Using Blade Element Momentum Theory
A critical step in the beginning of this Senior design project was to decide what scale model we were going to build the large scale prototype to. Once we determined the size of the structure of the aircraft, we needed to figure out what size props (propellers) we would need in order to achieve enough thrust to lift the aircraft off the ground in a vertical take off (VTOL). The way we determine what size props we would need used the Blade Element Momentum Theory (BEMT). The theory behind this is quite involved, but basically the principles involve equivalence between the circulation and momentum theories of lift [Leishman, 2006]. So, what does this mean?
A basic explanation of how we applied this will start with the image below.
The image shows a top view, side view and isometric (3-Dimensional) view of a prop. The top view of the prop shows that the velocity at a small section is equal to omega (the angular velocity) times r (the radius). If you look at the cross-section of this prop, you will see what is shown in the side view of the image. Applying some basic aerodynamic principles to the airfoil, we integrated the lift across the length of the prop. Using this (lift = thrust), we were able to write a code that would show a graph of the thrust as a function of the radius of the prop. If we knew the speed we were traveling at, along with the thrust required to lift the aircraft off the ground, we could choose the size of the prop we needed. For more details, please go to the link below and check out the code we used! There are plenty of comments in the code that explain what we did along the way.
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