Stop viewing the Science Olympiad Helicopter event as just a “build.” Instead, recognize it for what it truly is: a fascinating optimization problem.

The Problem of Maximizing Duration

See a graph below for a generalized and simplified optimization problem:

In this graph, the function f(x) represents the goal, which we want to maximize. There is only variable, x, in this graph. In this highly simplified and non-realistic case, the function’s value (i.e. duration) only depends on one variable, x, (i.e. P/D.) In this scenario, there is only a single knob to turn: the propeller’s Pitch-to-Diameter ratio, P/D (Variable X). The output is the maximum Flight Duration, f(x). As shown on the graph, when P/D is at 1.4, the flight duration is the longest.

In reality, the problem is far more complex. We know the above curve would change if, say, the airplane’s trimmed flight speed is different. In addition to speed, there are many factors that would change the above curve. E.g. build-quality (q), pitch (p), washout (w), camber (c), rubber band length (l), rubber band density/weight, launch torque, etc. etc., all would affect the final duration (D). The function for our flight event can be written as D(q, p, w, c, l, …). Our flight event is a true multi-variable optimization problem. We are trying to find the perfect combination of every single factor to maximize D, duration.

The Foundation Principle: Dominating Factors

You might be asking: How do we approach this complex problem and find the perfect combination of all factors?

The secret is recognizing that not all variables affect the final duration equally or at the same stage. Some are far more influential than others. For example, as the simplified graph below illustrates, if the build quality is poor, no amount of precise pitch adjustment will significantly improve the duration. (Look at the cross-section of the graph on the right side, near the ‘bad’ extreme). Besides, the best duration we may achieve with a flawed build won’t be better than a well-built helicopter would have. (Look at the left side of the graph.) Simply put, we can’t trim our way out of a bad build!

The Staged Optimization Roadmap

As outlined in the “Helicopter Journey Roadmap” that I posted at Thingiverse.com, we must focus on identifying and working on the few dominating factors in three distinct stages:

• Stage 1: Master the Build. Focus on fixing the Build Quality variable to ensure a solid foundation.
• Stage 2: Perfect the Flying. Optimize flying techniques by mastering variables like rubber band length, weight, and launch torque, etc.
• Stage 3 and beyond: Master the Design. Fine-tune aerodynamic variables such as pitch, washout, and many other design factors.

The Importance of a Solid Foundation

This systematic approach is essential. At the 2023 SoCal Flight Workshop, several students brought their airplanes and ask me to trim. Instead of rudely pointing out the root problem (inferior kit and/or bad build quality), all I can say was: let’s trim our workshop (well-built, well-prepared) airplanes…, which did not need much trimming at all. 

Watch several high-flying Workshop airplanes at YouTube:

The point is, we have to ensure a solid foundation (excellent build quality) before tackling flying techniques like rubber band length, density/weight, and stretching, etc. Only after those foundations are solid, we can fine tune the airplane or helicopter design to win. This staged, systematic approach is the only way to conquer the complexity of this multi-variable optimization problem and reach the top of the leader board! Changing something that is not dominating, even if it is very critical for the final win, may be futile.

One final note. A multi-variable function’s solution space would need many graphs like this to represent. In fact, it is next to impossible to present in graphs. I will stop at this two-variable graph. Hope you got the idea. Feel free to contact me if you have any questions. I’d be glad to discuss how to navigate this complex multi-variable optimization space in more detail.

Cheers!

-AeroMartin 9/21/2025