I'm trying to design a fixed pitch propeller of diameter 1.8 m flying at 10000 ft going at forward velocity(85 m/s).
What I've done is take a series of airfoils (from root to tip), found the respective angle of attacks for each airfoil for which the $C_l/C_d$ ratio is max. I've then Added that to the angle of my resultant velocity (which I got from using 2300 rpm*(airfoil $r$) and an 85 m/s forward speed). This is now the angle at which my airfoils sits with respect to the vertical. Now for chord lengths, using the blade element theory,
$$ \mathrm{d}T=qc(\mathrm{d}r)\frac{C_l \cos(\phi)-C_d\sin(\phi)}{\sin^2(\phi)} $$
I've take $\mathrm{d}r=0.001\,\text{m}$ to approximate the $\mathrm{d}T/c$ for each small section of airfoil. I know $q$, $\phi$ and the co-effs. Now I have the $\mathrm{d}T/c$ for each airfoil that I've taken. Then I took the airfoil at approx more than half the overall radius and set $c$ as 0.15 m. So now I have the $\mathrm{d}T$ for that particular airfoil. Assuming I want thrust to be constant through out the propeller I used this value of $dT$ and the respective $\mathrm{d}T/c$ for the airfoils to get the remaining chord lengths.
Using these values for angle of attack and chord lengths I modelled my propeller.While modelling I reduced the chord lengths at the roots since the roots are more for structural stability than thrust generation and having a large value as chord length at the root could compromise the propeller.
I know that my propeller is modelled for a very specific forward speed, but I want to know if the math I used to approximate the chord lengths checks out. It seems to be okay since I'm getting the resultant angles to decrease along the length of the propeller and so do the chord length. But my theoretical overall thrust is around 3000 N while my CFD model is 1000 N (efficiency=60%). So I'm not sure if my model is bad or my theoretical calculation is off to the point I can't present it and say "This is why I've used these as the chord lengths"
