The thing about submarines is they are heavy. And the bigger they are the heavier they are. But it's easy to sink a boat right? We'll yes, but only if you're willing to fill it with water. Sinking a boat with 227 cubic feet of air inside means that the boat must weight more that the 227 cubic feet of water that it's going to push aside. That is about 7 tons of water! So to make the boat heavy enough to sink we add concrete, steel, or lead. And then we build in some tanks that can be flooded with water. It's the water in those tanks that will tip the scales and allow the submarine to slip under the surface with her precious cargo of air. So we have two types of ballast, "ballast weights" and "ballast tanks".
We calculated that 5 tons of ballast weight is needed in addition to get the submarine to sink after 35 cubic feet of water floods into the ballast tanks. Five tons is 10,000 pounds or about the same as two cars.
Concrete or Iron or Lead
Simon had all of these available to him for ballast weight. Concrete is the least expensive, and you'd thing it would be heavy enough but the problem is that that 5 tons of concrete takes up too much space. Concrete only weighs about 150 pounds for each cubic foot. The water being pushed aside weighs 62.4 pounds per cubic foot, so you'd need almost 1 cubic ft of concrete for every 2 cubic feet of air to take down. That's not going to leave much room inside.
So what about steel? It's much better. A cubic foot of steel weighs 490 pounds and will drag down more than 7 cubic feet of air. (1) The CAD model shows the amount of steel that would need to be set on the floor in order to total 5 tons. (2) But compare that to the next CAD model that shows the lead needed. Lead weighs a whopping 708 pounds per cubic foot!
(3) The lead will need to be added to Argonaut Jr. after it is in the water because the wooden wheels will never take the 5 tons of extra weight. So the lead must be fit in around the ballast tanks and the divers hatch in the bottom. And it will be set in as bricks so it can be moved a little at a time in and out of the hatch.
Bow and stern anchors hung on each end of the Argonaut and were lowered by capstans near the center of the boat. Or the anchors were possibly lowered from the capstans and just swung up over cleats at the bow and stern. Either way these anchors could be lowered to the bottom, allowing the Argonaut Jr. to rise off the bottom and give a diver room to clear the bottom of the sub when moving thought the bottom hatch. These anchors also make up some to the ballast weight on Argonaut Jr.
We've decided to make them adjustable so different configurations can be tested. We'll make lead anchors that can have 20+ lb disc added as needed. The top of the anchor will be a cone shaped lead cast around an eye bolt so we can tie onto it and also cast around a piece of all thread that sticks down so we can add or remove disc from the stack. Each anchor will weigh about 125 pounds or 250 pounds together.
Getting back to the surface is important. The submarine may be taking on water or the air supply could fail and prevents us from blowing the water out of the ballast tanks. For those emergencies we use drop weights. A drop weight is just something heavy that you can through overboard and make your boat lighter. The anchors are two obvious drop weights. If we lower then all the way then the rope can let go from the winch, allowing the anchors to fall to the bottom. If the submarine is ambient and the divers hatch can be opened then we can simply lift additional weight from the floor and drop them out the hatch. Finally additional drop weights will be installed between the wooded frames below the floor. Turning a handle inside the submarine will move a latch below these weights and allow them to fall free, immediately making the submarine 3,100 pounds lighter.
We don't know exactly where Simon put the ballast tanks inside of the Argonaut Jr., but we can see the plumbing that would have vented the tanks so they could flood. Both sides of the top hatch trunk have pipes that likely each connected to a ballast tank on below. When the vents were opened, another valve in the floor would have been opened to allow water to flood into the ballast tanks. When boat is heavy enough to slowly sink the valves would be closed.
If the anchors were hanging below the boat then they would have touched bottom first. Once the anchors were sitting on the bottom, they would no longer be pulling the Argonaut Jr. down, so the boat may have then floated off the bottom by it's anchor ropes. This would have given a diver plenty of room to slip out the bottom hatch onto the ocean without having to crawl out from under the submarine.
When Simon wanted to roll the Argonaut across the bottom, he would simply raise the anchors so the wheels took on there weight. On the bottom the Argonaut Jr. would have only weighed a hundred pounds or so. And the weight could be increased by adding more water to the ballast tanks, or by blowing water out the bottom of the tanks using the air stored in the air tank.
Ballast Tank Size and Freeboard
It's all about trade-offs. The bigger you make the ballast tanks, the higher you are out of the water when they are empty. The height out of the water is called "freeboard". The more freeboad the better, because it keeps waves from pouring into the submarine when you have the hatch open on the surface. But the bigger you make the tanks the less room you have for crew and equipment inside the submarine. After you bang your head a few times you will start wishing you had more room. :)
1/4 Scale Model Ballast Testing
We built a scale model which allowed us to also test the displacement, freeboard, and ballast weight calculations.
submarine to exit thought the divers hatch in the bottom.
A diver leaving the sub will increase the sub's buoyancy by the equivalent water weight of his volume.
Because the air pressure inside the submarine is equal to the water pressure outside the diver's hatch, you can open the bottom hatch and the water will only lap at the opening. But as you drop out of the hatch, an interesting thing happens. As you slip below the water, the water rises up through the hatch. Inside the submarine, you were taking up space. As you exit the submarine air moves to fill the space and it moves out of the way of the water that is pushing up through the bottom hatch. So how much water comes in? If you filled a bath tub to the rim, and then got in and floated, the water that spills over the side will weight exactly what you weigh. That is your displacement. But part of you is floating above the water. If you held onto the sides and pulled yourself completely under then you would spill a little more water out. Now the water on the floor is equal to your volume. If you put it in a box that could be measured in cubic inches. So if a 180 pound diver gets out of the submarine, then a little more that 180 pounds of water is is going to rise up in the divers trunk. And that's just perfect because the anchors are only holding the Argonaut Jr. down with about 200 pounds so if water in the trunk replaces the weight of the diver and the submarine stays on the bottom. And if 5 or 10 pounds of extra water is added, that is no problem either because the Argonaut Jr. is pulling up against the anchors with about 50 pounds of force. Even if that is reduced to 40 pounds the submarine will not sink back to the bottom. However it is important to keep the extra water in the divers trunk. If air is added to the inside of the submarine then the extra water will be pushed out making the submarine too light; and it will lift off the bottom and start on its way to the surface without the diver!
I took an old regulator apart and it looks like no problem to rig it by putting the diaphragm on the end of a pipe with a float inside. The float could extend to the bottom of the sub and would transfer the psi at the bottom of the hull to the valve which would be 18 inches higher in Argonaut's case. We could have one on each side and that would give us 60 cfm which would be more than enough. On most dives the decent speed will be controlled by how fast you crank the submarine down to the bottom where the anchors will be sitting.
The valves in the top of the ballast tanks are used to fill and release air and they are common PVC ball valves. The valves in the bottom of the tank are more complicated. For most dives they will be locked open, allowing the water to enter and leave the tanks when air is vented or forced into the tanks. But they will be closed when back on the surface. The ballast tanks are below the water line even when the Argonaut Jr. is on the surface. So having them closed allows for the air pressure in the tanks to be release without water flooding in through the bottom. This allow for the tank to leak or for work to be done through the inspection hatch with the submarine still in the water. It also lets almost all of the water to be expelled from the tank so the wood has a chance to dry out. These bottom "flood valves" must also act as check valves; automatically opening to let excess pressure inside the tank to vent safely into the water. The air system will have about 150 psi of pressure above the pressure inside the sub, so if a ballast tank was pressurized to force the water out with the bottom valve accidentally left closed, the pressure would be enough to cause the tank to explode.
Occasionally we may want to close the bottom valves during a dive. This is a dangerous procedure if not closely monitored but it has advantages. A ballast tank that is left open at the bottom is called a "soft tank". Soft tanks on submarines are commonly completely flooded with water during dives. If a portion of the tank had air remaining inside, the air would compress as the submarine descended and as the air compressed the submarine would lose some of it's displacement and sink faster. So in order to trim a submarine we want "hard tanks". A hard tank can have some air left inside in order to make easily adjust the submarine's displacement as needed. If the submarines displacement is adjusted so that it is just slightly negative then it will slowly sink deeper. And slowly changing depth is important for an ambient submarine because time is needed for additional air to flow into the cabin and for the passengers to equalize their ears to the change in pressure. With the valves in the bottom of the ballast tanks, the Argonaut Jr. will be able to add air as needed to the tanks in order to adjust the submarines displacement and then close the bottom flood valves so the pressure inside the ballast tank and the volume of air tapped does not change as the submarine descends. The danger is that the pressure of the air inside the submarine and the water outside the submarine will become too much for the tank and the tank will implode. To avoid this, only the two smaller ballast tanks on either side of the divers trunk should be used as hard tanks and the submarine should not descend more than 20 feet after closing the flood valves.
Slow descents can easily be done in the Argonaut Jr. without
using the hard tanks. To do some the boat is simply trimmed so
that it still has 50 to 100 pounds of negative buoyancy when the
ballast tanks are completely flooded. To trim the boat in this
manner it will be necessary to add up the weight of the passengers
and add or remove some of the lead weight ballast as needed.
To submerge the submarine the fist step is to lower the two anchors
until they are sitting on the bottom. That will make the boat
200 pound lighter. Then flood all of the ballast tanks.
The boat would now normally be 50 to 100 pounds heavier than it's
displacement and begin to sink, however it will remain on the
surface with just a little of the conning tower out of the water.
The reason is that anchors that weigh over 200 pounds are on the
bottom an not weighing down the boat. Now you only need to
turn the cranks to pull in the anchor rode, that's "rope" to you
land lubbers. Because the anchors are 200 pounds and the
submarine has less than 100 pounds of positive buoyancy; the anchors
will stay on the bottom and the submarine will descend only as fast
as you wind in the line.
We have started on the ballast tanks. Lots of clamps and even more very sticky epoxy and a friend to help is all it takes. The next night Kay and I completed setting in the rest of the ballast tank partitions.
The numbers below are estimates and the actual numbers have turned out better, as hoped, because we tried to be concretive in our estimates. For example we calculated the weight of the hull without accounting for the 60 gallons of epoxy we used to make it waterproof. And we built the steel structure of the drop weight out of much heavier than needed steel. So our estimated 1,482 pound for the hull actually came out to 2,560 pounds. That means we need less lead ballast. And our estimated 3,102 pounds for the drop weights turned out to be 3,633 pounds or 528 pounds over the estimate. Another good thing as is reduces the amount of lead required inside the hull by 1,660 pounds, so instead of 7,353 pounds, we only need 6,803 pounds inside.
|Argonaut Jr. 2010 - Buoyancy Calculations - Version #4|
|Water Weight||0.0361||Lbs/Cubic In|
|Marine Plywood Weight||0.0187||Lbs/Cubic In|
|Lead Weight||0.3520||Lbs/Cubic In|
|Main Body Horizontal Cross Section Area||6655.00||Sq In|
|Height, Bottom to Deck||57.50||Inches|
|Main Body Volume||382662.50||Cubic In|
|Conning Tower & Divers Trunk Below Hull Bottom Vol||10656.00||Cubic In|
|Total Body Volume||393318.50||Cubic In|
|Total Body Displacement (Vol x Water Weight)||14198.80||Lbs||14198.80|
|Plywood Volume, Hull Sides (3/4")||17280.00||Cubic In|
|Plywood Volume, Everything Else (1")||29744.50||Cubic In|
|Interior Wood Beams||16149.00||Cubic In|
|Total Interior Wood Volume||63173.50||Cubic In|
|Hull Wood Weight||1182.68||Lbs||1182.68|
|Exterior Framing/Wheels Positive Displacement||246.61||Lbs||246.61|
|Axel & Steering Hardware||200.00||Lbs||200.00|
|Ballast Tank Area - Sides||522.00||Sq In|
|Ballast Tank Area - Forward & Aft Tanks||3536.00||Sq In|
|Ballast Tank Height||15.00||In|
|Ballast Tank Volume||60870.00||Cubic In|
|Scuba Tanks (6)||210.00||Lbs||210.00|
|Other Hardware and Equipment||75.00||Lbs||75.00|
|Ballast Weight (Lead)||10140.00||Lbs||10140.00|
|Drop Weight and Internal Weights|
|Lead Drop Weight Volume||8821.61||Cubic In|
|Lead Drop Weight Mass||3105.21||Lbs|
|Lead Drop Weight Mass (Less Displacement)||2786.75||Lbs|
|Lead Required Inside||7353.25||Lbs|
|Interior Lead Volume||20889.92||Cubic In|
|Lead Floor Area||1440.00||Sq In|
|Lead Height from Floor||14.51||In|
|Divers Trunk Volume||8712.00||Cubic In|
|Divers Trunk Displacement||314.50||Lbs|
|Ballast Tanks||66120.00||Cubic In|
|Conning Tower||10656.00||Sq In|
|Main Body Horizontal Cross Section Area||6655.00||Sq In|
|Main Body Freeboard (Tanks - CT / Cross Section)||8.33||In|
|Air Consumption||Cubic Inches||Cubic Feet|
|Total Interior Volume||393318.50||227.61|
|Ballast Tanks Volume||60870.00||35.23|
|Interior Lead Ballast Weight Volume||20889.92||12.09|
|Interior Framing Volume||63173.50||36.56|
|Crew and Equipment (Estimated)||20000.00||11.57|
|Interior Air Volume||228385.08||132.17|
|Expoy and Glue||7.00|
|Fixed Ballast Difference||9.91|
|Crew and Equipment||14.61|
|Total Lead to Add to Interior||28.82|
Modern regulators have a maximum flow rate of 30+ cubic feet per
minute @3000 psi
An 80 cubic foot scuba tank only holds about 77 cubic feet.
Scuba guidelines recommend 1 foot / second max depth changes.
New regulators have an inhale and exhale effort measured as between 0 and 2 column inches of water (ciw.) 2 ciw equals 0.072 psi sensitivity, which is the equivalent of 0.00491 atmospheres.