# High-Speed Flight: Commercial Supersonic Flight Challenges and Opportunities

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Prime Mover Lab’s webinar last month on high-speed flight covered a range of topics, including briefly touching on the challenges for commercial supersonic flight. The conversation inspired me to dig further into this topic area. Buckle up because…

Author’s note: ballistic flight refers to projectile motion governed by Newtonian mechanics (eg space capsule unpowered re-entry). Maverick did not go ballistic!

Supersonic Flow Fundamentals

Before we dive into the current state-of-the-art, a detour to define basic terms and concepts is warranted.

Supersonic flight denotes a vehicle whose speed (magnitude of the velocity vector) is faster than the local speed of sound (a). Aerodynamicists LOVE to non-dimensional things so it’s easier to compare their performance. For supersonic flight, the non-dimensional number of choice is the Mach number.

A Mach number greater than one (M>1) means you are in the supersonic flow regime. (The hypersonic flow regime begins with Mach numbers greater than five, because the flow physics change substantially. More details to come in the next blog!) It’s worth noting that the speed of sound for an ideal gas is a function of the temperature. For an aircraft, you can think about temperature varying as a function of altitude, as measured in the 1976 Standard Atmosphere. Earth’s atmospheric temperature profile also varies both spatially and seasonally. This natural atmospheric variance is one of the main reasons why aircraft fuel performance varies depending on the route and its conditions.

How does supersonic flow differ from subsonic flow? Traveling faster than the speed of sound creates a local discontinuity in the flow, also known as a shock wave. There is an almost instantaneous step change increase in static pressure, temperature, and density across the shock and the post-shock speed shows a similar step drop in value.

Flow physics in the supersonic flight regime are reasonably well modeled in 1-D via the normal shock relations. While the shock wave itself is an irreversible process, on either side of the shock the simplifying assumptions of isentropic flow (ideal gas, adiabatic, inviscid, irrotational flow) can be applied to get a closed-form solution. To keep this blog light on equations, it’s more illustrative to view the normal shock relations plotted, to understand just how much each quantity changes with increasing freestream Mach number.

You might ask, what’s the point of a 1-D model? Aircraft are 3-D! Aerodynamicists, in addition to loving non-dimensional numbers, also love scaling laws. They provide a framework for thinking about the largest first order effects of the flow physics. From the chart above, the biggest takeaway is that pressure scales with velocity squared. The practical design implications for aircraft are that the faster you go, the larger the pressure loads and the more thrust you’ll need to overcome the resultant induced drag force. Pressure scales linearly with freestream density and linearly with the cross-sectional area of the aircraft, so aircraft designers have a few variables to trade during conceptual design. (Fun fact: subsonic aircraft cruise at a much lower altitude (~35,000 ft) than supersonic ones (~60,000ft). This is a design choice!)

Aerodynamic Design Fundamentals

In aerodynamic design, the function determines the form. In other words, aircraft look the way they do as a result of the flow physics they are required to fly through. Subsonic aircraft have soft rounded shapes with smooth continuous gradients in radius of curvature — the design intent is to keep the flow smooth and attached for as long as possible to reduce drag.

Author’s note: I’ve not yet mentioned the transonic flow regime. Today’s commercial passenger jets tend to cruise at M~0.85, which means their wings encounter transonic flow phenomena during flight: there are local shockwaves on the upper surface of the wing (the suction side of the airfoil) that cause the flow to detach early and create a much higher drag coefficient. In 1969 NASA Langley researcher Dr. Richard Whitcomb designed the supercritical airfoil to be optimized for transonic flow. The supercritical airfoil shape enables aircraft designers to trade between increased subsonic cruise speed before encountering the transonic drag penalty OR thicker wing sections reducing structural weight and enabling higher lift at lower speeds. Dr. Whitcomb is also credited with the area rule, which is applied to the fuselage of supersonic jets.

In contrast, supersonic aircraft have sharp leading edges. The design intent is to reduce drag by keeping the shock waves attached and as oblique as possible. The pressure drag dominates over viscous skin friction drag for supersonic aircraft, contributing ~85% of the total drag force. While aircraft designers optimize the outer mold line of the vehicle for cruise conditions, most supersonic aircraft also have variable geometry for the subsonic flight regime. Some famous examples: the Concorde’s articulating droop nose and the F-14’s variable swept wings. Of note, while the SR-71’s engine had linearly translating spike, its purpose was to optimize supersonic flight performance by keeping the oblique shock attached to the engine inlet. For readers who’d like to learn more, I highly recommend reading P.W. Merlin’s “Design and Development of the Blackbird: Challenges and Lessons Learned”. (Link goes to a free copy available on NASA Technical Reports Server. #Patreon4NASA)

Sonic Boom Suppression Research

With our background tour of the fundamentals complete, we’re ready to dive into the state-of-the-art research on aerodynamic design for sonic boom suppression. To recap, we learned earlier that there is an abrupt pressure rise behind a shockwave — the birthplace of the sonic boom. (Sound is a pressure wave.) Flying at a higher altitude, in less dense air, reduces the sonic boom by reducing the absolute pressure and increasing the path length for sound energy to dissipate on its way to the ground.

A normal shock is the strongest discontinuity that can be created at a given speed — making the shockwaves more oblique lessens their strength and thus the resultant sound. This translates to a long pointy outer mold line for low-boom supersonic passenger aircraft. That guiding principle is used on both NASA’s X-59 design and JAXA’s D-SEND2 research aircraft. Supersonic aircraft designers also minimize the strength of the shockwaves that propagate towards the ground by placing features that can disrupt flow, such as engine inlets, on the upper surface of the vehicle. For completeness' sake, long and pointy isn’t the only design paradigm for low-boom design. There is an MIT biplane concept that reduces noise by canceling out shocks.

The goal of NASA’s quiet boom demonstrator was not to make the quietest design for that size of aircraft, but rather to create a supersonic demonstrator that can provide the ground noise data necessary to re-write the rules for overland supersonic travel. A recent IEEE Spectrum article does a great job covering the history behind the FAA’s sonic boom noise regulations. To summarize here for brevity: overland supersonic flight has been banned in the US since 1973. The FAA’s regulatory ban was informed by the extensive flight testing they completed a decade prior. In 1964 citizens of Oklahoma City experienced 8 sonic booms per day for nearly 6 months. The FAA’s study of ~1,200 flights garnered 15,000+ noise complaints and damaged property claims (cracked brittle materials); 25% of the Oklahoma City population was not in favor of the sonic boom noise.

The X-59’s design goal for ground perceived noise is 75 decibels, roughly 8 times quieter than the Concorde. (Average urban background ambient noise levels are between 60–70 dB.) As seen in the below images, the X-59 is predicted to meet its design requirement across its entire sonic boom ground footprint.

The X-59 is scheduled to begin flying in 2022, with the critical community noise data being collected starting in 2024. The flight tests will also provide data to help validate simulation tools and put experimental error bars around the design predictions. Knowing the pre-test accuracy of modeling and simulation results enables supersonic aircraft designers to scale up the low-boom design principles for large passenger vehicles with sufficient design margin for success.

Commercial Supersonic Flight Market

The commercial supersonic flight market can be divided into two segments: smaller-sized business jets that carry less than 20 passengers and larger-sized commercial passenger jets that carry over 50 passengers.

There are currently two entrants to the larger passenger jet supersonic commercial market: Boom and Exosonic. Boom, a Prime Movers Growth portfolio company, has a commanding lead in this market segment, as evidenced by the 65–88 seat Overture’s design maturity and their recent order with United to enter into service in 2029. Boom has also made tangible technical progress, de-risking through its XB-1 demonstrator airplane, scheduled to fly in 2022. Exosonic, the newest entrant to the commercial supersonic market, has a 70-seat low-boom conceptual design. Exosonic graduated from Y Combinator in March 2020 with \$150K of funding and was awarded a \$450K STTR grant to collaborate with Stanford on transitioning their design for a military cargo application. Whether Exosonic can leverage their initial work into a larger program as hypersonic startup Hermeus recently did with their \$60M DOD award remains to be seen.

Building aircraft is a capital-intensive business. Despite a \$10B backlog of orders for 300 of its low-boom 12-passenger business jets, Aerion Supersonic closed in May 2021. There are two remaining entrants for the supersonic business jet market: Spike Aerospace and Virgin Galactic. Spike Aerospace has a mature 18-passenger low-boom design, which they are aiming for market entry in 2028, targeting lucrative routes overland in markets such as Asia. Meanwhile, in August 2020, Virgin Galactic announced its plans to develop a 19-passenger low-boom business jet, partnering with Rolls Royce for the propulsion and NASA for the aerodynamic design.

While the current investment opportunities for commercial supersonic flight are limited, if NASA’s X-59 does successfully change overland supersonic flight regulations, more startups may emerge. We at Prime Movers Lab are obviously excited about this space given Prime Movers Growth’s investment in Boom, so we are eager to see how the next generation of engineers push the envelope to sustainably advance the speed of commercial air travel.

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