Human Foot Morphology
Human foot morphology is intimately related to the fitting of the shoe. We study the human foot morphology in order to improve the fit of mass-produced shoes. The size and shape of a shoe is determined by the shoe last on which it is manufactured. Foot size is used to determine the shoe size, and foot shape provides information on how to design the last shape.
How to measure foot dimensions
Shoe size is represented by length and ball girth in the Japanese Industrial Standard. The foot length and foot circumference of a human foot correspond to these two measurements respectively. Foot measurements are taken with the subject standing barefoot and with weight distributed equally on both feet.
The distance between the Pternion (the rearmost point of the heel) and the tip of the longest toe is measured pararell to the foot axis. The foot axis is the line connecting the Pternion and the tip of the 2nd toe.
Foot circumference (Ball of foot circumference)
Foot circumference is measured with a tape so that the tape passes over the Metatarsale tibiale and the Metatarsale fibulare. The Metatarsale tibiale is the most medially prominent point on the head of the first metatarsal bone, and the Metatarsale fibulare is the most laterally prominent point on the head of the fifth metatarsal bone.
Distribution of foot dimensions
Secular change has progressed in Japan. Younger people tend to have longer and narrower feet.
The distribution of foot sizes is related to production planning: how many and what size of shoes should be produced to satisfy the consumers. There are wide variations in foot size, but the sizes follow a normal distribution curve. The following data are derived from two anthropometric studies: one is on foot dimensions by the Japan Leather and Leather-Goods Industry Association in 1987 (JLIA), and the other is on whole body dimensions of young adults by the Industrial Products Research Institute in 1991 and 1992 (IPRI).
In Japanese adult males (18-60 years), foot length ranges from 21.1 to 28.7 cm and foot circumference ranges from 21.9 to 30.2 cm.
In Japanese adult females (18-60 years), foot length ranges from 19.4 to 26.3 cm and foot circumference from 19.8 to 26.3 cm.
Female feet are typically narrower than male feet of the same length.
In the Japanese system, shoe size is determined by length and circumference. Shoe size indicates the size of the foot that fits the shoe, not the size of the shoe itself. Foot length is measured in cm. Since foot circumference varies widely even when the foot length is the same, there are shoes of the same length with different circumferences. A shoe with average circumference is called width "E". It becomes "EE", "EEE", "EEEE", with increasing foot circumference, and becomes "D", "C", "B", "A" with decreasing foot circumference. To accommodate the variations in foot size, shoe lengths change by 0.5 cm. Circumference of the shoe changes in 0.3 cm increments. In the JIS for shoes, the sizes range from 20A to 30G for adult males, from 19.5A to 27EEEE for adult females, and from 10.5B to 26G for children.
Foot size distribution
The most frequently observed foot size is 25EE in adult males and 23E in adult females. People with very large or small feet, or very wide or narrow feet may have difficulty in finding shows that fit their feet. Industrial products are expected to cover the whole range of the variation, but, in practice, it is impossible.
Due to secular change, Japanese have become taller by more than 10cm in the last 100 years. Foot size has also changed in the last 100 years. There is a inter-generational difference in foot size. In the younger generation, feet are generally longer, but narrower.
A foot may become deformed during childhood.
Foot growth stops at a younger age than height growth. Feet stop growing at about 14 years in boys and 13 years in girls.
Another conspicuous change in feet is the increase in toe angles with age. The big toe gradually rotates laterally, and fifth toe rotates medially with age. Toe shape gradually narrows, probably due to wearing shoes.
Allometry of foot and grading of shoe last
Allometry is the change in size-related proportions due to growth. It is a widely observed phenomenon in animals. A large animal and a small animal have different proportions.
Small feet and large feet have different proportions. Large feet have an absolutely larger circumference but are relatively narrow.
In shoe last production, a standard size last is manufactured by hand. The lasts of other sizes are made by grading the standard last. Allometry of the human foot is taken into consideration when grading lasts.
2-dimensional foot shape
The bending foot axis is a shape characteristic important in shoe fitting. Most Japanese feet are more or less outflared.
A medial axis (skeleton) of a foot outline is used to summarize the 2-dimensional foot shape. The medial axis corresponds to the approximate midline of the long direction. The medial axis flexes in most feet, that is, most feet are outflared. Three regression lines were fitted to the medial axis, and the degree of outflare is quantitized by using the posterior flexion angle.
The distribution of the posterior flexion angle is a normal distribution with a mean of 8.4 degrees in males (8.2 in females) and with SD of 4.03 (3.79) degrees. In the medial axis of shoe last outline, the posterior flexion angle is 0 degrees.
3-dimensional foot shape
The 3-dimensional foot shape is correlated with the flexion foot axis. The most important variation in Japanese 3D foot shape is that contrasting a 'standard' type and a 'flat foot'.
When human foot shape is measured 3-dimensionally, the shape characteristics of the sections are correlated with the 2-dimensional foot outline.
The most important variation in 3D foot shape is that which contrasts a flat foot with a "standard" type foot having a well developed plantar arch and a high dorsal arch.
How to introduce shape characteristics to last design
Free Form Deformation is introduced for the analysis of 3D foot shape and for designing a shoe last for outflared feet.
Last design by using Free Form Deformation
We developed a method of last design in order to introduce information on human foot morphology by using the FFD (Free Form Deformation) technique. FFD control lattice points are defined around an object, and the object is deformed by moving the control points.
In the figure, control points are defined around a "standard" foot, and the control points are automatically moved so that the "standard" foot deforms into a flat foot. Here the movement of the lattice points are considered as a transformation function from a "standard" foot to a flat foot. When a last is placed in the transformation function, a new last that would fit a flat foot may be obtained.
Transformation of a "standard" foot into a flat foot
This is an example. The movements of lattice points that transform a "standard" foot (blue figure) into a flat foot (red figure) were calculated. The pattern of the lattice movement represents the difference between the two feet. In top view, the resultant lattice points arranged in a "S" pattern represent the bentness of foot axis. In the side view, the lattice points moved downward at the tarsal part to represent the low arch.
A new last for the flat foot
An existing last was placed in the deformed lattice. The resulting last reflects the morphology of the foot. Though foot morphology is a very important aspect, the function of the last and the shoe should be also taken into consideration.