# What temperature is the vapor that forms around a maneuvering aircraft?

At what temperature does the vapor seen on aircraft maneuvering form? I know this highly depends on humidity, but is there a general calculation?

When doing my research, I found this page, but it only really talked about how air can't turn into water.

I'm fairly sure that the temperature this happens at is the dew point, but I'm not 100% sure.

• I may be nitpicking, but technically, it is probably mist or some other word describing suspended droplets formed by condensation, while "vapor" in a scientific sense is a usually transparent gas... Apr 21 at 7:55

I think I've linked to this resource in one of your previous questions.

NASA SP 514

On page 5 (pdf page 15), he derives an expression for the relative humidity around an aircraft.

$$RH_l=RH_\infty\, \frac{P_l}{P_\infty}\,10^{\left\{-\frac{2263}{T_\infty} \left[\frac{(T_l/T_\infty)-1}{T_l/T_\infty} \right]\right\}}$$

Sorry the font gets so small in the exponent. I'll write it another way...

$$A={-\frac{2263}{T_\infty} \left[\frac{(T_l/T_\infty)-1}{T_l/T_\infty} \right]}$$

$$RH_l=RH_\infty\, \frac{P_l}{P_\infty}\,10^A$$

The temperature $$T_\infty$$ must be in Kelvin for the number $$2263$$ to be correct.

The subscript $$l$$ means local -- at some point in the flow around the aircraft. The subscript $$\infty$$ means freestream -- at some point well ahead of the aircraft. I.e. the ambient conditions.

He is calculating $$RH_l$$, the local relative humidity.

Condensation begins when $$RH_l>1$$. The line between clear air and air with visible water vapor should be at $$RH_l=1$$.

We can immediately see that when the condensation will be visible depends on the ambient humidity $$RH_\infty$$, ambient pressure $$P_\infty$$, and ambient temperature, $$T_\infty$$. Furthermore, we can see that it also depends on the local pressure $$P_l$$ and temperature $$T_l$$.

I'm fairly sure that the temperature this happens at is the dew point, but I'm not 100% sure.

You are correct.

• Is this true also for rocket launches where vapor sometimes appears as a rocket goes transonic? Apr 20 at 14:40
• @StevePemberton, unless there is some nuance I'm missing I don't see how it would not be. Apr 20 at 15:01
• @MichaelHall Yeah it should be as the vapor cloud around an aircraft going transonic is lower pressure, so I'd assume it is with rockets also. Apr 20 at 17:12
• So does that mean if you could touch it with your hands, the vapor would be cold or hot? ;) Apr 21 at 17:03
• @J.ScottElblein, it depends on the temperature. ;) Apr 21 at 17:09