# How the planform geometry of rotor is designed for helicopter?

Rotor planform specially the tip is designed differently for different helicopter rotor. How the shapes are determined? For example I added 2 photos. How the dimensions of the tip or root of these rotors were determined?

First of all, a basic description of the aerodynamic environment encountered by the blades.

The airflow velocity $$V$$ seen by a rotating wing is the sum of:

• the speed due to the rotation around the hub $$=\omega R$$;
• the speed due to the forward velocity of the helicopter $$=V_f$$.

Those two speeds:

1. sum up when the blade in its rotation around the hub is rotating forward i.e. from the tailboom toward the nose and it's $$V=\omega R + V_f$$; at high forward speed, this sum can reach transonic value;
2. subtract when the blade in its rotation around the hub is rotating backward i.e. from the nose toward the tailboom and it's $$V=\omega R - V_f$$; at high forward speed, this difference can reach very low subsonic speeds (it actually becomes negative on some 40% of the blade span toward the hub).

The following picture from this paper shows this effect (higher speeds on the right/advancing blade and lower speeds on the left/retracting blade):

That means that the velocity seen by blade continuosly changes from a maximum (the sum at point 1.) to a minimum (the difference at point 2.) during each revolution. In particular, the tip is the part of the blade experiencing the highest changes in speed and therefore the highest aerodynamic load.

There's a third aerodynamic aspect that is also important for the design of the blade tip:

1. each blade leaves a wake behind it; this wake is stronger where the bladewise change of lift is stronger and this happens towards the tip; as seen (previous point 1.) toward the tips lift can be very high but then it suddenly goes to zero where the blade ends; this sudden change in lift leaves a very strong vortex behind, which is called tip vortex; now, when a blade bumps (literally) into the tip vortex released by the previous blade, the airflow is locally strongly perturbed (this is the source of the typical "flap-flap-flap" noise of slowly descending helicopters). The following picture from this paper shows two tip-vortices (number 3) shed by two blades:

So, now that we know the three main aerodynamic conditions the blade (and especially its tip) must undergo in its flight, we can try to figure it out how it should look like. Due to the previous point:

1. $$\rightarrow$$ the blade tip should be thin, with a short chord, with a leading edge swept back and a tapered planform, basically just like the wing of a jetliner; all this in order to diminish and/or retard the rise of drag due to transonic effects (wave drag);
2. $$\rightarrow$$ the blade tip should be thick, with a long chord and no particular need of being swept or tapered; actually if we want to be fancy to comply with this point we could use a delta planform for the tip: delta wing are known to generate quite a lot of lift at high AoA and low speeds, exactly the aerodynamic environment of 2.;
3. $$\rightarrow$$ the blade tip should be curved down (anhedral) so that the tip vortex is shed into the wake in a lower position than the following blade and therefore doesn't hit it directly.

Well, blade's design is driven by some quite conflicting requirements.

To all of this we must obviously add the centrifugal force stretching the blade: a blade of a typical EMS helicopter resists a centrifugal force of some 40kN (4000kg, 9000 pounds). To resist that force you need a structure which is as much as possible aligned to this centrifugal force i.e. you just want a perfectly straight and rectangular blade. Yet another conflicting requirement.

I let you figure out which requirement took over in the design of the blades in your picture.