Estimating Route Time

Naismith's Rule

In 1892 a Scottish Mountaineer by the name of William Naismith devised a way of estimating the time it would take to complete a route based on distance. Quite simply he stated that it should take one hour to walk 3 miles, and adjusting a half hour for every 1000ft of ascent.

1 Hour = 3 miles + 0.5 hours /1000 feet

1 Hour = 5 km + 0.5 hours /300 m

This is a very simple rule, and assumes quite a few things. Firstly, it assumes a steady rate of 3 miles per hour, which is a fairly steady pace (Naismith was reportedly a very fit guy). Secondly, it assumes a fairly straight path and does not account for any obstructions.

Improvements / Exceptions / Adaptations

Many people realized that Naismith's rule, although simple was not very accurate. The calculation does not account for rough terrain, carrying loads, fitness level, and many other variables that could very much alter estimated times. Some people realizing this simply factored on adding 25-50% on to the estimated time. Others tried to further elaborate on Naismith's Rule.

A man named Bob Aitken decided that 5km/h was optimistic and only realistic in very optimal conditions, and therefore stated that 4km/h should be used for all other terrain.

Eric Langmuir in Mountaincraft and Leadership further elaborated on Naismith's rule to account for descent:

5 kilometres per hour

+1 hour per 600m ascent

-10 minutes per 300m descent for slopes between 5 and 12 degrees

+10 minutes per 300m descent for slopes greater then 12 degrees.

Another very simple variation on this rule:

4 km per hour +30 sec per contour line crossed

Yet another variation:

5 km/h easy going terrain

3 km/h easy scrambling

1 km/h rough terrain (sand, snow, brush)

+1h / 500m elevation up

+1h /1000m elevation down

+1h /5h fatigue

Another rule known as the Backpacker's Rule estimates 3.6km/h or 1 metre/sec

The Trantor Correction

Phillip Trantor also made corrections for fitness level. His corrections are based on how many minutes it takes a person to climb 300m in a 800m walk, and comparing that to how many hours quoted by the Naismith's Rule, giving you the modified result. To furthur compound this you should drop a fitness level if your are carrying a 20kg pack, walking into a headwind, travelling at night, or ground conditions are poor.

One thing the Trantor Correction does account for is fatigue. If plotted out, you will notice that fatigue seems to make its most obvious impact around the 10h mark.

Conclusion

Route planning is a very important aspect to any hike, or survival situation. However, above are only rough estimations, and the only way to accurately determine the time is will take is to know your speed, and route. Next I may try and elaborate on these estimations. It is also worth it to note that these calculations are based on Scottish terrain, and universities have found that in the Munro mountains the Naismith rule is within 25% accuracy.

Calories: Determining Calories Expenditure Hiking

Well there are many calculators out there that will determine the calories expenditure whilst hiking, backpacking, etc, I find they are limited and often never give you any indication as to how they come up with their numbers. Well probing a little further I did manage to find tables here http://www.nutribase.com/exercala.htm . Although I find these can give us some idea, there are somewhat limited concerning pack size. What we can divulge from these is that there are two variables concerning calorie expenditure: pack weight, and the persons weight.

If we try to take a 110lb person with no pack (ie walking or hiking), and a 100lb person with a 10lb pack you will notice that the counts are not the same. You can try this with any combination.

The Twofold Problem

We need to figure out the rate of expenditure of calories, and the rate of how pack weight changes this. To figure this out we need to use old school quadratic equations, which is made much simpler by using a spreadsheet program. Without going hardcore into disseminating this data we arrive with two separate equations:

Increase of Cal Expenditure based on Pack Weight = 0.29 x (Pack Weight) +14.9
Calorie Expenditure of Person = 1.55 x (Persons Weight) + 0.25

Person A is carrying a 30lb pack, therefore their expenditure has increased by 23.6 Cal/30 min. If we look at the data we notice that it increases by 24 cal per weight group, close enough. Likewise if Person A is 175 lb carrying no pack we know that 271.5 cal/30 min is the expenditure, which is also very much in line with our data.

If we figure out the equations for we will notice that the slope of each group is equal to the result given by our equation for the increase in pack weight. Therefore if we can combine the two equations we can figure out any calorie expenditure at any weight, carrying any size pack. If you try this you may notice that your result will be a decimal point off, and in addition any answer will be per 30 min (this is not necessarily a bad thing, and the equation could be adjusted, but I think it provides for more accurate planning.)

The Equation

Calories Expended per 30 min =(Pack Adjustment x 0.1) (Persons Weight)
Pack Adjustment = 0.29 x (Pack Weight) + 14.9

or

Cal Exp / 30 min = ((0.29 (Pack Weight) +14.9) 0.1) x Persons Weight
Cal Exp / hour = (((0.29 (Pack Weight) +14.9) 0.1) x Persons Weight) x 2
 
Person A weights 170lb carrying a 30lb pack.

Cal Exp / 30 min     =  ((0.29 (30) +14.9) 0.1) x 170
                               =  ((8.7 +14.9) 0.1) x 170
                               =  ((23.6) 0.1) x 170
                               =   2.36 x 170
                               =  401.2

If we compare 401.2 cal/30min with our table we see the table has 399. Not perfect but more then good enough for our purposes.

Conclusion

It is now possible based on this information to get a more accurate idea of your calorie expenditure. We can also now figure out diminishing results (ie carrying this much food is actually causing me to burn more calories then its providing), and properly plan. It should be noted however that any pack sizes greater then 30lb is purely speculative and based on previous data. Next I hope to be able to figure out this equation using a range of activities.

Survival – Calories

Survival is all about playing the calorie game. Calories are a unit of measurement devised by Nicolas Clemant for the measurement of energy. A calorie is the energy required  to raise the temperature of 1 gram of water 1 degrees Celsius.

1 cal = 1gm water raised by 1 degree centigrade

The calorie has been replaced as a scientific unit of measurement by the joule, however it is now used to measure energy content of food.

In its simplest form we need calories (i.e. energy) in order to live or accomplish tasks at hand, as most of us will already know. As our level activity increases so does our calorie consumption. The need to understand how this works is important for any survival situation, not only for planning purposes, but also simply to live.

To calculate how many calories we are using you use this formula:

Basal Metabolic Rate + Thermic Effect + Activity = Calories Expended

Basal Metabolic Rate

The BMR is the amount of calories the body expends simply to function. Even doing nothing your body is using up calories. To calculate exactly how many calories are being burned we can use these formulas:

Male BMR = 66 + (6.3 x weight in lb) + (12.9 x height in inches) – (6.8 x age in years)
Female BMR = 655 + (4.3 x weight in lb) + (4.7x height in inches) – (4.7 x age in years)

If Person A is a male, weighs 175 lb, is 6 feet tall, and 27 years old
BMR    = 66 + (6.3 x 175) + (12.9 x 72) – (6.8 x 27)
            = 66 + (1102.5) + (928.8) – (183.6)
            = 66 + 1847.7
            = 1913.7

This means that Person A needs to consume 1914 (rounded) calories per day minimum. To put that in perspective Person A would need to eat just less then four BigMacs per day to meet his minimum requirement, although I don't recommend it.

I used the Imperial system of measurement becomes in terms of a persons weight, and height it is more common. The metric measurements are as follows:

Male BMR = 66 + (13.7 x weight in kg) + (5 x height in cm) - (6.8 x age in years)                                     
Female BMR = 655 + (9.6 x weight in kg) + (1.8 x height in cm) - (4.7 x age in years)

Thermic Effect

Ironically enough the body must expend energy to make energy. The amount of energy needed to digest and metabolize energy is known as the thermic effect. To calculate how much energy is used up is rather simple, it works out to about 10%:

Thermic Effect = Calories consumed x 0.1

Person A decides to actually eat those four BigMacs (I am only using these as an example, because we all know what they are). The burgers come in at 540 calories a piece for a total of 2160. Because of digestion and the energy expended to metabolize the meal we lose 216 of those calories.

Activity Related Metabolism

Every time you get off the couch and do something, your body will use up more calories. This we probably all understand. Many people nowadays are trying to get rid of their extra calories their body has stored up in their body for self image purposes. In a backpacking or survival situation we need to conserve all the calories we can.

I will delve more into activity related metabolism in another post. However, for the sake of demonstrations:

Person A is hiking through the woods for six hours with a 10lb pack on. Based on previously attained data we know that a 175lb person carrying an additional 10lb will expend 623 calories an hour. During this hike Person A expended 3738 calories.

Adding it all Together

We now know all this information required to figure out exactly how many calories were expended.

BMR = 1914
Thermic = 216
Activity = 3738

Total Cal Expended = 5868 calories
Total Cal Consumed = 2160 calories

We are now running a calorie deficit of 3708. To put this in perspective one pound of body fat will supply you with approximately 3500 calories, therefore we have used up just over one pound of our bodies stored energy in addition to the 2160 calories eaten. If you start multiplying this by a multi day hike (which will probably include longer hiking days, and heavier packs), you can see how easy it is to run into a great deal of trouble in a short time. This is one reason why most survival manuals will instruct you to stay where you are. By not doing any activity and not eating, we can see that our BMR used up LESS calories then actually eating and going somewhere. Food for thought.