# How much thrust does the Lilium aircraft produce?

I have been researching the Lilium aircraft and can’t find information about thrust. An early version of this aircraft was 2 seats with a loaded weight of 1,400 lbs, 36 ducted fans and 320 kW peak power. They are testing a five seater also for vertical takeoff. Either the standard calculations for thrust are wrong in ducted fans or something else is going on. Any guesses?

The highest thrust is normally needed during hovering. During hovering thrust equals weight so the thrust generated by each fan should be simply:

$$weight/nr_{fan}$$

Since in these designs the total failure of some fans is always taken into account, $$nr_{fan}$$ is the minimum number of them which can sustain the flight (let's say some 80% of the total number). For the lilium, I suppose a bit more of thrust is needed during the transition to forward flight so the previous value has to be increased, let's say of some 10%. Obviously this final value doesn't take into account any aerodynamic interference

EDIT

Just out of curiosity I did some basic calculation. The thrust generated by an ideal not-ducted rotor is:

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

For a ducted rotor this increases of some 30%, the power being equal:

$$T = 1.3 \sqrt[3]{2 \rho A P^2}$$

From the pictures of the aircraft I would say that each rotor has some 20cm diameter and therefore $$A$$ becomes:

$$T = 1.3 \sqrt[3]{2 \rho (0.8*36 \pi 0.1^2) P^2}$$

where the number of rotors (36) has been multiplied by 0.8 to take into account the possibly failed rotors.

As said the max needed power could be some 10% higher than in hover to cope with the transition from hover to forward flight:

$$T = 1.3 \sqrt[3]{2 \rho (0.8*36 \pi 0.1^2)*(P/1.1)^2}$$

In hover thrust equals weight $$T = W$$. Using the ISA value for $$\rho$$ and the official 320kW for the total engines power we get some:

$$W = 737kg = 1620lb$$

which correlates quite well with the given max takeoff weight of $$1400lb$$

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