Nondimensional numbers and Similarity [Aerodynamics #4] 

Glad you enjoyed it! Good luck with your Masters program and I hope you find some interesting intersections of electrical engineering and aerodynamics.

Thanks for your patience! Just getting to comments after a short stint away. This is a good question. In these cases, there are multiple velocity scales (tip speed vs forward speed) and it is very hard to preserve all the non-dimensional numbers when scaling down. If you scale down in size, usually you need to increase velocity to compensate. This means, needing much higher rotation angular velocities of the turbine (to preserve tip speed ratio), which introduces all different sorts of problems. Definitely a challenge! Tip velocity is just a lateral velocity component, there is still usually a forward velocity. Typically, you choose based on which one is dominant.

Thank you!! I'm glad you like them

Thanks!! Glad you enjoyed them

My pleasure! I looked through the video again because I wanted to be sure, I am not sure where Cp (which is sometimes pressure coefficient) pops up, but I suspect you mean Cl instead, as in the lift coefficient? If so, I should say first that Cl does not *perfectly* stay the same at different scales. Other concepts like turbulence and Reynolds number come into play here. However, for the most part, it is sufficiently equal across a wide range of different scales. This is because take into account all the variables that impact lift when we scale the problem. A bigger airfoil would produce bigger force at the same air speed, but lift coefficient takes that into account by scaling with the area. Does this help at all? Otherwise, I think the text by Anderson might be helpful here. Otherwise, my video in fluid mechanics on non-dimensional numbers more completely goes over these concepts in a way that is not restricted to aerodynamics.

Awesome! I'm glad you like it

Thanks! Yep, I think you make a great point that the meaningful reference dimension (in this case length) is problem-dependent and often there are multiple to choose from. In this case, you could make the argument that the step distance is directly correlated to body length, so it would effectively be the same. Either way, there is a lot of wiggle room in choosing reference lengths.

@@prof.vanburen sure! this is just my rigorous nature :)). A human being can crawl too :p

You're welcome!

Confusingly, it's just a matter of convention. Often, constants are dropped when doing estimation analysis and the constant was dropped in Fluid Mechanics. However, in Aerodynamics the dynamic pressure (1/2 rho * u^2) is everywhere because it shows up predominantly in the Bernoulli equation, which is super important, so all the aerodynamic force/moment constants tend to be normalized by the 1/2 rho*u^2*L^2. There are different ways to derive the inertia force scaling and Aerodynamics and Fluid Mechanics approach it from a different perspective. Note that, even in Aerodynamics, Reynolds Number is defined with the 1/2 dropped.

The Wright Brothers were the first to controlled powered flight (this is a somewhat debated claim). Regardless of validity of being first, their name has become attached to the field of aerodynamics in the same way that Tesla and Edison are attached to electricity.