What is my apparent weight in water?

[brajesh]

TL;DR Summary

If I tiptoe in a pool of water, how much weight are my calf muscles lifting?

Hi,

I was wondering, what is my apparent weight in water?
For example, when I tiptoe on land, my calf muscles are pretty much lifting all my body weight.
But if I were to tiptoe with just my head out of the water, how much weight would my calves be lifting?
And as I move to shallower water, how can I compute what is the additional loss of buoyancy, or additional weight my calves need to support?

The reason I'm asking this question is that I've injured one of my calf muscle.
Part of my rehab exercises involve tiptoeing in the pool to exercise the calf muscle.
So I was curious about this question as I get better :)

 

[russ_watters]

Do you know Archimedes' Principle?

 

[berkeman]

And as I move to shallower water, how can I compute what is the additional loss of buoyancy, or additional weight my calves need to support?

What is your approximate percent body fat?

 

[brajesh]

What is your approximate percent body fat?

I don't know, my BMI is 28 if that helps?

 

[JT Smith]

Archimedes' Principle is worth looking at. High school physics level.

Humans are very close to neutral buoyancy until you include the fact that we contain gas in our lungs, intestines, etc. So the weight reduction you get when you're just ankles deep is very small, both because it's a very small part of your body and a relatively neutral buoyant part. The amount you get when thigh deep will depend on how much fat you have on your upper legs as fat is less dense than muscle and bone and blood. Once you get your torso in, that's when the effect is larger.

So it's hard to calculate. You'd need to know the volume of your limbs as well as their densities. It would be easier to measure it.

 

[Pratyeka]

https://en.wikipedia.org/wiki/Archimedes'_principle

 

[brajesh]

Do you know Archimedes' Principle?

I heard of the eureka moment he had in the bath tub which was something like "The upward buoyant force is equal to the weight of the liquid displaced by the body."

 

[russ_watters]

I heard of the eureka moment he had in the bath tub which was something like "The upward buoyant force is equal to the weight of the liquid displaced by the body."

Does this help you answer your question?

 

[jbriggs444]

It would be easier to measure it.

Personally, I have positive buoyancy with lungs full of air and negative buoyancy with them empty.

 

[kuruman]

Summary:: If I tiptoe in a pool of water, how much weight are my calf muscles lifting?

The reason I'm asking this question is that I've injured one of my calf muscle.

I hope your calf muscle is rehabilitated quickly. As you can see from the replies so far, calculating your apparent weight when you tiptoe in a water pool is a number that depends on determining two other numbers other than your normal weight: the level of the water around your body and the average density of the part of your body that is under water. As @JT Smith noted, it would be easier to measure your apparent weight.

I am curious about why you want to have a number for your apparent weight and how you think this number is relevant to the rehabilitation regime. Presumably you are doing this under the supervision of a physical therapist who has a plan to you. The usual advice from physical therapists is "push yourself to the limit of being uncomfortable but not in pain because that is where the benefit lies; if you feel pain, stop immediately." That's the advice I got when I rehabilitated my injured shoulder and I'm guessing that the advice to you was similar. In my case, I followed the advice and stretched rubber bands, some stiffer than others, that they gave me without needing to know a number for their effective spring constant assuming that they obeyed Hooke's law.

 

[JT Smith]

I found a study where someone was trying to determine if underwater weighing with one's head above the water could be used in place of full immersion when determining body fat percentage. Here are the averages for the male subjects in the experiment. It might be useful:

81.5 kg - weight in air
3.5 kg - weight fully immersed in water, air expelled from lungs
-0.8 kg - weight fully immersed, lungs full
6.8 kg - weight with head above water, air expelled
2.7 kg - weight with head above water, lungs full

 

[brajesh]

Wow yes, this really helps! The numbers make it easy to visualize and I'm about that weight. Thank you @JT Smith.

 

[brajesh]

I hope your calf muscle is rehabilitated quickly. As you can see from the replies so far, calculating your apparent weight when you tiptoe in a water pool is a number that depends on determining two other numbers other than your normal weight: the level of the water around your body and the average density of the part of your body that is under water. As @JT Smith noted, it would be easier to measure your apparent weight.

I am curious about why you want to have a number for your apparent weight and how you think this number is relevant to the rehabilitation regime. Presumably you are doing this under the supervision of a physical therapist who has a plan to you. The usual advice from physical therapists is "push yourself to the limit of being uncomfortable but not in pain because that is where the benefit lies; if you feel pain, stop immediately." That's the advice I got when I rehabilitated my injured shoulder and I'm guessing that the advice to you was similar. In my case, I followed the advice and stretched rubber bands, some stiffer than others, that they gave me without needing to know a number for their effective spring constant assuming that they obeyed Hooke's law.

I got curious while I was doing it. Your and others answers on this post have helped me understand buoyancy better.

 

[hutchphd]

So the weight reduction you get when you're just ankles deep is very small, both because it's a very small part of your body and a relatively neutral buoyant part. The amount you get when thigh deep will depend on how much fat you have on your upper legs as fat is less dense than muscle and bone and blood.

This is not really correct. The buoyancy depends only upon the volume below waterline which displaces water.
For instance, if all your weight was in your feet, you would not suddenly float when your ankles became submerged. The buoyancy supplied will be the same regardless. All that matters is your total weight.

 

[JT Smith]

This is not really correct. The buoyancy depends only upon the volume below waterline which displaces water.

Yes, you're right.