Getting Your Weight Belt Right… With Science!

The weight problem

The human body is naturally buoyant (it floats). For this reason, a scuba diver must add weight (usually in the form of a weight belt with lead blocks) to ensure he or she will be able to descend and ascend in a controlled manner.

Due to the multiple factors that influence the calculation of the required weight for a belt such as water type (fresh vs. salt), diver weight, body fat, gear, temperature, etc. setting it up a with the right amount of lead can be a daunting task. Especially for novice divers that are still learning the ropes of buoyancy control.

This, more often than not, leads to an “improper” weighted diver who is either too heavy or too light and struggles to maintain neutral buoyancy. As a result, the diver uses more air than necessary reducing the bottom time and increasing risk.

Many diving agencies have developed “rule of thumb” guidelines to calculate the required weight but these usually don’t take into consideration all the factors that affect buoyancy and the approximated suggestions need to be adjusted continuously.

To prevent this and help fellow divers, this paper describes the physics of buoyancy with the objective to describe a more accurate method to calculate the weight requirements for any diver and condition.

So, buckle your belt up (no pun intended) take your calculator out and get ready to uncover the actual weight you need to put on your weight belt for your next dive!

Understanding buoyancy

When a body is placed in a fluid, two main interacting forces determine if it will float, sink or remain suspended: The buoyancy force (Fb) and the force of gravity (Fg).

To determine the body behavior in the fluid consider the following table:

Fb > Fg

Floats – Positive buoyancy

Fb < Fg

Sinks – Negative buoyancy

Fb = Fg

Neutral – Neutral buoyancy

Determining the buoyancy force (Fb)

Buoyancy force is determined by three factors:

  • The submerged volume of the body (Vs)
  • The density of the fluid (D)
  • The force of gravity (g constant with a value of 9.81 Newtons/Kg)

Buoyancy force is calculated with:

F_b =D\times V_s\times g

Calculating fluid density (D)

Diving only happens in water! This makes the fluid density calculation a bit simpler, however, there are a couple of things that must be considered: Water temperature and salinity. To determine the density, use the following table(1):

Temperature (Celsius)

Fresh water \frac{kg}{mt^3}

Salt water \frac{kg}{mt^3}

4

1000

1024

5

1000

1024

10

999.98

1024.94

15

999.2

1024.15

20

998.3

1024.22

25

997.1

1022

30

995.7

1020.56

Calculating the volume (Vs)

For diving, this is the most complicated element to calculate. Several factors must be considered to accurately determine the submerged volume. To simplify the calculation, only the most relevant variables will be taken into account:

  • Body weight
  • Body composition: since fat floats and muscle tends to sink, this must be considered on an individual basis
  • Tank weight and volume

Body volume: to calculate the diver’s body volume, it is necessary to determine the amount of fat and muscle. I suggest that a simplified version of this calculation can be done by using the body mass index (BMI) as a guideline. To calculate BMI(2):

BMI=\frac{(\frac {weight (kg)}{height (mt)})}{height(mt)}

BMI can be related to the percentage of body fat and body density according to the following table(3):

Category

BMI

Body Density

Fitness

<18.5

1.282

Normal

18.5 – 24.9

1.01

Overweight

>25.0

0.808

With these elements, diver body volume (Vd) is calculated with body weight (Wd) and body density (Dd) with the following formula:

V_d=\frac{(\frac{W_d\times 1000}{D_d})}{1\times 10^6}

Note that the operations with the constants (1000 and 1×106) are used to maintain the unit of measure integrity. The final result is expressed in m3.

Tank volume: For an accurate volume (Va) calculation it is necessary to take into account pressure after compression (Pc – typically 210 bar), Volume of gas after compression (Vc – typically 11 lts) and atmospheric pressure (Pa – constant 1.01 bar). This is expressed in m3 and determined by:

V_a=\frac{P_c\times V_c}{P_a}\times 1.225\times 10^{-3}

Total volume: Once these elements have been calculated, the diver total submerged volume is obtained as follows:

V_s = V_d + V_a

Determining the force of gravity (Fg)

Gravity is calculated considering: The total weight (W) and the force of gravity (g)

F_g = W\times g

Calculating total weight (W): To calculate the total weight consider the two main elements: diver weight (Wd) and tank weight (Wt).

W = W_d + W_t

Tank weight (Wt) varies depending on the material (steel or aluminum), volume and ambient temperature. To determine the total tank weight use:

W_t = W_e + (V_a \times d)

 To determine the tank weight (We) refer to the following table(4):

Tank

Weight (Empty) kg

Aluminum 11 lts (AL80)

14.2

Aluminum 13 lts (AL100)

18.5

Steel 11 lts (Steel 80)

12.7

Steel 15 lts (Steel 108)

20.8

The weight of the tank gas will vary depending on volume and temperature. To determine the density (d), refer to the following table(5):

Temperature (Celsius)

Density (kg/m3)

5

1.269

10

1.247

15

1.225

20

1.204

25

1.184

30

1.165

Calculating the required weight

Once the buoyancy and gravity forces have been calculated. the required weight (in kg) for the belt can be calculated with:

B_w = \frac {F_b - F_g}{D \times g}

Compensating for exposure suit and other gear

Divers wear a variety of exposure suits to adapt to different conditions such as water temperature, potential hazards, etc. To calculate the required weight to compensate (Wc) for exposure suit buoyancy consider the following table:

Add per mm (fresh water)

Add per mm (salt water)

Exposure suit

Kg

Lbs

Kg

Lbs

Full body 1 piece

0.884

1.95

0.907

2.0

Shorty (no sleeves)

0.442

0.975

0.435

1

If the diver is wearing extra gear, add the required weight to compensate according to this table:

Fresh Water

Salt Water

Additional gear

Kg

Lbs

Kg

Lbs

Hood and gloves

0.435

0.96

0.453

1

Calculate the total weight

The total weight belt (Wt) will be determined by Bw plus the required compensation for exposure suit and other gear (Wc). Additionally, due to the weight blocks availability at most diving shops, this number needs to be rounded.

As a safety measure and personal preference, a margin of +/- 10% can be factored into the final calculation to get the recommended weight belt range:

W_t = round(B_w+W_c)

Recommended weight range = Wt +/- 10%

Putting it together, a practical example

The best way to understand these calculations is with real life example:

A diver needs to calculate the weight for the belt:

  • Diver weight: 86 kg
  • Diver height: 1.70
  • Water: Salt @ 20 Celsius
  • Tank: Steel 11 lts @ 210 bar
  • Exposure suit: full body 5 mm
  • No hood

Calculate Buoyancy force (Fb):

F_b =D\times V_s\times g

Density (D) = 1024.22 \frac{kg}{mt^3}

Volume (Vs):

BMI=\frac{(\frac {86kg}{1.70mt})}{1.70mt}=29.7, then Dd=0.808

V_d=\frac{(\frac{86kg\times 1000}{0.808})}{1\times 10^6}=0.106mt^3

V_a=\frac{210\times 11}{1.01}\times 1.225\times 10^{-3}=2.801mt^3

V_s = 0.106mt^3 + 2.801mt^3=2.907mt^3

F_b =1024.22\times 2.907\times 9.81=29\times 10^3 Newtows

Calculate force of gravity (Fg):

F_g = W\times g

W_t = 12.7 + (2.801 \times 1.204) = 16.07 kg

W = 86 kg + 16.07 kg = 102.07 kg

F_g = 102.07\times 9.81 = 1.0\times 10^3 Newtons

Calculate the required weight (Wt):

W_t = round(B_w+W_c)

B_w = \frac {29\times 10^3 - 1\times 10^3}{1024.22\times 9.81} = 2.78kg

compensate for exposure suit:

W_c = 5 \times 0.907 = 4.53 kg

W_t = round(2.78 + 4.53) = 7 kg

Recommended belt weight range: 6 kg – 8 kg

Final notes and recommendation

Please note that to give credit to the sources that were used during the preparation of this paper, links have been added where you can click for further reference.

Remember that it is recommended that a buoyancy check is performed every time you change the diving environment, gear or conditions. Ensuring that you are properly weighted will make the experience safer and more enjoyable.

Feel free to distribute or copy this material as long as you provide a reference to the source.

Obviously, the author can not take any responsibility on how a diver applies this information.

Happy diving!

-Stein

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Brief History of Squash

I love Squash! Not the the vegetable (or is it a fruit?) but the popular sport practiced across the world that for some reason that escapes my understading did not make the cut for the olympic games.

In any case, the more you know about something you like the more you can enjoy it. So, here you have a really brief story of squash. Hope you like it.

Squash traces its origins to 1830 in Harrow School, England where it was invented as an offshoot of the game of rackets. It began when underclassmen who either lacked the skills or seniority to play rackets, the popular game at the time, opted to hit rubber balls against the walls of alleys and courtyards. The students discovered that squashing balls against walls yielded a number of shots and required adept footwork that was enjoyable.

However, the game did not receive much attention until in 1864 when the first squash courts were built in the school. Its popularity spread fast especially among famous private schools and colleges and in exclusive men’s clubs. The sport debuted in North America in the 1880s.

That period saw the construction of four squash courts by St, Paul’s school, New Hampshire in 1884. Similarly, Honorable Cecil Edwards built a squash court at his Vancouver residence where pioneer players such as Bimbo Sweeney mustered the sport.

Another court was constructed in 1904 in Newfoundland at St. John’s Tennis club and others followed in Montreal, Toronto, Ottawa and later in Canada. By the 1950s, the game had caught up with the rest of the world.

Of interest is Hashim Khan, a squash player of Pakistani descent, who after working as a ball boy at a local British Officer’s court, went ahead to clinch the British Open title in 1951Currently, the top three countries that have consistently churned out squash champions are England, the United States, Egypt.

England, where the sport was founded continues to enjoy a massive following both as a sport and a recreational activity. Moreover, squash classes are offered at the college level.

Notably, the top squash player, Mohamed Eishorbagy hails from Egypt. Squash thrives in this country with budding players striving to attain the elite competition level and even to receive scholarships abroad. Similarly, the United States is home to new tournaments such as The US Open Squash Doubles Tournament that have played a pivotal role in boosting the sport in the country

-Stein

Am I a writer? Yes, I am a writer!

I love writing. For some reason, I find easier to articulate personal feelings, ideas or thoughts writing them down and thus have found in this blog an outlet to share those little personal treasures that I would probably not do otherwise.

But always wanted to test myself and see if I could write for money. How cool would that be? Do something that I totally enjoy and at the same time get paid for doing it!

I thought about trying it out  for a very long time but never really committed to it. Which translates into the intention of doing it was nagging me all the time but never actually tried… Until now…

Last week I got my first article accepted by a client and got paid!!! Yes, I admit it, this happened in the shady world of a content mill. Yes, I know, it was a short piece of a few hundred words and if you are familiar with the content mill dynamics you already know that the money I made will not allow me to leave my day time job anytime soon.

But that I actually tried instead of only thinking of “doing it some day” and someone considered the few words I put together worth some money is very satisfying and encouraging.

I will definitely keep trying. Who knows, maybe, just maybe, many years from now, with discipline and hard work this might turn into a more serious undertaking.

-Stein

Winston

 

winstonSir Winston Leonard Spencer-Churchill is one of the few characters in history that really inspires me. I know there are opposing camps when it comes to considering his contributions to this world and many, many different opinions regarding his personality.

All that aside, I believe that we all can agree that his famous speeches and writings show the ability that he had to transmit his message with clarity, force, and elegance.

Of all his work, there are two quotes that for me stand out and have been my favorite for a very long, time. I want to share them with you. Hopefully, you will find in them the same inspiration that I do every time I read them.

“Never give in. Never give in. Never, never, never, never—in nothing, great or small, large or petty—never give in, except to convictions of honour and good sense. Never yield to force. Never yield to the apparently overwhelming might of the enemy.”

-Winston Churchill

 

“I am a man of simple tastes easily satisfied with the best”

-Winston Churchill

-Stein