# Is this quadcopter specification realistic in terms of endurance?

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?

• Probably better on Drones SE but just look at it from an energy perspective. How much energy does it take to fly 8kg around for ninety minutes?
– Jim
Commented Sep 14, 2022 at 5:15
• It only boasts the 90 minutes at empty weight, or 45 minutes at 7.9kg. But I agree, this isn't an aviation question and is more suited for a drone SE or a battery SE.
– Max
Commented Sep 14, 2022 at 5:22

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.