Aircraft like the Concorde, the SR-71, or the Space Shuttle come in to land with an elevated skin temperature. The Concorde just spent 3 h cruising at M = 2, the SR-71 spent time at more than M = 3 and the re-entering Space Shuttle, who knows? Peak Mach number reached is said to be around 25 through all layers of the atmosphere. The skin temperatures reached by the two supersonic cruise aircraft (195 °F (90 °C) and 500 °F (260 °C), respectively) have a lot to say about the aircrafts’ design. The skin and structure of the Concorde is made with aluminum and the SR-71 with titanium. The Space Shuttle was covered with ceramic tiles that can stand the hellish temperatures of re-entry from space and are replaced as necessary after landing. Are these material choices associated with the flight Mach numbers? Very definitely. Are they due to friction? The answer is No, with a little bit of Yes.
Let’s look at the nature of friction. A friction force is experienced by a solid body (as our high school physics experiment again) whose motion is retarded by stationary surface like a brick sliding on the floor or a rope slipping through our hands. When a force, including a friction force, acts with a speed, there is an expenditure of mechanical power. In the case of friction forces, the mechanical power is converted to thermal power, heat. That is the nature of our experience with frictional heating and why automobile or aircraft wheel brakes get hot when used aggressively.
For fluids, liquids and gases, the situation is more complicated. Shearing forces acting on moving elements of fluid exert mechanical power that ends up in the fluid itself. For example, the oil in a journal bearing experiences such work expenditure and, as a result, the oil warms up. In many applications, such heating has to be dealt with by cooling of the liquid involved.
For unbounded fluids flowing past a surface, friction is manifest in the creation of a boundary layer on the stationary surface. Within the boundary layers, there are shear forces acting on adjacent moving elements of fluid. The heat generated is the product of this shear and the local velocity. At the bottom of the boundary layer, the shear is relatively large, but the velocities are small while the opposite is true near the edge of the boundary layer. There is, consequently, a zone of peak heat generation somewhere in the central region of the boundary layer. This heat is distributed by the motion of molecules and/or eddies within the boundary layer and plays a role (a very small one as it turns out) in heating the surfaces of our flight vehicles.
Is there another source of heat for the air passing along our high-speed airplane? Yes, and it is an important one. By its nature, the boundary layer air is forced to come to rest relative to the airplane, or at least slow down. The air that is so slowed brings with it its kinetic energy. When that kinetic energy source is large, as it is for high-speed flight, the local heating from the deceleration of the freestream air delivers kinetic energy converted to thermal energy that is not just significant, but dominant. That last statement has to be supported by plausible evidence.
Short of a detailed analysis, the best one can do is to make an order of magnitude assessment. That involves examining what physical quantities play roles and devising a figure of merit that characterizes the relative importance of two effects to be compared.
Such a figure is the ratio is of the heat generated by dynamic conversion of kinetic energy and the heat generated by the shear forces associated with friction. One can show that the ratio is closely related to and numerically similar to the Reynolds number (based on flow distance), a number that is numerically in the millions for a full-scale airplane. In short, frictional heating on a high-speed airplane is very small compared to the heating from the kinetic energy of the oncoming air. Engineers who have been concerned with this have established that the surface temperature on a surface like that of an airplane is typically somewhat less than the stagnation temperature of the air. Near a stagnation point (on the blunt nose) or line, however, like the leading edge of the wings, the temperature realized there is the full stagnation temperature. Thus, one can say, at least for conservative design purposes, that the entire vehicle is bathed with air close to the stagnation temperature.
This state of affairs is well illustrated qualitatively in the Space Shuttle sketch (Fig. 7.13) showing the leading edges white hot while the lower surfaces of the wings and body are also hot but cooler. NASA engineers equipped the leading edges as well as the bottom surface of the Shuttle with the best performance thermal protection system that they could devise.
Leaving the Space Shuttle aside, we can look at the temperatures experienced by the other two airplanes as representative examples and see how the stagnation temperatures at the conditions where they fly correlates with after-flight body temperatures. It is reported in practice that the Concorde operates skin temperature is typically between about 200 °F and 260 °F (93–126 °C) while that of the SR-71’s is typically near 500 °F (260) and sometimes as high as 1000 °F (540 °C).
The stagnation temperatures relevant to these airplanes can be estimated by making a few assumptions. Consider that we are flying in an environment like the stratosphere where the absolute temperature is about 400° R (-60 °F or -51 °C). The Rankine scale is identical to the Fahrenheit scale except that it is referenced to absolute zero temperature. For practical reasons, namely that temperatures near absolute zero are not in our everyday world, the Fahrenheit scale, still used in the US, employs some diabolical thinking that the temperature of freezing water (at 14.7 psi absolute atmospheric pressure or 101,000 N/m2) is exactly 32 °F. Because this scale is familiar, at least in the United States, we will stick with it. Table 7.1 shows the Fahrenheit temperatures reached at a stagnation point. What is apparent in this table is that a Concorde flying at M near 2 will be hot on landing. More so for the SR-71 that is capable of speeds greater than M = 3. Aluminum melts near 600 °F (315 °C) while titanium melts at over 3000 °F (1650 °C). The Concorde design could safely use aluminum, but the SR-71 had to employ a titanium structure. Note that our commercial airliner’s skin temperature is 20 °F (-7 °C), cold enough to face the possibility of ice build up under some conditions. Their leading edges are equipped with means to heat them and thus avoid worries with icing issues whose buildup might change the shape of the airfoil shape that was developed with such care.
Now consider that the Space Shuttle reached Mach numbers near 25. It ‘flew’ back into the atmosphere at speeds where surface temperatures reached are said to be near 2300 °F (1260 °C) and air temperatures higher yet!
The numbers in the table are estimates. Nevertheless, the good correlation between observed vehicle temperatures with the stagnation temperatures seems a sufficiently strong to able to say, with a good deal of certainty, that friction per se plays a very small role in contributing to airframe heating of these examples.