For a closing velocity of 80 ms\({}^{-1}\) a single 2 mm rain droplet may exert a pressure of up to 120 MPa on the blade surface [35]. The amount of kinetic energy transferred into the blade from an ensemble of falling hydrometeors is dictated by:  
1. The closing velocity between the hydrometeors and the blade. Variations in wind turbine rotational speed are a function of incident wind speed (WS) at the hub-height (Figure 1a). The rotational speed of the wind turbine blades during typical operation exceeds the terminal fall velocity (\(v_{t}\)) of hydrometeors and hence generally dominates the closing velocity between falling hydrometeors and wind turbine blades. A range of approximations have been proposed to describe the dependence of hydrometeor \(v_{t}\) on their diameter (\(D\)), phase, morphology and density [39]. Estimates shown in Figure 1b are computed using:  
\[v_{t,rain}\ =\ \kappa\left[\frac{\rho_{o}}{\rho_{air}}R\right]^{1/2} \tag{1}\]  
where \(R\) = droplet radius (m), \(\kappa\) = 220 m\({}^{1/2}\)s\({}^{-1}\), \(\rho_{o}\) = air density at sea level (kgm\({}^{-3}\)), \(\rho_{air}\) = air density at the altitude above sea level (kgm\({}^{-3}\)) [40]. Early research [41] suggested that droplet \(v_{t}\) should be calculated within three different diameter ranges. The following is valid for droplet diameters (\(D\)) > 0.05 mm (\(5\times 10^{-5}\) m);  
\[v_{t,rain}\ =\ B\left\{1-exp\left[-\left(\frac{D}{a}\right)^{n}\right]\right\} \tag{2}\]  
where for \(D\) = 5 \(\times\) 10\({}^{-5}\) m to 3 \(\times\) 10\({}^{-4}\) m, \(B\) = 1.91 ms\({}^{-1}\), \(a_{1}\) = 3.16 \(\times\) 10\({}^{-4}\) m and \(n\) = 1.754. For \(D\) > 3 \(\times\) 10\({}^{-4}\) m, the coefficients in Equation (2) are adjusted to \(B\) = 9.32 ms\({}^{-1}\), \(a_{1}\) = 1.77 \(\times\) 10\({}^{-3}\) m and \(n\) = 1.147. Figure 1: (a) Simplified wind turbine rotor speed (revolutions per minute, RPM) and tip speed (ms\({}^{-1}\)) as a function of hub-height wind speed for a typical wind turbine with a rated capacity of 1.5–2 MW (e.g., GE 1.5 SLE). Estimation of the tip speed from the blade RPM assumes a blade diameter of 83 m. Power production begins at 3.5 ms\({}^{-1}\) and ceases at hub-height wind speeds >25 ms\({}^{-1}\), thus no RPM or tip-speed data are plotted for wind speeds outside of this range. (b) Contours of the joint probabilities of terminal fall velocities (\(v_{t}\)) and hydrometeor diameter (\(D\)) based on 4 years of optical dishorometer data (2017–2020) from the US Department of Energy (DoE) Atmospheric Radiation Measurements (ARM) site at Lamont in the US Southern Great Plains (US SGP). Additionally, shown are \(v_{t}\) estimates as a function of \(D\) computed for rain droplets and half using Equations (1) and (3) (lines) and the following assumptions: \(\rho_{o}\) = 1.225 kgm\({}^{-3}\), \(\rho_{air}\) = 0.999\(\rho_{o}\), \(\rho_{i}\) = 900 kgm\({}^{-3}\). An approximation for the terminal fall velocity for hail is:  
\[v_{t,hail}\ =\ \left[\frac{8}{3}\frac{|g|}{C_{D}}\frac{\rho_{i}}{\rho_{air}}R_{h} \right]^{1/2} \tag{3}\]  
where \(R_{h}\) = radius of the hailstone (m), \(\rho_{i}\) = density of ice (kgm\({}^{-3}\)), \(\rho_{air}\) = air density at the altitude at which the hail is falling (kgm\({}^{-3}\)) and \(C_{D}\) = drag coefficient (0.55) [40]. Alternative, simpler forms have also been experimentally determined. E.g., for \(D_{max}\) < 2.05 cm:  
\[v_{t,hail}\ =\ 12.65D_{max}^{0.65}\] (4a) For \[D_{max}\) > 2.05 cm: \[v_{t,hail}\ =\ 15.69D_{max}^{0.35}\] (4b) where \(D_{max}\) = hailstone maximum diameter [42]. For hail \[D\) of 0.6 to 9 mm, the following has been suggested [43]: \[v_{t,hail}\ =\ 3.74D^{0.5} \tag{5}\]  
Virtually all droplets with \(D\) > 0.5 mm have sufficient inertia to deviate from the streamlines and impact the blade with an impingement efficiency ~1 and have a velocity at impaction close to \(v_{t}\)[14; 44; 45; 46].