How do you weigh an elephant without using a weigh machine?

Answer by Rory Young:

You can determine a good estimate of weight from an elephant's footprints or droppings.

Here is something I wrote about estimating the gender, stature, age and weight of elephants from their tracks.

Left hind foot imprint of an adult female elephant

Tracking has in recent times often been considered a general and vague skill, mainly useful for following animals and establishing rude estimates regarding the age of the tracks, the size of the animal and possibly a bit more information.

Highly skilled trackers have been able to convincingly show their ability to reveal detailed information of the animal. However, this was never taken seriously. It was seen as a tool but not as empirical and therefore you could “not take it to court” so to speak.

However, while this ancient skill was being practiced unchanged since time immemorial in the wild, in the universities of the Western world a new version of tracking was developing from scratch in a strange convergent evolution. They called it forensic science. Empirical information was used to categorically determine the accuracy of different hypotheses.  In 1892 in Argentina  Juan Vucetich applied the first systemized use of fingerprint recording to law enforcement.

Fingerprints are nothing more than “transfer tracks”. A good example of transfer track is a muddy footprint on a kitchen floor. In the case of fingerprints the mud is instead oil secreted naturally by the body and instead of examining them with the naked eye they are enhanced and “lifted” for later comparison.

So, what has all this to do with tracking elephants? Well, Natural Philosophers as scientists were originally known, developed many different disciplines and applied their use of empirical data to determine much else. Amazingly, they reinvented the skill of tracking in order to gather the information they needed to conduct their studies.

Twenty two years ago, as a young ranger, I listened to my tutor, Rob Clifford, explain that taking the circumference of an elephant’s front foot and multiplying it by two and a half would give you its height at the shoulder.
This was something that I found completely amazing.
I had grown up tracking and hearing tales of tracking. In all that time I had only learned by experience, mainly using the right side of my brain and the obvious. It was good and gave me a natural awareness and ability that I could build on. However, it was the first time I had heard of mathematics or scientific methodology being applied to determine specific information.

The scientists have been very busy. Trackers could greatly benefit by adding the results of scientific studies to their arsenals.
Although trackers themselves are not scientists; they are experts in their skill and often profession. They combine knowledge and practical ability gained over many years, often from early childhood, developing an amazing database, a set of skills and a highly developed intuition to become experts at what they do.
It is important that they do not let scientists take their job away from them, applying great knowledge but with limited skill. The trackers need to step up, whether professional trackers, hunters, guides or rangers, and start studying and applying this new knowledge (well not so new actually) and combining it with the more ancient knowledge.

Determining Stature in Elephants.
Why would we want to accurately determine the height of an elephant?
Interestingly an elephant never stops growing. They go through several different growth rates. They also slow right down at twenty five years old in the case of males and twenty years old in the case of females. That means we the age of the animal can be determined from its size.
Determining the age of elephants is very important for establishing the health and other status and other information pertaining to a population. 
Although elephants also use instinct they are very dependent on acquired knowledge from older elephants, especially regarding food and behavior.  It is important to have a healthy variety of ages within a population. With the current levels of poaching in Africa, particularly affecting bigger animals it is important to be able to properly analyze tracks.

Determining Stature From Tracks
The old rule of thumb I learned as a years ago is not bad but it is not accurate either.
When an elephant puts on or loses weight, whether because of illness, hunger, pregnancy or other reason, the width and circumference of the feet will change.

For this reason and other reasons the most consistent and reliable foot measurement to use to correlate to height is the rear foot length; it deviates much less than any other foot measurement with weight loss and other variables that affect circumference.
The foot is measured in a straight line from the base of the rear foot to the front of the same foot.
Now comes the tricky part, determining the formula to use.
A general, rough, rule of thumb guide is 6:1. It is not accurate though, because the growth of elephants is not linear. Their growth rate changes throughout their lifetime.
Up to the age of nine years old the ratio of foot length to shoulder height is 5.83:1 Foot length at this age is recorded as below 43.67 Therefore to determine height at shoulder:  Hind Foot Length x 5.83 = Shoulder Height
Between the ages of ten and fifteen years old the ratio of foot length to shoulder height is 6.11 Mean foot length at this age is 43.67cm which should be used to determine the age group. Therefore: Hind Foot Length x 6.11 = 267cm
Between the ages of fifteen and twenty five years old the ratio of foot length to shoulder height is 5.82.  Mean foot length at this age is 49.81cm. Therefore to determine height at shoulder: 49.81 x 5.82   = 290cm
Between the ages of twenty five and thirty five years old the ratio of hind foot length to shoulder height is 5.68.  Mean foot length at this age is 53.32 cm. Therefore to determine height at shoulder: 53.32 x 5.68 = 303cm
Above the age of thirty five years the ratio of hind foot length to shoulder height is 5.74 .  Mean foot length at this age is 53.32 cm. Therefore to determine height at shoulder: 55.04 x 5.74 = 316cm
The average for all of these age groups is 5.83.
These figures were extrapolated from a study of elephants in Etosha National Park. Because heights vary according to different populations calculations can be made based on different mean heights for different age groups and a percentage difference applied in order to give a reasonably good basis for estimating height.

Determining Stature From Droppings
To determine stature using droppings the bolus diameter is used.  “Bolus” is the name given to a single round dropping.
The diameter is measured as one would measure any circle; across the widest part.
The following table shows the different formulas to be used for determining the size of male elephants:                                         
2-9.75 cms diameter                         Age =   0-5yrs                      Height at Shoulder = <160cm
9.75-12.25cms diameter                  Age =  5-10yrs                     Height at Shoulder = 160-200cm 
12.25-13cms diameter                     Age =  10-15yrs                  Height at Shoulder = 200-230cm
13-14cms diameter                           Age =  15-20yrs                  Height at Shoulder = 230-250cm
14-14.25cms diameter                     Age =  20-25yrs                  Height at Shoulder = 250-260cm 
14.25cms<  diameter                        Age =  25yrs <                     Height at Shoulder = >260cm
The following table shows the different formulas to be used for determining the size of female elephants:
15.5cm<  diameter                            Age = 25yrs <                      Height at Shoulder = >215cm
14.75-15.5cms diameter                  Age = 20-25yrs                   Height at Shoulder = 212-215cm
13.75-14.75cms diameter                Age =  15-20yrs                  Height at Shoulder = 205-212cm 
12-13.75cms diameter                     Age =  10-15yrs                  Height at Shoulder = 185-205cm 
10-12cms diameter                           Age =  5-10yrs                     Height at Shoulder = 160-190cm
2-10cms diameter                             Age =   0-5yrs                      Height at Shoulder = <160cm

Shoulder Height to Age Table.
                Females                                                                                                                Males
Age (years)  Shoulder height (cm)                Hind Foot Length                              Age (years)          Shoulder height (cm)
<1yr                       <110cm                                                                 <1yr                       <105cm
1yrs                        105-115cm                                                           1yrs                        105-115cm
2yrs                        115-130cm                                                           2yrs                        115-130cm
3yrs                        130-145cm                                                           3yrs                        130-140cm
4yrs                        145-155cm                                                           4yrs                        140-150cm
5yrs                        155-160cm                                                           5yrs                        150-160cm
6yrs                        160-170cm                                                           6yrs                        160-170cm
7yrs                        170-175cm                                                           7yrs                        170-175cm
8yrs                         175-180cm                                                              8yrs                         175-185cm
9yrs                         180-185cm                                                              9yrs                         185-190cm
10yrs                       185-190cm                                                              10yrs                       190-200cm
11yrs                       190-195cm                                                              11yrs                       200-210cm
12yrs                       195-200cm                                                              12yrs                       210-215cm
13-14yrs                  200-205cm                                                              14yrs                       215-220cm
15-17yrs                  205-210cm                                                              15yrs                       220-230cm
18-23yrs                  210-215cm                                                              16-17yrs                  230-235cm
60                            215-220cm                                                              18yrs                       235-240cm
60<                          220<                                                                        19yrs                       240-245cm
                                                                                                                20yrs                       245-250cm
                                                                                                                21-22yrs                  250-255cm
                                                                                                                23-24yrs                  255-260cm
                                                                                                                25-26yrs                  260-265cm
                                                                                                                27yrs                       265-270cm
                                                                                43.67                       28-30yrs                  270-275cm
                                                                                                                31-33yrs                  275-280cm

Estimating the Weight of an Elephant Using its Tracks Or Droppings
If the age and or height at the shoulder has been determined either using tracks or droppings then either can be used to estimate weight using the following table.
The following data has been taken from estimates used in zoos for feeding and medication purposes.
Age (years)                                          Height (m)                                           Mass (kg)
0                                                              0.85                                                        120
1                                                              1.15                                                        300
3                                                              1.30                                                        400
6                                                              1.50                                                        600
10                                                           1.90                                                        1,200
15                                                           2.20                                                        1,600
40                                                           2.60                                                        2,400
In theory height can be determined from stride length. However, there is as yet no been no empirical studies to determine exactly what the ratios are.

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