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Ken1036

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I have these shoes and love them! And I will NEVER share photographs of them here because your photographic talents scare me.
 

MoosicPa

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That's fascinating sforum1. I've never seen anything like that. Thanks for the reference.
That twisted last must be exceptionally flexible, to flatten out when its worn.
My salesmen friend knows little about physics. He simply brought this issue to my attention.

Without using lab instruments, we can assess comparative shoe stability using some basic metrics (which given sform1's video may possibly be defied by some ingenious shoe craftsmen).

First, examine your EGs and JLs, hopefully representing a number of lasts from each maker. Now measure the narrowest part of the waist and the widest part of the ball of the sole. Let w = the waist (the narrowest part) of the sole and b = widest part of the sole (where the ball of the foot will lie). Now calculate the ratio: w / b. That's your waist-to-ball of the foot ratio. The closer w/b is to 1, the more evenly distributed will be plantar force exerted on your foot's sole when you take a step, and so the more stable your gait should be when you walk. I believe that for most lasts, you will find the EG w/b ratio is generally closer to 1 compared to JLs.

More specifically, we can actually measure how much pressure is exerted when we walk. Let p = f /a (pressure = force / area). However, because of the irregular shape of the shoe's sole, we have to adjust our calculations accordingly. We need a better measure of the distribution of the plantar force that's exerted when we walk. Let x = (1 - w / b). Given our specification: 0 < x < 1. We can now alter our original equation for pressure thusly: Pressure = (f / a)^x, and as long as x < 1, that should give us a nice decimal root function that is easy to measure and interpret. Therefore, as w/b approaches 1, x approaches 0, and the lower the value of p. A lower p means a reduction in the plantar pressure that's exerted on a specific area of our foot as we walk and the more evenly this pressure should be distributed.

In other words, that beautiful fiddle back waist that we all appreciate, is likely to cause our gait to be less dynamically stable compared to shoes that have wider waists.

Second, we can examine the aspect ratio of the sole relative to the ground, as well as the angle between the ground and highest point of the waist. Again, all things being equal, the greater that angle, the greater the disparity between our sole axis relative to our ankle angle, leading once again to a less stable gait, which is one of the reasons why women in 6 inch pumps have such a hard time walking. Now examine your EGs and JLs. I think you will find the JLs have a greater angle between the ground and waist, which will put greater upward pressure on the medial and lateral arches of the foot. Based on this basic analysis, walking in EGs should exert less plantar pressure on the posteroinferior tuberosity of the calcaneous (the back of the sole), which absorbs most of the pressure exerted when we walk, as well as reducing the pressure upon the 1st and 5th metatarsals at the front of the foot.

In conclusion, there are physical and biokinematic reasons (there are 33 joints in the foot) for my hypothesis that EGs may in fact be more dynamically stable than JLs, but I would have to conduct measurements and systematic analysis of a large sample from each brand to examine this hypothesis to an acceptable level of rigor.
:puzzled:
 

reidd

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That's fascinating sforum1. I've never seen anything like that. Thanks for the reference.
That twisted last must be exceptionally flexible, to flatten out when its worn.
My salesmen friend knows little about physics. He simply brought this issue to my attention.

Without using lab instruments, we can assess comparative shoe stability using some basic metrics (which given sform1's video may possibly be defied by some ingenious shoe craftsmen).

First, examine your EGs and JLs, hopefully representing a number of lasts from each maker. Now measure the narrowest part of the waist and the widest part of the ball of the sole. Let w = the waist (the narrowest part) of the sole and b = widest part of the sole (where the ball of the foot will lie). Now calculate the ratio: w / b. That's your waist-to-ball of the foot ratio. The closer w/b is to 1, the more evenly distributed will be plantar force exerted on your foot's sole when you take a step, and so the more stable your gait should be when you walk. I believe that for most lasts, you will find the EG w/b ratio is generally closer to 1 compared to JLs.

More specifically, we can actually measure how much pressure is exerted when we walk. Let p = f /a (pressure = force / area). However, because of the irregular shape of the shoe's sole, we have to adjust our calculations accordingly. We need a better measure of the distribution of the plantar force that's exerted when we walk. Let x = (1 - w / b). Given our specification: 0 < x < 1. We can now alter our original equation for pressure thusly: Pressure = (f / a)^x, and as long as x < 1, that should give us a nice decimal root function that is easy to measure and interpret. Therefore, as w/b approaches 1, x approaches 0, and the lower the value of p. A lower p means a reduction in the plantar pressure that's exerted on a specific area of our foot as we walk and the more evenly this pressure should be distributed.

In other words, that beautiful fiddle back waist that we all appreciate, is likely to cause our gait to be less dynamically stable compared to shoes that have wider waists.

Second, we can examine the aspect ratio of the sole relative to the ground, as well as the angle between the ground and highest point of the waist. Again, all things being equal, the greater that angle, the greater the disparity between our sole axis relative to our ankle angle, leading once again to a less stable gait, which is one of the reasons why women in 6 inch pumps have such a hard time walking. Now examine your EGs and JLs. I think you will find the JLs have a greater angle between the ground and waist, which will put greater upward pressure on the medial and lateral arches of the foot. Based on this basic analysis, walking in EGs should exert less plantar pressure on the posteroinferior tuberosity of the calcaneous (the back of the sole), which absorbs most of the pressure exerted when we walk, as well as reducing the pressure upon the 1st and 5th metatarsals at the front of the foot.

In conclusion, there are physical and biokinematic reasons (there are 33 joints in the foot) for my hypothesis that EGs may in fact be more dynamically stable than JLs, but I would have to conduct measurements and systematic analysis of a large sample from each brand to examine this hypothesis to an acceptable level of rigor.
Unsubscribed
 

oskrusa

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That's fascinating sforum1. I've never seen anything like that. Thanks for the reference.
That twisted last must be exceptionally flexible, to flatten out when its worn.
My salesmen friend knows little about physics. He simply brought this issue to my attention.

Without using lab instruments, we can assess comparative shoe stability using some basic metrics (which given sform1's video may possibly be defied by some ingenious shoe craftsmen).

First, examine your EGs and JLs, hopefully representing a number of lasts from each maker. Now measure the narrowest part of the waist and the widest part of the ball of the sole. Let w = the waist (the narrowest part) of the sole and b = widest part of the sole (where the ball of the foot will lie). Now calculate the ratio: w / b. That's your waist-to-ball of the foot ratio. The closer w/b is to 1, the more evenly distributed will be plantar force exerted on your foot's sole when you take a step, and so the more stable your gait should be when you walk. I believe that for most lasts, you will find the EG w/b ratio is generally closer to 1 compared to JLs.

More specifically, we can actually measure how much pressure is exerted when we walk. Let p = f /a (pressure = force / area). However, because of the irregular shape of the shoe's sole, we have to adjust our calculations accordingly. We need a better measure of the distribution of the plantar force that's exerted when we walk. Let x = (1 - w / b). Given our specification: 0 < x < 1. We can now alter our original equation for pressure thusly: Pressure = (f / a)^x, and as long as x < 1, that should give us a nice decimal root function that is easy to measure and interpret. Therefore, as w/b approaches 1, x approaches 0, and the lower the value of p. A lower p means a reduction in the plantar pressure that's exerted on a specific area of our foot as we walk and the more evenly this pressure should be distributed.

In other words, that beautiful fiddle back waist that we all appreciate, is likely to cause our gait to be less dynamically stable compared to shoes that have wider waists.

Second, we can examine the aspect ratio of the sole relative to the ground, as well as the angle between the ground and highest point of the waist. Again, all things being equal, the greater that angle, the greater the disparity between our sole axis relative to our ankle angle, leading once again to a less stable gait, which is one of the reasons why women in 6 inch pumps have such a hard time walking. Now examine your EGs and JLs. I think you will find the JLs have a greater angle between the ground and waist, which will put greater upward pressure on the medial and lateral arches of the foot. Based on this basic analysis, walking in EGs should exert less plantar pressure on the posteroinferior tuberosity of the calcaneous (the back of the sole), which absorbs most of the pressure exerted when we walk, as well as reducing the pressure upon the 1st and 5th metatarsals at the front of the foot.

In conclusion, there are physical and biokinematic reasons (there are 33 joints in the foot) for my hypothesis that EGs may in fact be more dynamically stable than JLs, but I would have to conduct measurements and systematic analysis of a large sample from each brand to examine this hypothesis to an acceptable level of rigor.
May I ask: what is w and b in your distribution of the plantar force equation?

Also, perhaps the fiddle back waist might be better suited for feet with high arches. On this case, the shoe would better harness the bottom of the foot, almost embracing it while bringing a stronger overall connection with the rest of the shoe as a platform.
 

sforum1

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May I ask: what is w and b in your distribution of the plantar force equation?

Also, perhaps the fiddle back waist might be better suited for feet with high arches. On this case, the shoe would better harness the bottom of the foot, almost embracing it while bringing a stronger overall connection with the rest of the shoe as a platform.
Furthermore, do w and b have to be reals, or are they allowed to take on imaginary values too?
 
Last edited:

Professor Χάος

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May I ask: what is w and b in your distribution of the plantar force equation?

Also, perhaps the fiddle back waist might be better suited for feet with high arches. On this case, the shoe would better harness the bottom of the foot, almost embracing it while bringing a stronger overall connection with the rest of the shoe as a platform.
Hello Oskrusa,

Thanks for your question. I hesitate to remark on issues related to shoe-making, but I'm not sure that arch-height and fiddle back waists are necessarily related. I own an hand-welted Enzo Bonafe that has a fiddle back waist, but with a relatively low arch. I'd refer your question to a shoe craftsman like DFWII, who has a life-time of experience creating shoes.

My point concerned the relationship between waist width and stability when walking, and I hypothesized that EGs, on average, have a wider shoe waist than JLs, which influences the overall stability of your gait. If I understood your question: w = the narrowest part of the waist, and b = the widest part of the midsole (where the ball of the foot rests). The w / b ratio is related, all things being equal, to the stability of your stride as a matter of basic physics. The wider the shoe waist, relative to the widest part of the midsole, the more stable your gait. I'm guessing that shoe makers could craft an ultra-thin waist if they wanted, but it would be a challenge to insure stability when walking.

More generally, you are correct that there is a natural variation in foot dimensions across the human population. I'm not an orthopedic surgeon. My specialization lies elsewhere. However, the biokinematics of walking is a fascinating area of research, and turns out to be quite complicated, since the human foot contains 26 bones, 33 joints, 20 muscles, 30 ligaments, and 100 tendons. Modeling the human stride is therefore quite challenging. Had I asked a surgical resident with a background in biomechanics to create a model of plantar pressure, they would have likely provided you with a set of differential equations with instrumental variables to capture the dynamic process of walking. My goal was therefore not completeness, but rather to provide the simplest and most intuitive formulation possible, that anyone can implement. Note that my previous message only contained a simple static equation, that does not capture change (i.e. is not dynamic), and to do so would require a more sophisticated model of the propagation of the heel strike across the rest of the foot, as well as the secondary strike of the metatarsals (front of the foot) against the ground. These are further not independent events, but happen according to a cycle that is slightly different for each person.

Each person has a unique foot profile, that is as personal as your foot print or fingerprint. So its not surprising that you have foot characteristics that make some shoes more suitable than others, regardless of purported shoe quality. The variation of foot dimensions is correlated with age, height, gender, and geographic origin (ethnicity if you wish). Given the distribution of foot variations across the human population, manufacturers must design shoes based on the population mean. Hence, the main motivation for different shoe lasts is not just aesthetic differentiation, but also to capture the general variation in foot dimensions across the target market, which today is global. That's why bespoke shoes may be the best option for people with foot dimensions that are relatively far from the mean values of the wider population. Orthopedic shoes may also be necessary for people with extremely variant foot dimensions or who suffer from various maladies that affect blood circulation in their feet, such as diabetes, leg aneurysms, or thrombophlebitis.

Once we normalize for scale, there are six dimensions of foot morphology. In order of decreasing variation these include: arch height, ball width, inter-toe length/distance, global foot width, hallux bone orientation, and midfoot width. These different categories capture over 90% of foot morphology variation. Furthermore, a higher BMI (Body-Mass Index = weight/height^2) results in wider ankles, a wider Achilles tendon and a higher toe orientation. Gender is also typically associated with ankle and heel width, and intensity of sports activities is also associated with wider heels and toe height. On average, the larger your shoe size, the more narrow your Achilles tendon, the narrower your heel and the lower your arch, although these characteristics vary significantly regardless of shoe size.

Anyway, I hope that answers your question.

Best Regards,
 
Last edited:

Professor Χάος

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Furthermore, do w and b have to be reals, or are they allowed to take on imaginary values too?
hahaha....I don't know sforum1....is your ruler divided into complex intervals? Perhaps you can use it to measure your imaginary shoe collection. Imagine if your shoes existed in two dimensions, then they would appear as a flat surface and you could skate on them. Alternatively, if your shoes existed in one dimension, they would appear as lines.......or even better..... zero dimensions, then your shoes would appear as points and you could carry your entire collection in your pocket.

Actually, I was waiting for you to produce another mind-bending video of some physics-defying shoe designs.
 

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