A couple weeks ago I wrote about how airfoil-less paper airplanes are able to fly, and answered a few of my own follow-on questions. A bit after that I received a request from another wonderful reader, this time asking about rubber band powered airplanes—in particular, how the rubber band engine contributes to the flight, and how the aerodynamic design factors are balanced.
I knew even less about rubber band powered airplanes than I did paper airplanes, so I was more than game to tackle this topic.
To answer this question, I specifically looked into the airplanes flown as part of F1 Free Flight competitions. Turns out there are two different types of competitions, with two types of model: indoor models and outdoor models.
The only scoring criteria is how long an airplane is able to stay in the air, with the two types of model accomplishing this in different ways. This is an even more specific “mission” than I’m used to—endurance matters for most UAVs, but actually going somewhere does too. Not so with these Free Flight models, and in fact some of them effectively just float in space to achieve their goal of maximizing flight time.
Let’s dig into how they do this.
A quite literal rubber engine
One of the first things I realized was that I entirely misunderstood how a rubber band engine actually works. I had assumed the band was wound around a central shaft and pulled the propeller as it unwound, like how a yo-yo spins.
I was pretty wrong. The rubber band isn’t wrapped like a spool of thread; instead, it’s twisted like a length of rope. One end is fastened at the tail of the airplane, and the band is twisted on itself until it can’t twist any more. This explains why the models have such long, skinny fuselages: the longer that central “spine”, the more rubber band you can fit.
So how do you spin a propeller with a rubber band? Just like with a typical internal combustion engine, you turn stored energy into kinetic energy. But instead of burning fuel, you take advantage of the rubber band’s elastic properties.
This uses the same physics as springs: the force required to either compress or extend a spring is proportional to the compressed or extended distance, multiplied by the spring constant, which is different for every material. A stiffer material has a larger spring constant and requires more force to displace, while a more flexible material has a smaller constant. And per Newton’s third law, the compressed or extended spring will rebound with the same amount of force once released.
The behavior of springs applies to many elastic materials, like rubber bands. So by twisting the band on itself, we’re adding a displacement from its “natural” state. And when the resistance holding the twists in place is released, it will unwind and apply the torque that was required to twist it in the first place, which spins the propeller.
A fun detail I found is that some model makers have a preferred “vintage” of rubber. Rubber bands manufactured at different times will have slightly different spring constants, and since the spring constant impacts how quickly the rubber band untwists in flight, competitors will seek out bands from their ideal rubber batch. Supposedly May of 1999 produced prime rubber bands.
Propellers for both indoor and outdoor models
I questioned how the rubber band powered models for indoor and outdoor competitions could be so different. But once I considered the conditions each flies in, it all made more sense.
Indoor models look incredibly delicate as they glide through the air like gently-falling snowflakes. Since they’re flown in large spaces, the most intense wind gust they’ll ever experience is probably someone opening a door—they can afford to be optimized for lightness.
On top of this, the indoor models’ propellers spin incredibly slow, on the order of a single rotation per second. I have a few thoughts about why that is:
- The lightweight models only need to generate a tiny amount of lift; for reference, the minimum weight for these models is from 2 to 5 grams. If you have a large wing area, you only need a little forward airspeed to generate enough lift, thus your propeller can generate the bare minimum of thrust.
- In videos, the propeller blades are proportionally pretty large and seem to have a high pitch (their angle with oncoming air). That means each rotation takes a bigger “bite” to move forward, resulting in fewer rotations needed overall. The larger blades may also encounter more resistance as they move through the air, which might slow the rubber band’s rate of untwisting.
- And finally, with such a small forward airspeed and blade width, Reynolds number effects might play a role. Airflow behavior substantially changes at very low Reynolds numbers—at this size and speed, the propellers are probably paddling through the air more than anything.
Remember, the sole purpose of these flights is to stay in the air as long as possible. Everything here is optimized to have the rubber band untwist as slowly as it can. And amazingly, that makes flights of up to 40 minutes possible.
The outdoor rubber band models have a very different strategy. In these competitions, the airplanes climb as high as possible; when the rubber band’s twists are exhausted, the aircraft turns into a glider.
These propellers are likely designed to generate as much thrust as they can for each rotation. They still have high pitch, but also narrower blades than the paddles of indoor models. These models are much larger too, able to navigate wind gusts while also accommodating more rubber band twists.
What’s interesting is this model ends up using two different energy changes in its flight. It exchanges the potential energy stored in the twisted rubber band for the kinetic energy of the propeller spinning. But it also exchanges the potential energy of altitude for the kinetic energy of airspeed.
Set it, and forget it!
The goal of flying for as long as possible is enough of a challenge, but these model airplanes add another layer: they fly entirely independently, with no autopilot or other control system on board.
Instead, the model makers “pre-program” their flight path with analog methods. The larger, more robust outdoor models have actuated control surfaces on timers. At certain intervals, the surfaces will be moved to pre-determined deflections, making the aircraft turn automatically and stay within the competition area.
I can imagine this requires plenty of analysis and testing. You can estimate how much deflection is needed for a certain bank angle, and extend that to how long you need to fly in the bank to complete a turn. But you also need to test and make sure your settings work as you expect, and you probably need to be judicious with your test cases so your airplane doesn’t get too beat up.
The outdoor models also have to transition from essentially a rocket to a glider. This requires dialed-in positive static stability, so the aircraft can level out when it reaches the right airspeed in a dive. This stability will also allow it to handle wind gusts while aloft: if the nose is pushed up, the aircraft slows, which drops the nose and speeds it back up.
Indoor rubber band powered models have a much more serene experience: all they need to worry about is not running into a wall. Once they have the correct wing and tail sizing to maintain stable flight, a slight asymmetry in the wings and tail will encourage them to fly in a gentle circle for the duration.
While it’s probably pretty minimal, they also need to counteract the torque generated by the spinning propeller, which will generate an equal and opposite rolling tendency. A crafty model maker could use this to their advantage when tweaking their aircraft.
What I find truly interesting is how, despite having the exact same goal of maximum flight time, the indoor and outdoor models are designed very differently due to their operation.
With a less challenging environment, the indoor models go the hyper-optimized route and reduce weight as much as possible to make the rubber band untwist as slowly as possible. Flying in variable winds, the outdoor models take the opposite approach and let the rubber band untwist quickly. But they trade that energy “loss” for altitude gain, and then take full advantage of their gliding ability to extend the flight duration.
It’s a fun illustration of how a single problem can have many solutions—the “right” one is just the one that fits the situation best.