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DISPELLING THE STEP LENGTH MYTH
Differences in step length for the left and right feet can
not lead to path deviation.
When a person takes a 20 in. step with the left foot, as
they walk the right leg has to be brought up to and then pass the left foot.
This action I have termed the "carry".
Thus, when the left foot takes a 20 in. step, the right foot
is "carried" for 20 in. Then, the right foot moves forward with a step of 25
in., followed by the 25 in. carry of the left foot. The total distance moved
forward by each foot is not just the 20 or 25 in. step, but also includes
the corresponding carry. Thus, for one full stride, the left foot would move
forward by a step of 20 in. PLUS a carry of 25 in., for total of 45 in., and
the right moves forward with a carry of 20 in. PLUS a step of 25 in., for a
total of 45 in.
Disregarding the carry is the critical error which leads to
the confusion. The carry equalizes the total distance traveled for each leg.
The only way to deviate from the straight path is for one or the other foot
to be placed off of the straight line during the step.
To see what I mean, try walking with extremely exaggerated
differences in the left and right step length (eg. left-25 in. and right-2
in.). If step length had anything to do with direction, after 1 or 2 strides
you should be pointing off of the straight line. You don't because the carry
of 2 in. for the left step and 25 in. for the right step means the total
distance traveled is still 27 in. for both feet. (Stride = carry + step)
For a person walking straight, left and right strides are
equal in length. In a turn, the stride lengths are different, but, the turn
causes the stride length differences, not vice versa.
Try this: Draw two lines on the floor. Make
them parallel and at a distance apart that is comfortable when you walk,
your normal walking base. Now step on the lines. Take a few steps, keeping
each foot to its line. This is the normal starting point for all of the
discussions that I have seen. This is a person who is walking straight. Do
you agree?
Now, while keeping your feet on the lines, walk along it
with any combination of step lengths that you like. Don’t worry about stride
lengths, you can’t control that, you can only control step length. Look at
the lines, or not, as long as you keep stepping on them. Have you stepped
off the line at the end of the room? No, you haven’t.
Now, imagine that the lines are in a room that is twice as
long as the first one. Now, do the same thing, taking whatever step lengths
you want for each foot (try 0” step length with one of the feet, or 2”). At
the end of that room, did you step off the line? No, you didn’t.
Do you think that at the end of a room a million times
longer you would be off the line? No, you wouldn’t. Because that’s not how
humans change direction when they walk. It just doesn’t happen that way.
It’s said that the height of foolishness is to continue to
do exactly the same thing while each time expecting something different to
happen.
SO THEN, “WHAT IS THE CAUSE OF PATH DEVIATION?”
Ironically, as it stands now, in order to answer that
question, we can’t ask that question. The first question to ask is ‘what is
the nature of path deviation’. What I mean is, how does path deviation come
about. What has to happen for there to be path deviation.
Luckily, there is only one answer needed for this.
Placing our feet off of the theoretical straight lines as we
walk is the thing we are doing that causes path deviation. It doesn’t matter
why we place our feet off the line, it doesn’t matter what controls it or
how, it’s enough that we do.
Assume a person is standing in the center at one end of a
football field. The goal is to walk to the center of the other side so we
can observe the path taken. Standard set-up. But we define four points as an
aid to the discussion. At the start, the right foot is on point A and the
left on point X. When we stop, the right foot will be on B and the left on
Y, when we are directly in the center of the target.
If a person where to walk a perfectly straight line to the
target, not only should they contact the target dead center, but we could
draw a line from A to B and from X to Y, and each right footfall would land
on the A-B line, and each left on the X-Y line. If this foot pattern was
observed, then we could say the person contacted the target dead center,
without question.
It could also be said that if we keep each foot on its
appropriate line, we will be walking a straight line to the target.
This begs the question, “what will happen if we don’t keep
our feet on the lines?” We won’t be walking a straight line to the target!
So, now, the question ‘what is the cause of path deviation’
can be answered by ‘path deviation is caused by placing our feet off of the
theoretical right and left straight lines’. That’s the only answer needed
for that question.
But it isn’t very useful. It is true, but in order to use it
we need to realize that when the question ‘what causes path deviation’ was
being discussed, the more direct question being asked was ‘what causes us to
put our feet off of the theoretical lines’.
Thus, the question is changed from ‘what causes path
deviation’ to ‘why do we place our feet off the theoretical lines’. This
profoundly simplifies the analysis, though it may not appear to at first.
Consider that you are the one standing in the football field
above. You’re at the start and there are actual lines connecting A-B and X-Y
in a straight line to the objective. As you look down at the lines and take
a step with the left foot you can easily put your foot on the line.
Continuing looking down with the right step, then left, etc. will end you up
at the dead center of the target. You don’t even have to look at the target
to accomplish this. As long as your feet touch the lines perfectly every
time, you will contact the target dead center, guaranteed.
Now, close your eyes and take a step with the left foot.
It’s unlikely your foot will land in exactly the same place it did when you
where looking (ie. dead center of the line). If the A-B and X-Y lines are
the zeros, the foot will be on the left or right side of its zero point by a
certain distance. This is the “foot offset”.
This will also cause the line of the leg (a line from hip
socket to heel point) to be at a certain angle from the current DOT. The DOT
is changed by the amount of this leg angle when the body moves onto the
planted foot in preparation for the next forward step.
Thus, for any step, we step out a certain length and have a
left or right offset, which changes the DOT. This is the first of the two
possible angular direction changes which occur during a step.
Varying foot offset is one way for a person to change
direction. The only other way is by changing the normal foot angle and
stepping out at an angle from the straight line. (Or, a combination of the
two, probably the most common.)
The normal foot angle is that which is most comfortable for
a forward step. If the foot has been planted so the foot angle is not
perfect for a straight step, there will be a slight angular direction change
when the rear foot is brought up to take its step.
Direction changes due to foot angle can come about in
several ways.
-
the foot is planted on the straight line with a non-zero
foot angle (a step turn),
-
the foot is planted on the straight line at zero foot
angle, but then twisted to give non-zero foot angle (a spin turn),
-
the person can plant the foot normally, but push off the
planted foot differently.
Foot offset combines with any of these, and the angular
change due to the offset (leg angle) will add to any other angular changes.
But, they all are just different ways to step off the
straight line at an angle.
With each step there are 2 possible angle changes. The first
from the foot offset as the body moves off the line to balance over the
front foot, the second is stepping out at a different angle due to variation
of the foot angle of the planted foot.
So, there are 4 potential angle changes per stride.
The offsets and angles for the left and right steps are most
likely (almost certainly) not going to be the same.
Each step will contribute its angular change to the DOT.
It’s the summation of the changes that determine direction. For example, if
each left step gave a 2 deg turn left, and each right step gave a 2 deg turn
to the right, the person would be walking straight, but turning with each
step.
ie. If the net direction change over a stride is zero, the
person will be walking straight, even if they’re turning with each step.
If the left gave 3 deg left and the right 2 deg right, the
person would be turning left at 1 deg per stride, and would be at 90 deg to
the original DOT in 90 strides.
For a 30” normal step with a 15” step-out length, an
increase in foot angle of only 2 deg. for one foot will cause a person to go
at 90 deg to the original DOT in 45 strides, or about 40 yds. The same
deviation occurs with a 1/2” foot offset. That’s barely perceptible.
Therefore, when a person deviates from a straight path, the
exact path is actually a line that is punctuated by angle changes at each
step, rather than a smooth curve.
Let’s go back to the room with two lines on the floor, and
step back on the lines. Try to step off one of the lines without doing one
of these things: 1) stepping to the side of the line with the front foot, 2)
placing your foot on the line, but with a different foot angle, (in a step
turn or spin turn, etc.) and then stepping out at an angle in the next step,
or 3) a combination.
Do one movement and then assume you are walking straight
again. ie. shift the frame of reference so the two lines correspond to your
new DOT.
And, then take another step. See where and how you put your
foot down with respect to the new lines. It will probably be similar shifts
and angles as seen in the previous steps, especially it there are no
direction cues. Maybe not exactly the same, but generally. People do things
in a regular way.
I believe I can study wandering by using a shifting frame of
reference and relating direction changes to variations in foot angles and
offsets.
Now there’s something to quantify. Experiments can examine
the effects of various factors on foot angles and offsets. Much easier than
answering the original question directly, but the original question is
answered each time another factor is described.
Anything you can imagine that will cause path deviation,
must do so by altering how the feet are placed when we walk compared to the
straight line.
A computer model has been developed which uses angles,
measures and positions at the instant of footfall, to produce realistic
footfall patterns. See Part II for details.
I believe a reasonable approach to the experimental work is
outlined below, see Part III for details:
In the first lab experiments:
-
define any terminology and descriptions that will be
used
-
run standard and control tests to uncover errors,
determine applicability and validate the method
-
develop general experimental protocols which can be used
by anyone
-
start getting offset and angle numbers under various
conditions
-
fiddle with the set-up to make data collection quicker,
easier and less sensitive to errors
-
take the real data and use the computer to determine
patterns
-
compare to larger scale to ensure applicability
The experiment is just variations of the football field
experiment, but with measurements for each footfall. I think it is much
better to start at the school gym scale and with the same subjects for many
tests. This will give an idea of scope and provide a feel for the techniques
without as much effort.
Form standards and controls:
-
“straight line” patterns
-
determine “straight” foot angles for several persons
-
see wander and correction patterns
-
start seeing offset and angle numbers and their ranges
-
start relating variations to conditions
-
see if one person can take the same test without biasing
it (ie. learning it)
-
see if smaller scale can be directly related to larger
-
and any other things we can think of
Collect and analyze data over a range of conditions and
subjects:
We MIGHT be saying things like: (I just made these up as an
example of the terminology)
-
to correct for wander, the majority of subjects used the
non-dominant leg with large foot offset and no foot angle change, in
each 2nd or 3rd stride, etc. OR,
-
most people use the dominant leg’s foot as the main
directional cue. There is much more variation in the non-dominant’s
offset and angle, leading to large changes of direction when stepping
out from the non-dominant foot.
Experiments could be devised to hinder the walk in various
ways and see how that affects the wander pattern, with specific respect to
individual angles and offsets. With a few current footprints of the lost
person, specific initial values could be obtained for use in the lost person
case.
If the same person can be used in more than one experiment,
a series of single conditions (like one shoe) could be looked at and a way
found to combine the data to predict the path with more than one condition.
Then, it can be checked by running the multi-condition test. This could lead
to a method to combine the data to predict paths for many combinations of
conditions.
A data base of experimental results could be compiled with
subjects from all over the world, using the internet, once a data collection
regime is better defined and the method validated. This would make good
projects for youth and outdoor groups.
Ultimately, there could be a list of general guidelines for
predicting wander paths, given a bit of footprint information from anywhere,
which would be useful over a wide range of ages and conditions. It may help
SAR to narrow a search area and end an ordeal more quickly.
I’ll leave it there for now. Experimental procedures, the
model, plots and analysis techniques will follow shortly.
If anyone sees any problems so far, please let me know so it
can be dealt with right away.
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Next
Part I (Page
1, Page 2) Part IIa Part IIb
(Page 1, Page 2)
Part IIc Part III
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