Pre-amble

This was a late night (4 am) writing exercise inspired by some online discussion I had been privy to. All mistakes are my own. Math is likely incorrect. There are MANY ways in which to improve upon this work, only some of which are addressed below. Please excuse the lack of equation formatting, turns out LaTeX plug-ins require upgrades! Minor edits may be ongoing!

Abstract

I investigate the effects of shockwaves and in light of aquarium hobbyists concerns regarding impulses potentially damaging glass tank walls. I compare the potential peak pressure experienced by the aquarium walls in the case of a manmade object travelling at 3 km/s at 0.1 km altitude to the theoretical strength of the glass walls and find that failure is unlikely to occur if the glass ratings are reliable. However, the silicone seams may be a point of weakness. Additionally, I did not evaluate the compound effects on glass strength from other damaging sources such as scratches, casual impacts, and long-term use. Suggestions to minimize the impact include the use of diffusion (reflecting barriers) and absorption (highly porous material converting kinetic energy to heat), though their efficiency is not evaluated. Lastly, I note some of the short-comings of this work.

Introduction

Impulsive events occur on a daily basis, of which the common aquarium is hopefully designed to withstand these bumps and knocks. For larger events such as meteor impacts and the passing of fighter jets, it is difficult to believe that the various aquarium manufacturers take these factors into account when setting out safety standards and designing their warranties. Recently, an innocent question was asked online, “How to protect my aquarium from shock waves caused by sonic booms?” (u/WassufWonka, 2024). This sparked a brief discussion that was rapidly quelled, though subsequent posts were made (u/memerobbin, 2024; u/laced1, 2024) and others discussing moderation. Before it concluded, some points were brought up, including the relative pressure caused by shockwaves from passing fighter jets, equilibrium pressure inside and outside of the aquarium, and whether aquarium glass was sufficiently strong enough against said pressures. Suggestions for limiting the impact including foam mats as padding, tape in cross designs, and transferring fish to buckets for the time being. A brief reassuring post from u/sldomingo (2024) appeared explaining how the shockwaves would be absorbed by water and not to worry before promptly being removed.

In this article, I briefly investigate the potential source of impulse, describe the range of pressures from the shockwave as it encounters the aquarium glass, and consider whether standard aquarium glass is sufficient to withstand these impulsive events. I also discuss the various ways in which an aquarium can fail from other events, and how one can mitigate the effect of shockwaves on glass with a brief note on the strength of silicone seals.

Methods

Source
Impulsive sources impacting aquariums can vary, including repeated finger tapping on the glass, a young toddler wrecklessly scratching glass with a set of keys while an absent-minded parent looks on, to the sonic booms from fighter jets overhead. Sonic booms are generated when an object moves faster than the speed of sound, causing a stacking of pressure waves “breaking the sound barrier”, a shockwave. This shockwave and can come from natural sources, such as incoming meteors, and manmade sources, such as space shuttle return or fighter jets.

The shockwave that is released travels at speeds higher than the speed of sound for several wavelengths, before relaxing and continuing to travel at the local speed of sound (ReVelle et al, 1976). The shockwave can be approximated as a cylindrical source. At sufficiently far distances, it can be approximated as a line source with one main overpressure event. We can estimate the range of overpressures from the shockwave using the generalized steps:

• Estimate the source energy available for sonic boom
• Convert source energy to overpressure at the surface

For expediency, I will use existing data on manmade hypervelocity objects. The return of Stardust suggests maximum overpressures of 1.153 +/- 0.096 Pa including several delayed infrasonic arrivals with equipment sampling frequency of 100 Hz (ReVelle and Edwards, 2007). Estimates of source energy range from 1.557E-6 to 2.437E-5 ktTNT (1 ktTNT = 4.185E12 J) for the first instance of infrasound arrivals with a distance of 32.6 km and height of 42.7 km. Secondary arrivals have a maximum overpressure of 0.207 Pa with around a 10 s delay, and estimated energies of 6.275E-7 to 1.206E-5 ktTNT when Stardust was at a distance of 26.1 km and a height of 32.07 km. Stardust had an initial return velocity of 12.9 km/s with simulations estimating a mean velocity of 3.0 km/s (ReVelle and Edwards, 2007).

Siber et al. (2024) also provided data on the OSIRIS-REx capsule return. For a point of reference, station A05 from the Gems station was located closest (~13 km away, height unknown), with a maximum amplitude recorded at around 1.5 Pa (Fig. 7). They found that the shuttle was travelling at approximately 2.9 km/s based on the seismic data. Notably, the shuttle achieved a theoretical maximum of Mach 45.6 at 95 km altitude, and the shockwave was estimated to be produced at 80 km altitude.

Theoretical Fighter Jet
Let us consider a theoretical fighter jet, capped at Mach 9.6 (3.3 km/s) per a google investigation. This is sufficiently close to the case of the estimated Stardust return. We now estimate the potential distance of a fighter jet passing by over a home in Beirut, Lebanon, let’s say 0.1 km (or 100 m). Considering the mountainous environment, lower flying does not seem particularly sensible, though certainly feasible. Let us also consider this the slant distance, as it is possible a plane would be flying directly overhead.

Scaling Laws
We can now use some of the existing scaling laws to estimate the total overpressure that may be experienced 0.1 km below a passing jet if we can assume scaling laws apply (I should probably find references for this, but I’ve been reasonably assured below 100 km this is not too silly to do), then del(p_1)/d_1=del(p_2)/d_2, which can be rewritten as del(p_2) = del(p_1)*(d_1/d_2)

For the first arrival, I found an overpressure of 619.2 Pa, and for the secondary arrivals, 85.6 Pa. For a point of reference, atmospheric pressure is 101325 Pa. The pressure exerted by water in a full tank can be estimated using an example of a 33 gal standard aquarium with dimensions of 48’’ x 13’’ x 12’’. Assuming the 12’’ dimension is the base, the area of the outwards facing walls are approximately 0.4 m² and 0.1 m² respectively. The pressure in the tank can be calculated using force, F=rho*g, with rho=1000 kg/m³ as the density of water, and g=9.8 m/s², gravitational acceleration on Earth. For the respective faces, the pressure exerted by the water in the tank is 24500 Pa (24.5 kPa) and 98000 Pa (98.0 kPa, or 0.098 MPa) respectively. Thus, the arguments that the pressure within the tank are greater than the impulsive events appears to hold.

Note that the pressure from the sonic boom in this case is within the blast radius, before viscous relaxation. The blast radius is ~3.0*R_0 (Ceplecha et al., 1998), where the characteristic blast radius R_0=1.05*M*d_m where M is the Mach number, and d_m is the diameter (ReVelle, 1976). Let’s say the blast radius is then 3*1.05*9.6*13.7 m = 414.3 m, greater than our hypothetical case of 100 m altitude. At a more realistic Mach number 3, the blast radius is 129.5 m. This suggests that our pressure estimations may be underestimations for this particular case.

Let us assume that the source of the shockwave from the OSIRIS-REx return was at a distance of ~81 km (assuming 80 km altitude), this corresponds with 1215 Pa at a distance of 0.1 km. Thus, we have a general range of overpressures, between 85.6 Pa and 1215 Pa from a shockwave. On the higher end of the estimated overpressures, this is about 8% of the pressure of water exerted on the long face of the tank.

For a 5 mm thick tempered glass pane, I found an average of 19800 psi compressive strength (I have misplaced this reference, Wikipedia suggests 10000 psi for a 6 mm pane), with Wikipedia giving glass a tensile strength of 1000 psi (Tempered Glass, n.d.; Strength of Glass, n.d.). Say the average tempered glass is 4x stronger than regular glass, this gives us a tensile strength of 1000 psi (6.8 MPa), several times stronger than the overpressure effect from a sonic boom (though later Wikipediaing suggests tempered gl. This suggests that there is no immediate concern that a single sonic boom from a nearby fighter jet travelling at Mach 3 will be of immediate concern.

Discussion

Contradictions
This is odd, many horror stories abound about surprise aquarium blowouts, or an accidental hit from a bb gun might be up to 0.5 kg of force over a 4 mm diameter pellet at 20 ft is actually around 3 MPa, half the compressive force glass can withstand. It’s not like we’re tearing around our aquariums either so tensile force doesn’t necessarily come into play. One consideration might be the strength of the silicone seals. Tensile strength of silicone sealant is around 0.5 MPa. Oh.

Now lets assume the glass may have some imperfections. A quick google shows that nickel-sulfide inclusions can be found in 1-2/100,000 6 mm tempered glass panes. An inclusion can result in localized tensile stress as high as 860 MPa (Glass Breakage – Nickel Sulfide Inclusions, n.d.), resulting in microfractures that are easily recognizable. These are primarily a concern in tension zones (say, the center of a pane for a long, starting to bow out aquarium).

Repeated microfractures can cause the weakening of a pane of glass. While I was unable to find the values of strength drop, a microfracture review with repeated loads found that cracks in glass follow progressive stages, with cracks formed by the procedure continuing to produce lateral cracks for hours afterwards (Zakiev et al., 2020). Overall, initiation and propagation of cracks are accelerated by the presence of water (a concern for those of us who scratch up glass with hardscape from the inside).

Minimizing the impacts of sound waves
Outside the blast radius, one can assume that waves propagate at the speed of sound, approximately 343 m/s. One can think of either reflecting the wave, or diffusing it rapidly over a short distance prior to the delicate glass. To destroy the incoming waves, it would be necessary generate acoustic waves constantly, in hopes that they would cancel out the incoming waves by means of perfect destruction. Alternatively, one can apply an acoustic panel, which purportedly absorbs sound by conversion into heat energy. I found that a 1-inch foam acoustic panel has a noise reduction coefficient of 0.4 on average (where 0.0 represents a surface that completely reflects sound), though I have not read the ASTM to review the power levels they evaluate (ASTM C423-23). Generally, the more porosity for a given area, the more reflections can take place in a short amount of time. Alternatively, one can diffuse the sound waves by strategically placing a number of flat panels in an attempt to reflect and stagger the effects. An interesting thought would be to place a curved reflector surrounding the aquarium, such that sound waves coming in from every direction would be reflected as evenly as possible.

Conclusions

Despite the very real threat of sonic booms occurring in certain places in the world, preliminary work shows that the failure of aquarium glass for hobbyists is likely to come from pre-existing damage, or repeated events. A single blowout for a relatively new, unstressed aquarium from a passing fighter jet appears unlikely (note that this is not advocating lack of caution!). However, points of failure include the silicone seams, and the aquarium is at greater risk if it has been exposed to prior stressors, thus unquantified. Diffusing or absorbing shockwaves may be possible, though the specific reductions in terms of energy translation and thereby impulsive pressure waves are not quantified in this work. Subsequent studies modelling these specific effects are under consideration, as is generating the impulsive source directly, rather than use of a scaling law, and accounting for cumulative effects such as secondary shockwaves, and ground shaking.  

References

u/WassufWonka, (2024). https://www.reddit.com/r/Aquariums/comments/1em8e77/how_to_protect_my_aquarium_from_shock_waves/  

u/memerobbin, (2024). https://www.reddit.com/r/Aquariums/comments/1enlnxg/how_do_i_keep_my_fish_safe/

u/laced1, (2024). https://www.reddit.com/r/Aquariums/comments/1enqlns/looking_to_protect_my_fish_from_loud_fireworks/

u/sldomingo, (2024). https://www.reddit.com/r/Aquariums/comments/1envm6l/why_aquariums_might_survive_a_sonic_boom_were/

ReVelle, D. O and Edwards, W. (2007). Stardust—An artificial, low-velocity “meteor” fall and recovery: 15 January 2006. Meteoritics & Planetary Science 42(2). pp. 271-299. DOI: 10.1111/J.1945-5100.2007.TB00232.X

Silber, E. A., Bowman, D. C., Carr, C. G., … (2024). Geophysical Observations of the 24 September 2023 OSIRIS-REx Sample Return Capsule Re-Entry. Accepted for publication in the Planetary Science Journal. DOI: 10.3847/PSJ/ad5b5e. arXiv: https://doi.org/10.48550/arXiv.2407.02420

Ceplecha, Z., Borovička, J., Graham, E. W. (1998). Meteor phenomena and bodies. Space Science Reviews 84(3-4). pp 327-471. DOI: 10.1023/A:1005069928850

ReVelle, D. O. (1976). On Meteor-Generated Infrasound. Journal of Geophysical Research 81(7). pp 1217-1230. DOI: 10.1029/JA081I007P01217

Tempered Glass. (n.d.) https://en.wikipedia.org/wiki/Tempered_glass. Retrieved Aug 9, 2024.

Strength of Glass. (n.d) https://en.wikipedia.org/wiki/Strength_of_glass. Retrieved Aug 9, 2024.

Glass Breakage – Nickel Sulphide Inclusions. (n.d.). http://www.sunshadeblindsystems.co.uk/wp-content/uploads/2014/04/Heatsoaking-brief.pdf. Retrieved Aug 9, 2024.

Zakiev, I., Gogotsi, G. A., Storchak, M., and Zakiev, V. (2020). Glass Fracture during Micro-Scratching. Surfaces 3(2). pp. 211-224. DOI: 10.3390/surfaces3020016

Standard Test Method for Sound Absorption and Sound Absorption Coefficients by the Reverberation Room Method – ASTM C423-23 (2023). https://www.astm.org/c0423-23.html. Retrieved Aug 9, 2024.