Christopher LuMs. GreenMath 10-2January 20th, 2018Nanobot Math investigationDimensions of my Nanobot Nanobots are the future of medical innovation. My goal is to design a Nanomachine that can deliver antibodies to cells. But what is a nanotechnology? Nanotechnology refers to technology that is measured in nanometers. A single nanometer is 110-7centimeters which is 10 million times smaller than a centimeter. Nanobots range from 1 nanometer to 100 nanometers diameter. The nanobot has to fit in a capillary because it is the smallest vessel found in the human body.

The size of a capillary ranges from 8-10 micrometers in diameter which translates to 6000 to 10000 nanometers. Since the capillary can only carry a single red blood cell at a time, the nanobot must fit between two red blood cells. The size of a red blood cell ranges from 6.2 – 8.2 micrometers in diameter. Since a blood cell with 8.2 micrometers in diameter would not be able to fit in a capillary that is 8 micrometers in diameter, we will not use capillaries that have a diameter of 8 micrometers but rather capillaries that are > 8.2 micrometers.

Since my nanobot will be 50 nanometers in diameter which translates to 0.05 micrometers, my nanobot can fit through capillaries that are >8.205 micrometers in diameter.Calculation for next (43233) =50965.01042(calculation 1)(5.096501041910-17)(2.

490810-19)=204.61298(calculation 2) My nanobot also needs to bring antibodies with it into the bloodstream to carry to cells. If my nanobot is hollow with a 1 nanometer thick shell.

My nanobot would be able to hold 50965.01042(refer to calculation 1) cubic nanometers of antibodies. However we have to switch cubic nanometers to volume and 50965.01042 cubic nanometers translates to 5.096501041910-17grams water. The mass of a single antibody is 150 kilodaltons which translates to 2.490810-19grams. My nanobot can hold 204.

61298 (refer to calculation 2) or 204 antibodies because there cannot be a fraction of an antibody.Calculation for next Paragraph(6.752103 )-(3223)=458.27982834241(calculation 1)0.

75210=17.67(calculation 2)My nanobot would need to release the antibodies at a point, so I created a cone where the antibodies could be released. The cone will have a 1.5 nanometer wide tube that connected the cone to the main body, The cone will be 12 nanometers long but 2 nanometers are shaved off from the top making the cone look like a volcano. The cone will also be hollow to make it as lightweight as possible and also allows more storage.

The shell of the cone will be 0.5 nanometer thick all the way down to the bottom of the cone. The base of the cone will be 15 nanometers wide and the peak of the cone will be 7 nanometers wide. The volume of empty space that the cone has is 458.27982834241(refer to calculation 1) cubic nanometers. I got the answer by subtracting 1.5 nanometers (the diameter of the tube) from both the base of the big cone and the smaller cone on the top, then I discovered the volume of both the small cone and the big cone.

The volume of the small cone is then subtracted from the volume of the big cone. To calculate the volume of the tube, 17.67cubic nanometers.

Calculation for Next Paragraph22 342 =24(Calculation 1)422=16(Calculation 2)4(24)+(22)=40(Calculation 3)221.2522 =9.8174770424681(Calculation 4)22.

511=5(Calculation 5)8(2.51)+2(11)=22 (Calculation 6)I added fins on my nanobot to guide it through the bloodstream, in the front and the sides. The fins on the top resembles the tip of an arrow, these fins are very thin to the point that it almost looks 2D.

The triangular fins have a base of 3 nanometers and a height of 4 nanometers, the poled that they are suspended to has a width of 2 nanometers a height of 4 nanometers and a length of 2 nanometer. The surface area of the fins is 24 nanometers squared (refer to calculation 1), the formula for the area of a triangle is BH2I multiplied it by 2 twice because once for the 2 fins and another time for the area of the backside of the fin. The volume of the pole holding the fins is 16 cubic nanometers (refer to calculation 2), and the surface area of the pole is 40 nanometers (refer to calculation 3) because one side of the pole is not visible.

The sides are similar in the way that the fins are paper thin, however this time the fins are made in the shape of a semicircle. The semicircle has a radius of 1.25 nanometers. The pole has a length of 2.5 nanometers, a width of 1 nanometer, and a height of 1 nanometer. The surface area of the semicircle is 9.

8174770424681nanometers squared (refer to calculation 4), the same calculations used on the triangular fins but this time find the area of a semicircle r22. This time there are 2 poles, 1 on each side. The volume of both poles combined is 5 cubic nanometers (refer to calculation 5). The surface area of the 2 poles on the side is 22 nanometers squared (refer to calculation 6).

My nanobot is going to be propelled by the fins on the side to deliver it to the target location. There will be a switch that will activate the the nanobot, releasing it’s load. There will also be a tracking device that will track where it is going so the load can be released at the right time. On activation, the nanobot will also need to self destruct, hence why it will be made from decomposable material. The material will be harmless in the bloodstream due to its size and the decomposable material that it is made out of. The nanobots will be injected into the bloodstream.

Why nanobots? Nanobots will be able to enter places that needles cannot touch and can also be used to cure specific cells. This is crucial in the cure for cancer and other diseases, for now mine is only to deliver the load to a specific location. Degree of Accuracy My nanobot may not be the most efficient in what it does but it is my design in what I believe is the most efficient way of carrying antibodies. However there are a few things that are not accurate, the actual area of the cone cannot be calculated because the sides connecting onto the sphere is very hard to measure because it is not in a shape that can be easily measurable. The volume of antibodies may not be accurate because there were many results and I used the result that seemed the most probable. There were also different results on the size of capillaries and the size of blood cells.

My nanomachine is also not natural so it may be targeted by white blood cells, and the production and price of materials is not determined. I could not determine how much antibody that a body needs so I made my model carry as much as possible, it may be too much or it may be too little. I also don’t know if the flaps and the arrowhead will help guide it to the directed location. In order to have a switch on the outside that controls the nanobot, the nanobot would need to have a switch inside it as well, which could take up more space or there isn’t switch that can be that small.