Sailing the Stratosphere: How We Discovered the Atmosphere's 'Goldilocks' Zone
Imagine trying to sail a ship across the ocean, but instead of moving your rudder or adjusting your sail, you simply change the winds around you. This may sound rather magical, but it’s exactly how we fly high-altitude balloons. Through this, we can set these platforms to float for weeks to months in the stratosphere, offering an eye-in-the-sky for everything from remote sensing to communications. These balloons fly without engines or propellers, and instead just change the winds they fly in. How do we do this? We leverage the stratosphere's unique diversification of atmospheric layers and regulate our altitude to float in a layer that has our desired winds.
For years, this promise of “wind-based navigation” has drawn in eyes. If we can successfully achieve it, one could steer these systems with remarkable energy efficiency. Despite the interest, a fundamental question remained: where in the stratosphere can we successfully “sail”? Are all altitude bands created equal, or is there a “highway in the sky” for navigation?
We address this question in our paper, “The stratospheric Goldilocks zone is critical for high-altitude balloon navigation," where we create a map of the navigational potential of the atmosphere itself.
The Creation of Our Map
From a first principles’ perspective, the idea is simple: navigability will require a diverse set of wind directions. If all the winds are blowing east, you can only go east. But then, if you add in a westerly layer, you can now go back and forth. And then a north layer... so on and so forth. Using this methodology, we wanted to build a global map of wind diversity.
To do this, we developed a method to score any vertical column of the atmosphere on a scale from 0% (where all winds are blowing in the exact same direction) to 100% (where a single wind layer can achieve any possible direction). The goal was to arrive at a metric that was simple, intuitive, and fast. We arrived on using the area of a polygon where the vertices are the normalized vectors of each wind layer. The area of a polygon works well because as the number of vectors increases, covering more directions, the area increases in diminishing amounts. The additional diversity gained from adding a North vector to a set of South, East, and West should be greater than adding a North-East vector to a set of North, South, East, and West. It can be shown that for a set of n vectors, if you optimally space them (equidistant around the unit circle), their hull area will be n/2 sin(2π/n) and will have the desired shape as n increases, leveling off to an area of π. Computing this area is quite fast with the shoelace method, and so it worked well for our large, desired dataset. We determined the diversity of 250 million wind profiles (across 5 years of global weather data) for each of the 338 different altitude bands we investigated. So, having this level of efficiency was key.
The 'Goldilocks' Zone
Through our analysis, we discovered a critical region for navigability in the stratosphere. The region is formed when the altitude ceiling is above 21 km, and the altitude floor is below 16 km. It’s in this region that major shifts and shears occur, allowing for many directions to be achieved in a tight range. Operating a balloon outside this range, either too high (all above 21km) or too low (all below 16 km), will result in a relatively homogenous operating band, offering little for navigability.
It would be great to simply operate a balloon at all altitudes, as then one would have the best chance of finding a target wind layer. Unfortunately, there are significant design constraints on what altitudes a balloon can fly at. Most current super-pressure balloons operate over a 5-6 km altitude band out of necessity. Otherwise, their balloon may pop or fall out of the sky. Furthermore, their altitude control systems are optimized for a specific density and thickness of the atmosphere. To support these constraints, we found where the optimal operating bands are based on how much range the system has and how much diversity is to be expected.
For zero-pressure balloons, they can operate at a much larger range of altitudes as they have no floor (able to fly all the way down to the ground if desired). But even here, bigger is not always better. We calculated the marginal diversity as the altitude ceiling continually increases, and found diminishing marginal returns above the Goldilocks zone. Increasing the altitude ceiling means making a larger (and likely more expensive) balloon.
Why This Matters
Our findings have clear implications for the future of high-altitude platforms. For balloon builders, like Urban Sky, this creates a quantitative framework to design balloons more efficiently and achieve more reliable navigation. By crafting the systems to fly within this Goldilocks zone, we can maximize our ability to navigate and persist over target regions.
Beyond engineering decisions, our work can inform policymakers. As the stratosphere grows in traffic, organizations such as the FAA and ICAO will need to update the rules of the sky. This research shows that arbitrarily restricting operating altitudes, such as by capping flights at the top of existing airspace (18 km), may unintentionally cripple the navigational capability of these platforms, undercutting their utility and safety.
This began as an internal search to ensure Urban Sky developed balloons to operate at altitudes to maximize navigability. The stratosphere didn’t offer a simple “more is better solution", but instead a nuanced environment centered on the Goldilocks zone, a region we expect to be critical for the future of stratospheric exploration.
To read our full paper in more detail, please follow this link: The stratospheric Goldilocks zone is critical for high-altitude balloon navigation.