Flow rate/s for T200?

[EliotBR (Eliot)]

Hi @shakeera,

@shakeera

Can you please give the step by step calculation using pitch and rpm… somewhere I saw pitch into rpm multiplication but here pitch in degrees…

The “pitch” being discussed here is the pitch angle of a single blade relative to the rotation plane of the propeller - “\theta” in the section cut in the following diagram:

As the propeller spins, each blade can be thought of as moving through the water like the thread of a screw. In an ideal case (with no “slip”), the maximum flow velocity is exactly equal to the offset between the rotational velocity and the pitch angle:

v_\text{max-flow} = v_\text{rot}\cdot \tan{\left(\theta\right)}

Rotational velocity is determined by the angular rotation rate at a given radius

v_\text{rot} = \frac{\text{RPM}}{60\frac{\text{seconds}}{\text{minute}}} \times 2\pi r'\ \frac{\text{m}}{\text{revolution}}

75% of the propeller’s tip radius is a common value for estimating propeller speed and flow rate, so

\begin{align} r'&= 0.75\times r_o\\ &= 0.75\times 38.1\text{ mm}\\ &\approx 0.0286\text{ m}\\ \rightarrow v_\text{rot} &\approx \frac{3600}{60\text{ s}}\times 2\pi \times 0.0286\\ &\approx 10.77\ \frac{\text{m}}{\text{s}}\\ \rightarrow v_\text{max-flow} &\approx 10.77 \times \tan{\left(22.5^\text{o}\right)}\\ &\approx 4.46\ \frac{\text{m}}{\text{s}} \end{align}

Substituting in the 12V RPM instead gives 3.81 m/s.

As @Adam mentioned though,

@adam

Bear in mind these speeds and flow rates are rough estimates based on some math and not true measurements, I would expect the real number to be lower. However, they should be reasonably accurate for estimation purposes.

Given the rough and maximal/ideal nature of the values, rounding down to the nearest 0.05 m/s seems reasonable to avoid too much false/inaccurate precision.

Note also that realistic flow rates depend on the relative incoming speed between each thruster and the water going through it, which is not considered or accounted for in the “theoretical maximum” calculations presented here.