B747 has a sweep angle of 37 deg and A380 has a sweep angle of 33 deg. If the main reason for sweep is to delay compressibility effects and increase operating Mach number, why does B747 cruise at a lower speed than A380?
From Wikipedia, the cruise speeds of the both airplanes are fairly similar:
A380, nominal wing sweep angle 33.5 degrees, cruise speed Mach 0.85
Boeing 747: nominal wing sweep angle 37.5 degrees, cruise speed Mach 0.84 .. 0.9, depending on the model.
So those numbers would contradict the claim in your question, but align with your expectations. There are several other things to consider. The nominal cruise speed of these planes is more dictated by efficiency, required power for a given speed, and fuel prices. The 747 is an older design, when fuel was cheaper, the general tendancy is that modern airplanes reduced the cruising speed slightly in favor of higher efficiencies.
considering the sweep, raw numbers:
- cos(33.5 deg)= 0.83
- cos(37.5 deg)= 0.79
So the difference of approx 4% here seems to reflect the difference in cruising mach numbers: the higher sweep of the Boeing 747 reduces apparent Mach number roughly by the same amount that it is flying faster.
Then, for both airplanes, and certainly for the A380, the wing aspect ratio is quite low. So there's a point to challenge how much the sweep actually angles differ, from an aerodynamic point of view. It may be very well that effective angles depend a lot more on local airfoil shapes, low aspect ratios, and other 3d effects than they depend on the nominal sweep angle.
All that said, the swept wing has more advantages than just reducing the apparent Mach number. There is
- enhanced aerodynamic stability around the yaw axis (this may even help in the event of asymmetric thrust due to an engine failure)
- enhanced mechanical stability of the wing itself under aerodynamic loads
- trim properties in transsonic aero regimes
The final design is then a result of many different considerations. Eg, IIRC, the wing span of the A380 had a limitation so it would "fit into standard airports", and there were likely some trade-offs in aerodynamics for that reason.
It's important to distinguish between three different Mach number definitions:
- Design cruise Mach I believe is 0.855 for the 747-8 and 0.85 for the 380.
- Maximum Operating (or Mmo) is 0.92 and 0.89, respectively.
- Demonstrated Maximum Diving (or Mdf) is 0.97 and 0.96, respectively.
Multiple factors effect drag from compressibility effects, especially the overall aircraft configuration area distribution along the longitudinal axis (ref. wave drag).
The question implies:
- that the maximum flying speed is mainly affected by the compressibility drag and;
- that compressibility drag is mainly related to sweep angle;
but this is not the whole story.
why does B747 cruise at a lower speed than A380?
Maximum flying speed depends on the equilibrium between thrust supplied by the engines and drag generated by the aircraft.
Thrust obviously depends on the technological development of the engines (which was for sure different between the first version of the B747 and the first version of the A380) and, among other factors, on temperature, density, humidity, height, ...
Drag depends as well on the technological development of (the surface of) the aircraft: its shape, how much surface can maintain a laminar boundary layer, surface finishing, eventual use of area-rule, type of airfoil used for the wing, ... Plus (induced) drag depends on lift as well.
So, maximum flying speed is affected by a lot of parameters and not only by compressibility. And upon this, also structural and/or aeroelastic (aka flutter) limitations can restrict maximum speed.
the main reason for sweep is to delay compressibility effects.
Compressibility drag is not influenced by the sweep angle alone.
If for example the area-rule concept has been used in the design phase then the geometry of the whole aircraft is important (area-rule is a particular smooth variation of the sectional area of the aircraft which minimises compressibility drag at transonic speed. Sectional area is the area that you get when slicing the aircraft longitudinally).
Another way to reduce compressibility drag is the use of supercritical airfoils, which have been for sure employed on the A380, not sure on the B747.
So, sweep angle is not the only parameter influencing the value of maximum speed or compressibility drag and its value is actually chosen as a compromise of many other (contrasting) requirements.
Bonus material about sweep angle: the point on the airfoil where the highest speeds are reached is around where its thickness is the highest. For a jetliner this point is important because it is the point where speed can reach transonic or supersonic speed with a relevant increase in drag. For this reason the real sweep angle to be considered for aerodynamic considerations is not the one at the leading edge rather the one passing through the highest thicknesses of the wing.