Is this quadcopter specification realistic in terms of endurance?

Question

According to the specifications, this quad-copter offers a 90-minute flight time on a 14S-14000mah Li-ion battery.

The propellers being used have a 22-inch diameter and have 8-inch blades and the Maximum Take-off Mass is 8.

Is it possible for such a quadrotor to have a such a high endurance? If so, could you please explain how?

Answer 1

As usual, the simple momentum theory is our friend in these cases:

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

Considering that in hover each rotor lifts ¼ of the total weight $W$ and that we have 4 rotors, the needed power becomes:

$P=4\sqrt{\frac{(¼W)^3}{2 \rho A}}$

where:

• $W=8\cdot9.81=78.5~\mathrm N$
• $\rho=1.125~\mathrm{kg}/\mathrm m^3$
• $A=\pi(22\cdot0.0254)^2=0.98~\mathrm m^2$

Substituting the values we get a total power of:

$P=234~\mathrm W$

According to the source, the electrical engines work at a voltage $V=50.4~\mathrm V$. The power of an electrical machine is $P= V\cdot I$, which translates into a current of:

$I=P/V=234/50.4=4.6~\mathrm A$

The battery has a capacity $C=14~\mathrm{Ah}$ and delivering that current it drains after a time of:

$C/I=14/4.6=3~\mathrm h$

This is obviously a maximum theoretical value that does not take into account many factors like:

• electrical engines are not 100% efficient;
• some electrical power is used by the onboard electronics;
• batteries are normally not made deplete completely;
• for manoeuvring, more thrust and therefore more power is needed than for hovering; but less power is needed in forward flight;
• simple momentum theory underestimates the needed power of some 15% in hover; and at the typical Reynolds number of drones the efficiency is worse; I'd say that the underprediction might be some 25%.

Factoring in all these points, the given endurance might be plausible.