Optimal Geometry for Flapping-Wing Flight

The Project

The purpose of this project is to find the optimal wing geometry for flapping-wing flight given the mass of the object that is intended to be lifted. Fixed wings are great for large aircrafts, but for smaller objects such as robots or individual humans, fixed wings can consume much more power than flapping wings (Gold, 2009). This project will calculate the power that is required to lift an array of different masses a constant height off of the ground for each different wing structure. I will create an array of wing structures to test against this model. These base wing structures will be tested with many variations in their dimensions for each mass and the data will be output into graphs so the untested measurements can be interpolated and the optimal wing geometry can be found.

The Solution

There are four main stages of insect and bird flight: downstroke, upstroke, pronation and supination. The pronation and supination are necessary so that the wing has less surface area on the upstroke than it does on the downstroke (Chin & Lentink, 2016). I have hypothesized that there may be a more efficient way of lessening surface area on the upstroke: folding the wing in half lengthwise on the upstroke and unfolding it on the downstroke. I plan to create a few “parent” structures such as the folding structure described, the pronating and supinating structure for birds, the propellor structure for helicopters, and any others as I come up with them. I will then increment measurements within the parent structures and test an array of masses against the model in order to determine how much power. The language I will be using depends on what I find this project to need as I research wing structures and fluid dynamics further. I may use Octave (basically a free version of Matlab) if I want to have a large array of numbers on which I want to apply the same operations, or I may want to use a more model-based program such as NetLogo if I find that I need more randomization and multiple simulations.

Progress

I have mostly been working on researching the different techniques living organisms use and all the force calculations that would be required. I have found many of the solutions to the needed calculations to be in the equations of fluid dynamics. I have also started deciding what I will not be accounting for such as the air density change caused by a flapping motion, since it is negligible at speeds under about 100 meters per second (Compressibility and Incompressibility, n.d.). I have also started working on the algorithm of the program, although I do want to wait until I have as much data as possible before I start the actual programming.

Predictions

I expect that this model will be able to find a structure that requires at most 50 Watts per kilogram since birds have been shown to require somewhere in the range of 40 to 120 Watts per kilogram (Knight, 2010). Currently, I am also predicting that the folded wing model I described above will be the optimal structure, but as I research further, I will likely find more advantageous structures.

Works Cited

Chin, D. D., & Lentink, D. (2016). Flapping wing aerodynamics. Journal of Experimental Biology. Retrieved from http://jeb.biologists.org/content/219/7/920

Compressibility and Incompressibility. (n.d.). Centennial of Flight. Retrieved from https://www.centennialofflight.net/essay/Dictionary/Compressibility/DI136.htm

Hartnett, K. (2018). What Makes the Hardest Equations in Physics So Difficult? Quanta Magazine. Retrieved from https://www.quantamagazine.org/what-makes-the-hardest-equations-in-physics-so-difficult-20180116/

Gold, L. (2009). To flap, or not to flap? Cornell Chronicle. Retrieved from http://news.cornell.edu/stories/2009/09/birds-fly-more-efficiently-airplanes-study-shows

Knight, K. (2010). How Birds Power Flight. Journal of Experimental Biology. Retrieved from http://jeb.biologists.org/content/213/16/i

Lehmann, F. O., & Pick, S. (2007). The aerodynamic benefit of wing–wing interaction. Journal of Experimental Biology. Retrieved from http://jeb.biologists.org/content/210/8/1362

Tobalske, B. W. (2007). Biomechanics of bird flight. Journal of Experimental Biology. Retrieved from http://jeb.biologists.org/content/210/18/3135