## Calculating Actual Resistance

### Incorporating Percentage Bodyweight into Weight Training Workloads

 ExRx.net > Weight Training > Calculations

 Adjusting BW Exercises Aligned Exercises Non-aligned Exercises

Workload prescriptions for progressive resistance training may be used to calculate:

• weight increases
• eg: increase of 5% after achievement of 12 reps
• warm-up resistances
• eg: 50% of workout resistance
• workloads based on a percentage of one rep max
• eg: 80% 1RM

Calculating the actual resistance of an exercise is important regardless if the workloads are based on the number of reps you can perform with a weight (e:g: 8-12 reps) or your one rep max.

With workloads based on a repetition range, once the upper repetition range is reached, the resistance is increased, typically 2.5% to 10%.

For example, let's calculate a weight increase 5% once 12 reps are achieved:

Shoulder Press
Weight to achieve 8-12 reps = 100 lbs
New Weight = 105 lbs

Once we know the workout weight, we can also quickly calculate a warm-up set resistance using 50% of the workout weight.

Now what happens when we perform and exercise that utilizes bodyweight in addition to added weight? Since the bodyweight contributes to a significant portion of the actual resistance, we must account for it by calculating the actual resistance:

Dumbbell Single Leg Calf Raise
Weight to achieve 8-12 reps = 10 lbs Dumbbell
Actual Resistance = 10 lb dumbbell + 200 lbs Bodyweight = 210 lbs
New Actual Resistance = 220 lbs
New Dumbbell Weight = 220 lbs (New Actual Resistance) - 200 (Bodyweight) = 20 lbs

So 20 lbs will be the new weight of the dumbbell once 12 reps are achieved with the 10 lbs dumbbell. Going from a 10 lbs dumbbell to a 20 lbs dumbbell may seem as though our resistance increased 100% if we did not understand the need to base the weight increase off of the actual resistance rather than only the weight of the dumbbell. If we would have not accounted for bodyweight, the new dumbbell weight would have been erroneously calculated to be no more than 11 lbs, far too light for a new resistance. So we calculate ~5% of the Actual Resistance which includes the bodyweight. Then we found the weight of the new dumbbell by subtracting out the weight of the body from the newly calculated Actual Resistance.

To calculate a 50% warm-up resistance we take the bodyweight minus half of the New Actual Resistance to arrive at negative number which signifies an assisted weight. However since there is no such machine as a Assisted Single Calf Raise Machine, we instead perform a Bodyweight or Dumbbell Standing Calf Raise with both legs

### Percentage of One Repetition Maximum Workloads

Many sports conditioning workouts are based on a percentage of One Rep Max, particularly heavy lifts such as Power Cleans, Bench Press, Squat, and Deadlift.

For example, normally we would have this scenario:

Bench Press
1 RM = 200 lbs
80% 1 RM = 160 lbs

Warm-up weight can simply be calculated by taking 50% of workout weight. In this case 80 lbs.

Now let's look at an exercise that utilizes bodyweight in addition to added weight in the form of a dumbbell between ankles or hanging from a dip belt around waist. To calculate 80% 1RM we must know Bodyweight:

Weighted Pullup
1 RM = 50 lbs (dumbbell)
Bodyweight = 200 lbs
1RM (Actual Resistance) = 200 + 50 = 250 lbs
80% 1RM (Actual Resistance) = 200 lbs
Dumbbell weight = 80% 1RM - Bodyweight = 0 lb

Since the workload is the same as the bodyweight, no additional resistance is required. If the New Actual Resistance were to exceed the Bodyweight, the new added weight can be calculated by subtracting the bodyweight from the Actual Resistance required. If the Bodyweight exceeded the New Actual Resistance, an Assisted Pull-up Machine can be used.

In the example workload above, 50% of the workout resistance would call for half of the bodyweight, meaning an assisted weighted Chin-up with 100 lbs (subtracted from the bodyweight) would be performed as a warm-up resistance. The same calculations can be applied to exercises like weighted pull-ups or dips.

### Machine Assisted Exercises

On machine assisted exercise, the weight placed on the machine subtracts weight from the users bodyweight, so the actual weight is the body weight minus the weight selected on the machine. To calculate a warm-up and a subsequent weight increase from the Actual Resistance.

Machine Assisted Dip
Assisted weight to achieve 8-12 reps = -30 lbs
Bodyweight = 130 lbs

To calculate Actual Resistance:

= Bodyweight + Assisted Weight
= 130 lbs + (- 30 lb) = 100 lbs
= 100 lbs

To calculate a warm-up weight from 50% of Workout Resistance:

= Actual Resistance * 50 - Bodyweight
= (100 lbs * 50%) - 130 lbs
= 50 lbs - 130 lbs = -80 lbs

To calculate a weight increase of 5% from actual resistance:

= Actual Resistance * 105% - Bodyweight
= (100 lbs * 105%) -130 lbs
= 105 lbs - 130 lbs = -25 lbs

### Exercises Utilizing a Percentage of Bodyweight

Many exercises utilize a portion of the bodyweight along with the added weight. For example, during Barbell Squats the weight of the upper body and a portion of the upper thigh are lifted in addition to the added weight. This is very similar to what occurs in the Deadlift. Although the upper body is angled forward at the bottom of the lift, it is lifted upward more directly against gravity along a very similar path as the added weight. In contrast the thigh rotates from a more horizontal position at the bottom of the lift to a vertical position at top, moving less directly upward against gravity.

So, how can we accurately calculate the bodyweight used as a load for these exercises?

de Leva's Segment Weight data
Segment Quantity Percent Extension
Whole Trunk 1 43.020 43.02
Total Arm 2 4.715 9.43
Total Leg 2 20.370 40.74
Total Percent:     100

Using normative data for the percentage weight of body segments we can calculate the weight of the move more directly upward with the weight (upper body). Using center of gravity of body segments we can calculate torque required to turn body segments from near horizontal to near vertical.

Step 1

Calculate weight of body segments that share similar center of gravity and move mostly upward with added weight, in this case upper body

Method A: Head + Trunk + 2 Arms = ~59.26% of total bodyweight
Method B: Total Body (100%) - 2 Legs (40.74%) = ~59.26% of total body weight

Step 2

Calculate torque from heavy body segments that rotate significantly against gravity, in this case torque from both thighs.

Weight of 2 Thighs * Thigh's Center of Gravity from Knee

From body segment data we know:

Weight of Thigh = ~11% of body weight
COG of Thigh = 0.43 of segmental length measured from proximal end (from hip)

So we need to sum the weight of both legs and determine the COG from the opposite end

= 11% (2 Legs) * (1-0.43)
= 22% * 0.57
= 12.54 % of total body weight

Note: We would end up with 17.79% if we had used de Leva's data.

% Body weight used = % weight of 2 thighs * COG from knee = [(2*14.47%) * (1-0.3854) COG] = 17.79%

Step 3

Add resistive forces of upward moving body segments (steps 1) to torque forces of upwardly rotating body segments (step 2). In this case we add the weight of the upper body with the torque from the thighs.

Percentage of body weight used as a load during Squats or Deadlifts = ~72%

Note: Using de Leva's data in step 2, total percent bodyweight would be approximately 77%

59.26% + 17.79%

Here are other examples of exercises using only one leg:

Step Ups or Single Leg Squats
Upward Moving = Total Body (100%) - 1 Leg (20.37%) = 79.63% of total body weight
Upward Rotating = Thigh Weight (11%) * Thigh COG (0.57) = 6.27%
% Body Weight used = Upward Moving (79.63%) + Upward Rotating (6.27%) = ~86%

Notice when Step-ups are performed with heavy weights, the lower leg assists in the initial push off, the hardest part of the movement. Never-the-less, the lower leg rises more directly against gravity with the body and added weight, whereas the upper thigh rotates against gravity.

Notice other exercises like the Split Squat and Single Leg Split Squat appear to only use a single-leg exercise but actually use both legs to lift the weight or at least the weight of the rear leg rests on a surface. On these particular exercises the upper body and thigh of rear leg travel upward, whereas the leg of the exercising thigh and the shank of the rear leg both rotate upward.

Split Squat or Single Leg Split Squat
Upward Moving = Total Body (100%) - 1 Leg (20.37%) - 1 Shank (4.57%) = ~75% of total body Weight
Thigh Rotation = Thigh Weight (11%) * Thigh COG (0.57) = 6.27%
Shank Rotation = Shank Weight (4.57%) * Shank COG (0.57) = 2.6%
% Body Weight used = Upward Moving (75%) + Upward Rotating (8.87%) = ~84%

Generally speaking, to calculate the percentage of bodyweight lifted upward, simply add up the percentages of all the body parts that are moving (or not moving) directly against gravity. If all but a few segments move, simply subtract the percentages of the segments that are NOT utilized from 100% (total body) to arrive at the percentage. Notice the percentages for the arms and legs are only for one each so if both limbs are utilized, you will need to multiply by two.

Next identify body parts that rotate upward significantly against gravity. Calculate the torque by multiplying the center of gravity of the body segments (from the fulcrum) by their respective segment weights.

And finally add the resultants to determine the percent body weight contributing to the exercise's resistance.

### Calculating Percent One Rep Max

What difference does accounting for the portion of body weight utilized as part of the workout resistance when calculating a percent of 1RM for the squat?

Barbell Squat
1 RM = 300 lbs barbell weight
Bodyweight = 200 lbs

Standard Method: One Rep Max (Without Percentage of Bodyweight Included)

Calculate 80% of 1RM

80% 1RM x 300 lbs barbell = 240 lb barbell

Modified Method: Body Weight Adjusted One Rep Max (Incorporating Percentage of Bodyweight Utilized)

Calculate Actual Resistance:

Bodyweight used = 200 lbs bodyweight x 72% utilized = 144 lbs
Actual Resistance = 300 lbs bar + 144 = 444 lbs

Calculate 80% of 1RM:

Gross 80% 1RM = 0.80 x 444 lbs Actual Resistance
Gross 80% 1RM = 355 lbs Actual Resistance

80% 1RM = 355 lbs Actual Resistance - 144 lbs body weight utilized
80% 1RM = 211 lbs barbell

We can see a lighter barbell weight is required to achieve the desired resistance when accounting for the lifted portion of the body (ie: upper body weight). Now let's see if this is consistent with findings in the literature...

### Estimating One Rep Max

Although 1RM Prediction Equations have been known to over or under estimate actual values for the bench press (Mayhew, et. al., 1995), it is interesting to note that Lesuer, et. al. (1997) found various prediction equations are more like to under estimate 1RM for the deadlift (under prediction of 9 to 14%) and squat (under prediction of 2 to 8%) as compared to 1RM prediction for the bench press (under prediction of 0.8 - 6%).

Using the Brzycki equation, let's compare how a one rep max can be estimated using both methods:

4 RM = 320 lbs barbell weight
Bodyweight = 200 lbs

Standard Method: (Without Percentage of Bodyweight Included)

Calculate 1RM

1RM = Barbell weight / (1.0278 - 0.0278 x reps)
1RM = 320 lbs / (1.0278 - 0.0278 x 4 reps)
1RM = 349 lbs barbell

Modified Method: (Incorporating Percentage Bodyweight Utilized)

Calculate Actual Resistance:

Bodyweight used = 200 lbs bodyweight x 72% utilized = 144 lbs
Actual Resistance = 320 lbs bar + 144 = 464 lbs

Calculate 1RM

Gross 1RM = Actual Resistance / (1.0278 - 0.0278 x reps)
Gross 1RM = 464 lbs / (1.0278 - 0.0278 x 4 reps)
Gross 1RM = 506 lbs

1RM = 506 lbs Actual Resistance - 144 lbs body weight utilized
1RM = 362 lbs barbell

Here, we can see how including the percentage of body weight in the formula increases the prediction of the 1RM by approximately 3.7%, a possible improvement in predicting 1RM using the data from Lesuer, et. al. (1997) as a guide.

### Adjusting Exercises Utilizing Nearly Full Body Weight

When making quick calculations at the gym, it may be sufficient to calculate the full bodyweight on exercises such as the Pull-up, Chin-up, Dip and Standing Calf Raise; as we did with the early examples above. Simplifying calculations in this way can decrease computations that would likely not make a large impact on the final workloads, particularly since weight increases can range from 2.5 to 10%, One rep Max calculations are not exact, and warm-up resistances can ranges from 1/3 to 2/3 of the workout weight. So discrepancies of a couple pounds may not be worth the extra arithmetic since precise calculations are typically not necessary.

However, some may want to include the actual body segments that are actually being fully lifted in attempt to calculate slightly more precise values. To determine what body segments to count as the actual load, tally the weight of the body segments that move upward against gravity, then add the torque forces of body segments that are close to horizontal and rotate upward, as explained above. Do not count body segments that do not move upward against gravity at all. You may however decide to or not to include smaller body segments that do not contribute a significant force to the overall load. Here are a few examples showing three options with greater detail to accuracy with small and possibly insignificant differences:

Calf Raises
A) Total Body = 100%
B) Body - 2 Feet = 100% - 2 (1.33%) = 97.34%
C) (Body - 2 Feet) + torque of (2 Feet - 2 Forefeet) = 97.34% + [0.50 COG x (2.66 - 0.66)] = 98.34%

Pull-ups / Chin-ups or Dips
A) Total Body = 100%
B) Body - 2 Arms = 100% - 2 (4.715%) = 90.57%
C) (Body - 2 Total Arms) + torque of 2 Upper Arms = 90.57% + (0.553 COG x 5.26) = 93.48%

The more forces in which you account, the more accurate the resulting figure. Although even more complex computations could be applied to further increase the accuracy of this percentage, we question the feasibility of such an approach since its application (ie: determining workloads) does not require an extremely high level of precision.

### 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
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):

= (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:

= [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.

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:

1. movement of segments requires extremely little effort
2. weight of segments(s) are very small in comparison to the added weight.
3. 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.

### Olympic-style Weightlifts

At first glance we might assume the hardest part of the Clean or a Snatch would be either (1) at the floor, where inertia has to be overcome and the joint angles are least advantageous, as with the deadlift (see deadlift analysis above), or (2) when the barbell has to clear the knees since the moment arm at the hip is longest and is required to open in angle (back angle was static until this point).

However we know that the major problem for missing a Snatch is not at these points, but rather failing to finish the extension. Similarly, the major failing point for the Clean is after the initiation of the second pull.

A diagram presented by Zatsiorsky & Kraemer (1995) show that the greatest force is applied to the upwardly traveling barbell at approximately 20% [2/10.2 relative height units] from the highest extended position (Position 5 vs 6). At this position the back angle is relatively high with the upper body center of gravity at a short perpendicular distance from hip (fulcrum of movement). When the greatest forces are being applied to barbell (hardest part of the exercise) the upper body is approaching an upright position and has already risen upward against gravity approximately 77% [1-1.9/8.2 relative height units] from the lowest position (Position 5 vs 1).

This is not to suggest that the lower body is not lifted in the Olympic-style weightlifts or that the weight is lifted beyond this point is primarily lifted with the upper body. In fact we know that the hips are the primary movers to drive the barbell upward. Unlike most weight training exercises performed at a slower motion, these lifts rely on accelerating the weight by transferring momentum from power of the hips to the bar can so it can be thrown upward.

We can clearly see the body rises upward with such force that the heels momentarily leave the floor. Bodyweight is obviously being lifted. However, the majority of height is obtained just before the highest forces are being applied to the bar. Therefore, it does not appear that bodyweight is a significant force in comparison to the weight of the barbell at the hardest portion of the exercises (AKA failing point). For this reason we believe that a percentage of bodyweight would not be required to calculate actual loads for these movements.

### Free Weight versus Machine Force Vectors

On free weight exercises, the direction of Resistive Forces are directed downward by 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
• 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

1. List exercises where the bodyweight is aligned with the added weight.
1. Also briefly describe the basic formula arriving at the percentage of body weight used in the exercise.
2. List exercises where the bodyweight is NOT aligned with the added weight.
1. Also briefly describe the basic formula arriving at the percentage of body weight used in the exercise.
3. 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.
4. 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.

### 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.

Zatsiorsky VM, Kraemer WJ (1995). Science and Practice of Strength Training. 2nd Ed, 39-40. See Textbook.

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