How do I determine the diameter of my propeller at high altitudes?

Question

I'm designing a electrically propulsed HALE UAS and I need to find the diameter of my propeller to find my thrust. Is there an equation for propeller diameter that doesn't rely on knowing my thrust or velocity. In particular an equation that is concerned with relative air density as this is meant to be optimum at high altitude cruise conditions.

Answer 1

You have the process of propeller sizing backwards. This makes the question unanswerable.

I need to find the diameter of my propeller to find my thrust.

Normally, you start with a thrust demand at a given speed and work form there. After all, the propeller is needed to compensate for airframe drag at that speed plus any climb requirements. Without that, you have a glider.

Another route is to start with the torque the engine can supply. Now the propeller has to be able to absorb this torque at the given speed, producing thrust. But you still need to check this thrust against requirements in order to get engine size right.

So please do yourself a favor and find out what thrust you need. The rest should be easy. Use 85% for efficiency to arrive at a suitable $\Delta$v and assume that half of all losses are from friction.

This lets you arrive at $$\frac{\Delta v}{v_{\infty}} = 2\cdot\left(\frac{2}{1+\eta_{Prop}}-1\right)$$ which becomes 16.2% of flight speed for an overall efficiency of 85%.