I have an engineering project to do this semester. I'm not going to get into the specifics, but I (and my group) are going to be building a submersible servo-driven vehicle (it is basically driving underwater). The vehicle will be made of 4" PVC piping (thin-walled sewer variant). It must be able to carry an orange as cargo (don't ask why). Here is a poorly drawn MS Paint top-down view of the proposed design. The T-shaped section is the part made of PVC. The bottom of the T is a screw-cap to allow access to the internal computer and allow the orange to be placed inside, as well as extra ballast. The two "wings" of the T (that have the small flat rectangles on the ends) are permanent flat caps with waterproof servos built in. The small flat rectangles are supposed to be the wheels. The large rectangle on the front is a sort of hydrofoil (it really is just going to be a bent piece of sheet metal duct-taped to the front). The direction of motion is denoted by the arrow.(adsbygoogle = window.adsbygoogle || []).push({});

The task at hand is to determine what wheel radius will provide the highest top speed for the vehicle. Two servos are in operation, providing 80 oz-in of torque each, with a transit time advertised as 0.23 sec/60* (or 0.72 revolutions every second). I decided to simulate the vehicle's motion in Excel to accomplish this, so I could easily manipulate all the different variables involved, and to be able to see exactly how long it will take the vehicle to go a certain distance (acceleration factored in).

The key to this is solving for the acceleration as a function of velocity, since acceleration is affected by drag which is a function of velocity. My mathematical procedure is here, and the variable reference is here (I understand that some of these terms are incorrectly defined, but I did this for the sake of ease of explanation to some of my group members who have less experience in physics. They are technically correct for this application). Apologies in advance, all units are imperial (feet, pounds, slugs) - it was more convenient to do it this way since the servo specs were in imperial units. I started with the amount of ballast I would need to load onto the vehicle, both to counteract buoyancy and to maintain traction with the ground. From there you just calculate the mass of the vehicle and then you can solve for acceleration. If someone could double-check to make sure I did this correctly, I would greatly appreciate it.

In addition, I would like to have a ballpark estimate for the drag coefficient. In my Excel spreadsheet, I'm assuming 0.8 which sounds reasonable to me, but I really do not know for sure. The sheet metal hydrofoil on the front is bent at around 30 degrees.

Other than that, in my Excel spreadsheet, I used 0.6 for the coefficient of static friction (rubber wheels on a wet concrete floor), a 0.161 ft^3 vehicle volume (for buoyancy calculation), and a reference area of 0.391 ft^2 (for drag calculation). With these parameters, I am getting that the ideal wheel radius is approximately 6 inches, with a top speed of ~2.35 ft/sec.

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# Calculating ideal wheel radius for submersible vehicle

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