Diving weighting system
Scuba weight-belt with quick-release buckle
|Uses||Buoyancy correction and trim adjustment of underwater divers|
|Related items||Buoyancy Compensation Device|
Divers wear weighting systems, weight belts or weights to counteract the buoyancy of other diving equipment, such as diving suits and aluminium diving cylinders. The scuba diver must be weighted sufficiently to be slightly negatively buoyant at the end of the dive when most of the breathing gas has been used, and needs to maintain neutral buoyancy at safety or obligatory decompression stops. During the dive, buoyancy is controlled by adjusting the volume of air in the buoyancy compensation device (BCD) and, if worn, the dry suit, in order to achieve neutral or positive buoyancy as needed. The amount of weight required is determined by the maximum overall positive buoyancy of the fully equipped but unweighted diver anticipated during the dive, with an empty buoyancy compensator and normally inflated dry suit. This depends on the diver's mass and body composition, buoyancy of other diving gear worn (especially the diving suit), water salinity, weight of breathing gas consumed, and water temperature. It normally is in the range of 2 kilograms (4.4 lb) to 15 kilograms (33 lb). The weights can be distributed to trim the diver to suit the purpose of the dive.
Surface-supplied divers may be more heavily weighted to facilitate underwater work, and may be unable to achieve neutral buoyancy, and rely on the diving stage, bell, umbilical, lifeline, shotline or jackstay for returning to the surface.
Free divers may also use weights to counteract buoyancy of a wetsuit. However, they are more likely to weight for neutral buoyancy at a specific depth, and their weighting must take into account not only the compression of the suit with depth, but also the compression of the air in their lungs, and the consequent loss of buoyancy. As they have no decompression obligation, they do not have to be neutrally buoyant near the surface at the end of a dive.
If the weights have a method of quick release, they can provide a useful rescue mechanism: they can be dropped in an emergency to provide an instant increase in buoyancy which should return the diver to the surface. Dropping weights increases the risk of barotrauma and decompression sickness due to the possibility of an uncontrollable ascent to the surface. This risk can only be justified when the emergency is life-threatening or the risk of decompression sickness is small, as is the case in free diving and scuba diving when the dive is well short of the no-decompression limit for the depth. Often divers take great care to ensure the weights are not dropped accidentally, and heavily weighted divers may arrange their weights so subsets of the total weight can be dropped individually, allowing for a somewhat more controlled emergency ascent.
The weights are generally made of lead because of its high density, reasonably low cost, ease of casting into suitable shapes, and resistance to corrosion. The lead can be cast in blocks, cast shapes with slots for straps, or shaped as pellets often named "shot" and carried in bags. There is some concern that lead diving weights may constitute a toxic hazard to users and environment.
- 1 Function and use of weights
- 2 Types of weight
- 3 Materials
- 4 See also
- 5 References
- 6 Notes
- 7 Sources
Function and use of weights
The primary function of diving weights is as ballast, to prevent the diver from floating at times when he or she wishes to remain at depth.
In free diving (breathhold) the weight system is almost exclusively a weight belt with quick release buckle, as the emergency release of the weights will usually allow the diver to float to the surface even if unconscious, where there is at least a chance of rescue. The weights are used mainly to neutralise the buoyancy of the exposure suit, as the diver is nearly neutral in most cases, and there is little other equipment carried. The weights required depend almost entirely on the buoyancy of the suit. Most free divers will weight themselves to be positively buoyant at the surface, and use only enough weight to minimise the effort required to swim down against the buoyancy at the start of a dive, while retaining sufficient buoyancy at maximum depth to not require too much effort to swim back up to where the buoyancy becomes positive again. As a corollary to this practice, freedivers will use as thin a wetsuit as comfortably possible, to minimise buoyancy changes with depth due to suit compression.
Buoyancy control is considered both an essential skill and one of the most difficult for the novice to master. Lack of proper buoyancy control is likely to disturb or damage the surroundings, and is a source of additional and unnecessary physical effort to maintain precise depth, which also increases stress.
The scuba diver generally has an operational need to control depth without resorting to a line to the surface or holding onto a structure or landform, or resting on the bottom. This requires the ability to achieve neutral buoyancy at any time during a dive, otherwise the effort expended to maintain depth by swimming against the buoyancy difference will both task load the diver and require an otherwise unnecessary expenditure of energy, increasing air consumption, and increasing the risk of loss of control and escalation to an accident.
A further requirement for scuba diving in most circumstances, is the ability to achieve significant positive buoyancy at any point of a dive. When at the surface, this is a standard procedure to enhance safety and convenience, and underwater it is generally a response to an emergency.
The average human body with a relaxed lungful of air is close to neutral buoyancy. If the air is exhaled, most people will sink in fresh water, and with full lungs, most will float in seawater. The amount of weight required to provide neutral buoyancy to the naked diver is usually trivial, though there are some people who require several kilograms of weight to become neutral in seawater due to low average density and large size. This is usually the case with people with a large proportion of body fat. As the diver is nearly neutral, most ballasting is needed to compensate for the buoyancy of the diver's equipment.
The main components of the average scuba diver's equipment which are positively buoyant are the components of the exposure suit. The two most commonly used exposure suit types are the dry suit and the wet suit. Both of these types of exposure suit use gas spaces to provide insulation, and these gas spaces are inherently buoyant. The buoyancy of a wet suit will decrease significantly with an increase in depth as the ambient pressure causes the volume of the gas bubbles in the neoprene to decrease. A dry suit will also compress with depth, but the air space inside is continuous and can be topped up from a cylinder or vented to maintain a moderately constant volume. A large part of the ballast used by a diver is to balance the buoyancy of this gas space.
Another significant issue in open circuit scuba diver weighting is that the breathing gas is used up during a dive, and this gas has weight, so the total weight of the cylinder decreases, while its volume remains almost unchanged. As the diver needs to be neutral at the end of the dive, particularly at shallow depths for obligatory or safety decompression stops, sufficient ballast weight must be carried to allow for this reduction in weight of gas supply. (the density of air at normal atmospheric pressure is approximately 1.2 kg/m3, or approximately 0.075 lb/ft3) The amount of weight needed to compensate for gas use is easily calculable once the free gas volume and density are known.
Most of the rest of the diver's equipment is negatively buoyant or nearly neutral, and more importantly, does not change in buoyancy during a dive, so its overall influence on buoyancy is static.
While it is possible to calculate the required ballast given the diver and all his or her equipment, this is not done in practice, as all the values would have to be measured accurately. The practical procedure is known as a buoyancy check, and is done by wearing all the equipment, with the tank(s) nearly empty, and the buoyancy compensator empty, in shallow water, and adding or removing weight until the diver is neutrally buoyant. The weight should then be distributed on the diver to provide correct trim, and a sufficient part of the weight should be carried in such a way that it can be removed quickly in an emergency to provide positive buoyancy at any point in the dive. This is not always possible, and in those cases an alternative method of providing positive buoyancy should be used.
A diver ballasted by following this procedure will be negatively buoyant during most of the dive unless the buoyancy compensator is used, to an extent which depends on the amount of breathing gas carried. A recreational dive using a single cylinder may use between 2 and 3 kg of gas during the dive, which is easy to manage, and provided that there is no decompression obligation, end-dive buoyancy is not critical. A long or deep technical dive may use 6 kg of back gas and another 2 to 3 kg of decompression gas. If there is a problem during the dive and reserves must be used, this could increase by up to 50%, and the diver must be able to stay down at the shallowest decompression stop. The extra weight and therefore negative buoyancy at the start of the dive could easily be as much as 13 kg for a diver carrying four cylinders. The buoyancy compensator is partially inflated when needed to support this negative buoyancy, and as breathing gas is used up during the dive, the volume of the buoyancy compensator will be reduced, by venting as required.
- The common 80 ft3 (11 litre, 207 bar) cylinder carries about 6 pounds (2.7 kg) of air when full, so the diver should start the dive about 6 pounds (2.7 kg) negative and use about 1/10 ft3 (2.7 l)of air in the BCD to compensate at the start of a dive.
- A twin 12.2 litre 230 bar set carries about 6.7 kilograms (15 lb) of Nitrox when full, so the diver should start the dive about 6.7 kilograms (15 lb) negative and use about 6.7 liters (0.24 cu ft) of gas in the BCD at the start of the dive.
- A twin 12.2 litre 230 bar with an 11 litre 207 bar deep deco mix and a 5.5 litre 207 bar shallow deco gas will carry 10.7 kilograms (24 lb) of gas, and while it is unlikely that all will be used on the dive, it is possible, and the diver should be able to remain at the correct depth for decompression until all the gas is used up.
In surface-supplied diving, and particularly in saturation diving, the loss of weights followed by positive buoyancy can expose the diver to potentially fatal decompression injury. Consequently, weight systems for surface-supplied diving where the diver is transported to the worksite by a diving bell or stage, are usually not provided with a quick-release system.
Much of the work done by surface-supplied divers is on the bottom, and weighted boots may be used to allow the diver to walk upright on the bottom. When working in this mode, several kilograms beyond the requirement for neutralising buoyancy may be useful, so that the diver is reasonably steady on the bottom and can exert useful force when working.
The lightweight demand helmets in general use by surface-supplied divers are integrally ballasted for neutral buoyancy in the water, so they do not float off the diver's head or pull upwards on the neck, but the larger volume free-flow helmets would be too heavy and cumbersome if they had all the required weight built in. Therefore, they are either ballasted after dressing the diver by fastening weights to the lower parts of the helmet assembly, so the weight is carried on the shoulders when out of the water, or the helmet may be held down by a jocking strap and the harness weights provide the ballast.
The traditional copper helmet and corselet were generally weighted by suspending a large weight from support points on the front and back of the corselet, and the diver often also wore weighted boots to assist in remaining upright.
Trim is the diver's attitude in the water, in terms of balance and alignment with the direction of motion. Accurately controlled trim reduces swimming effort, as it reduces the sectional area of the diver passing through the water. A slight head down trim is recommended to reduce downthrust during finning, and this reduces silting and fin impact with the bottom.
Trim weighting is mainly of importance to the free-swimming diver, and within this category is used extensively by scuba divers to allow the diver to remain horizontal in the water without effort. This ability is of great importance for both convenience and safety, and also reduces the environmental impact of divers on fragile benthic communities.
The free-swimming diver may need to trim erect or inverted at times, but in general, a horizontal trim has advantages both for reduction of drag when swimming horizontally, and for observing the bottom. A horizontal trim allows the diver to direct propulsive thrust from the fins directly to the rear, which minimises disturbance of sediments on the bottom, and reduces the risk of striking delicate benthic organisms with the fins. A stable horizontal trim requires that diver's centre of gravity is directly below the centre of buoyancy (the centroid). Small errors can be compensated fairly easily, but large offsets may make it necessary for the diver to constantly exert significant effort towards maintaining the desired attitude, if it is actually possible.
The position of the centre of buoyancy is largely beyond the control of the diver, though the cylinder(s) may be shifted in the harness by a small amount, and the volume distribution of the buoyancy compensator has a large influence when inflated. Most of the control of trim available to the diver is in the positioning of ballast weights. The main ballast weights therefore should be placed as far as possible to provide an approximately neutral trim, which is usually possible by wearing the weights around the waist or just above the hips on a weight belt, or in weight pockets provided in the buoyancy compensator jacket or harness for this purpose. Fine tuning of trim can be done by placing smaller weights along the length of the diver to bring the centre of gravity to the desired position. There are several ways this can be done.
Ankle weights provide a large lever arm for a small amount of weight and are very effective at correcting head-down trim problems, but the addition of mass to the feet increases the work of propulsion significantly. This may not be noticed on a relaxed dive, where there is no need to swim far or fast, but if there is an emergency and the diver needs to swim hard, ankle weights will be a significant handicap, particularly if the diver is marginally fit for the conditions.
Tank bottom weights provide a much shorter lever arm, so need to be a much larger proportion of the total ballast, but do not interfere with propulsive efficiency the way ankle weights do. There are not really any other convenient places below the weight belt to add trim weights, so the most effective option is to carry the main weights as low as necessary, by using a suitable harness or integrated weight pocket buoyancy compensator which actually allows the weights to be placed correctly, so there is no need for longitudinal trimming.
A less common problem is found when rebreathers have a counterlung towards the top of the torso. In this case there may be a need to attach weights near the counterlung. This is usually not a problem, and weight pockets for this purpose are often built into the rebreather harness or casing, and if necessary weights can be attached to the harness shoulder straps.
Types of weight
All or part of the weighting system may be carried in such a way that it can be quickly and easily jettisoned by the diver to increase buoyancy, the rest is usually attached more securely.
Breathhold and scuba divers generally carry some or all of their weights in a way that can be quickly and easily removed while under water. Research performed in 1976 analyzing diving accidents noted that in majority of diving accidents, divers failed to release their weight belts. Later evaluations in 2003 and 2004 both showed that failure to ditch the weight remained a problem.
- Shot belt redirects here.
Weight belts are the most common weighting system currently in use for recreational diving. Weight belts are often made of tough nylon webbing, but other materials such as rubber can be used. Weight belts for scuba and breathhold diving are generally fitted with a quick release buckle to allow the dumping of weight rapidly in an emergency.
A belt made of rubber with traditional pin buckle is called a Marseillaise belt. These belts are popular with freedivers as the rubber contracts on descent as the diving suit and lungs are compressed, keeping the belt tight throughout the dive.
The most common design of weight used with a belt consists of plain, rectangular lead blocks with two slots in them threaded onto the belt. These blocks can be coated in plastic, which further increases corrosion resistance. These weights are often marketed as being less abrasive to wetsuits. The weights may be constrained from sliding along the webbing by the use of metal or plastic belt sliders.
Another popular style has a single slot through which the belt can be threaded. These are sometimes locked in position by squeezing the weight to grip the webbing, but this makes them difficult to remove when less weight is needed.
There are also weight designs which may be added to the belt by clipping on when needed. Some weightbelts contain pouches to contain lead weights or round lead shot: this system allows the diver to add or remove weight more easily than with weights threaded onto the belt. The use of shot can also be more comfortable, as the shot conforms to the diver's body. Weight belts using shot are called shot belts. Each shot pellet should be coated[clarification needed] to prevent corrosion by sea water, as use of uncoated shotgun shot for sea diving would result in the lead eventually corroding into powdery lead chloride
BCD integrated weights
These are stored in pockets built into the buoyancy control device. Often a velcro flap or plastic clip holds the weights in place. The weights may also be contained in zippered or velcroed pouches that slot into special pockets in the BCD. The weight pouches often have handles, which must be pulled to drop the weights in an emergency or to remove the weights when exiting the water. Some designs also have smaller "trim pouches" located higher in the BCD, which may help the diver maintain neutral attitude in the water. Trim pouches typically can not be ditched quickly, and are designed to hold only 1-2 pounds (0.5–1 kg) each. Many integrated systems cannot carry as much weight as a separate weight belt: a typical capacity is 6 kg per pocket, with two pockets available. This may not be sufficient to counteract the buoyancy of dry suits with thick undergarments used in cold water.
Some BCD harness systems include a crotch strap to prevent the BCD from sliding up the wearer when inflated, or down when inverted, due to the weights.
A weight harness usually consists of a belt around the waist holding pouches for the weights, with shoulder straps for extra support and security. Often a velcro flap holds the weights in place. They have handles, which must be pulled to drop the weights in an emergency or to remove the weights when exiting the water. A weight harness allows the weights to be comfortably carried lower on the body than a weight belt, which must be high enough to be supported by the hips. This is an advantage for divers who have no discernible waist, or whose waist is too high to trim correctly if a weight belt is worn. These advantages may also be available on some styles of integrated BC weights. A weight harness may also incorporate a crotch strap or straps to prevent weight shift if the diver is in a steep head down posture.
These are weights which attach to the harness directly, but are removable by disengaging the clip mechanism. They can also be used to temporarily increase the weight of a conventional weight belt. Various sizes have been available, ranging from around 0.5 to 5 kg or more. The larger models are intended as ditchable primary weights, and are used in the same way as BCD integral weights or weight harness weighs, but clipped to the backplate or sidemount harness webbing, and the smaller versions are also useful at trim weights.
Backpack weight pouch
Surface-supplied divers often carry their weights securely attached to reduce the risk of accidentally dropping them during a dive and losing control of their buoyancy. These may be carried on a weight belt with a secure buckle, supported by a weight harness, connected directly to the diving safety harness, or suspended from the corselet of the helmet. Heavily weighted boots may also be used to stabilise the diver in an upright position.
In addition to the weight that can be dropped easily ('ditched'), some scuba divers add additional fixed weights to their gear, either to reduce the weight placed on the belt, which can cause lower back pain, or to shift the diver's center of mass to achieve the optimum position in the water.
- Tank weights are attached to the diving cylinder to shift the center of mass backward and towards the head or feet, depending on placement.
- Ankle weights, which are typically about 1 lb./0.5 kg of shot, are used to counteract the positive buoyancy of diving suit leggings, made worse in drysuits by the migration of the internal bubble of air to the feet, and positively buoyant fins. Some divers prefer negatively buoyant fins. The additional effort needed when finning with ankle weights or heavy fins increases the diver's gas consumption.
- Metal backplates made from stainless steel, which may be used with wing style buoyancy compensators, move the center of mass upward and backward. Some backplates are fitted with an additional weight, often mounted in the central channel, also called a keel weight.
- Steel diving cylinders are preferred over aluminium cylinders by some divers—particularly cold water divers who must wear a suit that increases their overall buoyancy—because of their negative buoyancy. Most steel tanks stay negatively buoyant even when empty, aluminium tanks may become positively buoyant as the gas they contain is used. High-pressure (300bar) steel tanks are significantly negative.
The most common material for personal dive weights is cast lead.
The primary reasons for using lead are its relatively low melting point and cost compared to other high density materials. It is also resistant to corrosion in fresh and salt water. Most dive weights are cast by foundries and sold by dive shops to divers in a range of sizes, but some are made by divers for their own use. Scrap lead from sources such as fishing sinkers and wheel balance weights can be easily cast by a hobbyist in relatively cheap re-usable moulds, though this exposes them to vaporized lead fumes.
Heavy metal toxicity
Although lead is the least expensive dense (SG=11.34) material available, it is a toxic substance causing biological damage to wildlife and humans. The Centers for Disease Control has stated that no safe level of lead exposure in children has been determined, and that once lead has been absorbed into the body, its effects cannot be corrected. Even a very small amount of exposure causes a permanent reduction in intelligence, ability to focus attention, and academic ability. Lead can be inhaled or ingested as either a metal powder or powdered corrosion products, however most lead salts have very low solubility in water, and pure lead corrodes very slowly in seawater. Absorption through skin is not likely for metallic lead and inorganic corrosion products.
Although it is inexpensive to recycle lead from other sources into homemade dive weights, pure lead melts at 327.46 °C (621.43 °F) and releases fumes at 482 °C (900 °F). The fumes will form oxides in the air and settle as dust on nearby surfaces. Even with good ventilation there will be lead oxide dust in the lead melting area.
Solid block weights can corrode and be damaged when dropped or impacting other weights. In flexible bag weights, the small pieces of lead shot will rub together when handled and used, releasing lead dust and corrosion products into the water. The amount of lead lost to the water is roughly proportional to the total surface area of the weights, and the amount of motion between contact surfaces and is greater for smaller sizes of shot.
Diving is also sometimes practiced in swimming pools for training and exercise. Swimming pools can be contaminated by lead weights. Many divers using the same pool with lead weights will over time increase the lead contamination of the pool water until the water is changed.
Other heavy metals have been considered as an alternative to lead. One example is bismuth which has a similar density (SG=9.78) and a low melting point. It is less toxic, and its salts are highly insoluble which limits absorption by the body. Tungsten (SG=19.25) is another possible replacement for lead, but it is very expensive by comparison, both as a material and to manufacture in suitable shapes.
Non-toxic materials such as iron (SG=7.87) can be used in place of lead and would not cause poisoning and contamination. However, the density of most such materials is significantly lower, so the dive weight needs to be of larger volume and therefore greater mass, to equal the negative buoyancy of the mass of lead it replaces. A lead weight of 1 kg would be replaced by an iron weight of 1 × (7.87/11.34) × ((11.34-1)/(7.87-1)) = 1.044 kg, a small additional load for the diver when out of the water.
Iron is also corroded much more easily in seawater than lead, and would need some form of protection to prevent rusting. Alloys of stainless steel are more resistant to corrosion, but, for the cheaper grades, need to be rinsed with freshwater after use to prevent corrosion in storage. The cost of shaping alternative materials may be considerably greater, particularly for small quantities. Stainless steel and tungsten dive weights for example are currently only obtainable by milling down a solid metal stock material in block or cylinder form, into the required shape. Direct casting of these materials in a foundry is possible, but would require high volume production for the casting processes to be cost effective.
Encapsulation of lead weights
Lead weights can be coated with a protective outer layer such as plastic or paint, and this is commonly used for lead abatement. This prevents the lead from corroding or being ground into dust by rubbing, and helps to cushion impacts. However the protection is reduced if the coating is cracked or otherwise damaged. Soft plastics may become brittle over time due to UV degradation from the sun and loss of plasticizers, leading to cracking and shattering. Encapsulation materials are usually of near neutral buoyancy in water, and reduce the average density of the weights, making the weights slightly less effective, and increasing the overall weight in air of the diving equipment.
- Buoyancy – An upward force that opposes the weight of an object immersed in fluid
- Buoyancy compensator (diving) – Diving equipment for controlling buoyancy by volume adjustment
- Archimedes' principle – Buoyancy principle in fluid dynamics
- Emergency ascent – An ascent to the surface by a diver in an emergency
- Jablonski 2006, pp. 33–35
- Beresford, M.: CMAS-ISA Normoxic Trimix Manual
- Knedlik, Thomas (26 May 2015). "Back-up Buoyancy by Thomas Knedlik". TecRec Blog. PADI. Retrieved 1 March 2016.
- Staff. "WorkCover Queensland". Diving and snorkelling equipment. Queensland government. Retrieved 1 March 2016.
- Staff (1997). "Diving at Work Regulations 1997" (PDF). Media diving projects: Approved Code of Practice and guidance. HSE. Archived from the original (PDF) on 5 October 2015. Retrieved 1 March 2016.
- Staff (1982). BSAC Diving Manual (10th ed.). London: British Sub-Aqua Club. ISBN 0950678619.
- Jablonski 2006, pp. 35–37
- Fead, Lou (1979). "Saving your own life: Is dropping your weight belt the right response?". Journal of the South Pacific Underwater Medicine Society. 9 (1). Retrieved 2013-04-09.
- Knight, John; Acott, Chris J (2003). "Depth gauges, contents gauges and miscellaneous equipment problems reported in the Diving Incident Monitoring Study". Journal of the South Pacific Underwater Medicine Society. 33 (1). Retrieved 2013-04-09.
- Caruso, James L; Uguccioni, Donna M; Ellis, Julie E; Dovenbarger, Joel A; Bennett, Peter B (2004). "Do divers in trouble drop their weight belts or integrated weights? A look at the ditching of weights in fatal recreational diving accidents". Undersea and Hyperbaric Medicine. Retrieved 2013-04-09.
- Scuba diving air Regulators, buoyancy compensators scuba diving equipment, information advice help with scuba gear products safety - Philadelphia Area Dive Shops Archived June 21, 2007, at the Wayback Machine
- Freediving and Spearfishing Equipment
- Mares - stand for diving Archived April 15, 2008, at the Wayback Machine
- Centers for Disease Control and Prevention - Lead Poisoning information - Prevention Tips https://www.cdc.gov/nceh/lead/tips.htm Accessed Feb 26, 2016
- CDC / Agency for Toxic Substances and Disease Registry, Case Studies, Lead Toxicity: How are people exposed to lead? http://www.atsdr.cdc.gov/csem/csem.asp?csem=7&po=6 Accessed Feb 26, 2016
- Osberg, Erik; Jones, Franklin D. (1971). Holbrook L. Horton (ed.). Machinery's Handbook (19th ed.). New York: Industrial Press Inc. p. 2192.
- Michigan State University, Occupational and Environmental Medicine, Lead Hazards from casting bullets, shot, and other objects or reloading, Sep 10, 2009 http://www.oem.msu.edu/userfiles/file/ABLES/LEAD%20HAZARDS%20FROM%20CASTING%20BULLETS-c07-10-09.pdf Accessed Feb 26, 2016
- The Risk of Lead Poisoning From Scuba Diving Weights, By Douglas Bigler, Infolific, Retrieved 02/21/2018, http://infolific.com/leisure/scuba-diving/lead-poisoning-scuba-diving-weights/
- Staff (March 16, 2010). "Evaluation of Concerns Regarding Elevated Blood Lead Levels and Contaminated Water in a Children's Wading Pool" (PDF). Massachusetts Department of Public Health. Retrieved 26 February 2016.
- Emergency Medicine News, April 2001, Volume 23, Issue 3, p 16, Laboratory Rounds, Bismuth Toxicity, Often Mild, Can Result in Severe Poisonings, DiPalma, Joseph R. MD, http://journals.lww.com/em-news/Fulltext/2001/04000/Bismuth_Toxicity,_Often_Mild,_Can_Result_in_Severe.12.aspx Accessed Feb 26, 2016.
^ Derivation of formula for equivalent apparent weight in water.
- Density = mass/volume, ρ = m/V so m = ρ × V
- Buoyancy in water: B = (ρ - ρwater) × V × g, where g = gravitational acceleration at earth' surface
- For two objects of different densities but the same buoyancy in water: B1 = B2 so (ρ1 - ρwater) × V1 × g = (ρ2 - ρwater) × V2 × g (g can be dropped from both sides)
- therefore: V1 = V2 × (ρ2 - ρwater) ÷ (ρ1 - ρwater)
- Also, for the same two objects in air (ignoring the buoyancy of the air): m1 = ρ1 × V1 and m2 = ρ2 × V2
- by substitution: m1 ÷ m2 = (ρ1 ÷ ρ2) × ((ρ2 - ρwater) ÷ (ρ1 - ρwater))
- so: m1 = (ρ1 ÷ ρ2) × ((ρ2 - ρwater) ÷ (ρ1 - ρwater)) × m2
- And the same works with SG in place of density: m1 = (SG1 ÷ SG2) × ((SG2 - SGwater) ÷ (SG1 - SGwater)) × m2
- And since SGwater = 1: m1 = (SG1 ÷ SG2) × ((SG2 - 1) ÷ (SG1 - 1)) × m2
- Substituting values for 1 kg lead, iron gives: 1kg lead × (7.87/11.34) × ((11.34-1)/(7.87-1)) = 1.044kg iron