Velocity-Based Terrain Coefficients for Time-Based Models of Human Movement

Few studies have calculated the relative difficulty of walking across different types of terrain (e.g. grass, asphalt, loose sand, and so on). Nonetheless, these relative values, called terrain coefficients, are integral, alongside slope, for generating computer models of human movement, whether for emergency planning, development, archaeology, the impact of ecological change on migratory patterns or any other purposes. Additionally, the few studies conducted evaluate this relative difficulty through metabolic rate measured through oxygen consumption. We demonstrate that these values are only appropriate for energy-based models (e.g. easiest routes), because it is unlikely that the relationship between metabolic rate and velocity is linear even when terrain is held constant. Rather, our work (returning to four terrains from these earlier studies and adding three additional terrains) investigates the relative effect different terrains have on a person's walking speed, finding the effects to be smaller, with statistical significance occurring on an entirely different scale from previous studies. Therefore, these terrain coefficients should only be used for time-based models (e.g. fastest routes).


Background
Intuitively, a person can think about how some terrains (paved path, dirt road) are easier to walk across than others (bog, loose sand). A computer model of human movement, however, needs to be informed of these differences through numbers called terrain coefficients, sometimes also called multipliers (Herzog 2014a). These terrain coefficients impose a penalty on movement through different terrains. Previous studies were conducted in the 1970s by a group of physiologists affiliated with the U.S. military, interested in the effect of land cover on energy consumption (Givoni and Goldman 1971;Soule and Goldman 1972;Pandolf et al. 1976;1977). As a result, these studies have concentrated on calculating terrain coefficients for young adult males.
Collectively, these studies calculated the terrain coefficients for walking across a total of nine different terrain types by measuring oxygen consumption to calculate differences in metabolic rate (see Herzog 2014a, table 3). Currently, computer models of human walking that factor terrain must rely on these values (presented here in Table 1), regardless of the population (male/female, old/young) or type of model employed (e.g. easiest route, fastest route). If a study involves movement across other terrains, then the values must be approximated by interpolating between the nine existing terrain coefficients. We had several questions: are terrain coefficients based on energy expenditure appropriate for models based on other variables (e.g. fastest routes)? Are terrain coefficients the same for males and females? Are they the same for different age groups?
Does the burden of carrying extra weight (particularly important for migration) have a measurable impact on terrain coefficients?  Givoni and Goldman 1971;Soule and Goldman 1972;Pandolf et al. 1976;1977;Yu et al. 2003;as summarised in Herzog 2014a) To help answer these questions, we measured the relative difficulty of traversing terrains through participants' velocities rather than oxygen consumption and metabolic rate, repeating four terrains from these original studies: blacktop/pavement, lawn grass, swampy bog, and loose sand.
Additionally, we sought to expand the range of existing terrain coefficients by evaluating three new terrain types: a decayed asphalt/gravel path, tall grassland, and disturbed ground in an abandoned stone quarry. All seven terrains were located in County Durham and Tyneside, England (Figure 1), and selected using the authors' knowledge of the region combined with preliminary site reconnaissance to assess the suitability of each site.

Methodology
We successfully recruited five male and five female participants across two broad age categories (20-35 and 36-50 years old) who participated for two days each across a total of six study days.
All volunteered and provided informed consent. Durham University's archaeology and anthropology ethics committees reviewed and approved the project. The project's sample size is comparable to previous studies, which included between 6 and 14 subjects (Givoni and Goldman 1971;Soule and Goldman 1972;Pandolf et al. 1976). To avoid the possibility of fatigue artificially increasing the value of a terrain coefficient, subjects were provided time to rest with lawn chairs, and access to free tea and biscuits. We measured 200m-long routes with a 30-metre tape measure and marked it with bright orange flags placed every 10m. Variance in path location between days was less than 25cm. The participants then walked the path one at a time in isolation at the pace that they found most comfortable. The time they took to complete the total 200m and the final 100m were recorded to the nearest hundredth of a second using handheld stopwatch apps on an Apple iTouch 4.0 and an Android (5.0) phone (see spreadsheet). Participants were given no guidance on how to proceed along the flagged paths except the suggestion that they take the route they found most comfortable while remaining within the terrain zone. Participants then repeated walking one at a time along the marked path with a weighted backpack equal to 30 per cent of their body weight as measured to the nearest pound on the first day of participation. This proportion of weight was sufficient in the original studies to cause a significant difference in performance (Soule and Goldman 1972).
Each path was 200m long -an arbitrary length that enabled subjects to fall into their natural stride, but not so long that they would be tired when walking the third or fourth terrain in a single day. That subjects did walk at a natural stride is demonstrated by the consistency in their velocities between the first 100m and the second 100m. This was particularly pronounced on the loose sand, where participants were placed in the middle of the track and walked 100m to the starting point.
On this terrain, participants' completion times were always equal to within a tenth of a second between the first and second 100m, indicating that 100m is sufficient for kinesthetic learning of a terrain and the development of a natural stride.
In three cases (tall grass, bog, and disturbed ground) finding a stretch of land with one consistent terrain type that remained level in an accessible area proved difficult. In these cases, a shorter stretch of land (100m or 50m) was chosen that could be walked forwards and backwards multiple times without obstruction (see Figure 1 showing routes mapped in Google Earth). On two http://intarch.ac.uk/journal/issue45/4/1.html 5/13 occasions weather conditions of high winds and rain prevented some participants from completing the full range of terrain paths and our data analysis was adjusted accordingly.
Following previous studies, the terrain coefficient value for pavement/asphalt was designated 1.00 and all other terrain coefficients were calculated as ratios relative to this value (see, for example, Soule and Goldman 1972). For each terrain we simply calculated the proportional increase in the length of time it takes for each participant compared to their baseline time traversing the same distance on pavement.

Results
The results show a statistically significant difference for all but one of the terrain coefficients (decayed asphalt/gravel path) compared to the baseline pavement value, which was artificially set to 1.00 in keeping with previous studies; however, the actual difference can be quite small (see Table 2). This represents the first of our conclusions, that different terrains have a significantly measurable impact on speed of transit. The coefficients representing the velocity at which participants traversed each terrain relative to their speed on pavement. Data were analysed using the one sample t-test to compare the mean of the participants' coefficients for each terrain against the reference value of 1.0 (normality was first verified with q-q plots). We have included the p-value of each test in the table to indicate statistical significance.
It is also interesting to investigate the variation of the terrain coefficients of each surface with population variables such as age and sex, and to see whether the burden of extra weight carries a significant penalty for each topographic type. So for each terrain we compared the performance of participants grouped according to these variables, to determine whether there is variation in each terrain coefficient between the groups. This was achieved with a two-sample t-test (unequal sample sizes and variances) comparing the means of the coefficients of the groups against one another for each terrain type. We took a 95% significance level on a null hypothesis that the average terrain coefficient of each group is the same.
http://intarch.ac.uk/journal/issue45/4/1.html 6/13 Across each terrain, comparison between groups of participants demonstrates that age is not a significant factor for relative ease of movement. The authors suggest this may be due to a lack of elderly participants, who are more likely to have joint problems like arthritis, or younger children unable to maintain a comparable pace to adults. Sex, however, can be significant (at the 95% level) depending on the terrain. In our study lawn grass was found to show a significant difference between the coefficients of men and women (men: 1.067, women: 1.002, p-value: 0.03). A possible reason for this may be found in a study by Saibene and Minetti (2003), who found that a soft surface allows for a longer stride; the short length of the lawn grass would also enable greater freedom of movement. It is, therefore, possible that the observed difference between men and women on lawn grass may be the result of longer stride lengths by the men (although this was not measured

Discussion and Scope
Comparison between the new, velocity-based terrain coefficients and the pre-existing, metabolic rate-based terrain coefficients highlights that the two are not interchangeable. In particular we were unable to fit a simple linear model between the two sets of coefficients. Significant differences in our study occur at the hundredth decimal point, so the penalty incurred in speed of walking upon different terrain types appears to be less severe than that associated with increased metabolic activity. Furthermore, we found the bog has a much higher terrain coefficient value than the loose sand, whereas the original study evaluating both bog and loose sand (Soule and other than those based on energy consumption. Likewise, the terrain coefficients from this study based on velocity should only be used in models based on time (e.g. fastest routes). Second, that the original studies used only young male subjects may not be an issue, but this should be confirmed with more studies, given the significant difference in performance between male and female subjects on lawn grass. Furthermore, statistical significance occurs on such a narrow scale that a difference of as little as 1.8 seconds across 200m is significant at the 95 per cent level.
Whether this statistically significant difference is meaningful in the real world will depend on the model and research question at hand. For example, does it matter in the real world that walking 5km through one terrain would take 1 hour while walking a parallel path through another terrain would take 1 hour 1 minute and 48 seconds? In what instances would a difference on that scale matter to a person? Undoubtedly, the answer to this question will be culturally specific and at least partially based on available time-measuring technologies. It is unlikely such a small difference, for example, would matter to a fourth millennium B.C. Mesopotamian for whom the concept of hours, minutes, and seconds are more than a thousand years away, and for whom all administration (including the rationing of workers) is calculated in days (Brown 2000; 2010; Englund 1988).

Future Work and Re-use Potential of the Dataset
Two of the main aims of publishing this article were: 1. highlighting the need to generate velocity-based terrain coefficients, and 2. sharing the terrain coefficients we calculated so that they can be used.
There are, however, still many more terrain coefficients to calculate. The World Wildlife Fund has identified 867 terrestrial biomes around the world (Olson et al. 2001). Ideally, both energy-and velocity-based terrain coefficients will be calculated for each unique surface of the Earth, so that researchers studying regions around the world will have appropriate terrain coefficients to use in their models. Generating these will require an enormous amount of research and it is hoped that by sharing our methodology, others will be able to calculate additional terrain coefficients. We will be launching a website (https://terraincoefficients.wordpress.com/) that will aim to collect and maintain a complete list of all known terrain coefficients.  If a route was in constant use for economic purposes, the vegetation was cleared either by repeatedly walking the path or by cutting the vegetation. Several prehistoric roads in wetlands have been recorded (e.g. the Eclipse track constructed by interwoven rods in Somerset, see Renfrew and Bahn 1996, 314-15). So for this class of paths, the path surfaces differed from that of the surrounding landscape (see also Herzog 2014a, section 5.3: 'Vegetation cover should be mainly considered in the context of path formation'). It might be more important to take the effort of building paths into account than the time needed to walk on walker-unfriendly terrain). For the reasons given above, velocity-based terrain coefficients for grass, light or heavy brush, swampy bog and ploughed fields are probably not appropriate for LCP calculations.

How the Dataset Relates to other Publications
The site catchment is 'the area around a site that would have been exploited by the site's occupants' (Renfrew and Bahn 1996, 242). Renfrew and Bahn refer to a publication suggesting a radius of 1 hour's walk for a sedentary agricultural site and a radius of 2 hours' walk for huntergatherer sites. For movement of hunters and gatherers some of the terrain coefficients are important. But farmers replace the initial vegetation by pastures and ploughed fields, they mostly use paths and the arguments given above concerning LCPs apply. Moreover, in many past farming societies, the use of wheeled vehicles and pack animals had an impact on human movement.
For people moving into an unfamiliar region or foragers searching for food, the target location is not known in advance.
People may adopt a strategy like Lévy walks to find food, an appropriate target location for the night or for building a new farmstead. For a mathematical discussion of such strategies see Lewis et al. 2013. On these walks foragers probably try to avoid terrain that does not allow fast progress.
So with a raster-based model for human expansion, the probability of an agent moving into a neighbouring raster cell can be computed based on the terrain coefficients. Mostly young, healthy and adventurous people walk away from their home to find a new place to live. Therefore focusing on this group of people seems appropriate. But it is quite difficult to reconstruct the vegetation cover of past times. Often, only estimates at a global scale are available (e.g. Romanowska 2015).
It is possible that the terrain coefficients can be used in non-archaeological models as mentioned in the summary of the article. For emergency planning in mountainous areas, data on the velocity of walking on trails, grassland, and forest is available elsewhere (Ciesa et al. 2014). However, nonarchaeological applications are beyond the scope of this review.

Detailed comments
The authors state that 'it is unlikely that the relationship between metabolic rate and velocity is linear even when terrain is held constant'. They also refer to the formula published by Lejeune et al. (1998) found that 'walking on sand requires 2.1 to 2.7 times more energy expenditure than does walking on a hard surface at the same speed', whereas the multiplier for running on sand is only 1.6. Please note that the formula presented by Givoni and Goldman (also used by Soule and Goldman) is the product of the terrain coefficient with a factor depending on weight, load, velocity, and slope, whereas the Pandolf et al. (1977) formula consists of a term depending on weight and load only (estimating the energy consumption of standing) plus the extra energy required for movement, and only the latter term is multiplied by the terrain coefficient.
Considering the fact that energy expenditure of walking normally is only about 50% above that of The reasons for increased time to complete the hill walk were mainly 'cold, wet, and windy weather and deep snow underfoot' (Ainslie et al. 2002, 182). This paragraph shows that the variability of most terrain factors is quite high.
The authors applied t-tests that require the assumption of normal distributions. So they check normality by q-q-plots. The quartiles given by Ciesa et al. (2014,  The anonymised data used for computing the new time-based terrain coefficients was not available to the reviewer. Additionally, it might be useful to measure the heart rate. From the heart rate, the weight of the participant and the distance covered, the calories burnt can be estimated. A stationary bicycle provides such an estimate. Small heart-rate monitors with low weight are affordable; carrying such a monitor most probably would not affect the results. Calculating the energy expenditure for walking a given distance must take both the increased heart rate and the velocity into account (cf. Ainslie et al. 2002).

Conclusion
The design of the study to generate the data and the results presented in this article are sound.
The main issue is the problematic application of these data in archaeological research.
In archaeology, terrain coefficients are mainly important for modelling human expansion. But most projects dealing with such models cannot afford a detailed landscape reconstruction including the climatic conditions and the vegetation. Moreover, it is hard to estimate the impact of the time required to pass an unfamiliar piece of land on the choice of the route taken. Personally, after (temporarily) losing a boot, I would probably return and try another direction, if nothing forces me to walk on in that bog. Maybe some ethnographic sources are available dealing with this subject?
Due to the variability of the terrain coefficients found in previous studies and owing to varying climatic, seasonal and weather conditions, analysis of the impact of each terrain coefficient within its interval of variation is recommended rather than relying on one value only.
In my view the significance of this article is limited, if simply the data presented are considered.
But if archaeologists do not just harvest the data but think thoroughly about the importance of these coefficients for their project, an important aim has been reached.

Response by de Gruchy, Caswell and Edwards
The limited range of terrain coefficients (energy-or time-based) remains an issue for studies of movement that factor terrain/land cover, and will remain an issue after the publication of this article. More terrain types need to be evaluated, results need to be replicated, and future studies should aim to utilise larger sample populations (more people).
As research into past mobility and routes develops, the need for robust terrain coefficients will only grow. For example, with the recent development of a means for quantitatively comparing a route model to a preserved or known historic/ancient route and for assessing the statistical significance than slope as a cost factor in movement.
There are many existing assumptions about what variables were important to people travelling in the past (saving time or saving energy, to name two of the most common). It is time to move beyond assumptions. In her PhD thesis, de Gruchy (in prep.) has quantitatively compared route models to preserved routes/hollow ways to demonstrate that the fourth and early third millennium B.C. inhabitants and travellers through the North Jazira (Northern Syria and Iraq) often did not value any such physical variables at all. In fact, physical variables (easiest, fastest, and shortest) frequently did a worse job at predicting the preserved route locations than randomness. One of the conclusions, therefore, is that cultural variables took precedence.
Herzog raises important points about the application for terrain coefficients that we fully agree with. The first is that a route in constant use may be cleared of vegetation. Researchers must think critically about surfaces before applying terrain coefficients -the surface of a route may not match that of the surrounding landscape. In order to select the correct terrain coefficient (a type of natural landcover, a dirt road, a paved surface), it would be ideal if there were data on the frequency and density of traffic required to wear away the vegetation of different terrain types.
In de Gruchy's (in prep.) study area of the North Jazira, the routes are preserved as hollow ways, erosional features for which the terrain coefficient of a dirt road would certainly be more appropriate than one approximating a type of steppe -but only once enough people travelled the