# Could Mach 1.4 be a better design point for SST?

There's been a number of recent proposals for design work on low-supersonic bizjets that would cruise at Mach 1.1-1.6, the common theme being avoiding a sonic boom.

The conventional wisdom is to avoid this range, and either stay subsonic or go all the way to Mach 2+, because you sacrifice some efficiency the moment you cross Mach 1:

• Sharp nose and supersonic airfoils result in lower L/D across the envelope.
• Thin airfoils add weight and require more fuselage space for fuel tanks.

On the other hand, staying at low Mach avoids a few other penalties:

• The 12:1 slenderness of modern widebodies translates well to a low-Mach SST, allowing for a similar cabin layout. This is critical.
• Skin temperature allows the plane to be built with the same resins as subsonic airliners.
• Less COL shift, higher AR wings, reasonable bypass engines make it easier to meet TO lift and thrust requirements.
• Speculatively, cruise altitude might be kept at FL450 to avoid stricter pressurization rules.

What I'm not sure is which set of factors matters more. It's difficult to glean from existing designs, as they're not really comparable between one another.

The Aerion's wing should behave well on landings, and it claims only a 22% fuel penalty for going supersonic. But its slender nose and long tail leave just 18% of its length for the cabin, so it can't be used as an airliner template.

This is probably caused by its role as a status symbol and regulatory weight limits; actual SST managed a proper length cabin, and the 2707 was even planned as a widebody. Thin wings have are also featured in some subsonic proposals, so they're not a total efficiency killer.

I'd imagine a Mach 1.x airliner to be a 779-sized twin, with 788-like seating capacity, area-shaped akin to the Sonic Cruiser, an ogive nose (F-16 style), Aerion-like trapezoid SNLF wings, nacelle engines.

The question is, could a low-Mach SST, if sonic boom was publicly accepted, be closer in efficiency to subsonics than to historic high-Mach designs?

To narrow down the scope, let's explicitly exclude:

• Whether there is any market for such an aircraft.
• Whether Mach 1.x is fast enough to make a difference.
• Engines, as it's a major subject in itself. Just assume a rubber engine matching a loose trend line of TSFC~=0.4*Mach.max.

Leaving in scope the technical subject of the efficiency loss imposed by the aerodynamics of supersonic flight. It comes down to how good a L/D can high-tech airfoils like SNLF and area-ruled widebody provide, with how little compromise on capacity, in the range of Mach 1.1 to 2. Fuel per seat-mile being the figure of merit.

To help set a baseline, I've plotted a mix of historic and calculated numbers for known aircraft:

To put the question in more formal terms, I'm looking to estimate the seat-miles/kg function's behavior for an optimal design in the low-supersonic range.

The red line assumes the worst-case scenario and is based on just stuffing seats into the AS2. The green line represents a best-case scenario based on claims with the Sonic Cruiser as a baseline. The truth is probably in between.

• While this question does have some concrete technical components, in its current form, it's a market analysis question -- and too broad to ask here without a thorough re-phrasing and scope shrink. – 0xdd May 28 '18 at 14:13
• I'm looking specifically for a technical-only consideration of realistically achievable efficiency. Whether there is a market for it isn't important in this regard. Edited to make it more clear. – Therac May 28 '18 at 14:29
• transonic is awful no matter what – user3528438 May 28 '18 at 19:16
• That's... Thanks for trying to help, I guess. That's the conventional wisdom I've mentioned, what we've all been told forever ago. Lately I'm coming upon increasingly more information that leads to me question it. From recent QSST studies, it appears that the "sonic barrier" simplification might no longer hold for some modern laminar and supercritical airfoils, being replaced by a gradual performance reduction across the transonic region, possibly with even less dip than my green line. It's still something I'd wait to hear more independent confirmation on before subscribing to it, though. – Therac May 28 '18 at 19:44
• I'm very sceptical about SNLF. It works on the tiny, non-lifting fin below an F-15, but scaled up to a real aircraft and on a lift-producing wing, the high Reynolds number will not leave much laminar flow. Mach 1.4 allows for less sweep and a simpler intake, but I cannot say whether this is worth it. – Peter Kämpf May 29 '18 at 5:02

The high end of the business jets has been in a race for higher cruise Mach numbers which has resulted in a top speed of Mach 0.935 so far (Gulfstream 650, Cessna Citation X). So there seems to be a market value for the top spot in cruise Mach. To improve this further, and substantially, the jump to supersonic speed is unavoidable. So far, the expense of developing such an aircraft for a rather small market has been too high.

On the other hand, a Mach 1.4 design will be much easier than one flying at Mach 2.0. The reasons are:

• Intake complexity: At Mach 1.4 a simple pitot intake with a single straight shock has acceptable losses, while Mach 2 demands a complex, adjustable intake with ramps producing a cascade of oblique shocks.
• Wing aspect ratio: In order to keep the wing's leading edge subsonic, a Mach 1.4 design can get away with 45° sweep while a Mach 2 design needs at least 60° sweep. The Mach 1.4 wing will be much better for take-off and landing, and for the subsonic legs of the trip.

On the other hand, transport performance at Mach 1.4 will only be ⅔ of that at Mach 2 for comparable L/D, so the Mach 2 design will win hands down if airliner economics are used to evaluate a design. As you said, if you venture into supersonic territory, you might as well go all the way to Mach 2 in order to optimize the profitability of the design. Mach 2 still allows to use a fixed-geometry wing and aluminium, so the overall complexity of the resulting design is still manageable. Beyond that, you need to buy more speed with increasingly more system complexity.

Dietrich Küchemann proposed an empirical formula for maximum supersonic L/D: $$\frac{L}{D}_{max} = \frac{4\cdot(M_{\infty}+3)}{M_{\infty}}$$ Using this as a yardstick will result in 12.5 at Mach 1.4 and 10 at Mach 2. Combine this with the Mach number in order to have something close to transport efficiency, and the Mach 2 design enjoys a hard-to-beat 14% advantage in economic value.

So the only sensible reason to design for Mach 1.4 is to capture the high end of the business jet market, where airliner economics don't apply but bragging rights at the golf course are more important.

• On transport performance, my concern was that Mach 2 SST were stunted by low passenger capacity. At just 2/3 of Concorde's weight a 757 carries 200+ passengers. I'd expect a low-Mach transport to come much closer to subsonic pax/ton ratio. Or do you think a M2 jet can also work efficiently with low enough slenderness for say a 3-3-3 configuration, without a major weight penalty? – Therac May 29 '18 at 6:03
• @Therac: When Concorde was conceived, it was designed for the passenger count of the biggest airliners of its days. By enlarging it a bit, the passenger number would be easy to increase. The slower design will have smaller engines and a lighter intake, but the structure would be essentially the same. Therefore, the passenger fraction would be a bit better, but not dramatically so. – Peter Kämpf May 29 '18 at 11:51
• Thanks. A couple clarifications, if you don't mind. Does this mean the Concorde's 20:1 slenderness ratio was just a product of target size, and a much wider 12:1 ratio is good for M2 as well? Also, I assumed different engines for M1.4 and M2, with different bypass rations and exit velocities, and thus different TSFC (0.5 and 0.7 respectively). Would that be incorrect? – Therac May 29 '18 at 14:49
• @Therac: TSFC goes up with Mach. The values for Mach 1.4 and 2.0 cannot be compared directly. And of course can the fineness be reduced, but then L/D goes down. – Peter Kämpf May 29 '18 at 17:08
• Yep, that's why I used TSFC=Ma*0.35 in the question; with that, lower mach gives ~1.6x less fuel per seat-mile and 0.85 another 2.3x over that. I'll try and do some economic math later, but for that - would ground hours per flight most likely stay constant for a faster plane? – Therac May 29 '18 at 17:25