Potential uses and benefits of hillwalking as cardiovascular exercise
Andrew Wang, 2017
The hills are often frequented by all athletes alike, as it is believed that walking up a steeper gradient makes your heart beat faster – a 24% gradient can increase your heart rate by 55% at a modest speed compared with walking on flat terrain. 
The relationship makes sense because heart rate is a good measure of how hard your body is working during exercise.  This article presents the results of an experiment that seeks to verify and quantify the effects of different factors involved in this relationship.
In the experiment, the heart rates of hillwalkers were tested in varying conditions and it was concluded with near certainty that this cause-and-effect relationship exists, leading to a whole range of possible applications.
The link could, for example, be exploited to solve the problem whereby mountain/trail athletes (e.g. runners, cyclists and hikers) want to know their heart rate with a higher level of accuracy and fidelity than can be achieved at present with other means. Such useful bodily statistics can be thus deduced by simply measuring the gradient of a hill, easily achievable with GPS technology.
An increased heart rate points to aerobic exercise and countless studies have linked this to good health (e.g. lower risk of coronary heart disease or stroke).  For example, regular moderate intensity aerobic exercise can result in weight loss.  Good cardiovascular health also points to these benefits. 
Heart rate is therefore something that one often wants to measure. For example, during hillwalking, an athlete may want to know accurately the number of calories burnt or whether they’ve reached their target heart rate, where the heart works best. Current smartphone tracker applications, which essentially guess using generalised algorithms,  are inaccurate and physical heart rate monitors are cumbersome. Instead of looking at technological ways of measuring this data, other potential factors may be considered– notably, the gradient, or slope of the path or road.
The research hypothesis was therefore that at any point during a journey (here hillwalking is considered), the body’s heart rate is positively affected by the gradient of the slope of the path at the point of travel – that is, there is a direct causal link. If the hypothesis is to be accepted, one can quantitatively measure the health benefits of hillwalking.
Exploiting the direct link between heart rate and gradient can help a number of future developments. For example, a bioengineering-inspired approach can make use of the findings to create better algorithms in mobile fitness trackers to more accurately show users relevant information about their bodies, such as calories burnt or instantaneous heart rate. In addition, civil engineers and contractors could determine the gradients of a particular exercise site to suit the desired heart rates of different people walking up and down it in order to optimise their health benefits.
A future treadmill manufacturer could tailor its program to create the most effective workout for any user by adjusting its gradient so as to reach the so-called target heart rate, where the heart works optimally without straining.
It is a widely stated online fact that a steeper gradient causes a higher heart rate,  although such literature lack causal analysis. In addition, papers on the topic have seemed to focus on those whose bodies would be the least fit, including old or overweight people,  as they would be at the most risk to diseases/conditions such as coronary heart disease or diabetes; these research studies may not be relevant to most people. 
Furthermore, these investigations tend to focus on biological effects on the heart rather than their implications, which are arguably more important for achieving the functionality of such studies.
This study carries out a causal analysis and proposes methods of exploiting the results to practically maximise relevant health benefits.
This research was done on a group of six relatively physically fit late teenagers, a period where the body generally approaches peak performance,  and where other environmental/hormonal factors such as puberty, pregnancy or smoking are less of an issue. This also makes the research relevant to the readers of this journal.
In this experiment, each member took their own heart rate twenty-one times over the course of a 4-day hiking expedition, on mountain slopes of varying gradients. The data sets of all 6 members’ heart rates and the group mean heart rate against gradient were analysed for a positive linear correlation, and then further tests were undertaken to investigate a causal link.
Due to external restrictions, any slope, for example a hill road or track, was modelled as a triangle; each point of measurement’s grid reference was noted and the average gradient was taken as the contour density on the path, calculated as ascent or descentdistance×100 where distance, the distance walked during measurement, is calculated using online OS mapping software.
The heart rate readings were taken without standing still, by counting the number of beats from the chest or wrist for 30 seconds, and then multiplying by 2 to obtain a “beats per minute” (bpm) value. Each day, the readings were taken over the course of the entire day.
Other factors, such as weather and path surface descriptors were also recorded at each location, across a variety of conditions to ensure that the experiment was randomised. Nevertheless, these factors were still statistically tested.
Analysis of the causal relationship used the following minimum “criteria”, which have been adapted from a widely-used system designed by epidemiologist Austin Bradford Hill: 
- Strength: the coefficients of correlation and determination are high and significant;
- Consistency: the result is the same when done by/at different people or places;
- Specificity: there is no other likely factor or explanation;
- Temporality: the effect occurs after the cause;
- Gradient: an increase in the cause leads to an increase in the effect, and vice-versa;
- Plausibility: there is a plausible mechanism between cause and effect;
- Coherence: the relationship is compatible with relevant theory;
- Analogy: relationships between similar causes and effects exist.
These criteria will be discussed in the analysis section of the article.
Since all measurements were solely human or computer-based and not instrument-derived, any inevitable error would be small, meaning that the measurements are considered accurate. The experiment is very repeatable and the analysis was based on the mean of 6 individuals to ensure reliability.
Tables 1-3 and Figure 1 present the raw and extracted experimental data and test statistics.
Table 1: correlation analysis of heart rate group means vs. gradient of slopes. Raw data is shaded, and test statistics are coloured yellow. The residual is how far the heart rate predicted by the best fit line is from the actual value.
Figure 1: graphical representation of means vs. gradients (the best fit line and its equation are shown).
Table 2: summary of heart rate residual means data grouped by weather / surface condition. Std. Dev. represents the sample standard deviation of the group
Table 3: t-tests undertaken based on Table 2
|Tests||Sun vs. Rain||Rain vs. Cloud||Sun vs. Cloud||Smooth vs. Bumpy|
Here, each of Hill’s causation criteria is assessed based on the analyses of the collated data.
The correlation of mean heart rates to gradients is strongly statistically significant (P<0.0005 when r=0.86 from Table 1) – this is shown in the clear linear relationship on the graph (Figure 1). Similarly, the coefficient of determination is high (R2=0.745) and there are no excessive outliers, ensuring the correlation’s strength. From Figure 1, the gradients and heart rates can be assumed to follow the bivariate normal distribution.
The same result was consistently shown across all 6 individuals of the group (where P<0.0005 for all members, except for one where P<0.001).
It also follows that there is an increase in heart rate when the gradient increases, and vice-versa.
Any possible third causal factors were also tested. Heart rate data in different surface conditions (smooth, bumpy) and weather conditions (sunny, rainy, cloudy) were compared, and 2-sample independent unpaired t-tests were undertaken to check for a significant difference between the group means. The alternate hypothesis for each test was that d≠0, where d is the difference between the means.
As indicated by Table 3, all test statistics were not significant (P>0.05) and hence there is insufficient evidence to accept the alternate hypothesis, and to suggest a difference in the heart rates under different environmental conditions. A similar association test on the time of day was done and the outcome was also negative (P>0.05 when rs=0.248 from Table 1). This suggests that there are no other likely factors that could contribute to the relationship; hence, the direct causal link is valid.
Naturally, temporality is maintained as the existence of a slope precedes the measurer.
Plausibility, Coherence, Analogy
The heart rate-gradient link is understandable and plausible from a physiological point of view, and is coherent with the findings of scientists and athletes alike (as discussed above). In addition, the effect is observable and analogous with any sample of people travelling up and down hills.
Since all of the Hill criteria for establishing a causal link between two variables were satisfied, as demonstrated in the previous section, the relationship is very likely (although not certainly) a direct cause-and-effect link rather than one that involves such a third factor (i.e. weather, surface, time of day).
The results therefore support the experiment’s research hypothesis, that the body’s heart rate is positively and directly affected by the gradient of the slope of the path at any point during hillwalking. One can hence conclude that mountain/hill exercising is beneficial for the body, as this heart rate increase will lead to better cardiovascular health (as mentioned previously), and that there are many practical uses of the result.
It must be noted that there are obvious limitations in this approach, for example varying blood sugar levels or tiredness on any one day, could affect the heart rates, and thus introduce a calibration error. Further experiments such as this one need to be carried out to see the effects of such external factors, and to extend this investigation’s applicability to other activities such as running or cycling. However, the experiment undertaken presents sufficient evidence to suggest a similar result for these other activities.
Application of Results
Having established the quantitative causal link between heart rate and steepness of slope, it is now possible to exploit the relationship to achieve some health-related practical benefits. For example:
A hiker would like to be able to measure his heart rate during walking so that he is aware of how hard his heart is working, and whether it is working optimally. First, a calibration exercise is done, where he goes out and obtains a few measurements of his pulse on different gradients:
Since the relationship is linear, it can be expressed as the equation of the best fit (least squares regression) line:
where y is someone’s heart rate at slope gradient x, and M and C are ‘calibration constants’ unique to each person.
Using this data, a best fit line can be plotted and he can obtain his own calibration constants M and C using simple statistical techniques.  In this example:
Now on future walks, whenever the hiker wishes to measure his heart rate simply (or perhaps automatically), he can easily do so by using the following formula (at point of measurement with slope gradient x):
This can be done automatically in a smartphone application, where a GPS service measures the slope gradient. This way, his heart rate can be continuously logged throughout the exercise, which visibly is more faithful and personalised than a tracker application that guesses these statistics.
Heart rate measurements of six teenage hillwalkers on different hill gradients were analysed to see if there was a direct causal relationship between heart rate and the gradient of the slope. Based on an assessment of the data against the criteria of a widely used system for establishing causation, it was found that the correlation was strong, and the effect of other likely factors (weather, path surface, and time of day) were insignificant. Thus, it was concluded that an increase in gradient of the slope almost certainly causes an increase in heart rate, and vice-versa.
This not only proves the conjecture, but provides a quantitative way of representing the relationship between heart rate and gradient of a slope. Walking (and by extension, exercising in general) on slopes increases a person’s heart rate, leading to cardiovascular health benefits.
This result has many practical uses, for example to individually maximise workout intensity or to give a user more accurate, personal bodily statistics, using linear formulae incorporating unique calibration parameters.
This also paves the way to autonomous body data collection, useful for the future of medical diagnosis and biomedical technology.
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About the Author
Andrew enjoys eating poached eggs and catching epic sunrises on morning runs, and is currently training for the upcoming Manchester Half Marathon.