Articles and Papers
Sasquatch: Size, Scaling, and Statistics
(part 2)Height and Height Factor
No complete body prints have been measured in conjunction with footprints of their respective owner despite the fact that a few such rare artifacts have been observed (as is the case for hand, knuckle, knee, and gluteal prints). A starting point is the Patterson movie. Patterson himself estimated that Sasquatch to be 7' 4" tall, while all other ex post facto estimators argued for lower values. Detailed image analysis of side views of that animal combined with superimposed pictures at the same site with an included height reference in the form of a graduated pole (Glickman, personal communication) have yielded a body height of 7' 3.5" (222.3 cm) with a foot length of 14.5" (36.8 cm) measured from footprints. This combination yields a foot-to-height multiplier ("height factor") of 6.04, a value that can also be expressed as the footlength-to-height ratio of 16.5%, as is done in the case of human foot-to-height estimates (Robbins, 1986). The rear views of the same Sasquatch, with its bent knees and slumped posture does not readily extrapolate to this height. There is reason to believe that in a setting without reference marks, observers underestimate the height of a Sasquatch by intuitively assigning anthropomorphic dimensions. More importantly than this one example, which remains under debate and could, furthermore, be ignored for the purpose of this analysis, the database contains a cohort of 89 sightings in which both the height was visually estimated and the corresponding footprint measured after the sighting.
| Descriptive statistics for foot length | Descriptive statistics for height |
|---|---|
| N = 89 Range 8.5" - 25" (21.6 - 63.5 cm) Mean = 16.6" (41.9 cm) Median = 16.5" (41.9) Standard Deviation = 3.2" (8.1 cm) |
N = 89 Range = 5' - 13' (152 - 396 cm) Mean = 8.1' (247 cm) Median = 8' (244 cm) Standard Deviation = 15.0" (38.19 cm) |
The mean height factor for this group with its slightly higher mean for foot length than the general population is 5.84, i.e., lower than that applicable to the Patterson Sasquatch. The change in the height factor with increasing size is borne out by the regression line for this set of data (Fig.7), which yields the empirical allometric formula
H = 29.624 * L0.42054
[H = height in inches, L = foot length in inches] (correlation coefficient = 0.558). The formula will benefit from subsequent revision by way of tightly established, paired measurements, but it demonstrates in principle one important feature, namely that Sasquatch feet grow allometrically, i.e. in substantial excess of general somatic dimensions. Thus, the term Bigfoot is not an empty phrase. Application of this formula yields a height of 9'5" (286 cm) for a 24" (61 cm) foot, 7'7" (232 cm) for a 14.5" (37 cm) foot, and 7' (214 cm) for a 12" (30.5 cm) footprint. It should be remembered that these values average male and female heights, hence the value for the 14.5" foot is higher than that applicable to the Patterson female. Visual inspection of the scattergram suggests that the formula in its present state might overestimate height for small footprints and vice verse at the high end. It has, however, the compelling advantage of not being dependent on the opinion of a single investigator.
Only time and additional data will tell how the slope of the curve (the scaling exponent) or its relative position (the constant) will have to be revised. As it stands, the foot length-to-height multiplier (height factor) is near 5.0 for the largest prints, about 6.0 for the mean and 7 or higher for the low end. Human ratios that I have sampled range from 5.1 to 7.2 and probably exceed these values below and above. Extrapolation to values at the time of birth is exceedingly risky, but a Sasquatch foot size of 3.5" (8.9 cm) and body length of 20" (50 cm) or more is in keeping with human and gorilla dimensions. These are 8.2 cm (3.2") and 9.3 cm (3.7") for foot length, and 50 cm (20") and 45 cm (17.7") for total body length for human and gorilla, respectively.
Fig. 7 — Scattergram of observed heights matched with their measured footprint lengths (N = 79). The computed regression line is indicative of a foot length that grows in excess of linear dimensions of the animal.
Foot growth in excess of the linear dimensions of the rest of the body makes sound biological sense, since the weight increases as the cube (actually as a power of 2.9 (McMahon and Bonner, 1983) of the height of the individual, but the support surface, the sole, only by the square. Therefore, the foot would experience increasing loading pressures unless this tendency was compensated for by differential growth. implications for plantar pressure in the Sasquatch will be explored below.
Gait
A large number of sequential tracks have been measured and recorded, but almost all of the records suffer from the same uncertainty, namely whether the step length was measured between footprints (i.e., from toe to next heel) or from one point on one foot to the identical point on the opposite foot, the correct method. The result is an inevitable average underrecording of step length by some amount of the referenced footprint length. This means that the values for step length presented are likely to be extremely conservative. In addition, normal step lengths grade continuously into slow amble and shuffling or, at the other extreme, into an accelerated pace and running. Additionally, trackways of short steps are easily recorded, whereas running footprints, with their long distances between footfalls, are much less likely to be recovered in the usual forested terrain.
The term stride is reserved for three sequential steps in a trackway, an indexing mode useful for measuring the step angle and the width of the trackway (Mossman and Sarjeant, 1983). Gait is the generic term for quadrupedal or bipedal locomotion and pace is taken to be synonymous with step. Most footprints have obviously been imprinted in the absence of human observers (except for 89 sets cited above), hence, they presumably represent the most economical, average striding gait of the animal. Obvious shuffling foot steps in Green's collection of data have not been included as gait. Lastly, favored step length is a composite that conveniently combines such factors as weight, leg length or hip height, and natural pendulum periodicity of arms and legs in one measurable unit.
Fig 8 — Scattergram of step length as a function of foot length (N = 297). The Y-2 axis shows the corresponding speed, if a cadence of 85 steps per minute is applied. The lower, computed regression line shows the minimal average pace length, the upper line shows the estimated transition from walking to running (150% of normal step length).
The step file consists of 297 records, whose footprint statistics closely match that of the general list of foot lengths above. The step length for the mean foot length is 5.0' (152 cm). The computed regression line (Fig. 8, lower line) provides us with a low estimate of Sasquatch step length, given the underreporting of running steps and the ease of finding short steps in succession. The Patterson Sasquatch walking cadence amounted to 85 steps per minute as extracted out of the data of the film (recorded at 16 frames per second; Bayanov et al., 1984; Krantz, 1992) (960 frames per minute film speed : 11.25 frames/step = 85.3 steps/min). For a human step, that cadence is either uncomfortably slow if the step is long, or if short is appropriate to an old or debilitated walker. If this cadence is multiplied by the step length (70"; Gimlin, 1997), a speed of 5.7 mph (9 km/h) is obtained. If it is applied to other sizes of Sasquatch feet, a conservative walking speed emerges, which closely corresponds by coincidence in miles per hour to the step length in feet (Fig. 8, Y2 axis). Admittedly, the walking cadence is inversely related to increasing leg length and weight (Heglund et al., 1974), but the stride length increases with size. Incidentally, the gait of the Patterson Sasquatch lies only moderately above the regression line in congruence with its observed "unhurried" retreat from the scene.
The slapping sound of Sasquatch footfalls ("as if it had flippers on"), reported occasionally for one walking on a suitably hard surface like a blacktop, suggests a different foot placement than in man. There is also longer bipedal "double support" during the stride cycle (Krantz, 1992), an adaptation that reduces peak forces during heel-strike and toe-off and divides the body weight more evenly between the two feet. The frequently reported pattern of a standing Sasquatch swaying from side to side as if to shift the weight from one foot to the other may be related to plantar loading and its intermittent relief. Half footprints, which are not uncommon (Heryford et al., 1982; Hewkin, 1987), in which only the anterior part of the foot is imprinted, are indicative of a simian metatarsal hinge (Meldrum, personal communication). This anatomical detail suggests a hominoid rather than hominid nature of the Sasquatch since the human arch appears to have substantial paieontological antiquity (Johanson et al., 1994).
The Sasquatch has evidently evolved a peculiarly long stride with a long arm swing, a slow cadence coupled with prolonged ground contact of the feet (Krantz, 1992) and a suppression of vertical body oscillation, a so-called compliant walk (Alexander, 1977). This bent-hip, bent-knee bipedal gait is deviant from the human stiff-legged mode and has been frequently commented upon by eyewitnesses for its conspicuous fluid grace ("like riding on a bicycle" or "cross-country skiing"). An identical mode of walking was suggested for Australopithecus afarensis (Stern and Susman, 1983), albeit in the absence of any reference to, or presumably knowledge of, Sasquatch gait.
Sighting records collected by Green contain variable reports of running Sasquatches. For example, at initial encounter, 13% were running, while upon departing 9% ran and the rest walked away. Despite the fact that efficiency of locomotion rises substantially with speed (Heglund, 1985), such running as occurs in the Sasquatch seems to be restricted to short bursts of speed to reach cover, during which the metabolism for a Sasquatch could rise approximately ten to twenty-fold (Jungers, 1985a) and, hence, would be used sparingly. The transition of walking to running has been established at about 5.6 mph (9 kph) for man, although speed walkers, with their decidedly unnatural hip action, exceed 8 mph (13 kph) (Alexander, 1977; Cavagna et al., 1977). Experiments such as I have done myself indicate that the transition to running occurs at about 150% of normal human step length. In the Sasquatch the fastest walking cadence that has been observed is about 140 steps per minute, or 160% of the Patterson rate. A 150% value of normal step length, inserted into the graph (Fig. 8, upper line), indicates a level at which the animal most probably shifts from walking to running.
Only 6% (18 of 297) of the trackway records exceed this extrapolated boundary, a function of an underreporting of running trackways for the reasons pointed out above, and a presumptive reluctance of these heavy animals to run at all in their customary terrain. Scaling formulae for quadrupeds for both speed and cadence at the transition in gait patterns are available (McMahon and Bonner, 1983). These, if applied by weight alone to this biped (at the mean), indicate a walking-running transition of about 14 mph (22 km/hr) and a cadence of 120 steps per minute. The speed indicated in the graph is not applicable to running steps with their much higher cadence and speed.
The maximal speed that a Sasquatch is capable of attaining has not been reliably tracked, although many casual reports refer to observers driving in a vehicle parallel to a running Sasquatch. Before rejecting unbelievable sounding speeds or step intervals, it is well worth keeping human records in mind. For example, the world record walking speed over 20 km is about 11 mph (18 kph), the top running burst speed about 27 mph (43 kph), the longest single jump near 30' (9 m) and the longest triple jump — in effect three running steps — about 60' (18 m), all this with a physique of decidedly smaller scale than that of a Sasquatch.
Weight and Calories
Weight estimates are notoriously difficult to arrive at by visual observation due to the cubic ratio (exponent of 2.9 in man; McMahon and Bonner, 1983) of weight to linear dimension. Human ratios, especially when applied to footprints (Robbins, 1986), are clearly inappropriate. Some extrapolations have used the width of the dimensions of the heel or cubic volume of body parts (Krantz, 1992) or the width of the ball of the foot. Estimated or calculated weights for the Patterson Sasquatch (in Krantz, 1992) range from 280 lbs (127 kg) (Grieve), through 350 lbs (159 kg) (Gimlin), 500 lbs (227 kg) (Patterson and Krantz), 650 lbs (295 kg) (Willoughby, 1978), 800 lbs (363.6 kg) (Titmus and Green) to 2,028 lbs (920 kg) (Glickman, 1997). Glickman (1997) has used digital image analysis for producing correlative measurements between various frames of the movie, a process not readily verified.
I will here generate an estimating mode that will use measurements readily accessible to the reader. Specifically, I propose to use a scaling formula for weight of primates that has predictive value from tamarins to baboons (McMahon, 1971). This formula consists of an allometric relationship between chest circumference (C) and weight (W), presumably for the functional reason that the lung volume, and by implication respiratory exchange, scales isometrically with body mass (Stahl, 1967). Since gorillas reach maximally 250 kg (550 lbs) in the wild (Willoughby, 1978), and have been reported to attain 287 kg (631 lbs) in captivity (Raven, 1950), it is prudent to include values for these large primates. To this end I have added 10 pairs of gorilla measurements (Mountain and Lowland gorillas; from Willoughby, 1978, and Napier and Napier, 1967) and recomputed the regression formula of MacMahon (1971). The original formula was
C = 17.1 * W0.37
(C = chest circumference in cm; W = weight in kg), while the formula that includes the gorillas is
C = 17.57 * W0.39
with a correlation coefficient of 0.956. The recomputed formula has the additional gratifying feature that it is satisfactorily applicable to human dimensions.
Fig. 9 — Allometric plot of chest circumference against weight. Data from tamarins to baboons from MacMahon (1973), gorillas added (see text) and curve recalculated. The box represents the Patterson Sasquatch
The Patterson Sasquatch chest circumference can be estimated by taking the chest width from the oblique rear views in the Patterson movie (with an included vertical foot [14.5"] for scale). These film images (frames 61 and 72), printed on display stock and commercially available, are slightly over one-half second removed from each other, hence, the distance increase is negligible, especially in view of the camera distance of approximately 120' (37 m). Also, the two photographs have the same photographic magnification, as can be verified by reference to objects in the background common to both images. The foot measures 27 and 28 mm in length, respectively. Since no amount of tilting can make the foot appear longer than its actual size, I will equate 28 mm to 14.5" (1.931 mm/inch) in the plane of the animal. The width of the chest, measured between two imaginary lateral points a short distance below the axilla, measures maximally 32 mm, a value that has to be corrected for the rotation of the body away from the line of sight. This angle was averaged at 40 degrees by Krantz (1992) and calculated at 41.4 degrees by Glickman (1997). The raw width value is corrected by dividing it by the cosine of this angle. This operation yields 42.7 mm, or a 22.1" (56.1 cm) chest width of the animal. Glickman (1997) has calculated the ratio between chest width and depth to be 0.67, while that measured ratio in Mountain and Lowland Gorillas falls between 0.69 and 0.74 (Raven, 1950; Schaller, 1963 ). An average of 0.71, used here, gives a chest depth of 15.7" (39.8 cm).
These two measurements, of which at least the first can be extracted from a single image with minimal conjecture or mathematical manipulation, compare as follows to values in the literature:
| Author | Chest Width | Chest Depth | Calculated Circumference |
|---|---|---|---|
| Krantz (1992) | 17.6" (44.7 cm) | 15.2" (38.6 cm) | 51.0" (130 cm) |
| Green (1968) | 22.0" (55.9 cm) | 19.0" (48.3 cm) | 64.6" (164 cm) |
| The author | 22.1" (56.1 cm) | 15.7" (39.8 cm) | 60.0" (152 cm) |
| Glickman (1997) | 31.4" (79.8 cm) | 20.9" (53.1 cm) | 84.1" (214 cm) |
I invite the readers to obtain the images in question and try to verify to their own satisfaction these values, short of waiting for the first preserved Sasquatch corpse. The largest quoted chest circumference requires the obliquely projected chest width to be 40 mm wide, a distance that extends well beyond the edges of the chest in the picture, or else a foot that is 18.1" long.
Next, one can apply a simple engineering formula (Bosch, 1970) for an approximation of the circumference of an ellipse
Circumference = 3.33a + 2.95b
where a and b are the half axes of the ellipse. The value for the chest circumference by this method is 60.0" (152.4 cm). When this value is entered into the scaling formula,
C = 17.6 * W0.392
(C = chest circumference in cm, W = weight in kg) and the equation is solved for W, a weight of 246 kg (542 lbs) emerges. Lest the reader place excessive faith in the precise numbers, I should caution that a millimeter of raw width measurement translates into roughly 20 kg (44 lbs) of calculated weight, and an extra 0.5" foot length adds 10 kg (22 lbs). The range of weights in the plotted gorillas suggests a weight range for a Sasquatch of the Patterson site of between 180 and 310 kg (400 to 700 lbs)(fig.9). Both lean and paunchy Sasquatches have been observed. Since gorillas are rather barrel-chested in relation to their weight, their inclusion drops the calculated Sasquatch weight 33% from 369 kg (812 lbs), a weight which is obtained with the original formula of MacMahon (1971), based only on smaller primates.
On the assumption that chest circumference scales linearly with height of the animal, I have scaled the Patterson values (slightly below the mean as a female) to the calculated mean heights and generated a comparison table (Table 1).
| Foot | (cm) | Height | (cm) | Chest | (cm) | Weight (kg) | (lbs) |
|---|---|---|---|---|---|---|---|
| 12" | 30 | 7' 0" | 213 | 58" | 146 | 222 | 488 |
| 14" | 36 | 7' 6" | 228 | 62" | 156 | 264 | 581 |
| 15.6" | 40 | 7' 10" | 239 | 65" | 165 | 299 | 658 |
| 16" | 41 | 7' 11" | 241 | 65" | 165 | 305 | 671 |
| 18" | 46 | 8' 4" | 254 | 69" | 174 | 349 | 768 |
| 20" | 51 | 8' 8" | 265 | 72" | 182 | 388 | 854 |
| 22" | 56 | 9' 1" | 276 | 75" | 189 | 430 | 946 |
| 24" | 61 | 9' 5" | 286 | 77" | 196 | 472 | 1,038 |
Since the reference heights are derived from a formula that is conservative, the weights are most likely more so. A sobering detail concerning scaling from skull dimensions is the observation that a comparison of predicted to actual weights produced a range from -60% to +30% deviation in larger monkeys and small apes (Smith, 1985). It is hoped that chest circumference is a closer predictor.
Several corollaries accrue from increased weight in this primate. First of all, large size alone provides the quickest access to dominance over other species in the environment, of which the most formidable competitor must have been originally the Grizzly bear, though diurnal in habits. The Sasquatch, in contrast, is compellingly nocturnal (see Appendix 1). Most adaptive for the Sasquatch is the increased resistance to cold since the radiative body surface increases with the square of the linear dimensions, whereas the heat generating mass increases at roughly the third power. The climate of much of the range, to which the records of this article pertain, is wet and maritime, decidedly unpleasant to man for much of the year unless suitably equipped, though not frigid, while the inland areas experience much more severe winters.
Increased size also implies high mobility and a correspondingly large home range. A rare, individually identifiable Sasquatch was sighted over a span of 8 years in several locales in Washington and Oregon, the most distant sites having a linear separation of more than 150 miles (240 km). If we take this distance as a lifetime radius of activity, we get an area (πr2) Of more than 70,000 sq. miles (180,000 sq. km) of forested terrain. This value encompasses a substantial portion of, for example, Washington State and cannot be considered indicative of any particular home range. Also, it emphasites the difficulty of any contemplated scheme of organized study of the species other than to concentrate on regions of recent sightings.
Secondly, according to Kleiber's Law (McMahon and Bonner, 1973), which states that the basal metabolic rate scales as the 3/4 power of mass, a massive animal needs less energy input per gram of body weight than a small one does. This means that a Sasquatch can get by with a relatively smaller amount of food than a smaller animal. Nonetheless, if we use the calculated weight (W) of a Sasquatch at the population average (299 kg) and apply the scaling formula
Kcal/day = 67.6 * W0.756 (Kleiber, 1961),
a basal caloric consumption of about 5,000 calories per day is found. With exercise and inclement weather this value can double or triple. Hence, a diet that is minimally omnivorous, if not slanted toward carnivory for the sake of calories, especially during the winter, is required to fulfill that demand. Bipedal gait, seemingly as efficient as a quadrupedal gait (Rose, 1984), can be viewed as an adaptation to becoming an endurance hunter in the very demanding terrain inhabited by the Sasquatch.
Eyewitness reports tell of White-Tailed Deer (Odocoileus virginianus), Mule or Black-Tailed Deer (Odocoileus hemionus), and American Elk (=Wapiti) (Cervus canadensis) being killed by having their heads crushed or their necks twisted without claw marks or bite wounds. The head was sometimes separated from the body and the body cavity torn open with the internal organs missing, while the hide-covered carcass remained on occasion. The latter has been found sometimes partly hidden under branches or deposited in a tree, in all cases surrounded by appropriate footprints. If we published weight ranges for the three species, assign about 25% to internal organs, and a caloric value of about 500 calories per lean pound (Watt and Merrill, 1963), then we can estimate a caloric content of the innards: 12,000 - 35,000 calories for 0. virginianus, 20,000 - 50,000 for 0. hemionus, and 60,000 - 90,000 for C. canadensis. These values would rise dramatically (about 3,500 cal/lb) with the inclusion of retroperitoneal fat stores around the kidneys. A Sasquatch would probably engage in "binge" eating punctuated by lean periods, as has been described in dramatic and picturesque detail for the Eskimos by Mowat (1951). Examination of the database with an eye to exploring whether the Sasquatch builds up fat in the Fall has shown that "skinny" vs. "fat" Sasquatch sightings are evenly distributed throughout the year.
The initial organ selectivity may have its root partly in the nutritive value of the internal organs, generally adorned with fat, and partly in their friable nature, which is especially more easily dealt with by the flat molars of a primate as compared to the carnassial teeth of carnivores. Possible retention of the carcass would "ripen" the meat and soften its texture, allow for hypothetical winter storage, and contribute to the often noted "rotten meat" aroma of a Sasquatch at close range.
Scaling formulae for average daily food intake by herbivores
kg food/day = 0.157 * W(kg)0.84
or carnivores
kg food/day = 0.234 * W(kg) 0.72
(Bourliere, 1975) provide amounts of 19 kg (41 lbs) and 14 kg (31 lbs) per day, respectively, for the average Sasquatch, whose consumption with a mixed diet would lie between these values.
Additionally, partial carnivory limits the species to low biomass density, i.e., numbers of animals per given area, and thereby reduces its social structure, if any, to small and sparse groups (McNab, 1963), in congruence with the rarity of grouped sightings or footprints.
Finally, scaling of body weight to brain size in primates has been pursued by numerous authors (e.g., Armstrong, 1985; Martin, 1984; Martin and Harvey, 1985; Stephan, 1972), all of whom provide allometric formulae. An exploration of these leads to various results, with the brain size of the average Sasquatch ranging up to 770 cc. This estimate could be grossly in error if it is subsequently found that the Sasquatch has evolved a brain size above the trend applicable to the Great Apes. By comparison, the brain of mountain gorillas averages 532 cc with a range from 420-685 cc (Raven, 1950). I am loath to pursue this subject in view of the uneven brain evolution among the primates, the absence of head anatomy of the Sasquatch and the diversity of scaling formulae. In the absence of any reports of cultural traits or fire use, very minimal and primitive tool use, and inferred low sociality of the Sasquatch, we are reduced to conjectures regarding their need to remember a presumptive large home range.
All of these traits argue against an evolutionary need of complex communication, as is needed in the transmission of cultural acquisitions. Nevertheless, the vocal abilities of the Sasquatch, aside from potent screams, roars and growls, range well beyond those of Great Apes and suggest proto-linguistic faculties or even primitive communication (Berry and Slate, 1976; Berry and Morehead, personal communication and recordings; Kirlin and Hertel, 1980).
As an aside, the often reported prodigious upper body strength of the Sasquatch can be profitably viewed in the light of human weight lifters in whom lifting ability rises as the 2/3 power of their weight (Lietzke, 1956). If one uses the formula
Weight lifted (lbs) = 28.71 * W (lbs)0.6748
for maximum human weight lifting ability, extrapolated to the weight of the average Sasquatch (299 kg), it yields 1,300 lbs (610 kg). The build of the Sasquatch, in parallel with that of Great Apes, indicates muscle insertions more distal to joints with an attendant rise in the mechanical lever arm. This factor, together with presumptive larger muscle cross-sections, suggests that its real capability is apt to be much greater than that of man, though probably not expressed in the motivated fashion of a competitive weight lifter. Their reported ability to tip over a commercial trailer, lift rocks in excess of 230 lbs to unearth rodents in rock slides, or throw basketball-sized rocks in a high are seems not unreasonable in this light (Green, 1978, 1980a).
From: Cryptozoology Vol. 13: 47 - 75