Equations

FCEase Manual

When considering the relationship between Strength and Endurance, a mathematical relationship has been recognized and developed for sometime.

This equation developed over the years from the realization that a single maximum effort (muscular strength) and maximum repetitions with a submaximal load (muscular endurance) are related. Logan and Forman (1961) described the concept as the 'Strength - Endurance Continuum'.

Berger (1969) derived an equation for predicting the maximal load value for chin ups and dip exercises from the number of repetitions performed.

1RM = ß x No. chin ups + body weight

This equation was found effective for two (2) dissimilar exercises so it appeared reasonable that a quantitative relationship existed for other lifting movements. The mass lifted in the chin-ups and dips was the body weight. Using Bergers ß value and mass values, a mean co-efficient (0.034) was determined. Thus the equation:

1RM = L x [(0.034 x R) + 0.966)]

Where 1RM = estimated one maximum repetition (such that the lift cannot be immediately repeated)

L = load lifted in kilograms or lbs

R = number of repetitions of lift completed.

Doolittle and Kaiyala in 1988, validated this equation using 42 firefighters who were tested for 1RM and were then selected to perform repetitions at 90%, 80%, 70%, or 60% of their 1RM.

When the equation was applied, correlation between actual and predicted values resulted in R²value of 0.85 and standard error of prediction of ą 3.11 kg (6.84 lbs).

Other studies have proven similar results, i.e., Pollock et al (1978) found that the average individual should be able to complete 12 - 15 repetitions at 70% 1RM. If 30 repetitions are used, a 50% of 1 RM load is resultant.

To facilitate the use of this equation, the common factor of (0.034R + 0.966) has been isolated and called RF. RF is substituted where R = number of repetitions performed.

example: 5 repetitions RF = 1.2

10 repetitions RF = 1.3

(refer to Data Input Sheet for full table)

This makes the use of the equation very simple to either:

Predict Safe Maximum Lifts from submaximal endurance loads

Compare and correlate actual observed S.M.L. to predicted S.M.L. - these values should be within 10%.

This therefore allows a submaximal load to be used to predict a one repetition maximal load (1 RM) with accuracy.

There are some limitations however:

Some industrial workers in clinical settings will quit the repetitive lifting at about 25-30 repetitions because of boredom even though they could have continued the process. Thus if the load was too light, the large number of repetitions possible would render the equation invalid due to low motivation leading to too few repetitions achieved to maintain this equation. The results are accurate up to 30 repetitions. From 30-50 repetitions, the results appear in the tolerable limit, however, it is not recommended for repetitions above 50.

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The equation therefore is valid as it accurately describes the mathematical relationship of the 'Strength - Endurance Continuum' and may be employed for estimating 1RM for dynamic loads using both arms. It is also effective for use with either gender.

The equation 1RM = L x [(0.034 x R) + 0.966] can be used to predict a safe maximal load from performance using a submaximal load.

WorkHab does not use 1RM but prefers to use the terminology "Safe Maximal Lift (SML)" which is the ability to perform three lifts safely rather than a one-time maximal load. This allows a safety margin and provides a lift capacity of an occasional level.

To predict S.M.L. using a submax load, a weight L is chosen. This should be a weight the client feels he/she can lift continuously for 30-35 repetitions. The test is carried out until the client can no longer lift the load. The number of repetitions is counted and inserted into the equation.

Safe maximal lift "predicted" = L x [(0.034 x R) + 0.966]

L (Load) = a weight chosen by the client which they feel they could lift 30 to 35 times

R (Reps) = consecutive repetitions performed until client is unable to safely complete another repetition (see safe lifting guidelines).

To make this easier, a Repetition Factor RF is used. Therefore the equation is:

S.M.L. = L x Rf

Rf =

1.2 where client performs 5 reps
1.3 .........................................10 reps
1.5................................... .......15 reps
1.7 ..........................................20 reps
1.8.................................... ......25 reps
2.0 ..........................................30 reps
2.2 ..........................................35 reps
2.4 ..........................................40 reps
2.5 ..........................................45 reps
2.7 ..........................................50 reps
2.8 ..........................................55 reps
3.0 ..........................................60 reps

Example:

The client is required to lug bags of cement weighing 45kg from pallet into a wheel barrow as part of his/her job. This is an infrequent activity (2 bags per 8 hour day) but is essential for return to his/her job.

The client is still demonstrating pain behaviors and is currently unlikely to exert himself/herself maximally during a 'safe maximal lift test' because of fear of reinjury. The client is then asked what weight he/she feels can be lifted for 30 to 35 repetitions. The client chooses 20 kg to attempt. The lift is a floor to bench lift. He/she is able to safely perform 42 repetitions with 20 kg before stopping.

Safe maximal lift ('predicted') = L x [(0.034 x R) + 0.966]

S.M.L = 20 kg x [(0.034 x 42) + 0.966]

S.M.L. = 20 kg x (1.428 + 0.966)

S.M.L. = 20 kg x 2.394 (RF factor)

S.M.L. = 48 kg

Using the shortened version, the equation would be:

SML = L x Rf where R = 42

Rf = 2.4

SML = 20 kg x 2.4
= 48 kg

This equation therefore predicts that functionally, the injured client could perform this activity. The bags weigh 45 kg and falls under the Safe Lift Guidelines when considering only two lifts every eight hours. This provides the case manager or treating therapist some valuable information regarding the client's abilities not previously available.

Using the same strength/duration relationship it is possible to use the following equation to accurately determine the maximum load for repetitive activities called Max Tolerable (M tol) where:

M tol = (0.586 - 0.019F) x 1 RM

Where F = number of executions/min where F = 1 - 20 reps/min
1RM = maximum load x 1 repetition

To further simplify this equation, an endurance factor E can be used where

E = [0.586 - (0.019 x F)] i.e.:

E =

0.57..........where.........F= 1/min
0.55 ............................F= 2/min
0.53 ............................F= 3/min
0.51 ............................F= 4/min
0.49 ............................F= 5/min
0.47 ............................F= 6/min
0.43 ............................F= 8/min
0.39 ............................F= 10/min
0.36 ............................F= 12/min
0.32 ............................F= 14/min
0.30 ............................F= 15/min
0.28 ............................F= 16/min
0.24 ............................F= 18/min
0.20 ............................F= 20/min

M Tol = E x SML

(WorkHab has substituted SML for 1 RM as mechanism for safety.)

Example 1

During an F.C.E. a safe maximal lift was recorded of 36kgs from floor to bench. This obviously is the maximum load this client can safely perform in an isolated situation. He actually has to perform an activity where he needs to load 50 potted plants weighing up to 15kgs onto the back of a truck in 10 minutes, twice a week.

The S.M.L. of 36kgs does not give us this information accurately. By applying Equation 1, this can be simply evaluated.

M Tol = (0.586 - 0.019F) x SML

By using E where E = 0.586 - 0.019F the calculation is easily applied.

The frequency is 50 reps in 10 minutes or an average of 5 reps / min.

E therefore = 0.49

M Tol = 0.49 x 36 kg

M Tol = 17.6 kg

So this immediately tells us that this client would be capable of performing this task at this pace for this time period.

Example 2

A client is required to unload a pallet of packages of flour weighing 2kgs each. There are 200 packages/pallet and it takes 20 minutes to unload a pallet. This means the frequency of lifts is 10 reps / minute to unload the pallet. If the overhead SML = 12 kg, could the client safely perform this task?

M (max Tolerable) = [(0.586 - (0.019 x 10 reps/min) x 12 kg (SML)]
                                M = (0.586 - 0.19) x 12 kg
                                M = 0.396 x 12 kg
                                M = 5 kg

Again using the shortened version:

E = (0.586 - 0.019R) where 1 rep/min E = 0.57
                                                2 rep/min E = 0.55
                                                (See table on previous page)
                                                 (R = 10 rep/min) E = 0.39

M = E x L
M = 0.39 x 12 kg
M = 5 kg

In this work situation, a client's Maximal Tolerable Lift is closely 5 kg which has been calculated from a S.M.L. of 12 kg. So this client can safely return to the aspect of the job.

Based on the Strength Endurance Continuum it can be calculated that the SML or E = 1.0 can be used for situations where the frequency is up to 3 reps/hour or 1 rep every 20 minutes.

For frequencies over 3 reps/hour (1 rep every 20 min) and up to 60 reps/hour or 1 rep/min, use E = 0.75.

The equation is less accurate for values over 20 reps/min, so it is recommended that for reps over 20/min that E = 0.20 be used.

Supporting documentation:

Doolittle and Kaiyala Research (1987, 1989)
Consensus meetings on Safe and Effective Lifting (1993-1995)
Astrand and Rodahl (1970)
Guidelines for Exercise Testing and Prescription (1985)
NIOSH Guidelines for frequency
Worksafe Australia
U.S. Department of Labor

What information needs to be included in report:

Note changes in heart rate during evaluation.

Note ability to safely lift a certain amount of weight for certain number of repetitions or time.

Any breakdown in performance of lifting over time or with additional weight.

Note pain issues.

Note inconsistencies observed during the evaluation

Deficits as determined during testing.

Recommendations based on clinical interpretation of this data.

Note SML for the same lift height/distance as the task.