What is the point where air friction heat overcomes air cooling?

Let’s say a body of air is at the freezing point, 0 degrees C (could be any temp really, I’m just choosing this as a convenient example). You are passing through it propelled by … something … with variable speed. At lower speeds, presumably like a “cool breeze” you would cool off faster. But at some point while you’re increasing speed, that doesn’t happen any more. I recall that at least some supersonic aircraft like the SR-71 heat up a lot, to the extent that they need to be made of special materials that won’t melt.

At what point does that happen? And what are the variables that might change the point at which it happens?

Not an expert but I would imagine the altitude (and by extension the density) would have a big effect

First, let’s dispel the notion of “friction” heating. At speeds where the air gets heated up enough to matter, the problem is compression heating. Air heats up when you compress it; this is true whether you capture the air in a diesel engine and squeeze it with a piston, or slam it into a flat surface so fast that it’s crushed by its own momentum. The latter phenomenon is the issue here: the hottest surfaces on a supersonic object are the surfaces facing forward, where the air is moving the slowest and has been compressed the most. On an aircraft, this is primarily the nose and the leading edges of the wings, but the air still isn’t back up to slipstream-speed as it passes along the rest of the aircraft, so there’s still plenty of warmth there as well.

Bernoulli’s equation governs the relationship between pressure, density, and velocity in a moving fluid:

P[sub]1[/sub]+0.5*rho[sub]1[/sub]V[sub]1[/sub][sup]2[/sup] = P[sub]2[/sub] + 0.5rho[sub]1[/sub]*V[sub]2[/sub][sup]2[/sup]

The subscripts 1 and 2 denote two different states of the fluid. In your case, state 1 has P=101 kPa, T1 = 0C, and V1 = the velocity of your aircraft. state 2 is the condition of the fluid after it’s slammed into the nose or wing of the aircraft and reached its lowest relative velocity (call it V[sub]2[/sub] = 0). For liquids, the density is constant, and so you can solve this equation by itself directly for P2. For air, the density changes as you go from state 1 to state 2, and so you need to add another equation for adiabatic compression:


“gamma” is the ratio of specific heats; for air, this is 1.4.

Now you have two equations, and two unknowns (P2 and rho2), so you can solve for your unknowns.

Once you’re done with that, you know P[sub]1[/sub], T[sub]1[/sub] and P[sub]2[/sub], so now you can figure out what your final temperature T[sub]2[/sub] is using another equation related to adiabatic compression:


The math gets a little bit easier when you have access to software that solves systems of polynomial equations while simultaneously calling up thermodynamic properties of substances. Assuming a vehicle moving through air at sea level (so P[sub]1[/sub]=101 kPa) and T=0C, I came up with this:

V[sub]1[/sub] (km/hr)     T[sub]2[/sub] (C)
0		0
100		0.5366
200		2.137
300		4.773
400		8.403
500		12.97
600		18.4
700		24.64
800		31.6
900		39.2
1000		47.39
1100		56.09
1200		65.24
1300		74.77
1400		84.65
1500		94.83
1600		105.3
1700		115.9
1800		126.7
1900		137.7
2000    		148.9

The point at which “heating overcomes cooling” will depend on what temperature you’re trying to maintain on your moving object. From the table, you can see that 600 km/hr results in a stagnation temperature pretty close to “room temperature” - although if you’ve ever ridden a motorcycle in a T-shirt when it’s 18C out, then you know it still feels pretty damn cold. OTOH, if you’re inside a capsule so that the 600-km/hr breeze isn’t ruffling your shirt, then 18.4 C just feels slightly chilly.

Passenger jets travel at something close to 900-1000 km/hr, but they do this at an altitude where the ambient pressure, temperature, and density are much lower; ambient temperature at cruising altitude is somewhere around -50C, and the result is that the stagnation temperature ends up being something close to 0C.

Am I correct in noting that the terms in the above equations seem to scale linearly with pressure? What I’m getting at is that if my observation is correct, then ambient pressure shouldn’t matter in finding the equilibrium speed and temperature, because less dense air would cool less but also heat less equally. It would seem (besides the makeup of the aircraft itself) that it should just depend on ambient temp and speed.

In the aircraft I fly, at 400 knots and ~FL300 the temperature rise is around 13°C, that is the temperature displayed on the cockpit OAT gauge is about 13°C more than the true air temperature.

Interesting point. I tried using higher initial pressures, and the final temperatures didn’t change. The thing that matters is initial temperature.

Also worth noting that at very high altitudes where the density is very low, the rate of heat transfer is very low. So when the space shuttle Columbia was coming down with a big hole in its wing at many thousands of km/hr, it was exposed to air at thousands of degrees, but at very low density; it would have taken a long time for that thin, hot air to cause the damage it did.

400 kts = 741 km/hr, for which my math predicts 27.4 C. The temperature you read will depend on the placement of the thermometer. If it’s right in the center of the nose of the aircraft, then I’d expect something close to 27C, but if it’s in a small pitot tube where it’s subject to peak temperature only at the front of the tube (and something closer to slipstream temp on the sides of the tube), then your 13C rise makes sense.

I like Machine’s clarification of compression, plain old why-the-basketball-pump-gets-hot.

But how does friction fit in? Even as a definition?

Eg, smooth wing skin to sandpapery to bumpy to full-on aerodynamic surfaces–when/are compression physics must admit or even cede control to other components? (Golf ball bumps, etc.)

In fact, I just thought of reconfigurable skin materials in aircraft being used for aerodynamic control as a thing of heavy research for the military. (Although I really don’t know where the tech curve stands or is projected.)

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Form drag is the drag associated with air hitting forward-facing surfaces and causing an increase in pressure; it’s also associated with air not following the rearward-facing surfaces and causing a drop in pressure.

Friction is more synonymous with skin drag, i.e. with forces due to the viscosity of the fluid and the shear strain that occurs between the boundary layer that’s adhered to the skin of the aircraft (relative speed = 0) and the air much farther away from the aircraft (relative speed = max). If you’re in a short, fast vehicle like a fixed-wing aircraft (or if you’re a sheet of plywood oriented perpendicular to the wind), form drag tends to dominate. If you’re in a long, slow-moving vehicle like the Hindenberg (or if you’re a sheet of plywood oriented parallel to the wind), skin drag tends to dominate.

Machine Elf’s explanation of compression heating is pretty comprehensive from a first principles perspective but there are additional considerations when considering a high supersonic (M>2) or hypersonic (M>5) speeds. The heating, as noted, occurs because of compression of the air in front of the vehicle, and so the amount of power generated by the vehicle depends largely on the amount of surface area on the forward aspect of the vehicle; however, the temperature developed on any particular part of the vehicle depends on the proximity and orientation to the shock field, compression or expansion of the field in view of a location, and any interactions between separate shocks that can create heating augmentation. The transfer of heat to and from the vehicle occurs almost exclusively by radiation rather than the convective heating or cooling that occurs at sonic speeds, so local heating rates at supersonic speeds are more highly dependent on vehicle geometry and Mach number than ambient pressure.

To complicate this, some vehicles such as base entry capsules, use ablative shielding in which the heating causes evaporation of a thin layer of the surface which absorbs heat and is carried away outside the outer mold line (OML) and cools as it expands, ensuring that the upper surface of the OML sees only low heating rates, hence why the Apollo and Gemini capsules had very little external insulation on the conical surface compared to the blankets and ceramic panels that covered the underbelly and much of the upper wing area of both the US SLS Orbiter Vehicle and Soviet Buran vehicle.

At supersonic speeds there is essentially no direct contact between the external flow field and the surface of the vehicle, so small features such as wing chevrons, vortex generators, or other surface roughness items have little effect on heating as long as they don’t protrude into the flow field. For analysis of heating of supersonic flow the fluid inside the shock boundary is typically treated as motionless with respect to the vehicle and frozen (chemically inert) with empirical factors to address ionization effects. In the case of really high altitude, very low pressure conditions where the density is such that the atmosphere is in free molecular flow rather than a fluid continuum, the heating has to be simulated using what are called Direct Simulation Monte Carlo (DSMC) methods which simulate individual particle interactions with the vehicle surface which almost exclusively depends on the amount of frontal surface area and degree of ionization of the ambient atmosphere.

This is one of the many reasons that a capsule-style reentry vehicle returning from orbit makes more sense than a spaceplane configuration, at least within the limitations of current materials and thermal protection systems. It also illustrates the problems with entry and descent onto Mars; it’s thin atmosphere provides enough of a medium to create significant heating, but is too thin to provide significant cooling or aerodynamic braking below a certain airspeed for a reasonable sized surface, which requires either a very low density deceleration system or a large parachute-to-payload mass ratio, which is basically untenable for payloads significantly greater than 1 metric ton in mass.

There are some tricks you can play to direct heat away from the vehicle or reduce drag by intentionally creating a shock field that is offset from the OML (e.g. a forward aerospike or creating shock-shock interactions in regions relatively insensitive to heating) but again, surface roughness or small local features inside the flowfield don’t really play into this. There are also theoretical systems that can either carry away heat from a highly heated area, often using chilled propellants such liquid hydrogen and regenerating the energy from heating to help drive propulsion system cycles or spraying a protective ablative film that evaporates, carrying away the heat energy, but none of these have been successfully employed on a hypersonic or space reentry vehicle to date due to reliability concerns.


Im now going to re-read and think about the two above posts (and thank you).