Do commercial airplanes cruise at Mach number higher than the critical Mach number? And what is the critical Mach number of airplanes like B777 or A330?

  • $\begingroup$ Given that exceeding critical mach in an airplane not designed for supersonic flight can lead to departure from controlled flight I'd say they probably cruise below critical mach. $\endgroup$ – GdD Feb 17 '20 at 10:59
  • $\begingroup$ I guess by exceeding Drag Divergence Mach Number (Mdd), there is a significant rise in the drag. There won't be any issue if the plane is flying at Mcrit or in between Mdd and Mcrit, right? $\endgroup$ – Pavan Feb 17 '20 at 12:03
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    $\begingroup$ @GdD critical mach is the lowest airspeed at which the airflow reaches Mach 1 over some part of the airframe. That does not necessarily mean departure from controlled flight. In this video you can clearly see the normal shock wave dancing back and forth across the wing as an A320 exceeds critical mach in cruise flight. And on a 737. And on a 757. $\endgroup$ – Fiddlesticks Feb 17 '20 at 12:03
  • $\begingroup$ @Pavan According to this document, the max cruise Mach number for most of the airliners cited is simply equal to the drag divergence Mach number, Mdd. But that is not the same as Mcrit. $\endgroup$ – Fiddlesticks Feb 17 '20 at 12:53
  • $\begingroup$ @Fiddlesticks Mdd is more than (typically more by 0.1) Mcrit. But, flying very close to Mdd will increase drag significantly. So, don't you think it is better to fly between Mdd and Mrit? $\endgroup$ – Pavan Feb 18 '20 at 6:09

The critical Mach number $M_{crit}$ is defined as the lowest Mach number at which the airflow over some point over the airfoil reaches supersonic speed, that is, Mach 1. Usually, flying greater than $M_{crit}$ will produce a normal shockwave perpendicular to the flow, at the point of minimum pressure on the airfoil. I must note that if flying slightly above $M_{crit}$, there is a possibility of the isentropic recompression of the fluid, which means that no shockwave will be formed and thus no losses in form of the entropy will occur. This is especially the case with supercritical airfoils flying slightly above $M_{crit}$.

Critical Mach number for a typical transonic airliner is not equal to divergence Mach number $M_{dd}$. In fact, many aircraft will exceed $M_{crit}$ during the cruise, which you can see on the following video:

. I believe that the average value of $M_{crit}$ is around $0.78$ for today's airliners like A320 or B737.

Exceeding $M_{crit}$ does not mean the aircraft reached $M_{dd}$ or is about to lose control. Control difficulties may be possible if $M_{mo}$ is exceeded.

For A320 and B737, the maximum operating Mach number $M_{mo}$ is $0.82$. This is primarily due to the buffet (and ultimately high-speed stall/shock stall) and (or) flutter occurrence. Exceeding normal speed range may cause flutter to appear. It also may put the aircraft in grave danger if shock stall occurs. Shock stall will occur if the shockwave formed on the airfoil is too powerful and separates the boundary layer. In this case, the airfoil pressure distribution changes and introduces an intensive nose-down pitching moment. To avoid such scenarios, the aircraft are limited with Mach number as well. There might be some corrections on the $M_{mo}$ from the divergence Mach number standpoint, but $M_{dd}$ is not the primary reason why such aircraft are limited with respect to Mach number.

  • $\begingroup$ Exceeding Mmo cannot cause flutter to occur (by regulations). I think what you mean to say is buffet. $\endgroup$ – JZYL Apr 17 '20 at 19:20
  • $\begingroup$ What I meant to say is exceeding the normal speed range may cause flutter to appear... Transonic buffet will always be present if the aircraft is experiencing shock stall, since these two phenomnenos are very closely related. $\endgroup$ – Darjan Apr 17 '20 at 20:07
  • $\begingroup$ Flutter is possible only if you exceed Mdf, which is an extra margin over Mmo. You won't encounter shock stall up to Mdf either, as they've been flight tested there. Buffet is the only thing you will experience above Mmo. $\endgroup$ – JZYL Apr 17 '20 at 20:10
  • $\begingroup$ As you know, a transonic buffet is a condition where a separated turbulent boundary layer strikes the airframe with considerable force causing high amplitude vibrations. On a swept-wing aircraft, the separation will start at the wing root and work its way out towards the wingtips. As the first signs of separation will take place at the wing root, the transonic buffet will act as a consequence to "warn" the pilot to stay out of such high velocities. $\endgroup$ – Darjan Apr 17 '20 at 20:52
  • $\begingroup$ If the speed increases further, more wing will suffer from boundary layer separation and buffet will become even more severe until reaching the point where expressed nose down tendency will occur or result in the possible structural damage of the aircraft.The point is, the buffet acts as a warning sign to stay out of a shock stall, buffet should not happen in the first place,if it happens,this means that the shock stall is already gaining strength until it becomes impossible for the pilot to control the aircraft. Staying out of shock stall means eliminating the buffet in the first place. $\endgroup$ – Darjan Apr 17 '20 at 20:52

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