What is the downwash speed on a typical helicopter?

Question

On a typical 2 or 4 seat helicopter like a Robinson R22/R44, at full throttle at 20ft ASL, if you put a Wind Speed Meter/Anemometer about 10ft below the blades and halfway along a rotor blade's span, about what speed should it read?

Answer 1

What you are searching for is called the induced velocity $v_i$. It can be calculated in a good approximation via the following formula:

$v_i = \sqrt{\frac{F_n}{2 \rho S}}$

With $F_n$ being the weight of the aircraft, $\rho$ the air density, and $S$ the disk area. This formula assumes an "ideal" rotor, therefore air is uniformly accelerated over the rotor plane without losses.

Here are some example values for light, medium and heavy weight helicopters as well as a tilt rotor at sea level for the MTOW (Maximum Take-off Weight):

• Robinson R-22 (light weight helicopter): $7.34 \frac{m}{s} \approx 24.1 \frac{ft}{s}$
• Airbus H135 (medium weight helicopter): $10.01 \frac{m}{s} \approx 32.8 \frac{ft}{s}$
• Leonard AW139 (heavy weight helicopter): $13.55 \frac{m}{s} \approx 44.5 \frac{ft}{s}$
• Boeing V-22 Osprey (tilt-rotor helicopter): $20.24 \frac{m}{s} \approx 66,4 \frac{ft}{s}$

Real-life adaptation

In reality however, the rotor plane is not a continuous plane which accelerates air, as assumed by the momentum theory. In reality the airspeed over the rotor plane rises linearly outwards, as the velocity rises linearly over their span (a rotor segment spins faster the more distant it is from the rotor hub). The situation is roughly as follows:

However as you ask about about a point halfway along a rotor blade, the induced velocity is pretty much the mean induced velocity as calculated above. Additionally, the stream tube does not contract very fast, therefore the induce velocity might be a bit higher, but not by much. Sophit states in his answer that the stream tube contracts by a factor of 2 over the rotor diameter, which would be 25 feet for the R22, therefore at 10 feet it is perhaps 10ft/25ft = 0.4 about 40% faster. Given that, an the fact that I estimate the full throttle thrust to be about 20% of hover thrust at MTOW, the induced velocity of an R22 would then be about $11.36 \frac{m}{s} \approx 37,3 \frac{feet}{s}$.

Answer 2

Airflow around rotors can be extremely complicated (NASA source):

Estimating the airspeed in exactly one point is therefore very difficult and is normally done only if the point belongs to the helicopter. Anyway a good approximation of the average flow field under a rotor can be obtained via the simple momentum theory by which the rotor is assumed as a thin disk imparting the air a jump in its pressure (source):

As visible in this picture, airspeed increase from 0 far above the rotor to $v$ by the rotor and to $w$ beneath it. This particular airspeed shape is termed "vena contracta" (dashed line). For a rotor of disk area $A$ generating a thrust $T$, the momentum theory returns a speed $v$ by the rotor of:

$v=\sqrt{\frac{T}{2 \rho A}}$

As said, under the rotor the airflow keeps on contracting and the speed increasing, reaching a value $w=2v$ at some one-diameter distance under it. Further below airspeed will eventually decrease due to viscosity.

Being in hover thrust equal weight, from that equation it is easy to calculate the speed at the point you indicated in your question. Considering the point halfway between $v$ and $w$ and given the main rotor area of 46m² and the MTOW of 620kg for a R22, we get at sea level:

$w=1.5\sqrt{\frac{620 \times 9.81}{2 \times 1.225 \times 46}}=12m/s$