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14^th March 2008 - Fred Curls

Curls are the most important exercise in a lifter's arsenal. They will give one massive biceps and improve ones attractiveness to women of dubious moral characteristics. Here I copy the curl of Fred Hahn (lifting guru and Chuck Norris lookalike) and make a comparison between our performances.

A Guide to Power

The following still won't improve your lifting one iota.

In Force I covered the basic force equation;

Force = Mass's Weight + Mass's Acceleration = F_T = F_W + F_A = mg + ma = m(g + a)

I further noted that it was the muscles that generated the force F_T, i.e. F_T is not mysteriously generated from acceleration.

In Physics I discussed the 'dangers' of fast reps and calculated from the equation;

Displacement = Velocity² / 2×Gravitational Acceleration = s = v²/2g

That it only took 8 mm for the weight to decelerate from 0.388 m.s^-1 to 0 m.s^-1.

In this article I discuss how to calculate wattage (plus a few other things):

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To work out, with physics, how much a muscle can lift would require a complex model for example like this.

Even so, such a model is built on observing real world muscle contractions - in other words to work out power outputs would require observation of an actual lift. Here's an example;

EZ FRED CURL 350
46 kg × 2.134 secs positive
56 kg × 3.834 secs positive
57 kg × 4.467 secs positive
58˝ kg × 2.533 secs positive (half rep)

Let's look at some of the figures that can be calculated from the 46 kg and 57 kg weights as shown in the video.

The times were determined from the video (30 frames per second) and the range of motion was measured from pixel distances which were converted to an actual vertical displacement of the barbell of 0.522 metres;

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Weight

Weight = Mass × Gravitational Acceleration

46 kg × 9.807 m.s^-2 = 451.1 Newtons
57 kg × 9.807 m.s^-2 = 559.0 Newtons

As F = ma so W = mg... gravity is equivalent to acceleration.

Velocity

Velocity = Displacement / Time

0.522 m / 2.134 s = 0.245 m.s^-1
0.522 m / 4.467 s = 0.117 m.s^-1

This is average velocity.

Work

Work = Force × Displacement

451.1 N × 0.522 m = 235.5 Joules
559.0 N × 0.522 m = 291.8 Joules

Work in this case is the potential energy gained by the mass in it being raised - if the mass were then dropped to its start point it would gain kinetic energy equal to the potential energy lost... it is not dropped so the potential energy is absorbed by the muscles.

Power

Power = Force × Velocity

451.1 N × 0.245 m.s^-1 = 110.3 Watts
559.0 N × 0.117 m.s^-1 = 65.3 Watts

Power is a measure of energy expended per unit time, in this case a watt is a joule per second.

Impulse

Impulse = Force × Time

451.1 N × 2.134 s = 962.7 N.s
559.0 N × 4.467 s = 2497.0 N.s

Impulse is force times time, it comes from the F = ma formula and is an expression of a change of momentum, hence;

Force = mass × acceleration = ma = m((v - u)/t)

Ft = mv - mu = m(v - u)

Where v is final velocity and u is initial velocity. Thus if I applied 451.1 Newtons for 2.134 seconds to a 46 kg mass (in the absence of gravity) it would accelerate at 9.807 m.s^-2 from 0 m.s^-1 to 20.9 m.s^-1. If I applied 559.0 Newtons for 4.467 seconds to a 57 kg mass (in the absence of gravity) it would accelerate at 9.807 m.s^-2 from 0 m.s^-1 to 43.8 m.s^-1.

I've wedged my elbows against my torso, so these figures are generated almost solely by elbow flexion.

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FRED CURL
40.8 kg × 13.330 secs positive

I'm going to assume that Fred has the same vertical displacement of 0.522 metres that I do;

Weight

Weight = Mass × Gravitational Acceleration

40.8 kg × 9.807 m.s^-2 = 400.1 Newtons

Velocity

Velocity = Displacement / Time

0.522 m / 13.330 s = 0.039 m.s^-1

Work

Work = Force × Displacement

400.1 N × 0.522 m = 208.9 Joules

Power

Power = Force × Velocity

400.1 N × 0.039 m.s^-1 = 15.7 Watts

Impulse

Impulse = Force × Time

400.1 N × 13.330 s = 5333.5 N.s

Thus if Fred applied 400.1 Newtons for 13.330 seconds to a 40.8 kg mass (in the absence of gravity) it would accelerate at 9.807 m.s^-2 from 0 m.s^-1 to 130.7 m.s^-1.

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Let's assume for argument's sake that we are actually both equal in terms of curling strength.

Then it could be argued that my 110.3 Watts and 65.3 Watts figures compared to Fred's 15.7 Watts are better for stimulating 'power' gains. On the other hand if impulse (weight times time) figures are more important for say 'strength-endurance' then it could be argued that Fred's 5333.5 N.s compared to my 962.7 N.s and 2497.0 N.s figures are better.

There is also the fact that I used a heavier weight than Fred so the force generated by the arms is greater in my curl so it could be argued that greater force is better for greater strength.

If I am actually stronger than Fred then my wattage and force figures would be exaggerated whilst Fred's impulse figures would be under-exaggerated. On the other hand if Fred was actually stronger than me then my wattage and force figures would be under-exaggerated whilst Fred's impulse figures would be exaggerated.

It should be noted that the calculations do not take into account force differences from acceleration - I am assuming they would have a relatively small effect, being that this is a 'strict' lift.

It is also very important to note that the figures in themselves don't mean that say a high wattage means that the muscles wattage generating capacity is being stimulated. Certainly specificity implies this, certainly evolutionary logic would suggest this... however only actual observation of the results can lead to correlational figures. To flaty assume one from the other would be just that... an assumption.

17^th March 2008