Exploring Leverage & Force in Exercise Science

[Trooper149]

Hi all, not exactly a physicist however I am finding that the expertise of those in this field, would be massively appreciated in the field I am currently delving into - exercise science. Specifically an understanding of engineering physics.

As described above, in short I am trying to work out how much force is exerted by the abs during a single rep of the hanging leg raise (best search online to know what I mean), for the tempo of 1.5s up and .5 seconds down.

I have been looking up leverage, torque, fulcrums, etc and while I think I have the right formula, I would greatly appreciate second perspectives.

With this said, here are some figures:
-the total weight of the lower body (load) to be lifted is 36.4kg
-the total length of the lower body (loading arm) is 1.15m
-the abdomen connects into the loading arm at .1m
-when performing the leg raise, we are lifting from a dead hang position (0 degrees) to a right angle (90 degrees) parallel with the ground
-the arc of movement is 1.8m

With all this said, the equation I have followed is: (load to be lifted X by loading arm length X by length of arc)

36.4kg X 1.15m X 1.8m = 75.6NW/KG (75.6kg of force I think?)

My reason for asking is there is plenty of information and knowledge available on basic weightlifting and application of volume, however the information surrounding body weight training is a lot more vague and is far more dependent on levers. Combine this with the fact that a lot of experts in this field are more successful marketers than coaches. With this said, I would really like to learn the application of levers in bodyweight training and how much force is produced by muscles during certain exercises.

I have attached a copy of my equation in an excel document.

Cheers and Happy Easter

 

[jrmichler]

The next step is a free body diagram (FBD). A free body diagram (search the term) is a stick figure with weights and key dimensions. It has two purposes:

1) To show exactly what problem you are solving, and to communicate (to yourself and others) that you properly understand the problem.

2) To put the necessary information in one place. A good FBD makes the actual calculation easy.

Some (not all) of the key information is the location of the center of gravity of the legs, the location of the hip joint, and the location of the attachment for the abs. I'm not clear on anatomy, but I sort of kinda think that the quads and abs both attach to the pelvic bone. A proper FBD clarifies that.

 

[Trooper149]

Hi there

Many thanks, have done so and have reviewed some of the information: I needed to make a few adjustments so please disregard the previous stats and consider only of what I post now.

Athlete Stats:
Weight: 75kg
Height: 1.9kg
Leg Length: 1.15m
Length of Hip Girdle to Bottom of Sternum: 0.35m
Length of Sternum to top of Head: 0.45m
Weight of both legs together: 29.79kg
Weight of both legs and the weight of 66% of trunk: 51.3kg

The Hanging Leg Raise is divided into 2 phases. The 1st phase includes the hip flexors lifting the legs to 90 degrees so they are parallel with the floor. The spine should stay perpendicular with the ground. In phase 2, the abdominals then lift the pelvis complete with the already lifted legs and hip girdle to 45 degrees. Total degree of motion: 135 degrees.

Some other information that may be useful:
-the abdominals begin at the base of the sternum and connect onto the lower point of the pelvis.
-the hip flexors begin in the low back and expand across the top of the pelvis and insert about one third of the way down the thigh.
-the count tempo for this exercise is 1 second up and 2 seconds down

To give folk an idea of what the goal is: it is to create a formula (via excel) by which we can calculate the amount of force produced/volume shifted by the abs and hip flexors during the hanging leg raise. Ideally I would like to have a formula which I can simply input someones stats and parameters of the exercise and get a returned value. Most exercises operate as close as possible to ones centre of gravity and utilise external weights.

E.g. a back squat of 80kg external weight for 5 reps over a duration of 15 seconds. Add in an extra say 30kg of upperbody weight which is also being lifted by the legs. You can quite confidently take 80kg+30kg, multiply by 5 = 550kg of volume and divide by 15 seconds = 36.6kg of volume shifted/force produced per second. Because the body is lined with its centre of gravity, the overall leverage/torque is 0 or negligible.

With bodyweight training however, you are using the bodys own weight and a lot of tension is created by levers. This makes calculating the actual amount of work done, a lot more difficult (at least for myself).

Appreciate any other perspectives. Have included an FBD and my adjusted excel formula for all to look at. Note, I have only created a formula for the first phase, not the second as I am still working on that.

 

[jrmichler]

Your FBD is a good start. Now make all lengths to scale, muscles pull in straight lines except where wrapped around a bone, the pelvic bone needs to be a rigid link, the sternum is a horizontal distance from the spine, add distances from attach points to pivots, and add the center of gravity and mass of each link. Then simplify as much as possible.

 

[A.T.]

...muscles pull in straight lines except where wrapped around a bone, ...

The problem is the redundancy of the muscles which makes this an under-determined system. There are various hip flexors with very different effective lever arms, allowing for a wide range of muscle activations which all produce the same motion.

 

[Trooper149]

Appreciate the perspectives, it is an ambiguous question hence I am pursuing it. There are many factors that simply are difficult to determine such as:
-which muscles (and therefore aspects of total bodily mass) are included as part of the loading weight
-which muscles amongst the deep and superficial core as well as hip flexors are taking what percentage of weight
-the angle of motion as you proceed through the movement. As you pass 90 degrees, loaded weight will assume an angle which will subject it to less resistive force from gravity
-insertion points of particular muscles will vary and thus provide different actionable forces

Ultimately the result we are going to get at this point will not be accurate however if we were to assume that the body was of a solid nature and not a squishy/organic/flexible nature then we could get the basic formula down. After that, further investigation can be given to finer nuances.

Appreciate the feedback so far, it's certainly helped me ask further questions with regards to this.

 

[jrmichler]

You are on the right track. One way to tackle complex problems like this, and my preferred approach, is to start with a two dimensional model. In a two dimensional model, the hip joints are hinges, and the leg flexor muscles do not exist. The work is done by a simplified ab attached at a single point (in side view) at each end, and by a similarly simplified single quad muscle.

Does the pelvic bone rotate during this exercise? If so, it can be modeled with a hinge at the backbone. Keep it as simple as you can until you get answers, then add complexity to refine those answers. Continue until you run out of energy (likely) or have considered the effect of every muscle involved (not likely).

 

[Trooper149]

Now that you have said it, I think I will pursue that approach. I very much threw myself against the wall in treating it as a 3D model and have found myself getting bogged down.

Best simplify and start from the ground up.

If its ok, can I keep this thread open so I may bounce questions back and forth and put up what I have learned so far?

Many thanks again

 

[jim mcnamara]

Threads stay open by default.