Mechanical power generation through sub-ambient passive radiative cooling

Abstract

A Radiative Cooling Engine is described. The engine leverages the principle of radiative cooling, a natural phenomenon where objects emit thermal radiation to the cold space above, to generate mechanical and / or electrical power. However, unlike conventional solar-based systems that rely on direct sunlight, the Radiative Cooling Engine operates efficiently during nighttime hours when solar energy is unavailable. The engine can be implemented using a modified low-temperature differential (LTD) Stirling Engine that is configured to exploit the temperature difference between the earth's surface and the cold night sky to generate mechanical power that can be used for various purposes.

Description

MECHANICAL POWER GENERATION THROUGH SUB-AMBIENT PASSIVE RADIATIVE COOLINGCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to, and the benefit of, U.S. provisional patent application serial number 63 / 681 ,542 filed on August 9, 2024, incorporated herein by reference in its entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] Not ApplicableNOTICE OF MATERIAL SUBJECT TO COPYRIGHT PROTECTION

[0003] A portion of the material in this patent document may be subject to copyright protection under the copyright laws of the United States and of other countries. The owner of the copyright rights has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the United States Patent and Trademark Office publicly available file or records, but otherwise reserves all copyright rights whatsoever. The copyright owner does not hereby waive any of its rights to have this patent document maintained in secrecy, including without limitation its rights pursuant to 37 C. F. R. § 1 .14.BACKGROUND

[0004] 1. Technical Field

[0005] The technology of this disclosure pertains generally to mechanical and / or electrical power generation, and more particularly to harnessing ambient radiation for power generation so that power can be generated at times when solar-based methods are unavailable, particularly during nighttime.

[0006] 2. Background Discussion

[0007] Many power conversion devices work by exploiting the temperatureUC-2024-579-2-PCT -1-difference between two objects. A typical example is a sun-earth system, where the temperature difference between the sun (6000K) and the earth (300K) is utilized by photovoltaic cells or solar thermal devices to harvest energy directly. The sun, however, is not always accessible, and peak power consumption often occurs well after peak generation from such a system. This timing mismatch precludes the ability to rely solely on the sun’s energy in a zero-emission future without significant storage capacity.

[0008] There are also two-temperature systems that can generate power based on a temperature differential between the earth (300K) and outer space (3K) and which can be accessed 24-hours per day. For example, radiative cooling can be used to passively cool objects below ambient temperature by exhausting heat toward the sky. While the emitted power flux then can be utilized to generate electricity, for example, such devices often require low- bandgap or rare-earth materials that are difficult to scale.

[0009] To produce power through radiative coupling between the earth and space, a device should be able to emit heat from the local environment and emit the heat toward space. Ideally, the emitting object in the device would have a strong emission signature, such as between 8 pm to 13 pm, thereby allowing the radiation to pass through the atmospheric transparency window to directly couple to space. This phenomenon also allows the earth to exhaust heat to space at night, which can be a potential mitigation strategy to reduce global temperature increases.

[0010] For terrestrial devices, it is difficult to directly couple to space. However, coupling to the cool sky can be sufficient for reducing energy consumption by passively cooling buildings and other structures. This approach can also be used to convert the local ambient radiation into electricity.

[0011] Though functional, the above-described methods require either low- gap semiconductor devices or thermoelectric generators to convert radiative heat into electricity, and are not readily scalable. Additionally, power output is relatively low and fabrication generally requires rare earth elements.UC-2024-579-2-PCT -2-BRIEF SUMMARY

[0012] This disclosure describes apparatus and methods for generating mechanical power from the earth’s ambient radiation using a modified low- temperature differential (LTD) Stirling engine. Year-long, outdoor experiments were conducted and demonstrated that temperature differences >10°C can be sustained during most months, resulting in the generation of >0.1 mW of mechanical power. The apparatus was also adapted with a fan to assess useability for circulation, and experiments demonstrated circulation >0.3 m / s with a volumetric flow rate that exceeds 5 cfm, which is sufficient for CO2 circulation in greenhouses and residential buildings.

[0013] By way of example, and not of limitation, a Radiative Cooling Engine (RCE) according to this disclosure comprises a LTD Stirling Engine that is modified to generate power by exploiting the temperature difference between the earth's surface and the cold night sky. In one embodiment, the apparatus may comprise several components as follows:

[0014] (a) Stirling Engine. A LTD Stirling engine is the core component of theRadiative Cooling Engine and responsible for converting thermal energy into mechanical work. The Stirling engine operates on a closed-cycle regenerative thermodynamic process, where a working fluid alternately expands and contracts, driving a piston or displacer to produce mechanical motion.

[0015] (b) Thermal Coupling. The bottom side of the Stirling engine is configured to be thermally coupled to the earth's surface. This ensures efficient heat transfer from the ground to the engine, serving as the heat source.

[0016] (c) Radiative Surface. The top side of the Stirling engine is equipped with a large radiative surface area to maximize heat exchange with the cold night sky. This surface is coated with a thermally emissive material to enhance radiative cooling efficiency.

[0017] This technology presents an approach to harnessing ambient radiation for mechanical and / or electrical power generation, particularly during nighttime when traditional solar-based methods are unavailable. Unlike existing technologies that rely on semiconductor devices or thermoelectric generators, the Radiative Cooling Engine employs a low-temperatureUC-2024-579-2-PCT -3-differential (LTD) Stirling Engine or similar device configured to exploit radiative cooling from the earth's surface to the night sky.

[0018] Aspects of the Radiative Cooling Engine include, but are not limited to:

[0019] 1 . Utilization of a simple and scalable Stirling engine design, allowing for cost-effective deployment.

[0020] 2. Modification of the Stirling engine design with a large top plate coated with a thermally emissive material to optimize radiative surface area.

[0021] 3. Thermal coupling of the Stirling engine with the ground ensures efficient heat transfer, enhancing engine performance.

[0022] 4. Demonstrated ability to achieve sufficient temperature differentials for engine operation under varying sky conditions throughout the year.

[0023] 5. Potential applications extend beyond power generation, including air circulation in greenhouses, showcasing versatility.

[0024] 6. Comparative analysis suggests competitive power output with state- of-the-art solid-state devices but at significantly lower manufacturing costs.

[0025] 7. Future improvements could further enhance performance, such as using helium as the working fluid or optimizing radiative coupling to the night sky.

[0026] 8. Global impact potential, with visualization of energy production around the globe, and promising applications in space exploration and terraforming missions.

[0027] Overall, the Radiative Cooling Engine presents a promising solution to augment renewable energy sources, offering a sustainable and versatile method for mechanical and electrical power generation, particularly in regions with limited access to sunlight or during nighttime hours. The Radiative Cooling Engine holds promise for a wide range of applications beyond power generation, including air circulation in greenhouses and other controlled environments, and applications in space exploration and terraforming missions.

[0028] Further aspects of the technology described herein will be brought out in the following portions of the specification, wherein the detailed description is for the purpose of fully disclosing preferred embodiments of the technology without placing limitations thereon.UC-2024-579-2-PCT -4-BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The technology described herein will be more fully understood by reference to the following drawings which are for illustrative purposes only:

[0030] FIG. 1 is a schematic diagram of an embodiment of a Radiant Cooling Engine according to the present disclosure shown in context for operation at night.

[0031] FIG. 2A through FIG. 2C are diagrams of an embodiment of a mount providing a lower coupling surface for a Radiative Cooling Engine according to the present disclosure.

[0032] FIG. 3 is a plot showing emissivity / absorptivity characteristics of different thermal coatings for the upper radiative surface of a Radiative Cooling Engine according to the present disclosure.

[0033] FIG. 4A is a graph showing downwelling infrared from sky and solar irradiance plotted throughout the evening and into the night.

[0034] FIG. 4B is a graph showing temperatures of engine plates of a Radiative Cooling Engine according to the present disclosure compared to ambient air for the time period shown in FIG. 4A.

[0035] FIG. 4C is a graph showing engine frequency and temperature differential of a Radiative Cooling Engine according to the present disclosure for the time period shown in FIG. 4A.

[0036] FIG. 5A and FIG. 5B are plots showing seasonal effect on performance of a Radiative Cooling Engine according to the present disclosure. FIG. 5A shows average recorded temperatures for the bottom and top engine plates during runs throughout the year. FIG. 5B shows the associated average engine frequency and temperature differential for overnight runs.

[0037] FIG. 6A through FIG. 6F illustrate power conversion analysis and applications of a Radiative Cooling Engine according to the present disclosure. FIG. 6A shows plots of mechanical power against temperature differential for a range of cold plate temperatures. FIG. 6B presents results of voltage sweeps across an attached DC motor and shows maximum power point for mechanical to electrical power conversion at a range of engine temperature differentials. FIG. 6C is a bar graph that denotes the remaining mechanical power available and the electrical power extracted (plus motorUC-2024-579-2-PCT -5-losses) when a DC motor is attached to the engine’s flywheel. FIG. 6D is a schematic showing an axial fan blade attachment along with hot wire anemometer used to measure air speed. FIG. 6E maps air speed in front of the engine flywheel when the engine is converted into an axial fan. FIG. 6F is a plot of air speed and frequency against engine temperature differential.

[0038] FIG. 7A through FIG. 7C are examples of data used for power characterization of a test Radiative Cooling Engine according to the present disclosure. FIG. 7A shows frequency measured as the engine is manually brought to a near stall and then allowed to ramp back up to steady state. FIG. 7B shows instantaneous power calculated through extraction of the angular acceleration. FIG. 7C shows measured plate temperature during the test.

[0039] FIG. 8A through FIG. 8D show experimental results for a Radiative Cooling Engine according to the present disclosure. FIG. 8A is a plot of engine frequency plotted versus temperature difference. FIG. 8B shows replots of data using the modified Beale Equation in order to extract engine average Fill Factor of approximately 0.26. FIG. 8C and FIG. 8D show experimental data replotted with different Fill Factors.

[0040] FIG. 9A and FIG. 9B show test configurations of a Radiative Cooling engine according to the present disclosure. FIG. 9A is a circuit diagram for DC measurement. FIG. 9B is a schematic of the Radiant Cooling Engine tested.

[0041] FIG. 10A through FIG. 10D show test results for a Radiative Cooling Engine according to the present disclosure, with and without DC motor attached. FIG. 10A is a graph of engine frequency over time showing a measured frequency of approximately 6 Hz. FIG. 10B is a graph of engine power over time showing 1 .8 mW of available mechanical power. FIG. 10C is a graph of engine plate temperatures showing a small drift in temperature once the motor is attached. FIG. 10D is a graph showing associate power levels.

[0042] FIG. 11 A and FIG. 11 B illustrate axial fan conversion of a Radiative Cooling Engine according to the present disclosure. FIG. 11 A is a graph showing engine frequency and temperature difference over time. FIG. 11 B is a flow diagram illustrating motion of the fan blade over time.UC-2024-579-2-PCT -6-

[0043] FIG. 12A and FIG. 12B show experimental results of the Radiative Cooling Engine converted to a fan. FIG. 12A is a graph showing engine frequency with associated maximum air speed measured in front of the fan. FIG. 12B is a graph showing engine plate temperature profiles.

[0044] FIG. 13 is a schematic illustration of a Carnot engine utilizing the sky as a heat sink and the earth as a heat source.DETAILED DESCRIPTION

[0045] This disclosure describes a Radiative Cooling Engine (RCE) for generating power, such as mechanical or electrical power, or both, using a low-temperature differential (LTD) that is modified for radiative coupling to the night sky and thermal coupling to the earth's surface.

[0046] It will be appreciated that a LTD Stirling engine generally has a top plate, a bottom plate, a displacer between the top and bottom plates, and a flywheel. The LTD Stirling engine operates on a closed-cycle regenerative thermodynamic process, where a working fluid (typically air) alternately expands and contracts, driving a piston or displacer to produce mechanical motion. Small temperature differences between the plates are converted into motion of the flywheel. If one plate is sufficiently warmer than the other plate then the flywheel will turn. Some LTD Stirling engines can operate with a temperature differential as small as 1 °C.

[0047] By way of example, and not of limitation, FIG. 1 schematically illustrates a Radiative Cooling Engine 100 according to this disclosure that is based on the operation of a low-temperature differential (LTD) Stirling engine 102. The top plate 104 is configured to be radiatively (e.g., Electromagnetically) coupled to the night sky 200 and cool below ambient air temperature. The bottom plate 106 is configured to be thermally coupled to the ground 202 and remains warmer, as radiative access to the night sky 200 is blocked by top plate 104. This radiative imbalance creates the temperature differential that drives the engine.

[0048] In the Radiative Cooling Engine 100 illustrated in FIG. 1 , the Stirling engine's top plate is replaced with a top plate 104 that has a large radiative surface coated with a thermally emissive material. As a result of the largeUC-2024-579-2-PCT -7-radiative surface area and thermally emissive coating, top plate 104 is configured to be coupled to the night sky 200 through passive radiative cooling. The radiative surface of top plate 104 is oriented skyward to use the night sky as a cold sink.

[0049] The Stirling engine's bottom plate 106 is thermally coupled to a custom mounting base 108 that is configured for thermal coupling to the earth's surface for use of the earth's surface as a heat source. Bottom plate 106 rests on mounting base 108 and mounting base 108 in turn rests on the earth's surface 202 (e.g., after any intermediate vegetation 204 is removed). Mounting base 108 includes a plurality of spikes 110 that extend into the earth's surface 202. As a result, bottom plate 106 will be in thermal contact with the earth’s surface 202 through mounting base 108 and spikes 110, thereby ensuring efficient heat transfer from the earth's surface to the LTD Stirling engine.

[0050] Optionally, temperature sensors (not shown), such as resistive temperature detectors (RTDs), may be employed to monitor the temperatures of the top plate, bottom plate, and ambient air, for example.

[0051] Contextual Terminology

[0052] As used in this disclosure the terms earth's surface, ground and the like are not intended to be limited to the interface between the outermost surface of the earth and the atmosphere but can include underlying soil or other material. Additionally, any of the terms earth, earth's surface, ground, soil, and the like can be interpreted as referring to the terrestrial body (i.e. , the earth) that supports the Radiative Cooling Engine and to which the Radiative Cooling Engine is thermally coupled.

[0053] As used in this disclosure, the terms sky, night sky, and the like can be interpreted as referring to the atmospheric expanse that is away from the surface of the earth. References to the top plate pointing toward the sky or skyward, or being oriented toward the sky or skyward, can be interpreted as pointing or being oriented away from the earth, which could be directly upward (normal to the earth's surface) or at an angle in relation to the surface of the earth.UC-2024-579-2-PCT -8-

[0054] Earth Surface Coupling

[0055] As described above, Radiative Cooling Engine 110 uses the earth’s surface 202 as a heat source. However, simply placing bottom plate 106 directly on the ground might not provide good thermal conduction due to vegetation, uneven soil, and other surface anomalies. To couple bottom plate 106 to the earth's surface 202 with good thermal contact, bottom plate 106 can be thermally coupled to mounting base 108 that in turn is thermally coupled to the earth's surface 202.

[0056] FIG. 2A through FIG. 2C show examples of a mounting base 108 constructed in the form of a circular disc that has approximately the same base diameter as bottom plate 106. The disc can be fabricated from a thermally conductive material such as aluminum and include several holes through which spikes 110 can be embedded. Spikes 110 can be pressed directly into the earth's surface 202 to a suitable depth (e.g., 5 cm) so that mounting base 108 can maintain direct thermal contact with the earth's surface. It will be appreciated that a plurality of spikes will increase the contact surface area between mounting base 108 and the earth's surface 202, and hence increase the thermal transfer capability of mounting base 108. Additionally, thermal paste such as silicone-based thermal compound can be applied between the upper surface of mounting base 108 and the lower surface of bottom plate 106 to ensure uniform heat transfer between the bottom plate and the mount as well as to minimize slippage.

[0057] Thermally Emissive Coatings

[0058] Also as described above, the upper radiative surface of top plate 104 is coated with a thermally emissive material. Two different types of emissive paints were tested for the coating; Avian Black-S and AcryShield 400. As can be seen in FIG. 3, the thermal emissivity of both paints were measured to be quite similar and both paints performed successfully during field testing. Additionally the most suitable commercially available coatings were found to have emittance of about 0.95. The optimal coating would have emissivity approaching 1 .0 for wavelengths above approximately 2.5 microns, which is possible through the use of meta-material manufacturing.UC-2024-579-2-PCT -9-

[0059] Surface Area of Upper Radiative Surface

[0060] Another characteristic of top plate 104 is that it has a generally larger radiative surface area than bottom plate 106 to maximize heat exchange with the cold night sky. For example, and without limitation, the ratio of the surface area of top plate 104 to bottom plate 106 could typically range from about 1 :1 to about 20:1 .

[0061] It will be appreciated that the power available to the Radiative Cooling Engine will be the power radiated from the upper radiative surface of top plate 104, which is measured as a power density, W / m2. The larger the radiative surface, therefore, the more power available for the engine to convert. It may be difficult specify a minimum size requirement but, based on the size of typical LTD Stirling engines, a surface area of below about 1 cm2would be smaller than the cross-sectional area of the engine and may represent a reasonable lower bound.

[0062] Surface Area of Lower Thermal Coupling Surface

[0063] Because bottom plate 106 and mounting base 108 are in direct thermal contact with the earth's surface 202, the heat transfer coefficients of bottom plate 106 and mounting base 108 are more important than their surface areas. Ideally, the heat would be conductively transferred as quickly as possible. The thermal conductivity of copper is about 400 W / m / K and would be able to transfer heat very effectively. A minimum contact area has not been determined, but it will be appreciated that the contact area can be increased by increasing the area of contact rather than the area of the plates. In this regard, spikes 110 will provide additional contact area.

[0064] Additional Considerations

[0065] There are mechanical limitations to the size of the Radiative Cooling Engine since the Stirling engine's main cylinder and displacer need to increase in diameter as the size of top plate 104 increases to generate increased power. As the displacer needs to move infinitesimally close to, but never contact, either top plate 104 or bottom plate 106 during the engine cycle, the engine cannot be infinitely large because thin surfaces are vulnerable to warping as their area is increased.

[0066] Positioning the flywheel 112 (see FIG. 1 ) to the side of the StirlingUC-2024-579-2-PCT -10-engine would allow for maximum radiative coupling, since placing the flywheel above top plate 104 as illustrated in FIG. 1 will block some of the sky from view of the radiative cooling surface of top plate 104. Another option would be to build the engine internally.

[0067] It will be appreciated that it is desirable for a Radiative Cooling Engine to achieve the best practical thermal contact with the heat source (earth or other surface) and the best practical thermally emissive top plate.

[0068] In use, top plate 104 is pointed directly upward (normal to the earth’s surface) to be most effective. Top plate 104 can, however, also be pointed toward the sky at angles (e.g., pointing toward the blue or the clouds in the sky). In principle, mirrors could be used to block out the sides so that the top plate is only "seeing" some smaller angular spread.

[0069] Instead of replacing the top plate of the LTD Stirling engine as described above, top plate 104 can be placed on top of, and affixed to, the top plate of the LTD Stirling engine. In that configuration, thermal paste such as silicone-based thermal compound can be applied between the lower surface of top plate 104 and the upper surface of the top late of the LTD Stirling engine promote uniform heat transfer.

[0070] Instead of the bottom plate 106 and mounting base 108 being configured as separate components, bottom plate 106 could be combined with mounting base 108 or replaced with a disc structure that is the same or similar to mounting base 108.

[0071] The effectiveness of the Radiative Cooling Engine will decrease if exposure of the top plate to the sky is decreased. Therefore, the top plate should not be covered with a shade or other material that absorbs or reflects thermal radiation. Additionally, if the Radiative Cooling Engine is bordered by walls, the walls could limit exposure to the sky. In that case, it might be possible to strategically position mirrors around the engine to effectively increase the field of view of the sky.

[0072] Experimental Results - Power Generation

[0073] For testing, an outdoor experimental setup was constructed based on the Radiative Cooling Engine configuration shown in FIG. 1. The experimental setup comprised a modified Low-Temperature DifferentialUC-2024-579-2-PCT -11-Stirling Engine (Kontax Engineering KS90) with 12”x12” (30 cm x 30 cm) radiative surface area coated with Avian Black-S emissive paint. The engine has an approximately 160° view of the sky. Data was collected using RTD and photogate logging instruments, and radiative sensors (Apogee SL-510 Pyrgeometer and SP-510 Pyranometer).

[0074] FIG. 4A shows downwelling infrared radiation from the sky and solar irradiance plotted throughout the evening and into the night. These power fluxes control the temperature of the emissive top plate. The fluctuations in the downwelling infrared are caused by passing clouds, which emit strongly in the infrared due to high water content. FIG. 4B shows temperatures of the engine plates compared to ambient air throughout the run. The fluctuations in the top plate and air temperature match the fluctuations in the downwelling infrared, while the average temperature decreases as downwelling power decreases. FIG. 4C shows engine frequency and temperature differential. While the absolute temperature of the engine decreases throughout the night, the temperature difference and engine frequency remain approximately constant. Temporary increases in downwelling infrared, which decrease the engine temperature differential, are physically manifested in a slowing of the engine.

[0075] As can be seen in FIG. 4A, as the sun sets, the incident solar radiation tends toward zero and the measured downwelling infrared radiation from the sky steadily decreases. Temperatures of the engine plates and ambient air measured with resistive temperature detectors (RTDs) showed a steady temperature difference of ~10°C between the plates after sunset (see FIG. 4B), which led to a ~1 Hz rotation of the engine’s flywheel (see FIG. 4C). The engine’s flywheel was used as an optical chopper to measure the engine frequency using a photogate. This combination of monitors provided the ability to dynamically compare the engine’s performance with the sky’s radiative conditions.

[0076] Referring to FIG. 5A and FIG. 5B, experiments repeated throughout a year showed that a temperature differential sufficient for engine operation is achievable under most average night sky conditions. More particularly, FIG. 5A shows average recorded temperatures for bottom and top engine platesUC-2024-579-2-PCT -12-during runs throughout the year. Average monthly temperatures for the location where measurements were performed, are also plotted as a guide to the eye. This data reveals the correlation between engine operating temperatures and the local weather. FIG. 5B shows the associated average engine frequency and temperature differential for the overnight runs. Error bars show the maximum and minimum recorded values from datasets ranging from 1 to 10 hours.

[0077] While the absolute temperatures of the engine vary seasonally with the ambient (FIG. 5A), the engine temperature differential and frequency remain relatively consistent (FIG. 5B). The experiments showed decreased engine performance in winter months when more consistent rain and cloud cover were experienced, and above average performance in summer months when skies are clear and humidity is low. Similarly to how tropical zones remain warmer throughout the night than arid regions, this weather-dependent variance in engine performance is due to the strong thermal emission from H2O within the atmospheric transparency window. High concentrations of water in the atmosphere reduce radiative cooling power, thus optimal performance occurs with clear skies and low humidity.

[0078] In addition to field tests, a series of additional experiments were performed in the laboratory at specific temperature differentials to further characterize the power conversion potential of the engine.

[0079] More particularly, FIG. 6A shows mechanical power plotted against temperature differential for a range of cold plate temperatures. Error bars show standard deviation of the measured values. Solid lines represent the potential power denoted by the West Number, corresponding to different quality engines (FIG. 8A through FIG. 8D).

[0080] FIG. 6B shows maximum power point for mechanical to electrical power conversion at a range of engine temperature differentials with a voltage sweep across a DC motor attached to the engine. Solid lines are quadratic fits of the measured data points (circles).

[0081] The bar graph in FIG. 6C denotes the remaining mechanical power available and the electrical power extracted (plus motor losses) when a DC motor is attached to the engine’s flywheel.UC-2024-579-2-PCT -13-

[0082] In FIG. 6D, an axial fan blade attachment is shown along with a hot wire anemometer used to measure air speed.

[0083] In FIG. 6E, air speed in front of the engine flywheel is mapped when the engine is converted into an axial fan. Engine plate temperatures were 29°C and 7°C, simulating a typical greenhouse environment and an achievable radiatively cooled top plate temperature, respectively.

[0084] In FIG. 6F, air speed and frequency plotted against engine temperature differential. The shaded gray regions show the range of air speeds necessary to circulate CO2 to promote plant growth inside greenhouses and the ASHRAE recommended air speed for thermal comfort inside buildings.

[0085] In the experimental setup, the bottom plate temperature was controlled with a hot plate, and the top plate temperature was maintained with a custom water-cooling block. While monitoring engine frequency and temperature, the engine was started and allowed to reach steady-state, i.e. , constant rotation of the flywheel. By manually applying friction to the flywheel, the engine was slowed to a near stall, then allowed to ramp back up to steady-state. FIG. 7A shows frequency measured as engine is manually brought to a near stall and then allowed to ramp back up to steady state. In FIG. 7B, instantaneous power is calculated through extraction of the angular acceleration. Power is seen to be negative when friction is manually applied to the engine and then as the engine is allowed to reach steady-state, positive power is produced. Peak power output occurs just after the load is removed; i.e., the engine produces the most power when it operates just above its stall frequency. FIG. 7C shows measured plate temperature during the test.

[0086] This process was repeated for twenty-five different temperature differentials within the range of observed field measurements. Using equations of angular kinematics, the instantaneous power is calculated as:P = T ■ a) = la ■ ( / ) = !— dt a), where T, a), I, and a are the flywheel’s torque, angular frequency, moment of inertia, and angular acceleration, respectively. The angular acceleration is extracted as the time-derivative of the measured frequency and the engine power is determined at each set temperature difference (see FIG. 6A).

[0087] Referring to FIG. 8A through FIG. 8D, while Stirling engine frequency isUC-2024-579-2-PCT -14-non-linear with temperature, there is relative linearity of power output with respect to temperature differential over the measured temperature range. More particularly, FIG. 8A shows engine frequency plotted versus temperature difference. It is shown that frequency is not linear with temperature difference. While this curve is characteristic of the Radiative Cooling Engine of this disclosure, it is generally true for all Stirling engines that engine frequency and power are non-linear with temperature difference, as shown in the modified Beale Equation^). The equation,relates the key characteristics of a Stirling Engine (pressure of the working fluid (P), compressed / expanded volume (V), frequency (f), hot and cold temperature (TH, TC)) with a characteristic value, the Fill Factor (F), commonly known as the West Number, which accounts for any idealities of the engine itself, to predict the potential power output ( Wo). This correlation comes from Beale’s analysis of existing Stirling engines, adapted by West to include operating temperatures, for which the average Fill Factor of well-designed engines is 0.35 (in SI units). FIG. 8B replots the data using the modified Beale Equation in order to extract our engines average Fill Factor of approximately 0.26. (FIG. 8C and FIG. 8D). The experimental data replotted with different Fill Factors. The line fits shown here are those plotted in FIG. 6A.

[0088] In addition to directly producing mechanical power, the Radiative Cooling Engine can be modified to simultaneously generate electrical power (See FIG. 6B). To demonstrate this capability, a 3D-printed motor mount was designed to connect the driveshaft of a small DC-motor to the rotor of the Stirling engine.

[0089] FIG. 9A is a circuit diagram for DC measurement and shows a ammeter (A), a voltmeter (V) across 10 ohm variable resistor in series with a 100 ohm variable resistor, and a motor (M). A Stirling engine was placed on top of a hot plate to control hot side temperature. Keithley 2450 meters were used to monitor and record amperage and voltage across a variable load (0UC-2024-579-2-PCT -15-ohms to 110 ohms). Foil insulation was placed above the hot plate to limit temperature drift, an optical photogate was used for engine frequency measurement, and temperature detectors were used for plate temperature monitoring. The DC motor was attached to the front of the Stirling engine with the 3D-printed mount. The variable resistors were used to sweep the voltage across the motor. Components of the test setup 300 are schematically illustrated in FIG. 9B, which depicts hot surface 302 (bottom plate), displacer 304, radiative cooling surface 306 (top plate), displacer chamber 308, piston cylinder 310, piston 312, connecting rod 314, connecting pin 316, crank disc 318, DC motor 320, crankshaft 322, crank disc 324, connecting pin 326, and displacer rod 328.

[0090] The leads of the DC-motor were attached to a variable resistor load to find the maximum electrical power available for various engine temperature differentials (see FIG. 6B). While only a few percent of the mechanical energy is converted to electrical power due to losses in the DC-motor, approximately half of the mechanical energy of the engine was still available while the DC- motor is attached, enabling generation of both mechanical and electrical power simultaneously (see FIG. 6C and FIG. 10A through FIG. 10D).

[0091] Initially, while the engine is spinning freely, an engine frequency of approximately 6 Hz (FIG. 10A) and 1.8 mW of available mechanical power (FIG. 10B) were measured. At around t = 150 s, the engine is stopped. The DC motor is then attached, and the engine is restarted. The motor applies torque that reduces the engine frequency from its unloaded condition. With the engine attached, available mechanical power of 1 .1 mW is still measured (peak around t = 160 s), while the additional 26 pW of electrical power is converted by the DC motor (FIG. 6B). In FIG. 10C, engine plate temperatures during this run are monitored, which show a small drift in temperature once the motor is attached. During the measurement, the top plate temperature could not be controlled, so internal heat transfer from the working fluid and ambient heating effects from the electrical hot plate cause the engine top plate temperature to drift upwards. In FIG. 10D, the associated powers are plotted.

[0092] Note that there is opportunity for improved power extraction, and theUC-2024-579-2-PCT -16-mechanical-to-electrical power conversion efficiency could be maximized by designing a DC motor to match the radiative cooling engine’s torque and frequency.

[0093] Experimental Results - Air Circulation

[0094] Another application of the Radiative Cooling Engine of this disclosure is air circulation. To explore this approach, the engine’s flywheel was replaced with a custom 3D-printed fan blade, thus converting the Stirling engine into an axial fan (see FIG. 6D and FIG. 11 B). FIG. 11 A shows the engine’s frequency and temperature difference, and FIG. 11 B shows the motion of the fan blade over time.

[0095] The ambient temperature inside of a greenhouse (29°C) and an effective radiative cooler exposed to the night sky (7°C) were simulated. Air flow in front of the fan was monitored using a hot-wire anemometer (Dwyer 471 B) mounted to a two-axis translation stage (FIG. 6D). Positional air speed is plotted in FIG. 6E which shows relatively uniform radial air speed approaching 0.3 m / s, the air speed recommended to circulate CO2 in greenhouses. A separate temperature ramp was performed with the fan attachment and engine frequency and air speeds were measured across an expanded temperature range (FIG. 6F). FIG. 12A shows engine frequency with associated maximum air speed measured in front of the fan and FIG. 12B shows engine temperature profile.

[0096] At low temperature differentials, it was found that the fan is capable of moving air between 0.15 and 0.2 m / s, which is the air speed recommended by the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) to maintain thermal comfort inside buildings (see FIG. 6F). Additionally, at 0.2 m / s, the volumetric flow rate in front of the fan exceeded 5 cfm, which is the minimum per-person ventilation rate required by ASHRAE to minimize adverse health effects inside public buildings, such as libraries, courtrooms, and auditoriums. Utilizing the warm indoor environment as a heat source and radiative cooling on the roof as a heat sink, an efficiently designed radiative cooling fan could provide an entirely passive method of ensuring healthy breathing air in public places and promoting plant growth by regulating humidity and CO2 levels in greenhouses and growhouses.UC-2024-579-2-PCT -17-

[0097] Several improvements can be made to optimize engine performance. Internal engine friction and heat loss could be reduced using He or H instead of air as the working fluid. Power output can also be increased by pressurizing the gas. The radiative cooling power, and thus available power, can be increased by improving the radiative coupling of the top plater to the night sky. The use of a tailored radiative cooling material instead of commercial paint inside a thermally insulating vacuum enclosure would isolate the radiative exchange between the cold plate and the sky to maximize radiative cooling power around the clock. The radiative cooling power could also be increased by attaching the bottom plate of the engine to existing sources of waste heat in industrial, agricultural, or residential environments.

[0098] Global Application

[0099] Generating a temperature difference through radiative emission at night is broadly applicable in many regions of the world. Larger temperature differences and output power are possible under clear sky conditions.

[0100] To evaluate the potential performance of the Radiative Cooling Engine around the globe, consider the Carnot-limit engine 400 schematically illustrated in FIG. 13. The illustrated engine utilizes the earth’s surface as a heat source 402 and an ideal broadband radiative cooler (emitter) 404 radiatively coupled with the sky 406 as a cold sink, which would enable the engine to operate 24-hours a day by reflecting solar radiation while simultaneously emitting in the infrared.

[0101] Global data for Pabsorbed and THwere obtained from NASA as the downwelling infrared from the sky and the global surface temperature, respectively. The emitter temperatureand ultimately the engine power, can be calculated by combining the steadystate equation for heat flow of the isolated system above with Carnot’s law:^Net Pemitted Pabsorbed > [ ]UC-2024-579-2-PCT -18-and maximizing the output power, Pengine, for emitter temperature, Tc:where Pemittedis restricted to the blackbody emission of the cooler:

[0102] Average monthly downwelling infrared radiation and surface temperature were collected from NASA’s CERES and MODIS projects, respectively, as these two quantities control the upper limit of the engine’s potential temperature differential. The global surface temperature was used as the engine’s hot-plate temperature for the Carnot-efficient radiative cooling engine shown in FIG. 13.

[0103] To determine the optimal cold-plate temperature for maximum power generation, Carnot’s law can be combined with the steady state equation for heat flow between the ideal radiative cooler and the sky. Here, it is assumed that the engine plates are thermally isolated and that perfect radiative coupling between the cold plate and the sky is achieved. The average temperature difference across a Radiative Cooling Engine and the associated power potential around the globe during different times of the year can be calculated. The power density is highest in arid regions and mountain ranges, where downwelling radiation is lowest, and is close to zero in heavily forested regions, where the emitter cannot effectively exhaust heat to outer space. The best performance on average appears to occur in Saharan Africa, throughout the Eurasian Steppe, and, interestingly, during the summer in Antarctica. These regions are excellent targets for alternative power sources as renewable energy production is low.

[0104] As previously noted, radiative coolers have been theorized to slow global warming. The earth currently absorbs approximately 1 W / m2more than it emits, which causes a net warming effect. Radiative coolers offset this byUC-2024-579-2-PCT -19-enhancing earth’s emission. As it operates on the same principle, the deployment of a Radiative Cooling Engine can therefore also aid climate change mitigation. By trapping and converting a portion of earth’s heat to usable power, it is prevented from entering the atmosphere and contributing to global temperature rise.

[0105] Exemplary Implementations

[0106] From the description herein, it will be appreciated that the present disclosure encompasses multiple implementations of the technology which include, but are not limited to, the following:

[0107] A radiative cooling engine apparatus, comprising: a low-temperature differential (LTD) Stirling engine; a lower plate coupled to the engine and having a lower surface configured for thermal coupling to a heat source; an upper plate coupled to the engine and having an upper radiative surface configured for thermal coupling to a heat sink, the radiative surface having an emissive coating; wherein the lower plate has a smaller surface area than the upper plate; and wherein the engine converts thermal energy transferred from the heat source to the heat sink to a mechanical output from the engine.

[0108] The apparatus of any preceding or following implementation: wherein the heat source comprises the earth's surface; wherein the heat sink comprises ambient air; and wherein the engine operates when the earth's surface is warmer than the ambient air.

[0109] The apparatus of any preceding or following implementation: wherein the radiative surface of the upper plate is positioned toward the sky; and wherein the engine is configured to exploit a temperature difference between the earth's surface and a cold night sky to generate said mechanical output continuously.

[0110] A radiative cooling engine apparatus, comprising: a low-temperature differential Stirling engine; a lower plate coupled to the low-temperature differential Stirling engine, said lower plate having a lower surface configured for thermal coupling to a heat source; an upper plate coupled to the low- temperature differential Stirling engine, said upper plate having an upper radiative surface configured for thermal coupling to a heat sink, said upper radiative surface having a thermally emissive coating; wherein the upperUC-2024-579-2-PCT -20-radiative surface of the upper plate has a larger surface area than the lower surface of the lower plate; and wherein the apparatus produces a mechanical output in response to a temperature differential between the upper plate and the lower plate.

[0111] The apparatus of any preceding or following implementation wherein, when the upper radiative surface of the upper plate is positioned skyward, and when sky temperature is less than earth surface temperature at the lower plate, the temperature differential is the temperature difference between earth surface temperature and sky temperature.

[0112] The apparatus of any preceding or following implementation: wherein the heat source comprises a terrestrial body; wherein the heat sink comprises a location away from the terrestrial body; and wherein the apparatus operates when the heat sink is cooler than the heat source.

[0113] The apparatus of any preceding or following implementation: wherein the terrestrial body comprises the earth at night; and wherein the location away from the terrestrial body comprises the sky at night.

[0114] The apparatus of any preceding or following implementation: wherein the heat source comprises the earth at night, and wherein the heat sink comprises the sky at night.

[0115] The apparatus of any preceding or following implementation, wherein the thermally emissive coating comprises a material selected from the group consisting of Avian Black-S and AcryShield 400.

[0116] A radiative cooling engine apparatus, comprising: a low-temperature differential Stirling engine; a lower plate coupled to the low-temperature differential Stirling engine, said lower plate having a lower surface configured for thermal coupling to a heat source; an upper plate coupled to the low- temperature differential Stirling engine, said upper plate having an upper radiative surface configured for thermal coupling to a heat sink, said upper radiative surface having a thermally emissive coating; wherein the upper radiative surface of the upper plate has a larger surface area than the lower surface of the lower plate; and wherein the apparatus produces a mechanical output in response to a temperature differential between the upper plate and the lower plate; a mounting base, said mounting base having an upperUC-2024-579-2-PCT -21-surface, said mounting base having a lower surface with a plurality of spikes extending away from said lower surface, said upper surface of said mounting base configured to be coupled to said lower surface of said lower plate, said spikes configured to be coupled to a terrestrial body.

[0117] The apparatus of any preceding or following implementation: wherein the heat source comprises the terrestrial body; wherein the heat sink comprises a location away from the terrestrial body; and wherein the apparatus operates when the heat sink is cooler than the heat source.

[0118] A method for generating a mechanical output, comprising: configuring a lower plate of a low-temperature differential (LTD) Stirling engine for thermal coupling to a heat source; coupling an upper plate the low-temperature differential Stirling engine, said upper plate having an upper radiative surface configured for thermal coupling to a heat sink, said upper radiative surface having a thermally emissive coating; wherein the upper radiative surface of the upper plate has a larger surface area than the lower surface of the lower plate; thermally coupling the lower plate to a terrestrial body; orienting the upper radiative surface of the upper plate toward a location away from the terrestrial body; wherein the heat source comprises the terrestrial body; wherein the heat sink comprises the location away from the terrestrial body; wherein the low-temperature differential Stirling engine generates a mechanical output in response to a temperature differential between the upper plate and the lower plate.

[0119] The method of any preceding or following implementation, wherein said mechanical output is generated when the heat sink is cooler than the heat source.

[0120] The method of any preceding or following implementation: wherein the terrestrial body comprises the earth at night; and wherein the location away from the terrestrial body comprises the sky at night.

[0121] The method of any preceding or following implementation wherein, when the upper radiative surface of the upper plate is oriented skyward, and when sky temperature is less than earth surface temperature at the lower plate, the temperature differential is the temperature difference between earth surface temperature and sky temperature.UC-2024-579-2-PCT -22-

[0122] The method of any preceding or following implementation: wherein the heat source comprises the earth at night, and wherein the heat sink comprises the sky at night.

[0123] The method of any preceding or following implementation, wherein the thermally emissive coating comprises a material selected from the group consisting of Avian Black-S and AcryShield 400.

[0124] Terminology and Scope

[0125] As used herein, the term "implementation" is intended to include, without limitation, embodiments, examples, or other forms of practicing the technology described herein.

[0126] As used herein, the singular terms "a," "an," and "the" may include plural referents unless the context clearly dictates otherwise. Reference to an object in the singular is not intended to mean "one and only one" unless explicitly so stated, but rather "one or more."

[0127] Phrasing constructs, such as “A, B and / or C”, within the present disclosure describe where either A, B, or C can be present, or any combination of items A, B and C. Phrasing constructs indicating, such as “at least one of” followed by listing a group of elements, indicates that at least one of these groups of elements is present, which includes any possible combination of the listed elements as applicable.

[0128] References in this disclosure referring to “an embodiment”, “at least one embodiment” or similar embodiment wording indicates that a particular feature, structure, or characteristic described in connection with a described embodiment is included in at least one embodiment of the present disclosure. Thus, these various embodiment phrases are not necessarily all referring to the same embodiment, or to a specific embodiment which differs from all the other embodiments being described. The embodiment phrasing should be construed to mean that the particular features, structures, or characteristics of a given embodiment may be combined in any suitable manner in one or more embodiments of the disclosed apparatus, system, or method.

[0129] As used herein, the term "set" refers to a collection of one or more objects. Thus, for example, a set of objects can include a single object or multiple objects.UC-2024-579-2-PCT -23-

[0130] Relational terms such as first and second, top and bottom, upper and lower, left and right, topside and underside, front and back, proximal and distal, leading and trailing, and the like, may be used solely to distinguish one entity, action, or orientation from another entity, action, or orientation without necessarily requiring or implying any actual such relationship or order between such entities, actions, or orientations. Such terms are not intended to be terms of limitation read into the claims.

[0131] The terms "comprises," "comprising," "has", "having," "includes", "including," "contains", "containing" or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, apparatus, or system, that comprises, has, includes, or contains a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, apparatus, or system. An element proceeded by "comprises . . . a", "has . . . a", "includes . . . a", "contains . . . a" does not, without more constraints, preclude the existence of additional identical elements in the process, method, article, apparatus, or system, that comprises, has, includes, contains the element.

[0132] As used herein, the terms "approximately", "approximate", "substantially", "substantial", "essentially", and "about", or any other version thereof, are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. When used in conjunction with a numerical value, the terms can refer to a range of variation of less than or equal to ± 10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1 %, less than or equal to ±0.5%, less than or equal to ±0.1 %, or less than or equal to ±0.05%. For example, "substantially" aligned can refer to a range of angular variation of less than or equal to ±10°, such as less than or equal to ±5°, less than or equal to ±4°, less than or equal to ±3°, less than or equal to ±2°, less than or equal to ±1 °, less than or equal to ±0.5°, less than or equal to ±0.1 °, or lessUC-2024-579-2-PCT -24-than or equal to ±0.05°.

[0133] Additionally, amounts, ratios, and other numerical values may sometimes be presented herein in a range format. It is to be understood that such range format is used for convenience and brevity and should be understood flexibly to include numerical values explicitly specified as limits of a range, but also to include all individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly specified. For example, a ratio in the range of about 1 to about 200 should be understood to include the explicitly recited limits of about 1 and about 200, but also to include individual ratios such as about 2, about 3, and about 4, and sub-ranges such as about 10 to about 50, about 20 to about 100, and so forth.

[0134] The term "coupled" as used herein is defined as connected, although not necessarily directly and not necessarily mechanically. A device or structure that is "configured" in a certain way is configured in at least that way, but may also be configured in ways that are not listed.

[0135] Benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential feature or element of the technology described herein or any or all the claims.

[0136] In addition, in the foregoing disclosure various features may be grouped together in various embodiments for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments require more features than are expressly recited in each claim. Inventive subject matter can lie in less than all features of a single disclosed embodiment.

[0137] The abstract of the disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.

[0138] It will be appreciated that the practice of some jurisdictions may require deletion of one or more portions of the disclosure after the application is filed. Accordingly, the reader should consult the application as filed for the originalUC-2024-579-2-PCT -25-content of the disclosure. Any deletion of content of the disclosure should not be construed as a disclaimer, forfeiture, or dedication to the public of any subject matter of the application as originally filed.

[0139] All text in a drawing figure is hereby incorporated into the disclosure and is to be treated as part of the written description of the drawing figure.

[0140] The following claims are hereby incorporated into the disclosure, with each claim standing on its own as a separately claimed subject matter.

[0141] Although the description herein contains many details, these should not be construed as limiting the scope of the disclosure, but as merely providing illustrations of some of the presently preferred embodiments. Therefore, it will be appreciated that the scope of the disclosure fully encompasses other embodiments which may become obvious to those skilled in the art.

[0142] All structural and functional equivalents to the elements of the disclosed embodiments that are known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the present claims. Furthermore, no element, component, or method step in the present disclosure is intended to be dedicated to the public regardless of whether the element, component, or method step is explicitly recited in the claims. No claim element herein is to be construed as a "means plus function" element unless the element is expressly recited using the phrase "means for". No claim element herein is to be construed as a "step plus function" element unless the element is expressly recited using the phrase "step for".UC-2024-579-2-PCT -26-

Claims

CLAIMSWhat is claimed is:1 . A radiative cooling engine apparatus, comprising: a low-temperature differential Stirling engine; a lower plate coupled to the low-temperature differential Stirling engine, said lower plate having a lower surface configured for thermal coupling to a heat source; an upper plate coupled to the low-temperature differential Stirling engine, said upper plate having an upper radiative surface configured for thermal coupling to a heat sink, said upper radiative surface having a thermally emissive coating; wherein the upper radiative surface of the upper plate has a larger surface area than the lower surface of the lower plate; and wherein the apparatus produces a mechanical output in response to a temperature differential between the upper plate and the lower plate.

2. The apparatus of claim 1 wherein, when the upper radiative surface of the upper plate is positioned skyward, and when sky temperature is less than earth surface temperature at the lower plate, the temperature differential is the temperature difference between earth surface temperature and sky temperature.

3. The apparatus of claim 1 : wherein the heat source comprises a terrestrial body; wherein the heat sink comprises a location away from the terrestrial body; and wherein the apparatus operates when the heat sink is cooler than the heat source.

4. The apparatus of claim 3: wherein the terrestrial body comprises the earth at night; and wherein the location away from the terrestrial body comprises the sky at night.

5. The apparatus of claim 1 : wherein the heat source comprises the earth at night, andUC-2024-579-2-PCT -27-wherein the heat sink comprises the sky at night.

6. The apparatus of claim 1 , wherein the thermally emissive coating comprises a material selected from the group consisting of Avian Black-S and AcryShield 400.

7. A radiative cooling engine apparatus, comprising: a low-temperature differential Stirling engine; a lower plate coupled to the low-temperature differential Stirling engine, said lower plate having a lower surface configured for thermal coupling to a heat source; an upper plate coupled to the low-temperature differential Stirling engine, said upper plate having an upper radiative surface configured for thermal coupling to a heat sink, said upper radiative surface having a thermally emissive coating; wherein the upper radiative surface of the upper plate has a larger surface area than the lower surface of the lower plate; and wherein the apparatus produces a mechanical output in response to a temperature differential between the upper plate and the lower plate; a mounting base, said mounting base having an upper surface, said mounting base having a lower surface with a plurality of spikes extending away from said lower surface, said upper surface of said mounting base configured to be coupled to said lower surface of said lower plate, said spikes configured to be coupled to a terrestrial body.

8. The apparatus of claim 7: wherein the heat source comprises the terrestrial body; wherein the heat sink comprises a location away from the terrestrial body; and wherein the apparatus operates when the heat sink is cooler than the heat source.

9. The apparatus of claim 8: wherein the terrestrial body comprises the earth at night; and wherein the location away from the terrestrial body comprises the sky at night.UC-2024-579-2-PCT -28-10. The apparatus of claim 7 wherein, when the upper radiative surface of the upper plate is positioned skyward, and when sky temperature is less than earth surface temperature at the lower plate, the temperature differential is the temperature difference between earth surface temperature and sky temperature.11 . The apparatus of claim 7 : wherein the heat source comprises the earth at night, and wherein the heat sink comprises the sky at night.

12. The apparatus of claim 7, wherein the thermally emissive coating comprises a material selected from the group consisting of Avian Black-S and AcryShield 400.

13. A method for generating a mechanical output, comprising: configuring a lower plate of a low-temperature differential (LTD) Stirling engine for thermal coupling to a heat source; coupling an upper plate the low-temperature differential Stirling engine, said upper plate having an upper radiative surface configured for thermal coupling to a heat sink, said upper radiative surface having a thermally emissive coating; wherein the upper radiative surface of the upper plate has a larger surface area than the lower surface of the lower plate; thermally coupling the lower plate to a terrestrial body; orienting the upper radiative surface of the upper plate toward a location away from the terrestrial body; wherein the heat source comprises the terrestrial body; wherein the heat sink comprises the location away from the terrestrial body; wherein the low-temperature differential Stirling engine generates a mechanical output in response to a temperature differential between the upper plate and the lower plate.

14. The method of claim 13, wherein said mechanical output is generated when the heat sink is cooler than the heat source.UC-2024-579-2-PCT -29-15. The method of claim 14: wherein the terrestrial body comprises the earth at night; and wherein the location away from the terrestrial body comprises the sky at night.

16. The method of claim 13 wherein, when the upper radiative surface of the upper plate is oriented skyward, and when sky temperature is less than earth surface temperature at the lower plate, the temperature differential is the temperature difference between earth surface temperature and sky temperature.

17. The method of claim 13: wherein the heat source comprises the earth at night, and wherein the heat sink comprises the sky at night.

18. The method of claim 13, wherein the thermally emissive coating comprises a material selected from the group consisting of Avian Black-S and AcryShield 400.UC-2024-579-2-PCT -30-

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