Engineering Analysis: Drag Approximation Spring 2014 Innovative System Project for the Increased Recruitment of Emerging STEM Students
Outline • Drag equations • Variables explained • Density • Terminal velocity • Calculating time or distance
Drag Equations Drag Force Weight
Variables Explained Values for CD: What is Planform Area (S)? Planform area is the area (typically in square meters) that the flow (the atmosphere) “sees” as your object moves. So, if your probe is a sphere, then the planform area is a circle of the same radius of the sphere. If your probe is a torpedo shape, the planform area is still a circle, but the circle has a radius that is the largest radius of the torpedo. You can usually think of planform area as a cross-sectional area. (image from Wikipedia)
You’re My Density Venus Atmosphere Use the ideal gas law, and remember that density is mass divided by Volume. Assume pure carbon dioxide. BE CAREFUL – the units need to match up! (image and table from Wikipedia)
Terminal Velocity Terminal Velocity is when the force due to drag equals the force from weight. Therefore, the object no longer accelerates – it falls at a constant (“terminal”) velocity. Drag Force This is the terminal velocity for your probe Weight
Now that you have velocity Now you have solved for velocity, v. Note that since the velocity is constant, there is no acceleration, so we can use the following equation to find time (or distance if we already know the time): So, if you assume that your probe falls a certain distance, d, you can easily solve for the time of that fall.