The Bigfoot Field Researchers Organization (www.BFRO.net)

The BFRO is the only scientific organization
focused on the bigfoot / sasquatch mystery.


 

 

Foreword

This article is a condensation of a paper published by Dr. W. H. Fahrenbach in Cryptozoology, Vol. 13, pgs. 47-75 under the title: Sasquatch: Size, Scaling and Statistics. The original article contains more graphs and data, metric values, a substantial bibliography, as well as statistical and mathematical exposition. Due to its brevity, the usual cautionary comments have been largely deleted and the text may read here somewhat more definitive than is warranted.

Reprints are available upon written request from the author (Dr. W. Henner Fahrenbach, Ph.D. (Hennerf@bfro.net), Beaverton, Oregon), or else the entire journal volume, which contains several other sasquatch articles, can be bought for $22.00 from: Cryptozoology, ISC Secretariat, P.O. Box 43070, Tucson, AZ, 85733.

This article constitutes personal research and has in no way been aided or financially supported by the academic institutions with which the author is or has been affiliated.
 
 
 

Full Article Table of Contents

Abstract
Introduction
Methods
Results and Discussion
   Foot Length
   Ball Width and Width Index
   Heel Width
   Height and Height Factor
   Gait
        Pace Length
        Speed
        Gait Characteristics
   Weight
        Chest Dimensions
        Other Dimensions
        Weight Extrapolation
        Consequences of Weight
   Caloric Consumption
        Prey Food Value
        Brain Size
   Strength
   Plantar Pressure
        Plantar Pressure Comparison
        Foot Anatomy
   Growth and Life Cycle
        Infancy
        Adulthood
        Grouped Footprints
        Maturation of the Female
Other Traits Accessible to Statistics
        Nocturnality
        Sighting Duration
        Hair Color
        Change in Coat Color with Age
Summary
 
 
 
 
 

Abstract

Measurements and estimates on sasquatch dimensions, collected over the last 40 years in the Western U.S and Canada, were subjected to statistical analysis and extrapolation by scaling laws appropriate to primates and mammals. The study has yielded average population values for foot length and width, ratios of foot length to height, values for dimensions and weight, strength, plantar pressure, walking and running gait, speed, and a tentative growth curve as a function of time for the female of the species. Additional information is provided on such subjects as hair color and nocturnality. The results suggest a substantial population with traits deviant from those of other higher primates and man.
 
 
 

Introduction

Over the last half century several thousand eyewitness reports of sasquatch sightings, foot prints, and other circumstantial evidence have accumulated. Numerical values contained in the sources have not been explored statistically. A large sample size, as has resulted from combining all available data, and its statistical treatment also provide evidence as to whether the data are real or fictitious.

I have used unedited data. Excluded are only reports with preternatural content. These data lump both sexes and all ages into one set. Values derived from the Patterson movie of 1967 do not carry any special weight other than the chest circumference, for which it is the only source.
 
 

Methods

Most of the data were collected and computer indexed by John Green of Harrison Hot Springs, British Columbia, Canada, over the past 40 years. They have been further supplemented by some values published by Napier and Hewkin, by the records of the North American Science Institute as collected by the Bigfoot Research Project under the direction of Peter Byrne, by a small personal collection, and by a few details visible and measurable in the Patterson movie. All the data originate from the Western States of the USA (Alaska, Washington, Oregon, California, Idaho, Nevada, Montana, Utah, Wyoming, Colorado, New Mexico) and the Western Provinces of Canada (British Columbia and Alberta). Statistical calculations and graphing were performed with Statworks and Kaleidagraph on a Macintosh computer.

Many values are derived by the process of so-called allometric scaling, in which one unknown characteristic of an animal, for example the caloric consumption, is derived from a known one, like weight. Such formulae are derived from numerous samples of animals of varying sizes and take the graphic form of a straight line in a double-log plot.
 
 
 
 

Results and Discussion

Foot Length

Foot prints are the standard stock in trade of sasquatch research, and their sometimes inhuman length assures almost immediate measurement, even by first time witnesses. In all cases, the flat sasquatch foot print corresponds to a human foot outline rather than a human walking print, in which the arch may not touch a hard surface. Comparison of prints in a sasquatch trackway show a common tendency of the toes to be curled, thereby shortening the measured foot somewhat.

A collection of 706 footprints yielded an average length of 15.6" and a range of 4" to 27" (Fig. 1). The statistical treatment implies that more than 99% of the foot prints of this population are going to fall between 6" and 25". The graphic representation of the distribution is a bell-shaped curve, slightly more peaked than a normal distribution. This shape argues compellingly that the data originated from a single species rather than a multitude of overlapping species of different characteristics. It also means  that they were not produced fictitiously over 40 years by hundreds of people independently of each other, a process that would have generated a distribution with many peaks.

The slightly peaked nature of the curve suggests that the difference between mature male and female does not exceed 2" in foot length, or about a foot in height, on the average. The largest prints are most probably from males, also supported by eyewitness reports of such animals being more facially hirsute and devoid of breasts. The slight asymmetry of the curve to the left might be attributable to the contribution of juveniles smaller than the population mean and their attrition before adulthood.

As a telling comparison, the published set of data by Napier has been compared to this set (prior to its inclusion). The average length of its 59 foot prints is 15.5" and, thus, deviates by merely 0.1" from the larger population average.

Many of the data points represent a single measurement out of a trackway that might have extended over many yards or in some cases over several miles, where the ground and expertise of the investigator allowed uninterrupted tracking.

Undoubtedly, only a small fraction of the population of any species is ever represented by recorded foot prints, especially in forested terrain. With a life expectancy of around 40 years (see below), this collection of 706 prints over 40 years speaks of a substantial population, probably in the "low thousands", as speculated by Krantz.

Ball Width and Width Index

One of the characteristics of sasquatch foot prints that sets them apart from their human counterparts, aside from length, is the disproportionate width at the ball of the foot (Fig. 2), a ratio that is reminiscent of the foot of a human infant.

Descriptive statistics of 438 foot print widths yield a range of 3" to 13.5" and an average of 7.2". This width can be represented directly in relation to foot length, but a more instructive display is the ratio of width divided by length, called the width index. If these values (0.46 for the mean foot size) are plotted against foot length (Fig. 3), the calculated regression line shows a minimal decrease with increasing foot length, that is, the width increase lags slightly behind the growth in length.

This identical tendency has been studied in human feet over a range of 6"-12" foot length in 897 adult men and women by the NIKE Research Lab. Here, the relative narrowing of the foot is much more pronounced (Fig. 3, lower line). The foot of a 7’3" teenage basketball star measured 16.5" in length, but only 5.5" in width (width index 0.33).

 Almost the entire set of graphed sasquatch foot prints has a greater width index than average adult human feet do. Human infants have a width index of about 0.43 and the Patterson sasquatch 0.41.

Heel Width

The heel width histogram (Fig. 4) mirrors that of the foot lengths rather closely, though being lower in numbers (N=123). The widest sasquatch heels challenge one’s credulity unless one has seen the proportion of the heel to the size of the whole foot. Heels range from 1.5" to 9" in width and average 4.8".

As is the case with the ball of the foot, the heel does not grow in proportion to the length of the foot but lags behind, as the human heel does. The sasquatch appears to rely less on the heel plant in walking, but rather bears more of its weight on the broad anterior part of the foot, distal to the metatarsal hinge (see below) or, for that matter, more evenly distributed over the entire sole in the absence of an arch. In an expertly documented track of 14" prints, the imprint changed from a normal shape during calm walking to a round foot print, i.e., the anterior half of the foot, during running (step length changing from 4’ to 9’), in which the heel never touched the ground.

Height and Height Factor

No complete body print has been measured in conjunction with foot prints of its respective owner despite the fact that a few such rare artifacts have been observed (as is the case for hand, knuckle, knee, and butt prints). However, in 89 cases, the height of an observed sasquatch was estimated and its footprint length measured subsequently (Fig.5). Dividing the height by the foot length produces a "height factor", a multiplier to calculate height from foot length. This value, however, is not a constant but varies systematically with increasing size. The factor is 7 or higher for the smallest feet, about 6.0 for the mean and near 5.0 for the largest prints. Human ratios that I have sampled range from 5.1 to 7.2 and probably exceed these values below and above. This shifting ratio can be expressed mathematically in a so-called allometric scaling formula, which is explored in detail in the full article. It shows that sasquatch feet grow in substantial excess of general body dimensions (hence the justifiable moniker "Bigfoot").

This foot growth in excess of the rest of the body makes sound biological sense, since the weight increases as the cube 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.

The Patterson sasquatch, whose height has been derived by photogrammetric means by Glickman, is 7’3" tall, foot length 14.5", with a height factor of 6.04. The statistics suggest an average height for the population of 7’10" (foot length 15.6", factor 6.025), meaning females and males combined. Thus, the Patterson sasquatch, being a female, is below the population average for both foot length and height. A 24" footprint predicts a height of 9’5".
 
 

Gait

Gait is the generic term for quadrupedal or bipedal locomotion and pace is taken to be synonymous with step. The term stride is reserved for three sequential steps in a trackway. Step length is measured from one point on one foot to the identical point on the opposite foot.

Most foot prints that are found 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. 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 foot prints, with their long distances between footfalls, are much less likely to be recovered in the usual forested terrain. Consequently, the gait records are apt to err in the direction of being too low.

Pace Length

The pace file consists of 297 records. The pace length for the mean foot length is exactly 5.0’ (Fig. 5). The step length of the Patterson sasquatch lies only moderately above the regression line in congruence with its observed "unhurried" retreat from the scene. Given the walking cadence of that animal, extractable out of the movie, and its know step length, a reasonable speed of about 6 mph is obtained. Sighting records collected by Green contain variable reports of running sasquatches. For example, upon initial encounter, 13% were running, while upon departing 9% ran and the rest walked away. The upper line in the graph indicates approximately the step length at which the gait changes to running, about 6% of the total, a low figure for the previously mentioned reasons.

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 or a sasquatch running with galloping horses. 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, the top running burst speed about 27 mph, the longest single jump near 30’ and the longest triple jump - in effect three running steps - about 60’, all this with a physique of   decidedly smaller scale than that of a sasquatch. Extrapolation from step lengths and observed running cadence (about 140 steps/min) suggests a top speed of the sasquatch of 35-40 mph, the speed of a galloping horse.

Gait Characteristics

The sasquatch has apparently evolved a peculiarly long stride with a long arm swing, a slow cadence coupled with prolonged ground contact of the feet and a suppression of vertical body oscillation, a so-called compliant walk. 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"). A longer bipedal "double support" during the stride cycle is an adaptation that reduces peak forces during heel-strike and toe-off and divides the body weight more evenly between the two feet. Half foot prints, in which only the anterior part of the foot is imprinted, are indicative of metatarsal hinge. This anatomical detail, in which the middle of the foot can flex rather than having a rigid arch, is observable in the gorilla foot and is profoundly different from the human foot with its arch of substantial paleontological antiquity (see "Redwood Video", this website).

Weight

Weight estimates are notoriously difficult to arrive at by visual observation. Human ratios are clearly inappropriate. Some extrapolators have used the width of the dimensions of the heel, cubic volume of body parts, or the width of the ball of the foot, but the estimated or calculated weights for the Patterson sasquatch range from 280 to 2,030 lbs.

Chest Dimensions

There is, however, a scaling formula for primates that relates chest circumference to weight. This relationship, derived from data from marmosets to gorillas, can be applied to the sasquatch provided its chest circumference is known (Fig. 6). For the Patterson sasquatch, chest circumference can be extracted from enlarged prints of film images, which contain the 14.5" foot as a scale reference. From these, a chest width of 22" and a depth of 16" results, which corresponds to a weight of about 540 lbs. This weight is subject to considerable error, but clearly eliminates many of the high and low estimates from consideration.

Other Dimensions

For the sake of completeness, some other dimensions of the Patterson sasquatch that can be extracted from selected film frames, are cited here: Shoulder width: 33"; hip width: 24"; upper arm circumference: 22"; upper thigh circumference: 31"; knee circumference: 27"; [and from other sources] hand width at palm (with 16" footprint): 6"; wrist to base of fingers: 7"; wrist to end of middle finger: 11".

Weight Extrapolation

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 foot print / height / weight table (rounded values). The mean is represented by the 15.6" foot print.

Foot Height Chest Weight (lbs)

12"    7’ 0"   58"  490
14"    7’ 6"   62"  580
15.6" 7’ 10" 65"  660
16"    7’ 11" 65"  670
18"    8’ 4"   69"  770
20"    8’ 8"   72"  850
22"    9’ 1"   75"  950
24"    9’ 5"   77"  1,040

Consequences of Weight

Several corollaries accrue from increased weight in this primate. 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 habit. The sasquatch, in contrast, is compellingly nocturnal (see below). Most adaptive for the sasquatch is the increased resistance to cold with increased body mass. Increased size also implies high mobility and a correspondingly large home range, a characteristic that reduces its social structure to small and sparse groups

Caloric Consumption

The weight of an animal can be used to predict its basal metabolic rate, meaning its minimal daily caloric requirement, by a mathematical relationship (Kleiber’s Law), that is an extremely tight one. Application of this rule suggests 5,000 calories for the average sasquatch (as defined by the statistics). With exercise and inclement weather this value can double or triple.
Hence, a diet that is minimally omnivorous, if not slanted toward carnivory is required to fulfill that demand.

Prey Food Values

I will provide here some comparison data. Internal organs would yield 12,000-35,000 calories for White-tailed Deer, 20,000-50,000 for Mule Deer, and 60,000-90,000 for Elk. These values would rise dramatically (about 3,500 cal/lb) with the inclusion of fat stores around the body cavity. Reports exist for all of these species being preyed upon by sasquatch.

The initial selectivity for soft internal organs may have its root partly in the their nutritive value and partly in their friable nature, which is more easily dealt with by the flat molars of a primate. 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. Formulae for average daily food intake by omnivores suggest a needed weight of about 35 lbs of a mixed diet for the average sasquatch.

Brain Size

Finally, scaling of body weight to brain size in primates has been pursued by numerous authors. Application of these formulae leads to a predicted brain volume of about 770 cc, compared to that of the mountain gorilla of 530 cc with a range from 420-685 cc. 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 their large home range.

Strength

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. If one uses the pertinent formula for maximum human weight lifting ability, extrapolated to the weight of the average sasquatch, it yields a minimum of 1,300 lbs. 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. Their reported ability to pick up, carry and throw a full 50-gallon drum of diesel fuel (450 lbs), tip over a commercial trailer, or throw basketball-sized rocks in a high arc to discourage intruders seems not unreasonable in this light.

Plantar Pressure

If one refers to the preceding table of calculated weights and foot lengths, one can extrapolate plantar pressure for feet of different-sized individuals. It has been pointed out that the compressive strength of cartilage has certain inherent limits that can only be exceeded at risk of health and joint integrity of the animal in question. Additionally, compression of the sole beyond the limits of tissue pressure would collapse capillaries and eventually lead to tissue breakdown. Since any animal is likely to be optimally adapted to its weight, support and gait configuration, even the sasquatch would adhere to such general rules of body design.

Plantar Pressure Comparison

Admittedly, the following calculations have an element of circularity in them, so the resultant output should only be viewed as an approximation. Calculated sole pressure varies from 6 lbs/in2 to 12 lbs/in2. The Patterson sasquatch print, relatively narrow, covers between 60 and 65 in2 with a calculated weight of 542 lbs, translating into a plantar pressure of 8.3-9.0 lbs/in2.
Comparison values for the human foot are about 10 lbs for the contact area of the foot or 5 lbs/in2 for the entire sole (foot outline), a value that drops to about 2.5 lbs/in2 for a booted foot, a common reference in the field. Thus, a sasquatch foot print generally would be expected to show 4-5 times more pressure per area than a comparison boot print. Anecdotal reports often suggest higher weights, though generally without experimental backing other than jumping on one foot or carrying a second person without much effect.

Foot Anatomy

The sole of the sasquatch foot is probably several inches thick, as revealed by a small rock that was found to have deeply indented a sole. Usually, the foot shows no wrinkles or folds, though occasional scars. The thick sole pad, in man a tough connective tissue lattice filled with fat, presumably serves to distribute the weight on the sole in a much more even fashion than is the case in man. In any case, contrary to popular belief, plantar pressure in even large sasquatches does not appear to range exorbitantly beyond human values, as one would reasonably expect from anatomical considerations.

Growth and Life Cycle

Since almost all data presented here are gender neutral, it is next to impossible to extract values for presumptive sexual dimorphism. Beyond that, we have no idea of the age of any animal that has been sighted beyond comparing a juvenile one to the age of corresponding children. Here I have endeavored to apply what minimal data we have to estimate age and a growth curve, in this case of the female of the species. I should emphasize that this curve is predicated on the growth of feet rather than general somatic dimensions, which would follow a different curve.

Infancy

To fix the endpoints, I have taken the foot lengths of human neonates and mountain gorilla newborns as a starting point (about 3.5" for the sasquatch). The smallest, intermittently walking foot prints by a juvenile sasquatch that have been recorded are 4"-5" long. That length corresponds to the mean of the human foot at one year, which is the age that I have
arbitrarily assigned to these prints, although walking is probably initiated earlier than in man.

Adulthood

To fix the opposite, high end point of the graph, I have collected all records consisting of a single large set of prints accompanied by one set of "baby" foot prints (smaller than 7") on the assumption that the mother, by implication a mature, no longer growing female, is most likely the exclusive adult companion of a juvenile for the first few years of its life. The largest footprints of a presumptive female accompanied by an infant have measured 18.5".

Lastly, I have received three separate sets of timed foot print measurements (from three different observers), each stretching over several years, that were considered to originate from three growing animals. The set with the longest time base was used to produce the time axis for the graph, while the remainder was fitted to the resultant curve (Fig. 7).

The graph suggests a growth period in which average adult human height is approached at about age 8 with a foot length of 9-10". In some rare instances, 3’-4’ tall juveniles have been seen by themselves, although they are usually near their mother at that size and age.

Grouped Footprints

Additional speculative inferences can be drawn from combining this graph with rare multiple sightings and grouped foot prints. Surviving offspring seem to be spaced at intervals of 3-5 years, as estimated from presumptive "family" groupings of foot prints. A female with a very small, i.e., nursing, infant has never been observed, an indication that the mother can avoid absolutely all contact with man when in this vulnerable state. Records of family groupings of prints suggest that an older sibling will stay with the mother some years after the arrival of the next one, until about age 10, exhibiting its maternal attachment by occasionally "hitching rides" on the mother like the younger one.

Maturation of the Female

The female seems to reach sexual maturity at about age 9-10 (extrapolated from the smallest adult of a mother-infant pair), by which time she will be near 6’ in height. At this stage the female has been observed to keep male company and has developed small breasts, "pert" in an observer’s word.

By applying scaling formulae to the 660 lb body of the average sasquatch, a gestation period of about 9 months and an average life span (in captivity) of 36 years can be estimated. This life expectancy implies an occasional survival into the fifth decade, reports which account for descriptions of some animals as looking old and wrinkled, having "rotten, snaggle teeth" and unkempt, matted "angora goat dreadlocks" or patchy, worn hair. Survival times for gorillas in captivity range into the middle of the third decade of life.

Scaling formulae exist to calculate other biological aspects such as respiratory rate, heart rate and blood volume, limb proportions , tooth size, and organ weights, but these have not been applied.
 
 

Other Traits Accessible to Statistics

Nocturnality

The nocturnality of the sasquatch has been questioned on occasion. This trait can be considered from a statistical standpoint. Take a hypothetical area randomly seeded with sasquatches, evenly distributed during day and night. Their apparent temporal distribution will depend on them being seen by human observers. Assume a very conservative ratio of such alert observers during daylight as compared to the hours of total darkness in the mountains to be 20:1. A daylight observer will have a circular observational area with a radius of, say, 500’, over which recognition of the subject will be unambiguous, roughly 800,000 square feet. A nighttime observer has at best the expanding cone of headlights in one direction with recognition of a grey object at 300’ and an expanding width of illumination to 100’, a sector with an area of about 15,000 square feet. Factoring in the number of observers produces a ratio of 800,000 X 20 : 15,000 X 1, or better than 1,000 : 1. This 99.9% : 0.1% ratio describes how sightings should be distributed between day and night, a number that will get more extreme if flashlights or moonlight is the alternative illumination.

An actual ratio cited by Green consists of 735 daytime sightings (58%) and 540 during the night (42%), or a ratio of 1.38 to 1. If only sightings on roads are considered, the ratio shifts to 58% in favor of night sightings. This discrepancy can be interpreted as activity by the sasquatch that exposes it to being seen about 1,500 times more often at night than an even distribution would predict.

Duration of Sightings

Anecdotal reports suggest that a sasquatch, on being observed by a female or couple rather than one or more males, tends to linger longer. This impression suggests possible effects of less aggressive body language of women or recognition of the human female as inherently less threatening. Exploration of the available data in John Green’s database yield virtually identical duration values for the various categories of observers. However, no inferences can be drawn from this result, since the records do not state who broke off the encounter, that is, whether human females are more likely to terminate the sightings rather than the sasquatch.

Hair Color

The frequent question about predominant hair colors can be answered with 623 sighting records from John Green’s database. Slightly over 60% are listed as "Dark" or "Black", including such variants as brown-black, red-black, and dark brown. About 30% are described as "Brown", including dark-brown, light brown and red-brown. The "Grey" category (8%) includes dark and light grey, grey-brown, silver-grey, silver and silver tipped. "Light", off-white, white, and blond account for about 7%. The excess beyond 100% results from slight overlap in the categories. All purported sasquatch hairs in my possession (11 regional samples) show a reddish tinge under the microscope, lack a medulla and are indistinguishable from human hair. Efforts at DNA analysis were unsuccessful.

Change in Coat Color with Age

A suspected gradual darkening in hair color with adulthood was explored and not confirmed by the database, which produces identical height averages for coat colors grouped from dark through medium to light. Some tendency toward a geographical cline in coat color, i.e., lightening with higher latitudes, has been suggested in the literature with limited data.
 
 

SUMMARY

The presented statistics provide us for the first time with population averages and ratios that relate foot length, height and weight of the sasquatch in a manner not dependent on guesses, opinion or individual anecdotal accounts. I have speculatively pursued all attributes of the species that could be derived or inferred from the presented data by correlation or allometric scaling. It is very probable that the sasquatch population, being composed of animals with a long life span, few offspring, and little culling by predators will display wide physical variations, seen in such reported aspects as facial features, diverse coat colors, and the large variance in foot proportions documented here. The data, furthermore, are indicative of a sizeable population of a species that has adapted in a variety of ways (except development of intellect) to the demands of surviving in the montane environment of the North American continent.

© Dr. W. Henner Fahrenbach, Ph.D.
Beaverton, Oregon - October 2, 1999
 
 
 

 

Other Articles by Dr. Fahrenbach:

• Case Closure on the Murphy-Crook "Bell" News Story

 
• Status of DNA Tests on Purported Bigfoot/Sasquatch Hairs

 

Dr. Fahrenbach can be reached via e-mail at HennerF@BFRO.net