Tuesday, January 31, 2023

Water Supply and Water Carriers

As indicated in the previous article I read the following recently: Women work harder than men – our anthropological study reveals why. This got me thinking about the issue of fetching and carrying water from a distant location.

Now it seems that fitness trackers could be used for industrial engineering, work study and work measurement providing improvements over simple time measurement. It also seems they could be helpful in the undeveloped countries. 

Consider the common disparity where girls, their sisters and mothers often spend a significant amount of time each day collecting water from distant locations. It should be clear that counting foot steps is of little value, the daughters with shorter strides obviously travel the distance between home and the water supply with more foot steps. But do they do the task in the same time as their mothers or burn the same number of calories, and do they get closer to their MHR than their mothers and does their heart rate stay close to their MHR longer?

Not that we don't necessarily need any measurements to make an initial assessment. 

I recollect a recommendation of a minimum of 9 litres (L) of water per person per day to satisfy various needs: thirst and hygiene. WHO guidelines currently indicate need for 15 L or 7.5 L for short term emergency response. Assuming  a 4 person family then each family needs 30, or 36 L to 60 L per day.

I believe they typically carrying 10 L to 20 L at a time, and make around two trips per day, and the trips can be up to 5 km for both the outward and homeward trips, so 10 km round trip. Average walking speed is typically taken at  5km/h or slightly lower 80m/min. So each round trip is at least 2 hours duration, and the total time used for collecting water 4 hours per day. So rate of water delivery is 0.08 L/min to 0.17 L/min. 

When I turn the tap on water is supplied, depending on tap, at rates between 3.9 L/min and 29.6 L/min, with recommended flows being between 6 L/min and 12 L/min, hot water typically being the slowest. But there is a lot of wasteful industrial infrastructure to make that possible, plus need a large water supply to fill pipelines. If water supply is small, then transportation by container is preferable than piped water supply, as water in the pipes is basically lost.

Alternatively consider a small car, can travel at 50km/h and tow 700 kg. Assuming trailer tank is 200kg, then have 500kg available for water. So the 5km trip now only takes 6 minutes, the two way trip 12 minutes, and now have 500 L, to achieve 41.7 L/min. Assuming car achieves 10 km/L, then need 0.5 L of fuel for each trip, or 1 L for round trip. Assuming the fuel provides 41.8 kJ/g , and taking the density as 800 kg/cu.m, then using 400g of fuel for each trip, provides 16720 kJ of energy, and suggesting average power of 46.4 kW. However, also need yo consider all the infrastructure required to build and maintain the vehicles and produce and distribute fuel, and all the energy it also requires. 

So back to the capabilities of people. A typical recommendation is maximum load to carry is 25% of body weight. Consider that the youngest girl employed for this task is 5 years old, then have female body weights [14,24,45,65]kg for ages [5,10,18, older] years, except for the 65kg these are 5th percentile weights. For males have weights of [16,27, 56, 80]. Therefore females can carry [3.5, 6,11.25.16.25]kg and males [4,6.75,14,20]kg, which at 1000kg/cu.m equates to [3.5, 6,11.25.16.25]L and males [4,6.75,14,20]L of water. So to carry 10 L to 20 L of water typically carrying more than recommended. Also this is ignoring the weight of the container. If the weight of the container is small as would be if simple plastic bag, then can neglect but if a heavy 5kg to 10 kg clay pot, then it needs to be considered. {Note a plastic bag is light weight but not very robust and easily punctured}

So assuming main providers are able to transport 10 L per round trip, and need between 36 L and 60 L per day. Assuming can only make 2 round trips per day, so can only fetch 20 L/day, then need 2 to 3 people carrying water each day. which typically falls to children and mother, and of the children typically the girls. Assuming most only achieving the 36 L recommendation, then 2 people making total of 4 trips required. The above suggests that the father alone would only need make 2 trips to fetch 40 L of water: but assume he would be otherwise busy pulling a plough or something.

Now a wheeled or rolling container would require less force to move. Coefficients for rolling resistance can be as low as 0.001 for steel wheels on steel track, but our situation is likely rough undulating terrain and I don't have any values for such. So I will assume about 25% of force required to push/pull when on wheels. So 10 kg, only requires 2.5kg to push/pull, whilst 20 kg, requires 5kg to push/pull. As I don't have push/pull forces for children, I will assume the 25% rule as applies to carrying also applies to pushing and pulling, so the push/pull forces can apply are the same as the carrying capacities above.

So moving 20L within the capabilities of the 10 year old girl without exceeding recommended limit, but still a bit heavy for the 5 year old. Though the 5 year old doesn't have to fill the container, and could move 14 kg, or less if the weight of the container is significant. It now means the 10 year old can transport 40 L in two trips, and so only one person is required to fetch water.

Now Aquarolls hold 40 L and Hippo rollers 90 L, other more conventional wheeled containers hold 23 L. Hippo also suggests the effective weight when pushing/pulling is 10 kg, which drops our estimate of rolling resistance from 25% to approx. 11% of the load . So the 23L container requires 2.6kg to pull, and the 40L requires 4.4kg. Whilst the females have potential to move volumes of [31,54,101,146] L and the males [35,60,125,180] L.. So 5 year olds can only shift the 23 L containers, whilst those above 10 years can use 40 L Aquarolls, whilst only 18 year olds and older can use the Hippo's full of water.

On this basis only one person is required to make one trip to get 36 L of water using a 40 L rolling container, if they get the 40 L then they get 4 L reserve each day. But if can use the 90L Hippo, then it provides 30L surplus each day based on the higher recommended usage of 60 L. If they don't have a storage tank then they can get benefit from using more water if they use the 90L container.

If they have a storage tank, then they can store the surplus, and further reduce number of trips to make. It would take two trips to get 60L surplus, enough for a days needs. So they can rest every third day, or they can make two trips in a day (180L), and rest for two days or for the children they get 2 days at school. Or given mother can collect all water on her own, the children get to go to school.

Though there is another important factor, and that is the effort required to lift 90kg of water from where ever it is collected: if the container can be wheeled in and out off a water supply and filled, then not a problem. But if it has to be lifted in and out off  the water supply, then it is too heavy for one person to fill. Thus getting water in and out off the carrier container are other issues to consider.

The original assumption was they could travel at 5km/h carrying the load on their backs, in their arms or on their heads, it is assumed they can still travel at 5km/hr pushing/pulling the load. Also assuming that there is no change in the force applied, they apply the same force but are able to move a greater load.

So if F0 is the force to move an empty cart, and W0 work done to move an empty cart and the trip length is 's', then W0=F0.s for the outward trip, whilst if F1 is the force to move a full container, then  W1=F1.s is the work done to move the full container. The total work done for a single round  trip is W=W0+W1=F0.s+F1.s=(F0+F1).s, the total work done in a day was 2 round trips so Wt=2.W, but with the help of technology it reduces to a single round trip and Wt=W. {NB: If F0=F1, then W=2W1=2F1.s=F1(2s), and Wt=2W1=2(F1.2s)=F1(4s), that F0<>F1 is therefore significant.}

Noting that for the original method, the total distance travelled in a day was (2*2s=4s), whilst with the new method it is reduced to (1*2s). Also since speed has not changed and force not changed then Power, P=F.v has not changed. Not working harder, just spending less time working and therefore total energy use reduced (W=P.t).

Generally don't want to change the power. Consider recommended fuel intake is 8700 kJ, if don't gain or loose weight, then rate of energy usage is approximately 100 W, but at 25% efficiency then external work is at approximately 25 W. But from bicycling science book, can expect to sustain a power of 74.6 W for long periods, but to do so would require more fuel than the recommended daily input. We can therefore assume that work less than 25 W is easy work, whilst that above 74.6 W is hard work, and hard work requires increased fuel supply.

Now the mechanics of walking and pushing carts is complicated so I don't know the actual magnitude of forces involved. But for simplicity I will just convert the assumed 10kg pull force into Newtons, 10*9.81 = 98.1N. And assuming a 5000m trip W=98.1*5000 = 490500 J = 490.5 kJ. The human engine is about 25% efficient therefore need 490.5/0.25 = 1962 kJ of fuel (food energy), or 1962/4.18 = 469.4kcal (Calories) for the return trip moving the water, 1962/8700 = 0.23 or 23% of daily intake. Less would be required for the outward trip with the empty container. The trip takes 1 hour so P=W/t=490.5*1000/3600 = 136W whilst fuel consumption is 1962*1000/3600 = 545 W, or 469.4/60 = 7.82 kcal/min. As the power exceeds both 25W and 74.6 W, can say that shifting water is hard work, but can be made easier by travelling at less than 5km/h, which is viable if have fewer trips to make each day.

From other data walking at 5km/h, uses 280 W (J/s), this expect to take 1 hour, therefore energy use (fuel) is 280*60*60/1000 = 1008 kJ, or 1008/4.18 = 241.1kcal. Since this is walking without any additional load, the above calculation for walking with a load is probably correct order of magnitude.

Still another approach is using metabolic equivalents MET's from the compendium of physical activity. So looking at similar activities pulling a rickshaw requires 6.3 MET's, climbing hills with 21 to 42lb load is 8.3 MET's, or walking, 2.9 to 3.5 mph, uphill, 1 to 5% grade 5.3 MET's. Walking with baby stroller 4 MET's, or farming, hauling water for animals, general hauling water is 4.3 MET's. So our needs something between 4 MET's and 8.3 MET's depending on the terrain. Now chances are these are not calibrated for children, however will use anyway as just estimating. So for the 10 year old at 24kg weight, we get 4*3.5*24/200 = 1.7 kcal/min,  and 1.7*60 = 102 kcal which seems low compared to other calculations. So try 8.3*3.5*24/200 = 3.5 kcal/min and 3.5*60 = 210 kcal. It would seem MET's under estimate the fuel energy requirement, however some guidelines are provided to make corrections for various parameters. {Also I'm doubtful that all the activities come from actual measurements or detailed assessment of the specific activity listed.}

Now some women at the local gym on the Airdyne bike (arms and legs) can burn 10 kcal in 10 seconds, or 1kcal/s or 4180 W, as most gym equipment use calories for estimates of food energy and the Watt meter for useful external work and few people pay attention to the Watt meter, will just have to use the 25% rule, and so the useful external work is 1045 W or 1 kW, but this is only sustained for 10 seconds. A small engine on the other hand could output such power all day, as long as it has fuel.

A bicycle is typically about 4 times faster than walking, so the walking speed 5 km/h is increased to cycling speed of 20km/h, and so the 5km trip reduced from 1 hour to 15 minutes, saving more time, at least on the outward trip. The ordinary exercise bike at the gym, indicates my dodgy heart can sustain between 100W and 180W for 30 minutes, and travel anything from 15km to 20km, depending on the day, so speed varying between 30km/h and 40km/h. So if the trip is suitable for bicycle or tricycle then the time for the outward trip can be significantly reduced, the homeward trip with the water will be slower, noting that above estimate requires 136W just to move the water, with no reference to power to move person, moving at higher speed will need more power and will also have additional power requirements due to increased air/wind resistance. By comparison an electric cargo bike is typically powered at 250W with maximum cargo of 100kg or less, with rider of 100kg, so an ebike could help with the task, if had the infrastructure to charge the bikes battery.

School Experiment

It suggests a potential school experiment. Use fitness tracker to measure Calories (kcal) for walking  a reasonable distance (100 to 200m) without any load, then walk the same distance carrying increasing amounts of water, and produce a graph of litres carried against calories burned. Increase the water by 5 to 10 litres at a time, use a container which carry in a back pack or otherwise suitable for carrying in arms in front. The results should show that as the volume of water increases the calories burned increases. Also as the weight increases the travel speed decreases, until weight is too heavy to move, or distance can carry significantly reduced.

Then do the experiment with a roller container, or a container and some form of wheeled trolley. Again make several trips with different volumes of water and measure calories burned. Again increasing volume of water should burn more calories as more force is required to move heavier weights. Plot the two curves on the same chart. For any given volume less calories should be required by using the wheels compared to carrying.

References & Further Reading:

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[(31/01/2023) 16:26] : Original
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Measuring Work


An interesting article, however it would have more value if it used a more relevant measure of work effort than counting footsteps. A count of 12,000 steps versus 9,000 steps is not an indicator of more work (1.33 times), nor harder work. As with time measurement foot step counting is a poor indicator of work effort.

Also electronic foot step counters do not actually count foot steps, they have sensors which sense vibration, acceleration and movement, which is equated to a foot step. It is possible to be sat down but not still, and achieve a foot step count, it is also possible to be walking and get zero foot steps, they maybe fun but they are not reliable.

Similarly fitness trackers estimates of heart rate and calories burned are based on lots of statistical wrangling and assumptions, two different brands of trackers are likely to give different results. The point of counting steps is to estimate distance based on averaged length of stride, even though the tracker is calibrated to the individuals stride, a persons stride is not constant and is likely to vary during a trip. A measuring wheel will provide a better measure of distance, or a map will provide a reasonable estimate. Basically a fitness tracker is just a  wrist watch, measuring chunks of time and making assumptions about that time and calculating various things on the basis of assumptions about feedback from various sensors. Probably do as well with an ordinary wrist watch and do own calculations: point of tracker is it saves some effort and provides a more instantaneous result rather than at some time afterwards. It thus provides feedback allowing adjustment of behavior.

Also a few months back I read an article by an health and fitness writer, she was discussing the issues of couples exercising together and the 10,000 step recommendation. Basically if they go for a walk together, and they have different strides, then if one achieves the 10,000 steps the other will either be behind on their step count or in front. Assume that an average stride is less than 1m, then 10,000 steps is a distance less than 10km. Average walking speed is typically taken as 5km/h or the slightly less 80m/min, additionally typically expect to change mode of movement from walking to jogging/running at around 7km/h.

So assume a couple both complete a 5km trip in 1 hour, then on the face of it  they are both walking at 5km/h. Except their strides are not the same, so similar situation to different diameter wheels, the smaller wheel has to do more revolutions per minute than the larger wheel. Say one has a stride of 1m and the other 0.8m, a ratio of 1.25. Then one has made 5000 steps, whilst the other has made 6250 steps, or 83 steps/min compared to 104 steps/min.

So whilst completing the same external work, travelling 5km, the internal work of their bodies is different. Their elevated heart rates will be different, and the fuel each burns will be different. Do we also have a situation of one walking at 5km/h and the other running at 5km/h?

So what do we measure as work, and is it the useful external work of importance or is it the internal work of our bodies we need to measure or both?

Now in physics (mechanics), work done (energy) is the product of force(F) and distance(s)  to give (W=F.s) and is measured in Joules(Nm=J). Whilst power is work done divided by time (P=W/t=F.s/t=F.v where v=s/t) and measured in Watts (J/s=W). Also friction force is the product of the force normal to the surface and a friction coefficient (F=mu.N), the normal force is typically the weight of the object in Newtons (Weight=m.g=m 9.81). The friction coefficient is typically less than one, therefore less force is required to slide something than to lift it off the ground. Also rolling resistance is typically less than sliding resistance, so even less force is required to push/pull something on wheels.

Now the calories count on most trackers and gym equipment is an estimate of fuel used, not useful external work. The human body has an efficiency of around 25%, that is only 25% of the fuel used produces useful external work. So from the fitness tracker we can get calories, distance and time. We can estimate external work done (W) as 25% of the calories, we get velocity from distance and time, and can get an estimate of the force exerted from F=W/s, and power from P=W/t. The person with the higher force and the higher power is working harder. {NB; Working longer isn't considered working harder}

Now would expect the heavier person to exert the higher force, since distance is constant for both people, therefore expect work done W=F.s to be higher, and the time is the same for each therefore P=W/t will be higher. 

Except the person with the shorter stride is doing a lot more internal work, a lot more leg movements, possibly higher heart rate, and therefore expect to be burning more calories, but not expecting a higher force, and as over all speed is the same, not expecting higher power P=F.v.

But would expect similar power outputs only if smaller force is combined with higher speed. So would require looking at the mechanics of the activity in more detail, for example walking involves both vertical and horizontal movement, lifting an heavy body off the ground requires more force than lifting a lighter body, also sliding or rolling a heavy body requires more force than a lighter body. So who does burn the most calories for the task? Also who is operating closer to their maximum heart rate (MHR), as they would also be working their body harder.

Also need to take into consideration the environment. I recollect reading a book which indicated that traditional Canadian lumberjacks, with an axe, burned some 10,000 Calories (kcal) per day. But this isn't from the work alone, this is mostly just being in the cold. So two people operating in different environments will be burning different amounts of calories.

It is to be noted that sport, health and fitness have theories and equations to do some numbers on maximum heart rate (MHR) and calories. For example based on the various equations for MHR mine varies between 162.5 to 174.2 beats per minute. Exercise at about 90% of MHR is anaerobic metabolism, exercise is typically set around 65% to 85% of MHR. Would therefore expect work to be less than this as typically lasts for longer than exercise. MHR is dependent on age, with younger having higher MHR.

Energy needs are typically based on base metabolic rate (BMR) or resting metabolic rate (RMR), the equations for BMR are dependent on gender, weight, height and age. Total daily energy expenditure (TDEE) is then determined by using a multiplier to account for level of activity. With females typically having a lower BMR than males, so if all other parameters are equal women need less energy. Further given required energy reduces with weight and height, and women typically lighter and shorter, then even less energy required. 

This suggests that calorie counting possibly no better than step counting, as expect females to count more steps and burn less fuel for the same task compared to males. On the other hand if males are typically heavier then the force required to shift their weight is greater, so W=25%C, where C is the calorie count, may give a valid estimate of work done, and then a valid estimate of force from F=W/s. This poses a different issue: heavier people have to do more work for a given task. Therefore need to measure the task by some value which is constant, such as travelling 5km, or moving 90 L of water. Also consider weight ratio's and various other ratio's which assist in an equitable comparison.  For example an average fit person can generate about 3 Watts/kg for an hour, so the heavier they are the more power they can generate, but the more power they need to shift their weight. If weight has a negative impact on a task then the extra power may not be a benefit.

As well as calculating MHR it is also possible to estimate VO2 max, which is a measure of peak oxygen consumption during activity, oxygen being required for combustion of food/fuel. This being measured in ml/kg/min, which for a given body weight can be converted to L/min, and kcal/min and Watts, from VO2 max, exercise levels, or in our case work, can be based on oxygen uptake reserve (VO2R). If concerned with exercise type work, then there are formulae available for walking, running, cycling, arm cycling, and stepping. For other activities can use metabolic equivalents MET's from the compendium of physical activity. Ironing clothes for example is 1.8 MET's, cooking and food preparation is 2 MET's. carpentry general workshop work is 3 MET's, walking at 3 mph (4.8km/h) with light load 4.5 MET's. 

So from activity sampling, and time measurement can get an assessment of daily energy requirements from calculated MET's. Again this is based on fuel, not useful external work, again can estimate useful work at 25%. Note that in calculating energy in kcal or kJ from MET's that an allowance is made for weight. So the heavier person is using more fuel.

The sociologists work was with cultures in Asia, and one noticeable trait is that the males and females are typically not significantly different in height, breadth and weight: that is their basic skeletal frames are similar proportions. Any difference likely due to bone density and muscle mass, that is the males likely slightly heavier due to more muscle mass with stronger muscles wrapped around thicker heaver bones. So are the equations for BMR which vary by gender, valid for such culture? Males and females do have different body chemistry, but is it significant enough to alter BMR?

It does appear that there is no simple single measure of work. Work needs to be defined by multiple characteristics, such as distance, time, weight, energy and power. Also need to reference external work, and the internal work of the human body. If internal work being considered, then MHR and VO2 max, and fuel energy used are also useful measures.

However, hard work should be considered high force or high power, with duration also considered with respect to fatigue from work. Also working at a high percentage of MHR for longer durations may also be considered hard work.

However, time alone does not equate to hard work, 20 hours work versus 8 hours does not make the longer duration hard work. Similarly more foot steps per day does not equate to more work or hard work.

It does however seem that industrial engineering could benefit from the work of sports and fitness medicine, as can the design of human powered machines.

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[31/01/2023: 15:55] : Original
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