New Paper Airplane Distance Record

The Process

According to the Boeing press release², the team studied aerodynamics and origami techniques and spent over 400 hours perfecting their design. Over the 6 month project they created more than 20 different prototypes and folded hundreds of airplanes in their attempt to fly higher and further. Interestingly, the team used computer simulations to discover that the optimal angle to throw their airplane was at 40 degrees. We were curious about their prototyping process and simulation software that they used.

Fold'NFly: Please tell us about your process for refining your winning design. When you were testing a prototype, what sort of data did you collect and how did you decide what changes to make for the next iteration?

Garrett: Full-scale and paper airplanes have vast differences in their complexity, but both operate on the same fundamental principles. Some of the same design methodologies can be applied to both. One of these methods was our trial-and-error design process, both on throwing technique and aircraft design. For instance, we would theorize about an aspect of our plane we want to modify, fold it, throw it, and compare the distance to previous iterations to determine if the change was beneficial. While our database of flight data was not as developed as Boeing – St. Louis’, this testing method highlights the importance of rigorous experimenting in the real world.

Fold'NFly: You ran computer simulations to help improve your design. Can you please share some information about how you ran these simulations?

Garrett: The simulations were simple in comparison to what some people expect. For our purposes, we created a two-dimensional trajectory of our plane. This means the plane was able to go up/down and forward/backward. The "software" was Python code which is an open-source programming language. We decided to use Python since it's one of the languages of choice for our college classes.

The code that we developed is based around an Ordinary Differential Equation(ODE) solver. This may sound complicated, but it's just a way we solved the summation of forces in the forward/back and up/down directions for our plane. These forces give us accelerations on the plane, which gives us the change in velocity, which then allows us to solve for our horizontal and vertical distances that the plane has traveled. Using these distances, we can plot its flight path.

The main use of this code for us was two-fold (Ha). The first use was to find the maximum height of the airplane to pick an appropriate indoor space. Once we have the simulated flight of our plane, we can pick the tallest point on our flight path to find this. The caveat to this is that our coefficient of lift and drag are estimated using values obtained in testing. The second use was to find the best launch angle to throw the plane. We found this by simulating a variety of different throwing angles to choose the optimal one.

Fold'NFly: Did you start with a paper design and then create a digital twin for the simulations, or did you start with a digital 3D model and then reverse engineer how to fold it?

Garrett: We created a 3D model that was similar in nature to the final design, but not an exact replica. Additionally, we eventually 3D-printed this for personal display. The folding pattern was developed as we determined what features were most aerodynamically important in the design.

However, we never made a digital twin of our plane for testing purposes. The reason we could simulate the plane at all was because we already knew the fundamental forces of lift and drag acting on it. This is greatly beneficial because if we had the digital twin of our aircraft up to date with all the design changes, we would likely need to quit our full-time jobs. Not to mention the act of creating an accurate model induces errors which are separate from simulation errors. The moral of the story is that modeling the geometry of our plane would be very difficult and even more so to get an accurate model.

Fold'NFly: Can you share any more details about your simulation software?

Garrett: Here's some images of our code and subsequent output. The angle vs distance plot and optimizer graph is one of our key outputs.

Garrett: The optimizer plot [top left] is just for bug checking and seeing if the algorithm converged to a stable solution. It basically uses a slightly modified version of Secant Method. The angle vs distance plot [bottom left] is where we take the optimized CdA value and vary the release angle to find the best throwing angle. The useful data here is not only the best release angle, but also that the distance doesn't fall off too fast. This means the thrower doesn't have to be spot on to get close to the maximum distance.

The velocity vs optimal angle plot [right] plot was a case where we found information which is interesting, but not very practical for the thrower. It basically says the faster you throw, the lower angle you should throw to maximize distance. This is because as you go faster you will have exponentially more drag which "steals" away your velocity. To fight this, you need to throw lower to use what velocity you have to gain horizontal distance before it disappears from drag. Like I said before this is interesting but not very practical because for our velocity range the best angle only changes by 0.8-1 degree. This is too small to hit accurately for a thrower, and as we can see from the previous angle vs distance plot, small changes in angle from optimal don't affect distance too much. The reason I included this plot is because not every discovery needs to be a breakthrough. Sometimes you find information and relationships which don't seem useful but help you to understand the problem you're trying to solve.