# 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. – Andrius Feb 18 '16 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. – ROIMaison Feb 18 '16 at 13:45
• For us physics challenged readers, what does $\rho$ stand for? – TomMcW Feb 18 '16 at 19:43
• Sorry, $\rho$ is the density of the air – ROIMaison Feb 18 '16 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 |
| 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.