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Propeller Efficiency

There are two quantities of interest for propeller:

  • Thrust – $ T$ [N]
  • Torque – $ M$ [N$ \cdot$m]

In case of propeller, reference pressure is not taken into account when evaluating thrust and torque.

Dimensional analysis leads to a definition of propeller coefficients representing its performance. 8.1

  • Torque coefficient ($ k_Q$):
    $\displaystyle k_Q = \frac{M}{\rho n^2 D^5}\,,$(8.9)


  • Thrust coefficient ($ k_T$):
    $\displaystyle k_T = \frac{T}{\rho n^2 D^4}\,,$(8.10)


where $ n$ is the propeller speed [rev/s] and $ D$ denotes the propeller diamater [m].

The efficiency can be evaluated using the supplied power to the propeller ( $ P_\mathrm{in}$) and the useful power output ( $ P_\mathrm{out}$):

$\displaystyle \eta^{propeller} = \frac{P_\mathrm{out}}{P_\mathrm{in}} = \frac{TU_0}{2\pi n M} = \frac{1}{2\pi} \frac{k_T}{k_Q} J\,,$(8.11)

where $ J$ is the advance ratio and is given as the distance advanced by the propeller in one revolution divided by the propeller diameter, i.e., $ J=U_0/(Dn)\,$.