PrintableScience.com presents a Cartesian Diver featuring MakerBot’s AquaBot.
Delighting young and old alike for hundreds of years, the toy takes its name from the famous french philosopher, mathematician and scientist Renee Descartes who is credited with its invention. In addition to play potential, the Cartesian Diver provides a practical example of they physics of buoyancy and the ideal gas law.
The mechanics of a Cartesian Diver are quite simple. It is composed of two parts: The first part: a large usually transparent sealable outer container or chamber with flexible sides and filled with water, and part 2: the diver itself, which is smaller, contains an air channel or chamber and most often provides a flexible diaphragm that can be used to adjust the level of fluid in the air chamber of the diver by either expelling or sucking in water.
The design of a functional diver requires that when its inner chamber is completely full of water it will sink to the bottom of the larger container, and when the inner chamber is completely empty of water it will float to the top of the surface. Once these two extremes have been realized in the design, the toy is made functional by adjusting the static weight of the diver or the water level in the diver so that the tip of the top of the diver is floating just above the surface of the water in the larger container. This is called the state of “natural buoyancy”.
When the diver is naturally buoyant, it is placed in the outer chamber, which is then sealed, and if the container’s sides are squeezed the diver will sink to the bottom. When the sides are released, the diver will then rise from the bottom and float to its original state.
What happens in this process is that when the sides of the bottle are compressed it increases the pressure level inside the chamber, and while liquids cannot be compressed, the air in the chamber of the diver can. The consequence of compressing the air in the diver means is that water from the outer chamber is drawn up into the diver, increasing its weight until it no longer has enough buoyancy to float.
When the sides of the chamber are released, the pressure is reduced, the air in the cavity of the diver pushes out the water that was drawn in until it has shed enough water that it is light enough to return to its state of natural buoyancy.
Well enough physics. Let’s build our own Cartesian Diver.
Here’s what you’ll need to build your Cartesian Diver:
The pieces you’ve printed out on your 3d printer from the STL files which includes:
- the diver body
- the diver face plate
- the diver bottom cap
the diver plunger
you may also require
- the diver spray shield
- the diver stand
Also included are stl files for:
And for our outer container the following printed parts:
- bottle feet
- bottle helmet
- bottle rim
- bottle faceplate
You’ll require the following materials:
a bottle of Sparkling Ice Soda water - flavor is unimportant
- a rubber or latex balloon
- a variety of small nuts or washers
- a small piece of fine grit sanding paper
- gel Krazy Glue
- regular Krazy Glue
And finally the following tools:
- a large bowl
- cuticle scissors or a sharp razor blade or utility knife
We encourage you to use different colored balloons and to print the various parts of your cartesian diver out of different filaments. This will allow you to construct unique individual aquaBots if you have more than one child or one grandchild that you hope to amuse or gift with your Cartesian diver.
Our diver is a mashed up version of the Thingiverse AstroBot which we have affectionately renamed AquaBot. It was modified by hollowing it out and adding a pedestal to increase the volume of the air channel in the diver. In addition, we replaced the helmet’s visor with a hole to the air channel. This hole in turn will be covered with a piece of latex or rubber and serve as our flexible membrane for adjusting the level of water in our diver.
In its completed form, our diver is composed of 3 printed pieces. The diver body, the bottom cap and the face mask ring. The STL files supplied also provide for a small rounded plunger which we use for pushing in the rubber membrane. There’s also STL files for a diver stand and a spraying mask which are not required if your printer can print watertight objects.
While watertight is a word often used to describe a 3d object that has no unintentional gaps or holes in the STL file, we mean it literally. When you print your model, it can’t allow air out of the diver or water in… except through the hole in the bottom that was put there expressly for that purpose.
But don’t worry, if your prints are not watertight. Its a simple matter at this point to spray your diver with a sealant spray, such as the one shown here. If you only discover your diver is not watertight after you’ve finished construction you can use the printed stand and spray mask to help you apply the sealant later. the small pedestal gets the diver up off the surface so the sealer aerosol can reach underneath, and the spray mask prevent sealant getting on the balloons surface and interfering with its flexibility.
There is also an STL file for a balloon stretcher. Our goal is to have the rubber gently stretched from its resting state. We don’t want it as taut as in a completely inflated balloon though. If you find the stretcher we supplied is either too large or too small for the balloons you have it can easily be sized up or down to meet your requirements.
So let’s begin by stretching a balloon over our stretcher.
The next step is to take a little piece of fine sandpaper and use that to smooth out any rough edges on the face ring of our diver. Because that area of the diver is printed at an angle, it may not come out perfectly smooth, which is what we need in order to secure a watertight seal between the diver and the balloon rubber.
Next take some GEL Krazy glue or equivalent. Krazy Glue in GEL form provides us with just a little more bonding ability and helps eliminate any unevenness in our diver’s faceplate. Squeeze a small blob onto a flat surface. In the video we use the larger end of the ballon stretcher for this purpose… and then using the tip of the applicator, smooth out the blob until you get a light even layer of glue spread out over about a nickel sized circle on the board. Then take the diver, and lightly push it into the gel spread you’ve created. Move it around a little, but don’t push it in and hold it. We don’t want it to bond to the paddle, we just want to transfer an even coating of the glue onto the faceplate of the diver.
Having done that, press the diver’s faceplate onto the stretched balloon neck and hold it securely applying even pressure and without moving it around for about 30 seconds. This will give the glue enough time to set so that you can then remove your finger and allow the glue to cure for about another 15 minutes.
When the glue is dry, take a small pair of scissors, or razor blade to cut the diver free from the balloon. Do NOT pull the balloon off the stretcher, this will put too much strain on the rubber and it may pull free from the diver. Rather, cut away the rubber from around the diver while it is on the stretcher.
Once the diver has been cut free, then use your scissors or razor blade to trim around the outside of the faceplate until the rubber edge is flush with the faceplate’s edge. We find manicure scissors work best, or a single sided razor blade, but the key is sharpness. Even a slightly used razor blade will make getting a nice clean trim job hard to achieve.
If you have the time and resources, feel free to construct your diver out of different colored parts and or balloons. It provides you with the opportunity to craft unique individual aquaBots if you have more than one child or one granchild that you hope to amuse or gift with your Cartesian diver.
The next step is to secure the face mask ring. Press it onto the faceplate of the diver and a drop or two of REGULAR krazy glue will seep into the seam and seal it.
The next step of our construction is to determine the amount of weight we need to sink our aquabot when it is filled with water. ABS and PLA unweighted will both float on the surface of water, which is not what we want. As mentioned earlier, we want our diver, when filled with water to sink convincingly (but not as hard as a rock) when it is placed in the water. Here a little experimentation is required. Small washers, or nuts can be used and added to the diver until the desired effect is achieved. Get a large bowl and fill it with water… the best choice is a bowl that will easily let you get both your hands in.
One had to hold the model and the other to operate the plunger. Take a washer or two, pop it into the pedestal portion of the diver, snap on the base, put it in the water and see if it sinks. Its best if you perform this operation with the diver submerged, because we need to add just enough weight to sink the aquabot when it is completely full of water. Use the plunger you printed, and holding the diver upside down, so the hole at the bottom is facing upward while it is under water, pump out any remaining air.
Adjust the weight up or down and repeat the process until the diver, completely filled with water, sinks to the bottom of the bowl.
Now that you’ve determined the correct amount of weight, its time to glue the weights to the base plate of the diver. Remove your aquabot from the water, snap off the cap, remove the weight and dry your diver, weights and bottom cap fully.
You may have noticed during your buoyancy testing that your aquabot was tilted as it sank. So in gluing the weights to your baseplate, glue them slightly off-center. this will allow you to compensate for the tilt by rotating the base cap to achieve a level ascent and descent of your model before you seal on the bottom cap. Using krazy glue in moderation, glue on your weights so that they do not obscure the hole, and that they do not get in the way of the rim that is needed for gluing the baseplate to the diver body.
Once the weights have been glued in place and the glue has dried, return your diver to water, pump out all the air and observe your diver as it sinks. if it is tilted, give a slight turn to the bottom plate. Because you glued the weights slightly off center, you will be able to adjust the angle of your diver in the water by turning the base plate until the aquabot sinks and rises perfectly perpendicular.
Your Cartesian Diver is now complete.
The outer chamber used for our project is a Sparkling Ice 750 ml soda bottle. It was chosen for its compact size, and relatively inexpensive price. You can buy a bottle of it for about a dollar at your local grocery store. If you can actually drink the stuff, then its even more practical. You can use any size soda bottle you like, as long as it has a standard sized cap. Our diver is printed so that it will slip neatly into a standard size soda bottle opening. You could of course use a bottle with a larger opening as well. The main requirement is that it is sealable and that the sides are flexible. From an aesthetic perspective, you might want to avoid bottles that have designs or lettering embossed in the sides that obscure the view of the diver in the chamber. However if you wish to use the fancy bottle helmet and feet we’ve provided, it will need to be a Sparkling Soda bottle.
The next step is preparation of your water chamber. If you are using the Sparking Ice soda container as we did, then you’ll first need to remove the label. Remove it from the bottle, but take a little care… try not to squeeze the bottle too much or it will leave permanent crinkle marks. We used the small scissors to cut a little piece away which allowed us to remove the balance of the label easily.
The glue left on the bottle is soluble in Naptha… which you can pick up at any home improvement store. We just put a little on a folded up paper towel and the glue dissolved quite quickly. A second clean paper towel allowed us to remove any of the naptha and glue residue and we were left with beautifully clear bottle. As you clean your bottle notice that there are two very fine seams on opposite sides of the bottle. Take note of how they are positioned, as we’ll be using them for alignment purposes later.
First of all lets assemble the faceplate. Take the face collar, place a few dabs of glue on the inside lip and then press the logo plate face outward into the collar. The up and down orientation of the plate is not important at this time.
Once you have glued the logo plate into position and the glue has had an opportunity to dry, apply glue to the outer edge of the Helmets mask, and then, taking the collar with the inset logo plate, press it onto the diver, so that the M is in the proper orientation and hold the face collar into position until the glue dries.
Now its time to glue the head onto the bottle. First of all, screw the bottle cap that came with the soda onto the bottle nice and tightly… as tightly as you would if you were putting a cap back on a bottle of soda that you wanted to not loose its fizz. Then, do a test fit. Take the helmet and press it firmly onto the top of the bottle. You want to make sure that the bottle cap is inserted fully in the hole in the helmet, and you want to be able to do that so that the ears of the helmet line up with the seams on the side of the bottle. Aligning with the seams is not something you want to do after you’ve got the helmet in position as that may result in loosening, or over tighenting the the bottle cap that you’ve already put on with the right force.
If that all looks good, remove the helmet by from the cap by pulling and rocking it back and forth but not twisting it. Once removed, apply a liberal amount to the top edge of the bottle cap on the bottle, and slightly down its sides. Don’t over apply glue to the sides of the bottle cap or you run the risk of it bleeding down and cementing the cap to the bottle. We want it to adhere to the helmet only.
With the glue applied, push the helmet down onto the bottle cap, lined up with the seams on the side of the bottle. Make sure that the helmet is pushed as far as it can be. Having accomplished that, don’t rush the setting of the glue. An hour’s patience for a gelled krazy glue is not unreasonable for a lasting strong bond.
Once the glue has dried, you should be able to untwist the helmet and remove it easily. If you used the right amoutn of glue and gave it enough time to set properly, the bottle cap that is now glued to the helmet will be removed too.
Now take the soda bottle, and apply a generous drop of glue to the top surface of each of the legs of the bottle. Once that’s been accomplished, push the bottle into the foot base, making sure the bottle seam is aligned with the middle of the side of the feet.
You are now ready for final construction of your Cartesian Diver.
fill the bottle with water, up to about 1/3 of an inch below the neck of the bottom of the cap stem and set it aside.
Take your diver and submerging it in the water bowl use the plunger you printed to empty the air. At this point, you’re going to be setting the diver to its state of natural buoyancy. If you recall, natural buoyancy is achieved when just a small tip of of the AquaBots head is floating above water. So using trial and error adjust the floating level of the diver until the required effect is achieved.
To pump in more water, hold the diver upside down under the water level and use the pump to pump out air. To expel water, hold the diver out of the water right side up and use the pump to pump water out of the diver.
Once you have set the diver to its natural buoyancy, drop it into your water chamber and twist on the helmet cap snugly and securely.
Your cartesian diver is complete.
Simply adding pressure to the sides of the bottle with your fingers and thumb should sending your aquabot diving to the bottom of the container. Conversely, once at the bottom of your chamber, releasing the pressure on the sides of the container will result in your diver floating once again to the surface.