Aligned Exercises
For the above mentioned exercises, the added weight (point
of resistive force) is practically in-line with the center of
gravity of the body segments which also contribute to the resistive
forces. This means that the muscles exert the same effort lifting
each unit weight (eg: 1lb or 1kg) of body segment(s) as they
do lifting the same unit weight of additional resistive forces
(eg: barbell, dumbbell, etc.). 'In-line' means that the Point
of Resistance and the Center of Gravity of Body Weight Segments
are nearly aligned along a similar downward path of resistive
forces. For these exercises, we add up the segments that are
lifted (both upward moving and upward rotating) to find the contribution
of resistance from body weight. Then we can simply add those
forces to the additional resistive forces to find the Actual
Resistive Forces.
Non-aligned Exercises
So how do we determine the contribution of weight from the
body segments in these exercises?
Notice with these exercises that the center of gravities of
the added weight and the body segments do not align over one
another as do the previously mentioned exercises. Weight added
further away from the fulcrum exerts more relative torque on
the fulcrum joint than does the weight of the body segments.
If the point of resistive force is twice as far from the fulcrum
(moving joint or point) as the Center of Gravity of Body Weight
Segments. That means the Body Weight Segment exerts half the
force per unit weight as compared to the resistive force.
Alternatively if the point of resistive force is placed half
way between the fulcrum and Center of Gravity of Body Weight
Segments, the Body Weight Segment exert twice the force per unit
weight as compared to the resistive force.
Most of the non-aligned exercise are the former case where
the point of resistive force is further away from the fulcrum,
or movement joint, as compared to the Center of Gravity of Body
Weight Segments.
Algorithm for Adjusting
Percentage Bodyweight on Non-aligned Exercises
In Non-aligned exercises, we will determine the body segment's
torque relative to the added weight's torque at the most difficult
part of the exercise. This will allow us to determine the effective
resistance required to lift the body segment compared to the
added load.
Relative torque can be calculated by comparing the distance
from the joint fulcrum to both the added weight and the combined
body segment's centers of gravities (COGs). A ratio representing
this relationship is used to adjust the percentage body weight
value accordingly. If the center of gravity of the added weight
is further away from the fulcrum we effectively reduce the Bodyweight
Percentage figure by multiplying a COG Variation Ratio figure
less than 1. If the center of gravity of the added weight is
closer to the fulcrum, we effectively increase the Bodyweight
Percentage figure by multiplying a COG Variation Ratio figure
greater than 1.
COG Variation Ratio = Body Segment's COG / Added Weight's
COG
Adjusted Bodyweight Percentage Used = Bodyweight Percentage Used
* COG Variation Ratio
We are not attempting to calculate absolute load in non-aligned
exercises, so it not necessary to adjust numbers if the body
segment's COG does not move directly against gravity, as long
as the added weight moves in the same direction.
Begin with traced or printed photo of the subject in the position
of greatest effort, viewed perpendicular to the plain of movement.
On free weight exercises (eg: Barbells, Dumbbells, Weighted),
this is typically where the center of gravity of the combined
load (all lifted body segments and added weight) is the furthest
perpendicular distance from the fulcrum joint.
The combined center of gravity of multiple body segments can
be calculated using the Segmental
Method Formula and data from known averages of length, weight,
and center of gravity of each segment (see body
segment stats). The center of gravity of the added weight
is much easier to ascertain because the center of the dumbbell,
barbell, weight plate, etc., can easily be located.
The figures in the following example are simplified so this
concept can be illustrated more clearly:
 Weighted Vertical
Straight Leg Raise
Added weight = 10 lbs
Bodyweight = 100 lbs
Bodyweight Percentage Used: 40%
Segment Orientation: Thigh (horizontal), Shank (horizontal),
Foot (vertical)
Legs Center of Gravity = 15" from hip (joint fulcrum)
Added Weights Center of Gravity = 30" from hip
The greatest torque on this exercise happens to be when the
leg is horizontal, or perpendicular to the line of force (ie:
gravity). Since the added weight exerts 2 times relative torque
on hip as does leg's center of gravity that means we need effectively
reduce the Bodyweight Percentage Used figure by half. This will
allow us to calculate actual resistance relative to added weight.
So a COG Variation Ratio of 0.5 will be multiplied by a Bodyweight
Percentage Used of 40% to get the Adjusted Bodyweight Percentage:
COG Variation Ratio = Body Segment's COG / Added Weight's
COG = 0.5
Adjusted Bodyweight Percentage Used = 40% x 0.5 = 20%
To calculate Actual Resistance (relative to added weight):
= (Bodyweight * Adjusted Bodyweight Percentage Used) + Added
Load
= (100 lbs x 20%) + 10 lbs
= 30 lbs
To calculate a weight increase 5% of actual resistance
(new dumbbell weight):
= Weight of dumbbell + (Actual Resistance * 5%)
= 10 lbs + (30 lbs * 5%)
= 10 lbs + 1.5 lbs
= 11.5 lbs
And another example:
Barbell
Goodmorning
Barbell = 60 lbs
Bodyweight = 140 lbs
Bodyweight Percentage Used: 59% (body - 2 legs)
Upper body's Center of Gravity = 13" from hip (joint fulcrum)
Added Weights Center of Gravity = 22" from hip
COG Variation Ratio = Body Segment's COG / Added Weight's
COG = 0.59
Adjusted Bodyweight Percentage Used = 59% x 0.59 = 34.8%
In the Goodmorning, we're only including the upper body weight
and not the weight of the leg primarily because the legs do not
move significantly against gravity, unlike the torso is nearly
horizontal at the lowest position. Also the legs moves relatively
passively at the ankle to maintain center of gravity the body
and barbell over the feet. Therefore the movement of the legs
do not significantly effect the total workload.
To calculate Actual Resistance:
= [Bodyweight * Adjusted Bodyweight Percentage Used] + Added
Load
= [140 lbs x 34.8%] + 60 lbs
= 108.72 lbs
To calculate a warm-up weight (barbell weight) from 50%
of Actual Resistance :
= (Actual Resistance * 50%) - (Bodyweight * Adjusted Bodyweight
Percentage Used )
= 108.72 lbs * 50% - 140 lbs * 34.8%
= 54.36 - 48.72
= 5.6 lbs
To calculate a weight increase of 5% from actual resistance
(new barbell weight):
= Weight of Barbell + (Actual Resistance * 5%)
= 60 lbs + (108.72 lbs x 0.05)
= 60 lbs + ~3 lbs
= 63 lbs
Other Examples of Non-aligned
Exercises
 Weighted
Push-up
Lifted segments: Whole body - 2 whole arms
Axis of rotation: Toes on floor
Hypothetically, if we were to add resistance directly above the
center of gravity of the body the percentage of bodyweight used
would be considered 100% since the added resistance would encounter
the same mechanics as the bodyweight lifted. However since the
added weight is actually placed higher than directly above the
center of gravity, we would calculate a COG Variation Ratio <
1. This is because loads higher up on the back (away from fulcrum)
will seem heavier than if we were to place them at the body's
center of gravity.
Weighted
Sit-up
Lifted segments: Whole body - 2 whole legs
Axis of rotation: Hips are the fulcrum joint although waist initially
flexes
Weight can be placed on upper chest or behind neck, not only
effecting torque of added weight but also arm
positioning (effects segment's COGs).
Weighted
Crunch
Lifted segments: part of thorax, arms, and head
Axis of rotation: thoracic spine.
Weight can be placed on upper chest or behind head, not only
effecting torque of added weight but also arm
positioning (effects segment's COGs).
Weighted
Hip Abduction
Lifted segments: Whole leg
Axis of rotation: Hip
Measure at initial movement when weight is greatest perpendicular
distance from hip
Barbell
45 degree Hyperextension
Lifted segments: Whole body - 2 whole legs
Axis of rotation: Hips are the fulcrum joint although waist articulates
Measure when spine is horizontal - greatest perpendicular distance
from hip
Special Cases
Normally we would measure force at the point where the added
weight's and bodyweight's COG are the furthest perpendicular
distance from the fulcrum joint. In the case of the Weighted
Leg Raises, that is when the legs are straight just as the legs
and added weight are lifted from the floor. But notice in the
bent leg version as the weight is lifted upward both the added
weight and the legs COG travel much closer to the hip than during
the straight leg version. To account for the distinction of these
two variations, we propose to analysis torques ratios at the
midpoint, half way through the movement, or 45 degrees from the
lowest starting position.
Weighted
Incline Straight Leg Raise
Lifted segments: Whole Leg
Axis of rotation: Hip
Weighted
Incline Leg Raise
Lifted segments: Whole Leg (extended at bottom and flexed at
top)
Axis of rotation: Hips although knee articulates
Notice this movement is easier than straight leg version above
since the knees bend as the legs rise.
Notice that the Leg Hip Raise version involves hip flexion
at the top of the movement. Although Hips and knees bend initially
movement can be harder at the top, although paradoxically, both
COGs become closer to axis of rotation in that position.
Weighted
Incline Leg Hip Raise
Lifted segments: Whole leg + Pelvis + Abdomen
Axis of rotation: Lumbar or Thoracic Spine
Ambiguous Exercises
At first glance some exercises appear to be non-aligned exercise,
but after further examination we can see the added weight may
be sufficiently aligned, either directly over or under COG of
the sum of the moving body segments.
Weighted
Inverted Row
(Weight of body - arms) + added weight
Possible similar situation as Weighted Push-up (mentioned above).
The classification of this movement depends where the weight
is placed on the body. Although, unlike pushups mentioned above
where weight is placed higher up on back, the added weight on
the Weighted Inverted Row is usually placed closer to the center
of gravity of body, in which case it would be classified as an
aligned exercise.
There is however an ambiguity in what position to analyze
this exercise. At what point do we consider the hardest part
of this exercise? At the top of the motion, the elbow travels
the greatest perpendicular distance form the shoulder. On the
other hand, the body's center of gravity is furthest from the
fulcrum made by the heel and floor, assuming if the torso does
not travel lower than the elevated feet. The percentage of body
weight utilized actually turns out to be the same in any case.
This is because the added weight shares the same lever system
as the bodyweight.
 Straight
Leg Deadlift
On the Straight Leg Deadlift, notice at the bottom of the exercise
how the rear end falls back and the barbell is pulled in over
the feet. The foot (instep) position relative the the rest of
the body is indicative of the body's line of gravity, necessary
to maintain balance on a sagittal plane. Depending on how the
exercise is performed, the barbell may or may not be aligned
under the COG of moving body segments.
It is also interesting to note that the torso rotates upward
whereas the added weight travels directly upward against gravity.
One could argue that the torso also rotates upward in the Deadlift
and Squat.
With those exercises, however, the torso only rotates partially
maybe 45 degrees, but there is also a lifting component from
the thighs so we count the entire weight of the upper body plus
the torque of the thighs for the Deadlift and Squat.
If Aligned
If the barbell is aligned under the upper body's COG (head,
torso, arms) we add the torque of the upper body to the weight
of the barbell to calculate Actual Resistance (AR). This is because
the torso rotates upward whereas the barbell moves more directly
upward. The torque of the upper body is the horizontal distance
from this COG line to the hip fulcrum divided by distance from
the end of the segments (ie: vertex of head) multiplied by the
weight of the upper body.
A) Actual Resistance = Upper Body Torque + Added Weight
Upper Body Torque = Weight: Torso, Head, Arms x Upper Body COG
Distance from Hip / Total Lever Length
If Non-aligned
If it turns out to be non-aligned movement we will need to
factor a COG Variation Ratio into the Upper Body Torque before
adding that to the weight of the barbell. To arrive at a COG
Variation Ratio, first we calculate the COG line of the upper
body (head, torso, arms). We can then measure its horizontal
distance from the hip fulcrum. Next we measure the distance from
the weight to the hip fulcrum. But, unlike the Barbell Goodmorning,
the added weight does not share the same ridged lever system
as the torso. We would still however, measure the horizontal
distance from the middle of the dangling barbell to the hip fulcrum.
In this case the barbell would be held at a closer perpendicular
distance to the hip than the upper body's COG. So dividing the
Body's COG Horizontal Distance by the barbells COG Horizontal
Distance will result in a COG Variation Ratio greater than 1.
This is in contrast to the previously mentioned exercises where
the COG Variation Ratio was less than 1. From here we multiply
the COG Variation Ratio by the Upper Body Torque thereby calculating
the adjusted torque relative to the force required to lift the
barbell upward.
B) Actual Resistance = (Upper Body Torque * COG Variation
Ratio) + Added Weight
Discrepancy of Arm Movement
Some may argue that the arms travel upward directly against
gravity in-line with the barbell and only the torso and attached
head pivot at the hip. If we take that approach we should only
include the head and torso and not the arms when calculating
the COG for the upper body. This will shift the COG posteriorly,
possibly closer the barbell's COG line of force. Only if the
upper body's COG (minus the arms) is not in-line with the barbell's
line of force do we need to calculate a COG Variation Ratio.
In any case we would add the torque (if aligned) or adjusted
torque (includes COG Variation Ratio) of only the head and torso
to the full weight of the arms and barbell combined. So we would
use one of the modified formula depending on the alignment as
follows:
A) Actual Resistance = Head & Torso Torque + Arm Weight
+ Added Weight
B) Actual Resistance = (Head & Torso Torque * COG Variation
Ratio) + (Arm Weight + Added Weight)
Identifying Insignificant
Body Segments
Attempting to calculate actual resistances for every exercises
that have insignificant body segments in play may unnecessarily
complicating workload calculations. In a fitness or sports conditioning
setting, including certain segments will not likely make significant
effect on the resultant workload. Counting the resistive forces
for insignificant segments may not be necessary for the following
reasons:
- movement of segments requires extremely little effort
- weight of segments(s) are very small in comparison to the
added weight.
- segment(s) does not move or rotate significantly upward against
gravity
This means assessing a percentage utilized bodyweight will
not be required for every exercise. Examples of exercises likely
not requiring a percentage of bodyweight may include:
We should however account for the weight of body segment(s)
if its load is significant in proportion the added weight weight.
For example:
Some exercises may closer examination to determine if the
body segments are of significance. For example on Lateral
Raise, if 10 lb dumbbells are being used, the torque of the
arm would be a significant portion of the resistance. However
if 50 lb dumbbells are being used, then the torque of the arms
would not be significant enough to effect workloads.
In a physical therapy or scientific experimental settings
it may necessary to count these smaller body segments as part
of the total workload. This is because these lighter body segments
would make up a significant portion of the total workload in
comparison to the very light weights commonly used in a rehabilitation.
Interestingly, MedX weight training equipment was modeled after
their physical therapy and scientific testing apparatuses. Some
of these designs, such as the Lever
Side Lying Leg Hip Raise position the user of their side
to correct for measurement error due to gravity.
Keep in mind the orientation of an exercise can effect if
a body segment should be counted. For example, we would count
the upper body weight in a Sled
Squat since the body is in an upright position so the body
segments have to be lifted upward against gravity. In contrast,
notice body segments are no longer lifted against gravity during
the Sled Lying Leg Press, a very similar movement. Notice with
the Sled
Lying Leg Press, the body segments travel horizontal instead
of upward, so the upper body segments are no longer counted as
part of the resistance.
Actually at the hardest part of the movement the lower leg
prepares to rotate downward. For the reasons discussed above,
we would not need to subtract the weight from the added weight
on exercises have 'falling' body segments during concentric contraction
of the target muscle groups, except if those body segments make
up a significant portion of the weight, as they do in machine
assisted exercises, also discussed above.
However bodyweight is utilized if the body segment travels
vertically against gravity, or even at an upward diagonal angle,
like during a Sled
Hack Squat. Even though the resistance is reduced to approximately
71% at a 45° angle, both the resistances of the added weight,
sled weight, and the upper bodyweight are reduced the same so
they remain relatively proportionate
Free Weight versus Machine Force Vectors
On free weight exercises, the direction of Resistive Forces
are down, the direction of gravity for both the added weight
and lifted body segments.
However, when performing an exercise on a machines (eg: Lever,
Cable), the direction of resistive forces acting upon the added
weight can be redirected according to the design and use of the
machine. Where as any lifted body segments move against gravity.
For example in the Cable
Lying Leg Hip Raise the force of the added resistance is
redirected diagonally via pulley cable, yet the weight of the
lower leg and Hips is pulled downward vertically by gravity.
This can be more complicated to adjust the percentage of bodyweight
to a meaningful number.
In addition, even if we corrected for this difference of force
vectors, the amount of resistance provided my a machine can be
different from a free weight even when the same amount of weight
is loaded. To get an accurate estimate of actual weight, you
would need to access the mechanics of a specific machine to make
the necessary calculations to convert the weight placed or selected
on the machine to the equivalent free weight load.
However on machines where you are trying to determine the
percentage of bodyweight contribution to the resistance you may
need to estimate the actual force. Here are possible methods
of ascertaining actual loads on machines. Some methods are more
accurate, while others may be a bit extreme, so you'll need to
determine at what level of accuracy you require so you can determine
the best approach.
- Assume the weight the machine is the actual weight
- eg: 10 lbs = 10 lbs
- Least accurate method
- Estimate the weight ratio based on lifting trails and convert
weights accordingly
- 200 lbs 4 rep max on machine = 150 lbs 4 rep max on free
weight equivalent
- Therefore, 10 lb on machine = 7.5 lbs
- Contact the equipment manufacturer, ask them the conversion
formula for the machine
- Also ask them what method they used to arrive at their proposed
conversion
- Measure force with scale(s)
- Hanging (pulling) scales
- Load is pulled up in line with additional accessories:
- Chain(s), strap(s), or hook(s) and possibly pulley(s)
- Flat (pushing) scale
- Load is held up compressed scale in between
- If scale is placed under feet or on seat, body weight is
subtracted
- Construct a conversion formula accordingly
- Determine resistance using physics or mechanical calculations
- Lever machines
- will require length measurements
- may require the weights and center of gravities of the machine
lever components
- On selectorized machines, the actual weights of the plates
should be verified.
It would be idea to ascertain the resistance on a machine
at the most difficult point of the exercise. This point may vary
on machines where the point is effected by varying user heights
with different body segment lengths and resulting machine adjustments.
Force Analysis
To determine bodyweight percentages utilized in exercises,
we decided to estimate force with a torque analysis. This is
not an analysis of work, energy, or angular moment of inertia.
Although calculating work will likely result in comparable numbers,
we be believe that approach would have been more indirect.
Work would have included a distance component. When we say
an exercise is difficult, we typically are not referring to the
work required, we are more likely referring to the effort expended
at the hardest point of the exercise.
Our calculations do not attempt to measure forces within specific
muscles. Examining all the force vectors effected by origins,
insertions, and lever systems is far beyond the scope our objective.
Furthermore, we have not accounted for other extraneous variables
such as elastic energy of muscle, particularly biarticulate
muscles through passive
insufficiency, a third force assisting on some exercises
like at the bottom of the straight
leg deadlift and resisting on other exercises such as the
top of a straight
leg leg raises.
The purpose of these calculations are to determine actual
workloads so more accurate exercise prescriptions can be made
in the form of weight increases, warm-up resistances, 1 rep maximums,
and percentages of 1RMs.
Comprehension Quiz Exercises
After familiarizing yourself with incorporating a percentage
bodyweight in calculating workloads. Consider answering the questions
below to test your understanding these principles and concepts
discussed in this article. Provide examples by listing exercises
that fit into these descriptions (below). Try to provide unique
examples that are different from one another. For example don't
give both squat and hack squat as examples since they are somewhat
similar movements. Perhaps give an example of both upper and
lower body exercise with different characteristics
- List exercises where the bodyweight is aligned with the added
weight.
- Also briefly describe the basic formula arriving at the percentage
of body weight used in the exercise.
- List exercises where the bodyweight is NOT aligned with the
added weight.
- Also briefly describe the basic formula arriving at the percentage
of body weight used in the exercise.
- List exercises where certain body segment(s) may not need
to be assessed, and explain why these body segments would not
need be calculated as part of the load.
- Provide examples of exercises where the center of gravity
of the sum of the body segments moving against gravity could
be a greater perpendicular distance from the fulcrum joint as
compared to the added weight.
One Rep Maximum References
Mayhew JL, Prinster JL, Ware JS, Zimmer DL, Arabas JR,
M G, Bemben MG (1995). Muscular endurance repetitions to predict
bench press strength in men of different training levels. J Sports
Med Phys Fitness, 35 (2): 108-13.
Lesuer DA, McCormick JH, Mayhew JL, Wasserstein RL, Arnold
MC (1997). The Accuracy of Prediction Equations for Estimating
1-RM Performance in the Bench Press, Squat, and Deadlift. Journal
of Strength and Conditioning Research, 11(4), 211-213.
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Assisted Dip
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