The observations in this essay are mainly based on the calculations derived from a spreadsheet – Roman_campaigning.xlsx available at www.bandaarcgeophysics.co.uk/arch_intro.html - and contains information about the operation of the spreadsheet.

Note: the time format used is the International Standard ISO 8601 24 hour system, HH:MM:SS, e.g. '10:13:00' is 10 hours, 13 minutes and 0 seconds. In many instances in the text the use of seconds might seem overly precise but their use removes ambiguity, e.g. 10:13 alone could mean 10 hours and 13 minutes or 10 minutes and 13 seconds. The clock does run beyond midnight, e.g. 24:13:00 is 13 minutes past midnight. Distinguishing between a point in time and a period of time is dependent on context or preceding words, e.g. the words 'at' and 'by' typically precedes a point in time, while 'in' typically precedes a period of time. Unfortunately, there is no international standard to clearly distinguish the two.

Introduction

Early Imperial Roman armies, approximately 1^st Century BC to 2^nd AD, were impressive machines, powered by men, mules and horses, that traversed long distances, daily built fortified enclosures for night-time protection, and in this manner conquered much of the known western world.

This essay is intended to be read in conjunction with a spreadsheet – Roman_campaigning.xlsx (available at www.bandaarcgeophysics.co.uk/arch_intro.html) - that attempts to explain how the movement and fortification of Roman armies aided that conquest; how the men, mules and horses daily performed feats of marching and camp building that helped enable the conquest of peoples across the Mediterranean world and beyond. To that end, modern military and medical research figures relating to march velocities, rates of excavation and building, and the resulting energy expenditure and water requirements, have been sourced and factored into the spreadsheet.

The general aim of this work is to determine what Roman soldiers could reasonably be expected to have achieved in marching and building defences when the limits of modern examinations are allowed to govern the outcomes. It is not an examination of extraordinary feats, although they can be modelled in the spreadsheet.

There are a large number of parameters and metrics that govern the marching and building of defences, far too many to be described in detail, and certainly too many to discuss all of their permutations. Consequently this document will concentrate on a brief, general description of the spreadsheet, some observations arising and, in the appendices, the listing and description of the user inputs and calculated outputs.

General description of the spreadsheet

The spreadsheet caters for Roman armies ranging in size from one century (80 men) to eight legions (40,960 men). Variable velocity rates of march can be set for either on- or off-road marching using single or multi-column configurations. Times to complete the march, the energy and water consumption, and distances covered are calculated. The defensive ditch of the marching camp is V-shaped (triangular) with the option to include an ankle-breaker. The detritus from the ditch is assumed to infill a turf-constructed rampart of trapezoidal shape and, if selected, tituli. As for marching, times to complete, energy expended, etc. are calculated. As the defence construction proceeds, a match is made with extant camps in Britain allowing the examination of extant camps in terms of the size of army that could build, reasonably occupy and defend them. The user-defined variables give considerable control over many aspects of Roman army marching and camp building.

The spreadsheet contains the following worksheets:

'User inputs and camp building' - the main sheet for user inputs and reported calculations (Appendices 1, 2 and 3);

'March time, distance and energy' – calculations of march times, distance and energy expended (Appendix 4);

'Rampart building' – calculations for the time to build the rampart;

'Extant UK camps' – known marching camps in Britain used to cross-match with the calculated camps;

'Pandolf 1977 calcs' – base calculations of energy expenditure for marching soldiers;

'Example soldier day' – a simple description, together with timings and energy expenditure, of a typical Roman soldier's day.

From an initial selection of army size and march rate the user can alter a further 70 plus variables throughout the various worksheets (Appendix 1). For example, these range from the number of ranks and files of the marching army, the body weight of the soldier, to whether or not the latrines are dug inside the marching camp. It should be noted that the cells in the spreadsheet are not locked/protected, and that only the variables in the green coloured cells should be altered.

Approximately 70 individual parameters are reported to the user (Appendix 2) such as the lengths of the pack-mule train, the time to finish the march for the last soldier arriving at the camp, and the angle of the inward inclined sides of the rampart.

These user inputs and individual parameters are fed into the various worksheets to enable the calculation of march times, energy expenditure, the time taken to build the defences and a host of other outputs.

A brief description of the worksheet 'User inputs and camp building'

The overall strategy for the worksheet is to define a marching and camping Roman army, utilising most of the requisite parameters, many of which have been derived from modern examinations. For example, the number of soldiers arriving in the new camp per unit time is defined by the user, as is the number of diggers and rampart builders. Each digger has a length, width and depth of ditch to excavate, and the sum of the lengths for each digger determines the overall length of the ditch. This value is used to find a match between the calculated camps and extant camps in Britain. The matching extant camps aspect ratio, the ratio of side lengths, is assigned to the calculated camps. This action, therefore, applies the known evidence of Roman practice, for those particular camp sizes, to the calculations based on parameter choices and modern examinations, e.g. the rates for digging and rampart building are mostly derived from early 20^th Century British Army manuals.

The worksheet allows a user to specify nearly all of the known structures and designated areas within a camp, for example, the intervallum width, the number and widths of roads and whether tituli are built. In this manner users can build a detailed virtual camp, possibly modelling an extant camp, view the results and then decide what would have been possible for the soldiers to construct.

Knowing the construction and features within allows the calculation of various outputs that give an indication of the size of armies that built the extant camps. An example is the calculated output in column AD, the orientation and number of accumulating contubernium areas which is the area mentioned by Pseudo-Hyginus, the supposed author of De Munitionibus Castrorum (English translation in Gilliver, 1993, appendix 1), as being required for each 8-soldier unit and their tent etc. The user can expand the width and length of the Pseudo-Hyginus area. The number of contubernium areas per user-specified army is derived and these units are fitted into the then available strigified area (the area within the camp which is available for occupation by men and beasts, i.e. it excludes the intervallum, roads and any additional area specified by the user). Column AD remains red until the strigified area is sufficiently large to accommodate the contubernium areas required by the army.

Another measure of the required strigified area for the army in question is in column AE, the percentage of the required army area that fits into the cumulative strigified area. This also remains red while the total area required, for all individual soldiers, mules, carts, latrines and horses, is greater than the available strigified area. Typically column AE remains red for a little while longer than column AD because only whole contubernium areas can be fitted into the strigified area in AD – a function of the box-packing algorithm.

Another indicator of army size for the calculated camps is column AG, total soldier density per strigified hectare, which is similar to the commonly discussed archaeological term ‘density of soldiers per hectare’ (densities of 480, 690 and 1186 soldiers per hectare are shown in columns AM, AN, AO). The difference between the two terms is that column AG relates to the strigified area while the common term is nearly always a measure of density within the rampart or ditch. The strigified area is preferred in this work because it gives measures of soldiers etc., and the individual areas they might occupy that can be modelled according to variations in intervallum and road widths. Indeed, these variations can be set to 0 m resulting in direct correspondence with the common archaeological term. Conditional formatting is also applied to column AG such that densities roughly greater than 1186 are red.

In combination the red conditional formatting of columns AE, AD and AG indicate those camp sizes that could not hold the user-defined army (Fig. 1). There are other indicators of inappropriate camps for the army, for example, the number of soldiers required to defend the rampart (column AF) and the distance between the sharpened stakes used as a palisade (column AC).; in both cases the column will turn red once logical limits are approached.

The large number of parameters and calculations in this worksheet create a vast number of permutations, far too many to consider describing. However, the spreadsheet is relatively easy to use and has many comments to aid the user.

Other worksheets are briefly described in appendices 4, Sheet 'March time, distance and energy' and 5, Other ancillary worksheets.

Figure 1: an example of the conditional formatting in the worksheet 'User inputs and camp building', columns AC to AH. Red indicates a limitation in the camp size or the defence of the camp for the marching army. A band of rows without red across the first 5 columns (purple header) may indicate a suitably sized camp, in this case, equivalent to extant camps (column 6) Knockcross to Middlewich.

Observations

The following observations are not in order of importance but the reader may discern a logical progression. To aid the description of the observations a set of values, mainly based on the mean values of ditches in extant camps, has been used to create a standard configuration for the camp defences. These are: ditch 1.0 m deep, 2.5 m wide, ankle-breaker 0.3 m deep and 0.25 m wide; and the rampart, 1.1 m high, 2.0 m wide, with a fighting platform 1.2 m wide and all topped by a palisade 1 m high. The spreadsheet calculations indicate that this standard configuration could have been built by all armies irrespective of size, but dependent on march rate, surface and column disposition, by assigning four diggers and four rampart-builders from each contubernium arriving at the campsite, and have completed these defences within approximately 2:42:00 between c.18:20:00 and c.18:45:00.

The mean for ditch depths of 106 extant camps is approximately one metre (1.03 m, 0.44 m SD) (Fig. 2). The spreadsheet points to a number of observations that may explain this. For one legion marching in single-column, on-road, then a ditch 2.5 m wide and 1 m deep, with an ankle-breaker 0.3 m deep and 0.25 m wide, will be completed in 2:42:05 by four diggers and four rampart-builders from each contubernium – this is the standard configuration described above. Increase the ditch depth to 1.5 m and the time taken extends to 3:52:26. Ignoring small variations due to size, all armies will have completed a 1 m deep ditch by c.18:32:00; a 1.5 m ditch by c.19:42:00. There a number of points arising from these figures. To begin with, c.2:42:00 to dig a 1 m ditch (and build the rampart – see equality observations below) might have seemed appropriate and not overly onerous to the soldiers, especially as the digging could have been shared between all the defence-building crew (modelled in the spreadsheet). The same acquiescence might have been missing for the 1.5 m deep ditch, as a finishing time of c.19:42:00 lessens significantly the time given to the evening meal and care and maintenance of kit and body. In other words, producing a 1.5 m ditch might have had a detrimental effect on morale, and the health and vigour of the soldiers, unless mitigating steps were taken. One such might have been to have the 1.5 m ditch section dug by the first half of an arriving army and the remainder completed by the second half; clearly, this option would only be available to large armies (greater than approx. 5 cohorts, 2400 soldiers). It is noteworthy that only 11 of the 106 ditches in Fig. 2 are deeper than 1.5 m, the deepest being Ward Law (area 3.8 h) at 2.4 m and width 4.5 m, which would have taken 9:14:56 to complete at c.25:19:00, i.e. after midnight. It seems reasonable to suggest that these greater depths were excavated on at least a second day unless there was an overriding need for enhanced defences, and even then, continuing to build in darkness was probably not an option. As an aside, marching camps were re-occupied and ditches sometimes re-cut and/or deepened, but even so, the mean depth is only 1 m with 34.1% extended upto 1.4 m, ergo cutting deep ditches was not an imperative for the Roman army. A likely reason was that the overall width and height of the defences above ground level was more important, and that height could be most efficiently supplied by a palisade (see observation below, ‘A high palisade on top of the rampart was essential for an effective defence system’). Note: the 106 camps may not include any re-cut and/or deepened ditches; furthermore, the depths and widths have been gathered over many decades when standards of measurement and reporting have improved; plus, the population is skewed towards the larger, more impressive, camps.

The mean for ditch widths of the 106 extant camps (Fig. 2) is 2.5 m, 1.04 m SD. Increasing the width of a ditch costs less in effort and time than increasing the depth. In the standard configuration the width is set to 2.5 m and completed by c.18:32:00. Increase the width by 0.5 m and the time taken increases to 3:02:20 with completion at c.18:45:00. As already described in the paragraph above, solely increasing the ditch depth by 0.5 m extends the completion time to 3:52:26, with a finish at c.19:42:00. Of course, this time difference between the two of approximately an hour is in part due to the simple effect of digging nearer to ground-level, but is also due to being able to have two soldiers dig side-by-side at shallower, wider levels before being restricted to one digger at deeper levels (this is modelled in the spreadsheet). This depth-dependent limitation on digging efficiency is probably also why the ankle-breaker was dug; namely, a continuation of the triangular ditch to greater depths is costly in time and resources (energy, food, water), but digging a narrow extending slot below the triangle (or V-shape as often described) is relatively efficient, and as a trap for fallen attackers is probably more effective than the triangle shape alone. As will be discussed, the ankle-breaker is also a simple, efficient method to increase the effectiveness of the rampart and palisade.

Figure 2: Excavated ditch widths and depths of 106 extant marching camps. The green line is the average depth at 1.03 m and 0.44 m SD. The average width is 2.50 m and 1.04 m SD. The red line is a trendline with f(x) embedded in the graph. The areas of the camps range from Easter Powside at 0.4 h, to Lunan Head at 86 h. The deepest and widest data were selected from any reported range for a camp. Data sourced from Historic Environment Scotland (www.canmore.org.uk), National Monuments Record of Wales (www.coflein.gov.uk), Historic England (www.historicengland.org.uk) and a selection of European camps from Gilliver, 1993.

The size of the ditch does not scale with the areal size of 106 extant camps (Fig. 3). Put another way, large camps do not necessarily have large ditches and there is little correlation between area size and the size of the ditches; some small camps have large ditches and vice versa. The primary cause for this observation is the time it took to dig the ditch, itself a direct result of the effort required, i.e. a contubernium team assigned to build a section took the same amount of time irrespective of the army size, and the amount of available time when campaigning was constrained by such factors as march distance and the time required to prepare, cook and eat the evening meal. As far as the existing excavation data allow, this observation suggests that campaigning Roman commanders thought a depth of c.1 m and width c.2.5 m was sufficient - but on its own incapable of halting leaping warriors - when combined with a palisade height of c.2 m above ground level. If correct, therefore, other reasons for the overly-large ditches must apply: for example, a shortened march distance between camps with sufficient water and a need to occupy the soldiers; an expectation of imminent attack; as a punishment detail; for repeated training sessions; or the re-occupation of camps when some ditches were re-cut. However, and not intending to lessen the forgoing reasons, a camp occupied for more than one night is full of soldiers who need employing - further improving the defences would be good for discipline, morale, strength of soldiers and defence.

Figure 3: Bubble chart of camp area and excavated ditch widths and depths of 106 extant marching camps. The bubble size relates to the area of a camp in hectares. Otherwise the data is as Figure 2. Data sourced from Historic Environment Scotland (www.canmore.org.uk), National Monuments Record of Wales (www.coflein.gov.uk), Historic England (www.historicengland.org.uk) and a selection of European camps from Gilliver, 1993.

For armies greater than five centuries, a commonly sized one metre deep ditch and rampart defensive system took the same amount of time to build. This is partly a reiteration of an earlier observation which merits further comment. Of course, the correspondence in time to complete was simply a result of enough men completing their own sections in the same time, i.e. a contubernium of men in a small army completed their section in the same time as a contubernium in a large army, but there are more of them in the latter, hence, a longer defensive structure finished in the same time. The size restriction arises because armies of one cohort or less do not have enough men – soldiers and slaves – to complete the standard defensive system without producing a very small camp. For example, five centuries of soldiers (400 men), and assigning all soldiers to build the defences as they arrive at the camp-site, results in an unfeasible density of 1417 men per strigified hectare, only c.70% of the area required by the army would fit into that area and only 32 of the required 50 contubernium areas would fit (Fig. 4). Furthermore, the force is insufficient to defend the rampart by nearly 50% if the defended space per solider is 1 m, and only just sufficient, but with no reserve, if the space is increased to 1.5 m. To overcome these limitations, armies of five centuries or smaller had a number of options: decrease the sizes within the defensive structure, e.g. dig a 0.5 m deep ditch; increase the number of slaves from, the generally assumed, 2 per contubernium and have them assist in defence building; shrink road widths to, say, 4 m, enough for a cart; limit the intervallum width to a slim border around the strigified area; have the defence building crews dig two 1.524 m sections, one after another, but this option requires smaller defence parameters to avoid a very lengthy build-time, e.g. 0.5 m deep and 1.5 m wide ditch and commensurate changes in the rampart. However, these small armies probably did not individually campaign, being too small to defend themselves against most enemy forces. Furthermore, the majority of the extant small camps in Britain are situated close to the Hadrianic and Antonine walls or forts, and are usually described as construction or labour camps, which probably meant that the usual limitations, due to available time and men, did not apply.

Figure 4: Spreadsheet results for five centuries (400 men) building the standard defences. The red coloured cells show that the available soldiers are too few to build a camp large enough to house them. See text above for discussion. Note that the negative numbers, the consequence of trying to fit too large an army into too small a space, have not been suppressed in the spreadsheet because to do so considerably increased the computation time – such rows are to be ignored.

There may have been an equality of diggers and rampart erectors taken from the contuberniums assigned to defence-building. Furthermore, equality between the depth of the ditch and height of the turf and soil rampart, coupled with an equality of diggers and rampart erectors, results in the ditch and rampart being completed in approximately the same time. This is generally true for the modelled triangular ditch with ankle-breaker and a trapezoid shaped rampart composed of inclined walls two turves thick, front and back, the interior of which is infilled with the ditch detritus, and with a fighting platform two turves thick. Typically there is a small excess of ditch detritus that could have been used to raise the rampart or form steps, etc. These equalities would have considerably simplified the process of defence building. However, there are other rampart configurations that could have been chosen.

As a general rule, there is a greater time-cost to using earth infill in ramparts compared to filling the same volume with turves. For example, a 1.1 m high rampart with walls one turf thick, front and back, would take over two hours longer to build with a likely finish after sunset, and require an additional 2.3 m³ of earth infill per 1.524 m length section than one of the same dimensions but with two turves thick, front and back. This is due to the need to dig, carry, infill and tamp down the additional earth infill. Continuing with the example, a rampart 400 m long would require 603.67 m³ and 965.88 tonnes (density 1.65 tonnes/m³) of additional earth. Furthermore, this additional infill would have to be sourced from somewhere other than the ditch if the mean depth is accepted at 1 m. Double-thickness walls would also be more stable and robust. In consequence, the calculations strongly suggest that the Romans would have used double-thickness turf walls. The calculations in the spreadsheet assume that the turves were cut prior to the digging of the ditch from the area occupied by the defence complex and additional area as required in front of the ditch; this would have given the Romans sound footing within the rampart but made the approach to the defences slippery. The spreadsheet models all team members cutting turves and placing them in the intervallum ready for construction, i.e. turf cutting is the first, joint action of the whole team.

A high palisade on top of the rampart was essential for an effective defence system. As previously discussed, the spreadsheet suggests the Romans used an equality in depth of ditch and rampart height. To recap, a ditch 1 m deep, 2.5 m wide might be equalled by a rampart 1.1 m high, 2 m wide and with a 1.2 m wide fighting platform, all being completed within a few seconds of each other if there is also an equality of diggers and rampart builders. A system simple to implement and manage, and probably resulted in reliably reproducible results in most circumstances. Micro-management of soldiers would be low, and significant adjustments to sizes etc. not required; the senior officer would only have to state the depth of the ditch he required for everyone involved to know the overall dimensions of the defences (barring the lengths of sides). However, there is a problem in that a 2.5 m wide ditch and 1.1 m high rampart could easily be leapt by a charging warrior, which would result in either the warrior landing within the camp or colliding with and knocking off a legionary standing on the rampart. The warrior might die as a result of the collision, but the rampart could now be leapt by other warriors without opposition. In one rapid move the defences are rendered pointless. (Note: the average long jump distance for 16 year old boys is c.5 m., the best will jump over 6.5 m.) The simplest remedy, modelled in the spreadsheet, is to place a palisade atop the rampart made from sharpened stakes (sometimes called pila muralia) that soldiers either carried or fashioned at the new camp. Extant versions are 1.25 to 2.0 m long, waisted in the middle and tapering to sharpened points at either end. These could be thrust into the top of the front wall of the rampart, possibly to a depth of 1 m, which would anchor and support the turves, and also form a solid, protective barrier to missiles, slashing swords, poking spears and leaping warriors. The shield-equipped Roman legionary, standing directly behind the palisade, would form the mobile, active element of the defensive system; effectively, the earth, turf and palisade components were designed to protect the legionary, hence the whole camp and inhabitants. Sunk 1 m into the rampart, the palisade might have increased the height of the standard defences above ground level to 2 m (more than the average male height), and the total height from the bottom of the 0.3 m deep ankle-breaker to 3.3 m. An attacking warrior attempting to leap a 2.5 m ditch, followed by a 2 m high defended wall, would likely fail before slithering over 3 m to the bottom of the defences. The sharpened stakes may have been used as partially buried caltrops in the front wall of the rampart, but this solution would have been less effective against missiles, could be pulled out or scaled and may not have deterred a leaping warrior, but may have been a secondary deployment option if there were sufficient stakes. Note that, unlike the form of extant ditches, the archaeological record for ramparts is poor and, of course, any recorded heights are those that remain after c. 2000 years of erosion and slumping, hence, this study and others cannot make sensible use of these height data.

The area assigned to each contubernium defined by Pseudo-Hyginus is probably too small at 31.54 m² (8.88 x 3.552 m or 12 x 30 Roman pedes). The Pseudo-Hyginus area value is sometimes used in attempts to match historical, campaigning Roman armies to extant marching camps. These attempts usually use the whole area within the ramparts while this study uses the strigified area, i.e. the area within the ditch minus areas for the rampart, intervallum, roads and any user-specified additional area. Combining the Pseudo-Hyginus contubernium area with the standard defensive structure causes the first suitable spreadsheet value of the ‘required army area that fits into the available strigified area’ (column AE, => 100%) to match the ‘soldier density per strigified hectare’ (column AG) at c.1500 for all army sizes. Note that the camp has 10 m wide roads and intervallum and that, in addition to the contubernium area calculations, there are also values for mules, horses, carts, latrines and any user-defined area. This is a very high density of men, concomitant beasts and carts, a density very unlikely to have been practised, and suggests that Pseudo-Hyginus’ contubernium area is too small. However, increasing the dimensions of the Pseudo-Hyginus area by 1 m results in a density of c.980 men per strigified hectare, a value that could be considered as more plausible.

Densities of men per hectare greater than c.1000 is unlikely to be historically valid. High densities of 1000 – 1186 men/hectare are sometimes proposed by archaeologists and historians, especially for the camps at Masada or when the density is being assessed based on the Roman actus (length, 35.5 m). However, the preceding observation paragraph suggests a more plausible limit to densities might have been c.1000, possibly c.900, because the armies defined in this study will not fit into camps that result in such densities. Unfortunately, use of the spreadsheet has failed to find a lower density limit because there are too many unconstrained variables in the archaeological and historical record, e.g. the widths of roads and the intervallum or the number of cavalry.

The larger the army the greater the number of gates required to efficiently exit the morning camp. Furthermore, the number of gates used per type may have been balanced to ensure that all column types (men, mules, etc.) exited in roughly the same time. Amongst other benefits, this would allow marching columns of men, mules and carts, of roughly similar length, to efficiently form the marching order, for example a centre of mules and carts flanked by columns of soldiers. Such balancing of columns and available gates may have been well known to the Romans. An extreme emphasises the benefits: an eight legion army exiting a camp with two gates apiece for soldiers, mule and carts could take 5:41:00. In this case the mules take over 3 hours to exit but increase the number of gates to eight (some camps have 10 or more gates), assign four to the mules, and the total exit time decreases to just over 4 hours. Of course, there is an assumption that different types were assigned their own gates, which may be correct given that beasts quickly make ground difficult for men to traverse, especially in wet weather, but for large camps this would have involved some form of traffic-control within the camp.

Roman armies were extremely efficient construction machines. This is not a unique observation but does bear repeating. For example, a single legion, multi-column marching off-road 16 km, could have excavated 7237 tonnes from a 1 m deep, 2.5 m wide ditch by c.18:57:00, thereby producing a camp the size of St. Leonards’s Hill, one of the largest in Britain, with sides 738 by 1000 m enclosing 73.8 hectares. Only 72.30% of the soldiers, given a 1 m spacing, would be required to defend the ramparts and gates, but the density of men/hectare has fallen to 76, i.e. the camp could be built and defended, but the area enclosed is vastly greater than that required by 5120 soldiers. This efficiency arises because all the soldiers arrive in the camp in less than 20 minutes (velocity of march is 0.6706 m/sec and with a column of soldiers either side of a centre of mules and carts), and that time also separates the completion times of the first diggers from those that dig the equivalent of St. Leonard’s Hill. This mathematical outcome, inherent in such modelling unless some fuzzy logic is introduced, over-emphasises the efficiency of the Roman army which in reality would have taken more time to build the camp. Nevertheless, some Roman commander of a single legion could have produced such a large camp in similar time, assuming a little metronomic activity by his men.

A single legion could march 29 km on-road, in a single-column, at a velocity of 1.2741 m/sec, and complete the standard defences, sufficient for the whole army, by c.18:25:00 and with only c.1700 soldiers having arrived in the camp. In contrast, marching in a single column off-road at a velocity of 0.6706 m/sec, would have the last soldier arrive at 22:26:00 and the defences completed by 25:05:00, i.e. the next day. Clearly then Roman armies did not march 29 km off-road in single column, but the same army marching in multiple columns off-road could cover 16 km and complete the defences by c.18:46:00.

An eight legion army marching 16 km off-road in multiple columns at 0.6706 m/sec could have the standard defences completed by c.18:55:00.

On-road marches of 29 km, velocity 1.2471 m/sec, were possibly limited to three legions, probably two. Structuring the marching legions for typical road widths (variable, 4 to 10 m) limits the number of files per type, for example, soldier ranks might be limited to 4 abreast, mules to 2. For a full-compliment army of three legions this results in a total column length of 23.4 km and the time taken to pass a single point is 5:06:00. Crucially, the last soldier arrives at the new camp at 20:29:00, twilight for a mid-August day in Britain. Critically, the energy expenditure for soldiers not involved in the building of defences is 5694 kcal/day, while rampart builders working for c.2:57:00 expend 6467 kcal/day and require over 12 litres of water: these figures mean the soldiers are highly stressed, especially by heat, and this level of activity is unlikely to be sustainable day-after-day. In practice the time taken may have been longer, given that maintaining march discipline over such a length of time would be difficult, hence the probability that the limit for 29 km marches was actually two legions, the last soldier arriving at 18:46:00. A pragmatic solution in this scenario to armies larger than two legions may have been to shorten the march.

Off-road, single column marching was probably rarely employed except for small armies over short distances, or where the terrain channelled the force. In contrast, multi-column marching off-road creates a compact, defensible structure which reaches its destination more quickly, and uses less energy and water than a single column army. For example, two fully complimented legions marching 20 km in single column could have the last soldier arrive at the night camp at 21:35:00, the camp completed at c.20:52:00, non-builders expend 4669 kcal/day and the rampart builders may need 14 litres of water. If the army used multiple columns the last soldier arrives at 18:31:00, the completion of the camp occurs at c.20:45:00, non-builders expend only 4320 kcal/day and the rampart builders drink under 11 litres. In both single and multi-column marching off-road the high water values indicate that the rampart builders are being dangerously heat-stressed, even debilitated, by their activities, especially by the march distance. This is further support for the observation below that c.16 km marches off-road may have been close to the norm.

Under normal circumstances the camp defences were probably completed by c.18:30:00 to allow soldiers to cook, eat, wash and repair equipment and rest during the remaining daylight hours (roughly 2:30:00 during the high-Summer). If correct, this places a further limit on distances covered and the time taken to march for the first arrivals and those required to build the defences.

March distance of c.16 km for multi-column, off-road marches would seem to be a normal limit. For example, a two legion army marching such a distance would complete the standard defences by c:18:48:00. Except for minor variations, the same is true for all armies, including those of eight legions, assuming they built the same defences (barring length, of course).

For Roman armies campaigning in Britain, and most of Europe, the observations above probably would have governed the distances marched at the tens of kilometres scale. However, the need for adequate water at the campsite would dictate the march at the single kilometre scale. Placing the camp close enough to a sufficiently large supply of water was of critical importance to the Roman army. It is for this reason that a previous study (Kaye, 2013b) found that of 307 extant camps in Britain c.66% were within 100 m of a river(s) with a flow sufficient to meet the needs of the army, and c.90% within 300 m. There are, of course, other factors that govern the placement of camps (Kaye, 2013b). In summary, a Roman army might be distance-limited at the tens of kilometres scale by the need to march on- or off-road, i.e. circa 29 km or 16 km, respectively, but further limited at the kilometre scale by water needs to march, say, only 27 or 14 km, or indeed the reverse – to march a kilometre or two further.

Discipline on the march was very important to campaigning Romans. For example, assuming a great need, a full-compliment, five legion army could march on-road for 29 km with the first soldier arriving in the new camp at 15:22:00 and the last at a tenable 20:22:00, that is at dusk in the high Summer in NW Europe. In this example the number of files for the pack mules was set at 4, but if the file number is relaxed to 2, representing a loss of march discipline, then the last soldier marches for 14:29:00, expends 5947 kcal of energy and arrives at the new camp at an untenable 22:29:00. There are similar, size-scaled effects for all other marching armies.