Smoke Visibility Factor, Post-Volley - represents the smoke generated (or accumulated) from the previous (or prior) volley(s) plus the percentage of smoke generated from this volley. The percentage computed reduces the musketry effectiveness due to obscuring the sight of the defenders for the next volley.
  15. Attackers Remaining > 0? - the number of attackers remaining. If the count is zero or less then the attacker is destroyed. If the count is greater than zero then another simulation cycle will occur.

Rather than relying solely on the Gohrde three-point curve to quantify musketry effectiveness, two additional musketry effectiveness probability curves were constructed. Figure 4: Musketry Effectiveness Curve Comparisons illustrates these comparison curves. Since ranges are bounded by 0 and 450 yards, curves based on Beta distributions were examined. Curves fit to these data suggest two alternative musketry effectiveness curves.
The first curve, denoted 'Freitag I' (Beta parameters α=0.60; β=1.25) emphasizes Picard and Muller – Veteran trials with less emphasis on Scharnhorst. The Freitag I curve can be viewed as an upper bound on effectiveness given near ideal conditions on the firing range. Not only are the trial conditions ideal (volleys are not timed, weapons less likely to misfire, battlefield smoke dissipates before next volley, no panic from battlefield environs, etc.) but the firers are either well-trained or veterans of the art and science of firing their weapon.

The second curve, denoted 'Freitag II' (Beta parameters α=0.50; β=1.90), places more weight on the Muller – Raw trials and the single Gohrde data point with less weight on the Scharnhorst trials. Freitag II represents a lower bound on musketry effectiveness on the training ground since the firers do not have the training and expertise to produce the results of the veterans in Freitag I. In comparison, Nafziger II and Freitag II are similar with Freitag II yielding slightly higher casualty rates in the 50-150 yard range while yielding fewer casualties above 250 yards. For the simulation, Freitag II will be utilized.
Figure 4: Musketry Effectiveness Curve Comparisons


The assumptions for the simulation are as follows:

  • The attacking infantry marches at its regulated march rate (90 yards per minute) until either eliminated or defender is contacted. 
  • The defender's first volley is delivered exactly when the attacker reaches the distance as defined in the Input Parameters Table. 
  • Musket fire rate varies between 1 and 4 rounds per minute with Beta distribution and the defender maintains controlled volley fire throughout the attack. 
  • Musketry Effectiveness follows the Freitag II curve. 
  • Muskets fail/misfire following a Triangular Distribution with most likely failure rate equal to 15% but minimum and maximums are monotonically increasing for each successive volley. 
  • Muskets are repairable following a Uniform Distribution. 
  • The terrain between the attacker and defender is perfectly flat with no intervening obstacles. 
  • After the initial volley, only attackers in the front rank may be hit. The attacker can suffer a maximum of (Starting Total Number Attackers)/(Number of Ranks). For example, 100/3 = 33 is the maximum number of hits per volley. As casualties are incurred, the second (or third) rank move up to fill the gap in the attacker's line. Once the attacker has only one rank remaining, casualties will be reduced to account for the probability of having a hit fall within a gap. 
  • Hits missing the intended target are considered as a multiple hit on another target and ignored. A Multiple hit is defined as any hit not within 1.5 feet of the center of the target (defined as NOT P[-1.5<=x<= 1.5] with accuracy as N(0,1)) is deemed a hit on a nearby target. 
  • Casualties are reduced proportionately by the density of the smoke encompassing the defender. 
  • Smoke dissipates at a fixed rate dependent upon minutes between volleys.
Next Part 2: Simulation Studies

  1. Muir, Tactics and the Experience of Battle in the Age of Napoleon, p. 78.
  2. Rothenberg, The Art of Warfare in the Age of Napoleon, p. 65.

Wednesday, December 19, 2012

Musketry Effectiveness on the Early Nineteenth Century Battlefield - Part 1


Several years ago, I completed a course in simulation.  One of the requirements was to craft a project that used simulation techniques.  Topics were unconstrained so with an interest in military science, wargaming, and simulation, I chose to simulate musketry effectiveness on the 19th Century battlefield.  Below is the Part 1 excerpt from that project.  Comments encouraged.  On to Part 1 for motivation and review.
  
From the mid-1750’s through the mid-1850’s, the smoothbore musket was utilized as the principle infantry weapon on the battlefield. The loading and firing of the musket took as many as seventeen, well-drilled steps. To maintain control and overcome the inaccuracies of the weapon, tactics evolved emphasizing volley fire delivered by lines (ranks) of soldiers standing shoulder-to-shoulder and discharging their weapons in unison at the command of their officers. Not only did this deployment provide a sense of confidence and safety to the soldier but also provided the volume of fire necessary to ‘discourage’ an advancing enemy formation from bearing down on his position.

In these firing lines, two ranks of infantry could simultaneously discharge their musket. For example, a British company of 100 men would be drawn up in two ranks, each having a frontage of 50 men. While the company only maintained a frontage of 50 men, firing both ranks yielded a volley of 100 musket balls towards the target. Trained infantry could produce three or four volleys per minute on the parade ground but in battle, only two or three volleys per minute could be sustained in a protracted firefight.

On the battlefield, formations of men maneuvered in accordance to strict regulations. Both rates of advance and maneuvers were drilled to the point of becoming automatic. Each combatant nation maintained several prescribed rates of advance depending upon the situation. Often, these rates of advance were not standardized across nations. During an infantry charge, the attacker would quicken the pace to shorten the length of time needed to cover the ground between themselves and the defender. For the French, this quick pace was called the 'Pas de Charge' and equated to 120 paces per minute. Due to the length of the French pace, this march rate equated to 90 yards per minute.(1)

While many anecdotal accounts support the potential for devastating musketry volleys, little empirical evidence exists. The few field trials conducted during this period were carried out under ideal conditions and without scientific rigor. Three of the more famous musketry trials were conducted by Scharnhorst, Picard, and Muller. In each trial, soldiers lined up facing a target the size of an enemy company and fired volleys into the target at varying ranges.

In Scharnhorst's trials, a company of grenadiers (the most disciplined and trained classification of infantry) fired at a company-sized sheet at different ranges using six different types of muskets. The six columns for Scharnhorst's trials in the accompanying table represent one trial per weapon.(2) Instead of varying the weapon, Muller varied the quality of the firing soldiers between veteran (experienced) and raw (little training and no combat experience).(3) In all three trials, these data show, in general, an inverse relationship between range to target and casualty rates. That is, as the range decreases; the expected casualty rate increases. The results of these trials are detailed in Table 1: Musketry Trials Under Controlled Conditions


Table 1: Musketry Trials Under Controlled Conditions 

Plotting these data points yields the results in Figure 1: Musketry Effectiveness Under Controlled Conditions. Notice that Picard and Muller's (Veteran) results are quite similar while a distinct gap exists between Muller's two trials suggesting that the quality of the soldier firing the weapon was much more important than the quality of the weapon, itself.
Figure 1: Musketry Effectiveness Under Controlled Conditions 

In A Guide to Napoleonic Warfare, Nafziger used the Scharnhorst data as a baseline for his analysis and computed a non-linear regression to these data (this series is labeled, 'Nafziger I'). In order to compute a non-linear regression equation, two artificial data points were added to the analysis: (1) 100% hits at 0 yards and (2) 0% hits at 450 yards. The assumptions are that at 0 yards all muskets will hit a target and at 450 yards, even if a target is hit, no damage will be sustained. Not satisfied with these initial results, Nafziger added one historical data point obtained from an account of the Battle of Gohrde (labeled as the 'Gohrde' volley in the graphics) to the data series and recomputed the regression (labeled as 'Nafziger II').

Since details regarding the effectiveness of an individual volley in the battle are rare, the Battle of Gohrde provides a singular event. During this battle in 1813, a Hanoverian militia battalion sustained 27 casualties at a range of 70 yards fired by 66 French muskets for a hit percentage of 41%.(4) Superimposing the musketry effectiveness curve using the Gohrde point on Figure 1 yields Figure 2. 
Figure 2: Musketry Effectiveness Fit to Nafziger's Analysis 

Using the Nafziger II curve and the following assumptions, Nafziger concluded that four volleys would completely destroy an approaching attacker when both attacker and defender were of equal size. His assumptions were:
  • Two rounds per minute fired. 
  • The attacking infantry marches at its regulated march rate. 
  • The results of the Gohrde volley are typical and average. 
  • The first volley was delivered when the attacker reached 300 yards. 
  • The terrain between the attacker and defender is perfectly flat. 
One must note that Nafziger's conclusions regarding the complete destruction of the approaching enemy were actually computed at a one minute per volley rate rather the two minutes per volley rate in his assumptions. That error implies that casualty rates would be twice as large as stated in his original analysis.(5) 

Historical evidence suggests that the attackers were not typically eliminated while advancing on the defender. Often, the attacker's choices would be to either halt the advance short of contact and enter into a firefight or withdraw from musketry range. For the defender, if musketry volleys failed to persuade the attacker to halt the advance then the defender would withdraw as the attacker closed in on his position. Evidence also suggests that the first volley was usually the most accurate and delivered with the greatest care. After that first volley, muskets were more prone to misfiring and continuous volleys would reduce visibility as smoke choked the battlefield.

The problem, then, is to develop a musketry effectiveness model and simulate (in repeated trials) the expected number of casualties sustained by an attacker while advancing on a defender’s position. In addition, the number of volleys that a defender can deliver before being contacted by an attacking force will also be quantified. Taking these data, contemporary anecdotal accounts, and a number of simplifying assumptions, an event-driven analysis will be examined that models musket effectiveness on the nineteenth century battlefield. The objective of the simulation is to provide insight into the tactics employed and theoretical casualty rates on the early nineteenth century battlefield.

Next Part 2: The Model

  1. Nafziger, A Guide to Napoleonic Warfare, pp.6-7.
  2. Nafziger, pp. 11-12.
  3. Nosworthy, Battle Tactics of Napoleon and His Enemies , pp. 203-204. Nosworthy cites Hughes, Firepower p. 27 who in turn, cites Picard in La Campaigne de 1800 en Allemagne.
  4. Nafziger, pp.14-15. Nafziger draws this account from von Quistorp, B, in Die Kaiserlich Russich-Deutsch Legion, p. 99.
  5. See Nafziger, Table VII. Musketry Hits Based on Gohrde Curve p. 17 to verify computational errors.

Monday, December 17, 2012

Battle for the Bridges - Napoleonic AAR

Scott hosted a Napoleonic game using his beautiful 18mm Napoleonic collection and General de Brigade rules.  The scenario pitted Nordmann's Austrian Advance Guard attempting to hold the bridge and village as Morand's powerful division forced the crossing.  Scott moderated while Kevin commanded the French and I took the Austrians.

Initial positions show the jaeger holding the bridge while Vecsey's division approaches the village.  While the layout was expansive, only the area around the bridges witnessed much activity.
  
French initially have a battery deployed opposite the bridge while reinforcements pour onto the table.  Austrian grenz take up positions defending the village while the hussars pass through town to cover the lower bridge.

To counter the French threat at the lower bridge, Austrian hussars charge catching the French cavalry flat-footed.

French cavalry are sent reeling back across the bridge while a second French light cavalry regiment fords the stream below the bridge.

Morand sends skirmishers and legere to demonstrate against the jaegers in the wood line while major French efforts are made against the lower bridge.  French objective seems to be focused on an indirect approach on the village.

Nordmann's second brigade reaches the village and in an attempt to change orders, Froelich panics and his column back peddles into the third arriving Austrian brigade.  What a mess!  After a little embarrassment and a couple of turns, Nordmann begins to sort out his reinforcement arrival.  Unfortunately, the village has become a major bottleneck. 

Kevin leans, white knuckled, onto the table as the lone Austrian cavalry on the left is tasked with slowing up the entire French column.  In this delaying action, the Austrian cavalry repulse two French charges at overwhelming odds before being scattered.

Overview of the battle mid-game.  Austrians still have a major bottleneck as two brigades attempt to pass through the village simultaneously.  Skirmishing continues along the stream bank as the jaegers hold back the French.

Battle lines are beginning to form on the Austrian left as the French deploy across the stream and Austrians clear their traffic jam.  Austrian guns are brought up and unlimbered to protect the approaches to the village.  Still brash, Froelich crosses the upper bridge in pursuit of the legere.  Froelich's attack on the lone legere regiment ends in failure and consumes resources that could have been useful on the other side of the stream.

French cavalry charge the grenz but the grenz form square before the charge can hit home.  Unable to recall, the French light horse hit the square and are repulsed.

  Attacks go back and forth as opponents struggle to gain the upper hand.  In a bit of bad luck two full strength Austrian regiments fail morale checks and are dispersed. 


After the bloodletting, most formations are called upon to take brigade morale checks.  One after the other, both sides disengage as morale checks are failed.  In the end, the Austrians hang onto the village but both combatants are exhausted with few assets or willingness to continue.

Scott provided an interesting scenario with a few tactical problems for each side.  The Austrian commander faced one major problem and committed one major mistake.

The problem centered on Froelich's command failure and withdrawing his brigade into oncoming reinforcements.  The ensuing bottleneck in the village was a direct result of a tangle of orders and troops.

The mistake was in sending the headlong Froelich over the upper bridge to target one legere regiment.  Froelich's command would have been better employed on the village side of the stream to help shore up the defenses outside of the village.

Thanks, Scott! 

Wednesday, December 12, 2012

15mm Samurai Battles Project Update

Two more units for Samurai Battles have mustered out from the painting table.  This time, one unit of mounted Samurai and one unit of Ashigaru arquebusiers.  Again, the Peter Pig figures are really a pleasure to paint and the double hex basing is pleasing to my eye.

All of my other collections have a dullcote seal but with the Samurai project, I opted for a more matt finish.  To me, Krylon Matt Finish has always appeared too glossy but for these Japanese warriors, the slight gloss is appealing and seems to work.  Perhaps I prefer this matt topcoat on the Japanese because much of their gear was lacquered?  Perhaps, it gives the figures a more Old School look?  Whatever the reason, the lacquer on the helmets, armor, and weapons enhances their appearance.



    
Next up for the project is a unit of Ashigaru with swords.

As for the game, itself, I began work on reproducing the cards in the game.  Since the cards can't be purchased separately (that I can find), I am experimenting with creating my own set of Command & Colors and Dragon decks.  My thought is to create and then print out the card information and then affix these onto regular playing cards.  This approach solves two problems: obtaining the card decks and making a more durable product.
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