# VTOL Propeller Sizing and Executing a transition from VTOL to Forward Flight mission profile

Hi I am an engineering student, currently in the process of designing a compound UAV drone capable of both vertical and forward flight. I've made significant progress, having completed initial gross weight estimation, Wing Loading and powerloading estimation, wing, fuselage, tail, powerplant, and landing gear design, as well as weight estimations. Moreover, I've solved for the center of gravity at each component location using equations from Daniel Raymer and Mohammad Sadraey, resulting in minimal CG travel. This is the UAV that I have designed:

However, all these calculations have been based on single-engine estimations from Raymer as advised by my professor. My current hurdle lies in the VTOL (Vertical Takeoff and Landing) mission profile. I'm unsure about the rule of thumb for determining the diameter of the VTOL propellers and whether it's a critical aspect. Unfortunately, my professor hasn't provided much guidance regarding the VTOL motors.

Another challenge I'm facing is how to execute the required mission profile, as depicted below:

According to my professor, I need to gradually reduce the RPM of the VTOL mechanism while increasing the RPM of the pusher propeller. However, I'm concerned that this approach might impose excessive torque on my VTOL propeller. My alternative proposal is to go power-off once a certain height is reached and then increase the RPM of my pusher propeller as the aircraft glides. Nonetheless, I'm uncertain if the airfield space would be adequate for this specific mission profile.

Any advice or guidance on these issues would be greatly appreciated.

I'm unsure about the rule of thumb for determining the diameter of the VTOL

The rule of thumb is termed momentum theory, by which the thrust $$T$$ generated by a rotor is:

$$T = k\sqrt[3]{2 \rho A P^2}$$

where $$A$$ is the rotor area, $$\rho$$ is the density and $$P$$ the power needed to spin the rotor. This equation is strictly valid only at hover but being the highest thrust normally required in hover, then it's just perfect for your purpose. The $$k$$ is a coefficient taking into account the limitations of the momentum theory: a value of $$0.5$$ can be used in a conservative way.

Obviously $$T$$ equals weight $$T = W = mg$$, where $$m$$ is the mass and $$g$$ the gravity. Just divide it by the number of propellers you have in mind (4?).

According to my professor, I need to gradually reduce the RPM of the VTOL mechanism while increasing the RPM of the pusher propeller. My alternative proposal is to go power-off once a certain height is reached and then increase the RPM of my pusher propeller as the aircraft glides.

Just simulate both and compare the results, it might be that your approach work as well.

Theres lots of equations, here's one with empirical corrections. These calculations can be fairly inaccurate. You can always find the motor/prop combo that provides enough thrust for the weight. For 4 props at 50% throttle.

For transition you need to work out how much lift you gain relative to velocity squared. The thrust curve vs. RPM isn't linear either :)

I cannot upvote the answer related to blade momentum theory due to my low reputation ;) but it is way to go. Moreover, the following paper may help you with your project: https://www.mdpi.com/2226-4310/11/3/200

VTOL may need forward velocity to glide and transition is required to be executed gradually so that flow can be established over the wings. In the absence of airflow, a flying vehicle may fall into a flat spin.

Obviously, one can simulate both cases but that will require some CFD data at high AOA as linear methods lack the complexity of a separated flow over a falling aircraft.