# What phenomenon causes the increase of drag with rain?

I know that rain generally worsens the aerodynamic propeties of an aircraft.

I'm wondering what processes cause the increase in drag.

I'm mostly interested in General Aviation, thus relatively low speed and low altitudes.

Several things I can imagine, although the effects might be small:

• The water in the air makes it heavier, increasing the effective value of the air density, $\rho$
• Rain might lower the temperature, again having an effect on $\rho$
• Rain drops on the wing might cause earlier transition on the wing, increasing drag.

I hope somebody can clarify what magnitude these effects have, and if there are any more effects that cause an increase in drag when flying in the rain.

• On the glider rain drops can reduce glide ratio substantially. It depends on the wing profile but it can drop from 45 to 30. Commented Feb 18, 2016 at 13:37
• @Andrius, I know rain can change the glide ratio significantly, but I'm mostly interested in what causes these changes. I'll reword my question to make it a bit clearer. I'm also focusing more on the increase in drag, to keep a narrow focus. Commented Feb 18, 2016 at 13:45
• For us physics challenged readers, what does $\rho$ stand for? Commented Feb 18, 2016 at 19:43
• Sorry, $\rho$ is the density of the air Commented Feb 18, 2016 at 19:45

While Peter Kämpf already commented the effects I'll take a look at the numbers. Don't expect this calculations to be exact predictions, rather worst cases to know the magnitude of following effects:

• Mass increase due to rain drops
• Forces due to drops hitting the wing
• Early tripping of the boundary layer

After deducing some equations I'll feed them with the data of two different airplanes.

Mass increase due to rain drops

The dew layer you find on your airplane in the morning can reach a maximum altitude of 0.8 mm. Raindrops, which do not fill the complete wing surface, don't usually exceed 2 mm diameter.Therefore taking an average distributed height of $h_W=1mm$ for the water on the wing should be still a worst-case prediction.

$$m_{Drops}=\rho_{W} \cdot A\cdot h_W$$

$A$ is the projected area of the aircraft on the horizontal plane and $\rho_W$ water density.

Forces due to drops hitting the wing

Normal rainfall intensities are about 5 mm/hour and we already speak about violent rain with precipitation rates beyond 50 mm/hour. But let us take the heaviest rate ever measured: $I_R=38mm/min$.

Drops fall normally with $v_{Drop}=10m/s$.

To simplify the calculation I'll assume vertical rain and that once a drop hits the airplane it sticks to it. In reality you don't accelerate every drop to the airplane speed nor slow its vertical speed down to 0.

i) Drag increase

$$\Delta D= \rho_{W} \cdot I_R \cdot A \cdot v_{airplane}$$

ii) Lift decrease

$$\Delta L= \rho_{W} \cdot I_R \cdot A \cdot v_{Drop}$$

To calculate the total drag ($D=C_D\cdot \frac{\rho_{Air}}{2} V^2 \cdot A$) I've used $C_D=0.035$. $V$ is the cruise speed of the aircraft.

Early tripping of the boundary layer

While it's possible to find airfoil polars in rain searching the Internet, I'll first look at a "bugs influence" diagram where you can see the effect of small disturbances at the nose without other effects overlayed. Bugs and raindrops are similar in size, therefore the comparison should be valid.

Source

The polar above shows how the drag can double (100% increase)just because of some small disturbances at the leading edge. Keep in mind that in modern profiles the effect will probably be smaller. The next polar is from a transport aircraft airfoil.

Source

While not so important as in the glider airfoil, the drag coefficient increase (experimental results) is everywhere at least a two-digit percentage.

Airplanes

I've taken two airplanes with really different wing loadings: A1 would be something between the two Solar Impulse models and A2 a single engine four-seater like a Cessna 172. The last three rows give the drag, lift and mass difference as described above as a percentage of its total value.

|                       |            A1 |     A2 |
|-----------------------+---------------+--------|
| Mass m [kg]           |          1600 |   1000 |
| Area A [m^2]          |           210 |     20 |
| Wing loading [kg/m^2] |           7.6 |     50 |
| Cruise speed V [m/s]  |            20 |     58 |
| Lift L [N]            |         15696 |   9810 |
| Drag D [N]            |          1800 |   1323 |
| Drops mass mW [kg]    |           210 |     20 |
| Drag increase dD [N]  |          2660 |    703 |
| Lift decrease dL [N]  |          1330 |    127 |
|-----------------------+---------------+--------|
| dD/D [%]              |           147 |     53 |
| dL/L [%]              |           8.5 |    1.3 |
| mW/m [%]              |            13 |      2 |
|-----------------------+---------------+--------|


SUMMARY

For a normal GA airplane the water mass on the wings and the lift decrease influence due to raindrops hitting the wing even considering the worst possible conditions are low single digit percentages.

While drag increase due to drops hitting the wing is relevant in the extreme case I took here, under normal conditions it should be below single digit percentages too.

On the other hand the drag increase due to the early tripping of the boundary layer is at least a two digit percentage, at high lift coefficients even more.

Airplanes with lower wing loading are more affected with rain precipitation.

Fly a Schempp-Hirth Janus or a PIK-20 into rain. The effect will be dramatic. Make sure you have some place to land nearby! In both gliders your rate of sink will triple and the minimum speed will increase by maybe 20 km/h, so make sure you come in fast for landing while the wing is still wet.

The reason is the airfoil, the Wortmann FX 67-170. With 17% relative thickness and a very long laminar boundary layer, the recompression cannot be handled by a boundary layer which has been tripped near the leading edge. The consequence is flow separation already at moderate angles of attack if the wing is dirty from bugs or rain. The flight performance changes dramatically.

Then perform the same with a Schempp-Hirth Discus or an ASW-20. Sink speed will increase, but the effect is much less dramatic and the minimum speed will barely go up.

There is no general rule of thumb, and two of the three reasons you suspect are indeed the major effects: Added mass from the water film over all upper surfaces and early tripping of the boundary layer. In big aircraft where the transition happens close to the leading edge anyway the difference made by rain is very small. It might even help by increasing engine thrust: Rain will cool the air and by absorbing heat when vaporizing will lower the temperature rise in the compressor of a jet engine. Note that many early jets used water injection to increase engine thrust on hot and high airfields.

For small aircraft with their lower volume to surface ratios the mass increase is more noticeable, and if the airfoil was optimized for minimum drag in clean conditions the early transition will effect a dramatic change in a few cases. The airfoils of most powered aircraft are not nearly as sensitive to rain. Normally, those aircraft are flown VFR, and the drop in visibility caused by rain will be the biggest effect.

• This is a very good answer to the question specifically asked, but I think that there is an implied, more broad question about how rain effects "performance", rather than just increased drag. What I am referring to, is the obvious fact that rain is "falling". There is a force applied to the aircraft in a downward direction by both the rain, and the accompanying downdraft. Commented Feb 19, 2016 at 11:02
• @GregTaylor I tried to keep the question specific, which is usually good for the quality of the answers given. If you want to ask about the forces of rain falling on the aircraft, you're free to do so. When doing some research on this question I found answers to such a question here: airliners.net/aviation-forums/tech_ops/read.main/317372 This answer suggests that any forces caused by the rain are very small Commented Feb 19, 2016 at 14:00