Do bigger aircraft make a bigger sonic boom?

Question

I was watching an episode of MythBusters where they were trying to break glass windows and cups using a sonic boom generated by a F/A-18 Hornet, flown by the Blue Angels. In summary, they were unsuccessful at creating a boom that could shatter the windows, despite a mach speed pass within 200ft of the target building. In the last two passes they even flew straight at the building to focus the boom straight at the house, still no windows were shattered. **

But I've wondered, ever since, if they were unsuccessful because the plane was simply too small. What if the sonic boom had been generated by a B-1 Lancer or perhaps Concorde, which are several times larger than the F/A-18? Logically it seems that since you are displacing more air, the energy wave should have more energy. Then again, the plane isn't going any faster, so perhaps the surface area of the wave would be larger (because of the larger plane) but you wouldn't actually have any more energy at any given point?

Anyone know if a bigger plan than the F/A-18 would have a higher energy sonic boom? And could that cause glass to break?

Bonus point: A mathematical formula showing why, I love those things.

For those curious about what a sonic boom is to begin with, here's a wikipedia article.

**Just to clarify, for those who have seen the episode. A window is broken during the 200ft pass but they say that it only happened because the frame warped, not because the glass itself shattered. Their reasoning is that only that one window broke (out of several windows and glass cups in the area), and it had a pretty cheap frame on it.

Answer 1

The short version is that yes, larger aircraft create bigger sonic booms, but you still have to be flying very low (less than 100 ft.) and really trying hard in order to damage glass.

A sonic boom is so complicated that you will not find a simple formula to determine the strength. This article describes a modeling tool called PCBoom3 which can be used for sonic boom calculations.

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According to several different sites, like this one and this one, the size of the aircraft does affect the intensity:

Factors Affecting Sonic Boom Intensity

The intensity of sonic booms are affected by:

• Weight, size and shape of the aircraft.
• Altitude
• Attitude—orientation of the aircraft’s axes relative to the its direction of motion.
• Flight path.
• Atmospheric and weather conditions.

As the size and weight of the aircraft increases, the intensity of the sonic increases. This is because a larger aircraft displaces more air, and a heavier aircraft needs a greater force of lift to sustain flight. Thus creating a louder and stronger sonic boom.

and

General Factors Associated With Sonic Booms

There are several factors that can influence sonic booms -- weight, size, and shape of the aircraft or vehicle, plus its altitude, attitude and flight path, and weather or atmospheric conditions.

A larger and heavier aircraft must displace more air and create more lift to sustain flight, compared with small, light aircraft. Therefore, they will create sonic booms stronger and louder than those of smaller, lighter aircraft. The larger and heavier the aircraft, the stronger the shock waves will be.

NASA says that a typical sonic boom for the F/A-18 is about 1.4 psf and a different NASA page goes on to say:

Overpressure Sonic booms are measured in pounds per square foot of overpressure. This is the amount of the increase over the normal atmospheric pressure which surrounds us (2,116 psf/14.7 psi). At one pound overpressure, no damage to structures would be expected. Overpressures of 1 to 2 pounds are produced by supersonic aircraft flying at normal operating altitudes. Some public reaction could be expected between 1.5 and 2 lb. Rare minor damage may occur with 2 to 5 lb overpressure.

As overpressure increases, the likelihood of structural damage and stronger public reaction also increases. Tests, however, have shown that structures in good condition have been undamaged by overpressures of up to 11 lb. Sonic booms produced by aircraft flying supersonic at altitudes of less than 100 feet, creating between 20 and 144 lb overpressure, have been experienced by humans without injury.

Damage to eardrums can be expected when overpressures reach 720 lb. Overpressures of 2160 lb would have to be generated to produce lung damage.

Typical overpressure of aircraft types are:

• SR-71: 0.9 lb, speed of Mach 3, 80,000 feet
• Concorde SST: 1.94 lb, speed of Mach 2, 52,000 feet
• F-104: 0.8 lb, speed of Mach 1.93, 48,000 feet
• Space Shuttle: 1.25 lb, speed of Mach 1.5, 60,000 feet, landing approach

They also include a graphic that shows the difference in sonic boom between the F-18 and the Concorde, with the Concorde having a much greater sonic boom at the same alittude:

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This article specifically covers glass:

Glass. Poorly mounted, undamaged glass in the greenhouse was chipped by impact against nail holding points at a sonic boom overpressure of 12.1 psf. The same type of glass, which was already damaged, was further damaged at a designed overpressure of 7.9 psf. A large one-ninth of an inch thick window, intentionally precracked from corner to corner, was further damaged by booms of an average 6.5 psf overpressure.

So typical sonic booms generated by normal aircraft aren't going to create anywhere close to the 12.1 psf that they say is needed to chip "poorly mounted" glass, but the strongest sonic booms can get well over this.