I’ll preface this by noting that I wasn’t involved with the propeller design, but assuming I’m correctly understanding how the pitch angle is determined, then my result from a rough measurement on the CAD model is p_{0.75D} \approx 15.5°
I’ve asked internally to see if I can get confirmation on the value, in which case we can hopefully include a value in the technical details. That said, given we had quite different values, I’m curious how you went about calculating yours?
Thank you for working that out for me and I really appreciate you talking to the team about this.
If that is the same CAD uploaded to the website, I think it is quite different to the real propeller because it looks like a flat plate.
This was my method to work it out:
Your website has some data on the propellers which I used: Operating RPM @ 16V: 2751 RPM
Hence, rotations per second: 45.85 RPS
Then I estimate the flow velocity though the propeller: Thrust @ 16V: 5.63 kg (55.23 N) Power: 447.58 W Propulsive Efficiency (estimate): 70%
Velocity=Power/Force
V = ( 447.58 W x 70% ) / 55.23 N
Flow Velocity (Vf) = 5.67 m/s
Pitch = Vf / RPS = 5.67 / 45.85 = 0.124 m
This is a flawed way of measuring pitch as it does not account for slip, although, at the time this was the easiest way I could think of.
D_0.75 = 84mm
Using a right angle triangle to work out the angle:
Pitch Angle = TANH( Pitch/ Circumference_D_0.75 ) Pitch angle =TANH( 124mm/(84mm*PI) ) = 25 degrees
Subsequently I redid this with F=ma
Force = 55.2 N
Density (Rho) = 1000 kg/m^3
Mass Flow = Area x Velocity_exit x Rho
Acceleration = Velocity_exit - Intake Velocity (Intake is static = 0)
Therefore:
F = (Disk Area(A) x V_e x Density) x (V_e)
Rearranged:
V_e = sqrt ( F/(A x Density) )
Filling in values:
V_e = sqrt(55.2N / (0.009852m^2 x 1000kg/m^3) ) V_e = 2.37 m/s
Reducing this estimate for efficiency to 29% for the first method gives: Velocity = 2.35 m/s This speed seems much more reasonable as I have heard this prop is calculated to operate at ~3 kts Pitch = 0.051 m Pitch Angle = 11 degrees
This is only 4.5 degrees from your measured pitch. Because the calculated pitch angle comes from the real world data for the screws path through the water, it seems reasonable that this could be accounted for by the angle of attack of the flow to the blade. This gives the real pitch angle of 15.5 degrees.
I hope that makes sense, I’m not sure how to get notation into the post.
Following up on this, I’ve been told my approach was indeed correct, but apparently the public CAD model has the blades slightly modified for IP reasons. The measurement from the actual design file has been confirmed as 14°, which I’ve now added to the technical details on the product page
This is effectively a re-arrangement of my approach in this T200 comment, but with an included efficiency estimate (so you’re not the only one doing such calculations)
I’m assuming you meant \arctan here (i.e. \tan^{-1}), not hyperbolic tangent (\tanh)? That matches your calculated value, and makes follows your triangle logic description.
There’s a formatting section in the How to Use the Forums post, which covers the basics - the maths is essentially handled by LaTeX syntax, if you’re familiar with that