Why does the Falcon-9 booster make a triple sonic boom during flyback? An initial analysis Open Access

The SpaceX Falcon-9 rocket is the first orbital-class launch vehicle with a fully reusable booster stage (SpaceX, 2024). The 41.2-m long booster separates from the rest of the rocket while in the upper atmosphere and then descends through the atmosphere toward a landing pad either on land or at sea. Examples of a launch and landing are shown in Figs. 1(a) and 1(b), respectively. Because the booster descends at supersonic speeds, it produces a sonic boom (Anderson , 2024), referred to as a “flyback sonic boom.” While most far-field sonic booms are N-waves (i.e., consist of two shocks) (Maglieri , 2014), these booster-flyback sonic booms contain three primary shocks (Anderson and Gee, 2024; Anderson , 2024), as shown in Figs. 1(c) and 1(d). This phenomenon is not unique to the Falcon-9 booster, as the SpaceX Starship Super Heavy booster's sonic boom also has shown three distinguishable shocks (Gee , 2024). Understanding the Falcon-9 triple sonic boom may therefore shed light on whether all reusable rocket boosters are expected to produce a similar signature.

Such flyback sonic booms are high-amplitude acoustic events. Measured data from three Falcon-9 flights have been published by Anderson (2024). For observers farther than 2 km from the launch and landing locations, the sonic boom peak overpressure exceeds the peak pressures experienced during the launch. Within 2 km of the landing location, the sonic boom peak overpressures are generally between 6 and 10 pounds per square foot (psf). This drops to 2–3 psf at 10 km, with the triple sonic boom being clearly measured as far as 25 km from the landing pad and likely persisting even farther.

In the modern space age, other organizations throughout the world are also developing reusable vehicles that will use a similar flyback approach. Because this will result in an increase in the number of sonic booms around the landing facilities, it is important to ensure that accurate launch vehicle sonic boom models are developed and used. Sonic boom prediction software, like NASA's PCBoom software (Lonzaga , 2022; Page , 2023), has generally been designed and validated for use with air-breathing, aerodynamic-lift-producing jet aircraft, rather than rockets and reentry vehicles. Thus, these vertically descending, rapidly decelerating, blunt-body sonic boom sources provide a unique opportunity to further understand sonic boom formation and propagation. Although some organizations have used current models to produce prediction maps for Falcon-9 flyback sonic booms (FAA, 2020), such results only show final metric values, rather than full waveforms. This leaves whether the physics are fully understood and modeled as an open question. Some evidence suggests that models have been custom-tailored to match specific launch vehicles (FAA, 2020). This can be useful for predicting the sonic booms from a known vehicle under certain atmospheric and trajectory conditions, but does not necessarily produce a model that can be confidently ported to a new vehicle design or to other flight conditions.

Although there are many interesting features of Falcon-9 flyback sonic booms, this Letter's aim is restricted to determining why the booster produces a triple sonic boom rather than an N-wave. Although the effects of maneuvers are important for sonic boom predictions (Lonzaga , 2022; Maglieri , 2014), a maneuver-based explanation would not explain why a consistent triple sonic boom is measured at all locations ranging from near the landing pad to 25 km from the pad, and at all azimuths (Anderson , 2024). Additionally, the triple boom cannot be due to the exhaust plume from the engines during the landing burn, as the landing burn tends to occur after the vehicle is subsonic [see SpaceX (2023) for an example]. Thus, because the booster falls without engines on during the majority of the time that the sonic boom is produced, an explanation based on booster geometry is preferable. Such an explanation is demonstrated in this Letter using three complementary approaches. It should be noted that because this is an initial analysis, the primary goal is to see whether a triple sonic boom can be predicted in the far field, and the precise matching of that sonic boom to measurements remains an important part of future work. The first method, shown in Sec. 2, uses sonic boom theory coupled with nonlinear acoustic propagation modeling. In Sec. 3, computational fluid dynamics (CFD) simulations are used to visualize the flow field near the booster during flyback. In Sec. 4, photographic evidence from a booster flyback is used to visualize portions of the flow during an actual flight. Each method supports the conclusion that the booster's grid fins produce a forward-migrating shock wave that merges with a backward-migrating rarefaction wave produced by the lower portions of the booster, including the folded landing legs. This merging produces an additional central shock, explaining the triple boom signature.

In this Letter, the booster is modeled as an axisymmetric body of revolution with protuberances representing the landing legs and grid fins. While the vehicle is not completely axisymmetric, the triple boom is observed at all azimuth angles relative to the landing location (Anderson , 2024), which leads to the assumption that the flow field blends azimuthally during propagation. For simplicity, this blending is inherently accounted for by assuming an axisymmetric body from the start.

This modeling has two levels of detail. Figure 2(a) shows the booster modeled as a simple cylinder of equal proportions to the booster. Both the original geometry (black) and a modified geometry (blue) designed to better match an effective body shape are shown. Throughout this Letter, this geometry is referred to as the “Cylinder.” The F-function for this geometry is shown in Fig. 2(b). A more detailed approximation to the booster geometry is shown in Fig. 2(c), including the folded landing legs, grid fins, and a small protuberance near the top of the booster. Throughout this Letter, this geometry is referred to as the “Falcon 9.” The F-function for this geometry is shown in Fig. 2(d).

To account for the blunt shape of the booster during flyback (see Fig. 2), methods proposed by Gottlieb and Ritzel (1988) are applied to ensure more accurate shock placement. Because the goal is to model the far-field boom waveforms, it is assumed viable to accurately model only the general flow field, rather than to accurately match every detail of the geometry, as the near-field details will tend to disappear during propagation (Maglieri , 2014). There are three blunt features to which corrections are applied: the bottom of the booster (where the engines are located), the grid fins located near the top of the booster, and the actual top of the booster where there is an abrupt end to the geometry. These are all visible in Fig. 2. Although some other portions of the booster may also be considered blunt, the corrections that could be applied to these areas are assumed to have minimal impact on the far-field signature.

At the bottom of the booster, there is a detached bow shock. To account for the standoff distance between the shock and the body of the booster, an artificial body extension is added, ensuring that the shock occurs at the proper location. This is done for both the Cylinder and Falcon-9 geometries shown in Fig. 2. This extension can be represented by a cubic polynomial subject to the boundary conditions specified by Gottlieb and Ritzel (1988). Using the highly blunt Falcon-9 geometry, the original recommendation provided by Gottlieb and Ritzel (1988) produces an updated geometry that still greatly exceeded their suggested bluntness criteria. To correct for this, a related equation intended for blunt features on other portions of the geometry was used and found to more closely align with their bluntness criteria. This resulted in a larger standoff distance between the bow shock and the bottom of the booster.

The grid fins on the booster represent the most challenging aspect of this geometry. The fins allow airflow through the grid-fin structure while still producing a shock ahead of the fins. This can be observed in wind tunnel and CFD work by Bykerk (2022). Although Gottlieb and Ritzel (1988) did not consider blunt features that allow flow through, we treat it as a smaller protrusion than the physical grid fins. As shown in Fig. 2(c), the grid fins are modeled as a solid protuberance that extends about half as far as the physical grid fins. The shorter size ensures that airflow is not altogether impeded while ensuring that a shock is still produced. To model the flow on the other side of the grid fins, a linear taper in the geometry is used that returns the geometry radius to the same as the booster. Future research should investigate the most appropriate treatment of grid fins in sonic boom modeling.

For blunt features that face away from the flow such as the top of the booster, a different type of extension is applied to the body. This extension accounts for the flow after the body and the subsequent turbulent wake. The first portion of the extended geometry is a conical shape behind the top of the booster. The cone tapers to an amount specified by Gottlieb and Ritzel (1988) and then becomes a cylinder. This is used for both the Cylinder and Falcon-9 geometries in Fig. 2.

This equation is solved numerically using a hybrid time-frequency approach. The methods are described more completely in Gee (2005) and Gee (2008). Waveform distortion is calculated in the time domain via the Earnshaw solution while the geometric spreading, atmospheric attenuation, and dispersion are calculated in the frequency domain. The method uses adaptive steps based on the shock-formation distance (Anderson, 1974). When the steps are less than 1 mm, the method of Pestorius (Hamilton and Blackstock, 2008; Pestorius, 1973) is used to determine shock location and amplitude.

As the signatures are input into the equation, they are converted to functions of time using an assumed mean sound speed of 343 m/s and are resampled to 20 kHz. The time arrays are then scaled by $1/M∞$ to account for the fact that far from the vehicle, the waves approximately follow the Mach lines and thus the shocks are closer to each other than if they all propagate normal to the geometry. Additionally, when the initial pressure field calculated using Eq. (1) is input into Eq. (3), the pressures are large. For the Cylinder geometry, pressures around one atmosphere are estimated at one body length away from the booster (41.2 m). For the Falcon 9 geometry, the peak pressure excursions are around 10 atmospheres at the same distance. Such pressures are clearly nonphysical, as the rarefactions would be below vacuum pressure. This could be fixed by calculating the pressure at a farther distance in Eq. (1), but the required distance to have the pressure excursions drop to within one atmosphere would be around 100 body lengths, by which distance the near-field source function produced via the F-function is no longer valid, as Eq. (1) does not account for the nonlinear effects that would have substantially altered the flow field. Fortunately, when the signature at one body length away from the booster is input into Eq. (3), the peak overpressures rapidly decay to less than one atmosphere within the first 2 m of propagation. Within the first 7 m, the peak overpressures decay to within 0.5 atmospheres. Thus, outside of the first few meters of propagation, the flow field is assumed to be sufficiently accurate to capture the overall far-field sonic boom shape when propagated, though the overpressures are not expected to be fully accurate. This claim is substantiated by the similarity between the signatures produced in this section with the flow fields shown using computational fluid dynamics in Sec. 3. For both the Cylinder and Falcon 9 cases in this Letter, the signatures calculated at one body length away from the booster are used. As the purpose of this letter is to describe the overall waveform shape in the far field, this is an acceptable limitation. Future work should go toward accurately modeling both the waveform shape and overpressures simultaneously.

As the Cylinder and Falcon-9 near-field signatures are propagated to the far field, the two signatures evolve into, respectively, an N-wave and a triple boom. This propagation is animated in Mm. 1. In this animation, the Cylinder geometry produces a shock followed immediately by a rarefaction wave. This rarefaction wave ultimately migrates backward in the pressure signature and merges with the recompression shock near the top of the Cylinder. Although an interesting feature, we expect this rarefaction wave is not fully accurate. While the methods used here are essentially laminar, studies of turbulent supersonic flow over forward-facing steps indicate that turbulent separation can greatly complicate the flow field near the geometric discontinuity (Czarnecki and Jackson, 1975; Hu , 2022; Murugan and Govardhan, 2016). Additionally, Gottlieb and Ritzel (1988) suggest that inaccurate expansion waves can be generated near the front of blunt geometries when using F-function methods. Krasnov (1970) also discusses the flow around a body of revolution with a flat nose and shows that turbulence is an important consideration, forming a region of separated flow followed by a reattachment shock. While the accuracy of this rarefaction wave remains under investigation, the Cylinder signature does evolve into an N-wave. It is thus concluded that the far-field signature from a cylindrical geometry of equal proportions to the Falcon-9 booster is an N-wave, though a relatively large propagation distance may be necessary for the N-wave to fully develop from this geometry.

While the Cylinder geometry produces a far-field N-wave, the Falcon-9 geometry produces a triple boom that remains stable out to at least 25 km, as has been observed in measurements (Anderson and Gee, 2024; Anderson , 2024). Although the Falcon-9 geometry also produces a rarefaction wave at the base of the geometry, it is of little consequence as the rarefaction wave is almost immediately negated during propagation by a forward-migrating shock produced by the folded landing legs. This shock then merges with the front shock of the waveform. The folded landing legs also produce another, separate, rarefaction wave. As this rarefaction wave migrates backward in the signature, it merges with a forward-migrating shock wave produced by the grid fins. This produces a central shock that is more balanced and remains near the center of the signature. Thus, it is concluded that the far-field signature from a Falcon-9 booster geometry is a triple sonic boom.

To further illustrate and compare the changes in the waveforms with propagation distance, the signatures at four different distances are shown in Fig. 3. As the two signatures propagate, the Cylinder case produces an N-wave while the Falcon-9 case produces a triple sonic boom. These results demonstrate that a triple sonic boom can be predicted in the far field based on the booster geometry and that the triple sonic boom origin is likely related to the intermediate features of the geometry, particularly the grid fins. Because there remains some ambiguity over the accuracy of the rarefaction wave produced at the bottom of the geometry, the conclusion of this portion of the analysis is that the central shock results from a forward-migrating compression wave caused by the grid fins merging with a rearward-migrating rarefaction wave caused by the lower portions of the booster, including the folded landing legs. Further studies are required to determine the precise effects of the landing legs on the final far-field signature.

The second method used to determine the triple-boom origin is computational fluid dynamics (CFD). The results are shown in Fig. 4. For these simulations, two-dimensional unstructured meshes for both the Cylinder and Falcon-9 geometries were produced in gmsh (Geuzaine and Remacle, 2024) and the simulations were run in openfoam (OpenFOAM, 2024). The simulations were run at Mach 2.0 with the shockFluid solver for compressible flows. To reduce computational complexity, the flow field was assumed to be laminar. Assuming symmetry, the flow was only computed on one side of the geometries, with a symmetryPlane boundary condition on the bottom. The portions where the geometries were modeled used a zeroGradient boundary condition for the pressure and temperature and a slip condition for the velocity. Flow entered through the left boundary and exited through the top and right boundaries, which used waveTransmissive boundary conditions.

For the Cylinder geometry, three features persist at the edge of the computational domain. These arise from the detached bow shock, a rarefaction occurring at the base of the booster, and a recompression shock at the end of the geometry. Similar results were found in Sec. 2, where the central rarefaction wave in that analysis ultimately merged with the rear recompression shock. It remains unclear whether this rarefaction wave at the base of the geometry is accurate, as discussed in Sec. 2. For now, the conclusion is that if a more-complex simulation were run, including turbulence effects, this clear rarefaction wave would either not be present or would merge with the other shocks during propagation. The far-field result would then be an N-wave. Further simulations are required to verify this claim.

For the Falcon-9 geometry, three features also persist at the edge of the computational domain, but the structure is different from the Cylinder case. The front shock comes from the detached bow shock at the bottom of the booster. The rarefaction wave produced at the corner of the base of the geometry is effectively negated by a shock wave produced by the base of the landing legs, as was seen in Sec. 2. As also seen in Sec. 2, the folded landing legs produce rarefaction waves that merge with a shock wave produced by the grid fins. Such a rarefaction wave produced in the vicinity of the folded landing legs can be seen in near-field simulations by Charbonnier (2022). The trend for rarefaction waves to migrate backward in the shock system balances out the trend for the shock wave to migrate forward, producing a balanced central shock. Last, similar to the Cylinder case, a recompression shock occurs at the end of the geometry. In the Falcon-9 results, all three major shocks are observed to mutually diverge at the edge of the computational domain, suggesting that the three shocks will persist in the far field. While many of these same near-field flow effects can be seen in the wind tunnel measurements and simulations of Marwege (2022), Charbonnier (2022), and Bykerk (2022), the relationship between the flow features produced by the folded landing legs and the grid fins cannot be easily deduced either because their models did not include grid fins or their results did not contain details far from the model. Nevertheless, the fact that similar near-field flow structures are found in the literature substantiate the claim that the simulations in this Letter, although simplified, are sufficiently accurate for studying much of the overall flow field. The conclusion of this section is the same as Sec. 2, that the central shock in the triple boom is due to a forward-migrating shock from the grid fins merging with a rearward-migrating rarefaction wave produced by the lower portions of the booster, including the folded landing legs.

The final piece of evidence to determine the triple-boom origin comes from a unique photograph taken during the SpaceX NG-21 mission. While this analysis is not as technically rigorous, it presents a unique way to validate the results in Secs. 2 and 3. The original photograph is shown in Fig. 5(a). Condensation clouds form in regions of low pressure, where the conditions temporarily permit water in the air to condense (Campbell and Chambers, 1994). While the shocks themselves are not visible, these condensation clouds highlight important flow features that can help determine approximate shock locations. These features, illustrated in Fig. 5(b), point to the same conclusion as Secs. 2 and 3. Because regions of fluid expansion tend to form between shocks, approximate shock positions can be estimated. First, there must be a detached bow shock in front of the leading edge of the geometry, denoted by the letter “A.” This shock cannot be seen in the photograph, but its presence is inferred because all supersonic bodies have front shocks. Behind this shock, a condensation cloud forms that persists up until the grid fins, where the cloud abruptly becomes less pronounced. This suggests the presence of a strong rarefaction between the bottom of the booster and the grid fins. The sudden change in the local pressure suggests the presence of a shock located at the grid fins, denoted by the letter “B.” Following this, another condensation cloud appears at the top of the booster geometry. This rarefaction is related to the recompression shock (denoted by the letter “C”) expected at the end of all supersonic bodies. The final result is a shock system with three distinct features. Although the shock system drawn here is approximate and represents only the near-field fluid flow, the overall structure agrees with the results found using the other methods in this letter.

In this Letter, the Falcon-9 triple sonic boom has been explained. The first and third shocks are the typical shock structures expected from a finite body relating to the front and rear of the geometry. The extra, central, shock is formed by a combination of the grid fins and the lower portions of the booster, including the folded landing legs. These lower portions of the booster produce a rarefaction wave that tends to migrate toward the back of the shock system, while the grid fins produce a shock wave that tends to migrate toward the front of the shock system. When the two structures merge, a balanced shock forms that shows relatively little motion within the signature. The relative strengths of the rarefaction and shock waves determine the location of the final central shock within the sonic boom signature.

This conclusion is reached using three different methods. In the first method, sonic boom theory is used to produce an approximate near-field source function, which is converted to pressure and propagated numerically via the nonlinear acoustic Burgers equation. When the booster is modeled as a simple cylinder, an N-wave is produced in the far field. When the folded landing legs and extended grid fins are included, a triple-boom signature is produced in the far field. The second method uses computational fluid dynamics simulations to visualize the near-field flow around the booster, which agrees with the results in Sec. 2. The third method uses a unique photograph taken during a booster flyback where condensation clouds were visible around the booster. The condensation clouds highlight regions of low pressure, which agree well with the other two evidences.

While exciting, more research considering these booster flyback sonic booms needs to be completed. For example, simulations involving turbulent flow are needed to more accurately model the near-field flow around the booster, which could help determine what parts of the vehicle could be used to optimize the sonic boom signature. Although F-function methods can provide quick predictions, their use for blunt rocket boosters during flyback needs to be further validated. We suggest that near-field signatures from wind tunnel testing should be used as inputs into sonic boom propagation software to obtain more-accurate predictions. Last, the practical effects on structures, communities, and the environment from having a triple sonic boom should be investigated to determine whether the additional shock produces any extra effects beyond those produced by an N-wave.

The analyses for this work were funded by an appointment to the Department of Defense (DOD) Research Participation Program administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the U.S. Department of Energy (DOE) and the DOD. ORISE is managed by ORAU under DOE Contract No. DE-SC0014664. All opinions expressed in this paper are the authors' and do not necessarily reflect the policies and views of DOD, DOE, or ORAU/ORISE. We also thank the two anonymous reviewers and the associate editor, whose careful feedback improved and clarified many parts of this Letter.

The authors have no conflicts of interest to disclose.

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