Home » Blog » The Science of Passive Daytime Radiative Cooling: How Does it Work?

The Science of Passive Daytime Radiative Cooling: How Does it Work?

We’re the first to admit that zero-energy cooling sounds far-fetched. It may even sound downright impossible. But hear us out, because passive daytime radiative cooling (PDRC) relies on fundamental principles of physics. In this article, we’ll dive into the science of PDRC to explore what makes this cutting-edge cooling technology a reality. By the end, we hope you’ll join us in appreciating PDRC and its role in shaping a greener future. To get started, let’s warm up (or maybe cool down?) our imaginations.

A Frosty Morning

It’s just after sunrise on a late spring morning. You look out to see the grass covered in cold-white frost. You checked the weather last night and the forecast said nothing about sub-freezing temperatures! Your weather app gave a low of 39°F with clear skies and mild winds. How is it possible that the ground is covered in frost? This type of frost is called hoar frost. To comprehend its formation, even when air temperatures remain above freezing, we must first understand a concept called “thermal emissivity”.

All objects on earth emit energy in the form of infrared radiation. The efficiency at which an object emits infrared is known as its thermal emissivity. In fact, thermal cameras rely on this phenomenon of differing thermal emissivities and temperatures to generate images in pitch-black darkness.

But where does this emitted heat go?

Some of it is trapped and re-emitted by water vapor and greenhouse gases like CO2, but much of it travels through our atmosphere and into the cold of space. When an object emits more heat into space than it receives from the environment around it, it cools below nighttime air temperatures. This phenomenon is known as nighttime radiative cooling. Now, let’s reconsider the hoar frost that formed overnight, even with mild air temperatures. With a clear and still sky, the ground experienced enough nighttime radiative cooling to drop below freezing. Pretty cool. At least until the sun rises…

Sunlight Heats Everything, Right?

After the sun rises, the ground quickly rewarms and the hoar frost melts away in a matter of minutes. It would seem that once the sun rises, all objects absorb the sun’s energy and quickly heat back up.

But not so fast! While this is true for most objects, highly reflective materials like bright white paints resist heating under sunlight. Think of walking barefoot from a concrete sidewalk onto a scorching asphalt driveway. The massive difference in temperature is thanks to concrete’s ability to reflect much more incoming sunlight than asphalt. What’s the catch? The vast majority of materials that reflect sunlight also have naturally low thermal emissivity.

But what happens if you engineer a metamaterial that combines very high solar reflectivity with very high thermal emissivity? If you reach high enough performance in both areas, you end up with something that can stay colder than the air around it, even under noon sunlight! This phenomenon is known as passive daytime radiative cooling. Let’s break it down:

P – Passive: The material does not require any inputs, like electricity or water to function

D – Daytime: The material can function during the day, under direct sunlight

R – Radiative: The material emits infrared radiation, also known as heat

C – Cooling: The material chills to below the temperature of its surroundings

Passive Daytime Radiative Cooling – From Sci-Fi to Reality

For decades, man-made PDRC materials were relegated to the realm of science fiction. While considered a theoretical possibility, creating materials that combined nearly perfect solar reflectivity with efficient thermal emissivity proved difficult. 

However, the early 2010s saw significant advances in the physics subfield of photonics, or the science of using and controlling light particles. By 2017, physicists were able to create the first PDRC materials that stayed cooler than their surroundings, even under noontime sun. 

Interestingly, as is often the case, nature beat us to the punch. The Saharan silver ant is a small ant native to the Saharan Desert that has thousands of silver, triangular hairs covering its body. In 2015, researchers discovered that these hairs are perfectly tuned for passive daytime radiative cooling! Because of this adaptation, Saharan silver ants are one of the most heat resistant creatures on earth. In fact, they are able to survive temperatures of up to 128.5°F.

Key Scientific Principles of PDRC

Emissive Cooling: The primary principle of radiative cooling is thermal emissivity. Thermal emissivity is a measure of an object’s ability to emit thermal radiation. Objects with high emissivity are efficient radiators of heat. Radiative cooling materials have high emissivity properties, allowing them to release heat efficiently.

Selective Emissivity: To achieve efficient cooling, PDRC materials must act as selective emitters, absorbing and releasing thermal radiation only within a specific wavelength range. These wavelengths align with Earth’s infrared atmospheric ‘window,’ where the atmosphere is most transparent to radiation. Heat emitted within these wavelengths easily escapes through our atmosphere into the cold of space.

Solar Reflectivity: PDRC materials must have excellent solar reflectivity, enabling them to bounce back a significant portion of incoming sunlight. This keeps them from warming during the day, ensuring they emit more heat into space than they absorb from the sun.

Continuous Cycle: The radiative cooling process of PDRC materials is passive and continuous, offering an efficient and sustainable cooling solution. PDRC materials don’t rely on electrical or mechanical systems, making them cost-effective and simple to install.

Advanced Scientific Principles

Now that we know the basics, let’s jump into the deep end. Prior warning: if your eyes glaze over during science lectures, feel free to skip this section. If you thrive on scientific curiosity, this section is for you!

Earth’s Energy Budget and the Atmospheric Window

Earth’s energy budget is a fundamental concept in Earth science that describes the balance of energy entering and leaving our planet. The energy budget is primarily governed by the principles of energy conservation and the laws of thermodynamics. Solar radiation from the Sun is the primary source of energy input into the Earth’s system. If it is not reflected, incoming solar energy, known as insolation, is absorbed by the Earth’s surface, warming it. The Earth then re-emits this energy as lower energy infrared radiation. This outgoing longwave radiation is crucial for maintaining a stable climate.

The infrared atmospheric window is a key aspect of Earth’s energy budget. Most infrared wavelengths are trapped and re-emitted by oxygen, carbon dioxide, methane, and other gases in Earth’s atmosphere. This is what we refer to as the “greenhouse effect”. The atmospheric window represents a specific range of wavelengths in the infrared spectrum (around 8 – 13 micrometers) where our atmosphere is mostly transparent. Passive daytime radiative cooling materials target selective emissivity in these wavelengths. Most outgoing infrared takes the slow route, encumbered by red lights, roundabouts, and crosswalks. The atmospheric window represents a metaphorical superhighway to space for outgoing energy transfer.

Source: NOAA

Conservation of Energy

The first law of thermodynamics is crucial to understanding how heat transfers into and out of radiative cooling materials. This law states that energy cannot be created or destroyed, only altered or transferred. With high solar reflectivity, passive daytime radiative cooling materials bounce most insolation back into space. This represents a transfer of energy. At the same time, PDRC materials absorb energy and re-emit it through the atmospheric window. This represents both an alteration and a transfer.  

We know that air conditioners do not create cold, they simply transfer heat from an indoor location to an outdoor location. Similarly, PDRC materials do not create cold, they passively reflect and emit heat from a sky-facing surface to our upper atmosphere and outer space. For every watt of PDRC cooling power on Earth’s surface, there is an equal watt of heating power somewhere “out there”. Luckily, the vast heatsink of space is a basically unlimited renewable resource.

Kirchhoff’s Law

Kirchhoff’s law of thermal radiation states that for a given material at a particular temperature, the ratio of the emissivity (ε) to the absorptivity (α) is constant for a specific wavelength. In other words, a material that is a good emitter at a certain wavelength is also a good absorber at that same wavelength. 

Have you ever noticed that asphalt cools down faster than most other objects after sunset? This is Kirchhoff’s law in action. Asphalt is a reasonable approximation of a blackbody surface, or a material that absorbs and emits all radiative energy across all wavelengths. During the day, asphalt temperature quickly rises as it absorbs the sun’s incoming light rays and re-emits them in the form of thermal radiation. At night, asphalt continues to efficiently emit heat to the surrounding air, dropping towards thermal equilibrium faster than most materials. 

Passive daytime radiative cooling materials utilize Kirchhoff’s law by maximizing absorptivity (and thus emissivity) in the mid-infrared atmospheric window. This corresponds to wavelengths of roughly 8μm – 13μm. They also minimize absorptivity in the visible and near-infrared wavelengths of incoming sunlight. Achieving mid-infrared emissivity while minimizing solar spectrum absorptivity requires advanced material engineering. Armed with the understanding of Kirchhoff’s law, researchers and engineers use photonic structures and metamaterials to manipulate a material’s emissive and absorptive properties at different wavelengths.

Stefan-Boltzmann’s Law

Stefan-Boltzmann’s law describes how the total power radiated from a black body (an idealized object that absorbs all incident radiation) is proportional to its temperature raised to the fourth power. It plays a crucial role in understanding how PDRC materials perform at different ambient temperatures. The formula is:

P = σ * A * T4

Where:

P is the radiative power (in watts) emitted by the object.

σ is the Stefan-Boltzmann constant (5.67 ⋅  10-8W/m2K4).

A is the surface area of the radiating object (in m2).

T is the temperature of the radiating object (in Kelvin).

Notice that radiative power rises proportionally to temperature raised to the fourth power. In other words, as the radiating object gets hotter, it’s radiative power increases exponentially. While a tuned PDRC material will often stay below ambient temperatures, conduction and convection naturally cause the material to warm back towards ambient temperatures. As it warms, it’s cooling power increases.

Thanks to Stefan-Boltzmann’s law, PDRC materials continuously cycle in a self-correcting loop. This also means they reach peak cooling efficiency on hot summer days and minimize cooling on cold, blustery winter days. The result is a more sustainable and economically viable product that passively limits “over-cooling” when cooling is not needed.

Wien’s Displacement Law

Wien’s displacement law describes the relationship between the temperature of a black body object and the wavelength of maximum emission. It is expressed by the following formula:

λmax  =  b / T

Where:

λmax is the peak wavelength at which the object emits the most radiation.

b is Wien’s displacement constant (2.898 ⋅ 10-3m ⋅ K)

T is the absolute temperature of the object in Kelvin.

According to Wien’s displacement law, the peak wavelength (λmax) of the thermal radiation emitted by an object is inversely proportional to its temperature (T). As an object’s temperature increases, the wavelength of maximum emission shifts to a shorter, more energetic wavelength. Wien’s Displacement Law explains why white hot objects are hotter than those that are red hot. Consider the goal of PDRC to radiate in the specific wavelengths corresponding to Earth’s atmospheric window. With Wien’s law in mind, we can tune materials to reach peak atmospheric window emissivity at a specific target temperature. 

Advanced Optimization of Passive Daytime Radiative Cooling

It’s easy to think of the need for cooling for human comfort. However, there are thousands of cooling applications around the globe, each with different starting and target temperatures. For instance, a tent fabric used in Tucson, Arizona in the summer would see different operating temperatures than a roof film used to cool a telescope dome on a cold mountaintop in Chile.

Knowing the optimum temperature profile of a PDRC film allows engineers and architects to enhance the efficiency of radiative cooling by using smart design. Strategies like selective insulation and selective surface coating allow us to optimize the average target temperature of a surface. 

Large scale radiative cooling does not require this type of hyper-optimization. Temperature efficiency curves of existing PDRC materials already cool effectively for the vast majority of cooling applications. This type of optimization, while important, serves to create incremental improvements for specialized applications.   

Key Takeaways

Congratulations! If you made it through the advanced scientific principles section. You are now a PDRC pro. You know some of the scientific laws that physicists use to design PDRC materials that maximize radiative power and target emissivity at atmospheric window wavelengths. In addition, you know some of the techniques that physicists might use to further optimize PDRC materials for specialized applications in the future.

Applications of Passive Daytime Radiative Cooling

As a new technology, we are just beginning to explore the applications of PDRC. One thing is certain, passive cooling opens the door to a world of innovative and eco-friendly applications. Here are a few of our favorites:

Cooling Buildings

Radiative cooling materials can be integrated into the construction of sustainable buildings or added onto existing cooling systems as efficiency boosters. This reduces the need for traditional air conditioning. In our hometown of Tucson, it is common in older homes retrofitted with air conditioning for HVAC ducting to be run outside of the building envelope on top of a home’s roof. Even with internal insulation, these ducts heat like frying pans under the Arizona sun. When the HVAC system turns on, you get a delightful blast of hot desert air before the ducts cool back down. Applying radiative cooling film to these ducts significantly reduces energy use and helps mitigate these uncomfortable “hot shots“ from the air conditioning registers.

PDRC is a particularly important technology for individuals living in poverty. As is so often the case, economic disparity and housing discrimination have foisted inequitable heat risks onto poor and minority neighborhoods. In our home state of Arizona, low-income and latino neighborhoods are at higher risk for extreme heat. The poorest 10% of neighborhoods are on average 4°F hotter than the wealthiest neighborhoods nearby and low-income residents are much more likely to not own, or run, air conditioners. Targeting installations in these particularly hot neighborhoods, in partnership with city, county, and state governments and nonprofits can help level the playing field on heat inequality. 

Agriculture

These materials can be utilized in agriculture to protect crops and livestock from extreme heat while also improving agricultural yields. For instance, dairy farmers are acutely aware of the risk of heat on their production and animal safety. Overheating can drop milk production by 30% or more. By passively cooling barns, milking parlors, and calf housing, dairy farmers can reduce their energy and water usage, build resilient and sustainable farms, and house happier cows. And as the old saying goes, “happy cows make better milk”.

Data Centers

Radiative cooling can be employed to cool data centers, improving their energy efficiency and reducing the environmental impact of cloud computing. Data centers require 24/7 cooling to shed the heat produced by millions of machines that run our modern internet. Intelligently designing passive daytime radiative cooling into data centers means less energy-hungry air conditioning and a more resilient system overall.

Vehicles

Radiative cooling materials can be applied to the rooftops of trucks, buses, vans, and RVs to reduce demand on a vehicle’s air conditioner and therefore increase fuel efficiency. Because of their high reflectivity, consideration must be given to ensure materials are applied only where they will not cause glare for other drivers on the road. However, even on low vehicles like cars and crossovers, where glare considerations prevent permanent installation, car covers made from radiative cooling fabric can be used when parked in sunny locations. In testing, radiative cooling car covers kept interiors up to 54°F cooler than an identical uncovered car. Living in Arizona, we are not even joking when we say that you can bake cookies in your uncovered car during the summer.

Disaster Relief

Radiative cooling materials have multiple advantages when it comes to providing shelter after disasters. Without the need for energy, radiative cooling materials can be utilized even when grids are down or generator fuel is scarce. Self-adhesive radiative cooling films can be applied to temporary structures like containerized hospitals or food distribution trailers. Radiative cooling fabric can be used to make entire prefabricated tents or cooling fabric panels can be added onto existing tents.

In addition, radiative cooling films and fabrics are incredibly lightweight per watt of cooling that they provide. A single pallet of radiative cooling films and/or fabrics weighs under 950 lbs and covers over 13,000 ft². To actively cool the same square footage requires a 20-ton air conditioner that weighs roughly 4,500 lbs, a 40kW generator that weighs 3,600 lbs, and two gallons of diesel (14.2 lbs) every hour. Even if you are lucky enough to have an air conditioner and generator on-site, running the unit for just 2.7 days burns the same weight in fuel as the pallet of PDRC materials that will cool for the next decade. Given that post-disaster relief often arrives on cargo planes, every pound saved means more room for food, water, medicine, and personnel. 

Camping Tents

As avid Arizona campers, we never have a problem staying warm. A good sleeping bag and a couple of dogs do the trick perfectly. Unfortunately, staying cool during summer days is nearly impossible. Under intense afternoon sun, PDRC fabric tents can stay significantly cooler (by 20°F+) than traditional tents. And for glamping tents or yurts, the effects can be even bigger due to better wall insulation and larger roof areas. 

While a cool tent is nice luxury for the weekend desert camper, self-cooling tents can make a world of difference for unhoused individuals in hot climates. In some cases, it can even be life or death. We have made it a priority to work with reputable nonprofits to get passive daytime radiative cooling tents to those who need them most.  

Conclusion

Radiative cooling is a cutting-edge technology that harnesses the natural process of radiative heat transfer to cool down objects and spaces without the need for energy-intensive cooling systems. By understanding the science behind radiative cooling, we can appreciate its potential to revolutionize the way we approach cooling in a sustainable and eco-friendly manner. As our world seeks sustainable solutions for cooling, radiative cooling materials represent a promising step forward in the fight against climate change and energy waste. If you want to explore an application for PDRC materials, contact us to learn more about our PDRC films, membranes, and fabrics.

Ready to Jumpstart PDRC Adoption?

Coldrays is America’s first large-scale distributor of passive daytime radiative cooling materials. We are always on the lookout for partners with a shared vision for a better planet. Check out our passive daytime radiative cooling products or get in touch to learn more about building the future.

Love this post? Share it!
Chris Hiller
Chris Hiller
Articles: 8