<p>As usual, the simple <a href="https://en.m.wikipedia.org/wiki/Momentum_theory" rel="noreferrer">momentum theory</a> is our friend in these cases:</p>
<p><span class="math-container">$P=\sqrt{\frac{T^3}{2 \rho A}}$</span></p>
<p>Considering that in hover each rotor lifts ¼ of the total weight <span class="math-container">$W$</span> and that we have 4 rotors, the needed power becomes:</p>
<p><span class="math-container">$P=4\sqrt{\frac{(¼W)^3}{2 \rho A}}$</span></p>
<p>where:</p>
<ul>
<li><span class="math-container">$W=8\cdot9.81=78.5~\mathrm N$</span></li>
<li><span class="math-container">$\rho=1.125~\mathrm{kg}/\mathrm m^3$</span></li>
<li><span class="math-container">$A=\pi(22\cdot0.0254)^2=0.98~\mathrm m^2$</span></li>
</ul>
<p>Substituting the values we get a total power of:</p>
<p><span class="math-container">$P=234~\mathrm W$</span></p>
<p>According to the source, the electrical engines work at a voltage <span class="math-container">$V=50.4~\mathrm V$</span>. The power of an electrical machine is <span class="math-container">$P= V\cdot I$</span>, which translates into a current of:</p>
<p><span class="math-container">$I=P/V=234/50.4=4.6~\mathrm A$</span></p>
<p>The battery has a capacity <span class="math-container">$C=14~\mathrm{Ah}$</span> and delivering that current it drains after a time of:</p>
<p><span class="math-container">$C/I=14/4.6=3~\mathrm h$</span></p>
<p>This is obviously a maximum theoretical value that does not take into account many factors like:</p>
<ul>
<li>electrical engines are not 100% efficient;</li>
<li>some electrical power is used by the onboard electronics;</li>
<li>batteries are normally not made deplete completely;</li>
<li>for manoeuvring, more thrust and therefore more power is needed than for hovering; but less power is needed in forward flight;</li>
<li>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%.</li>
</ul>
<p>Factoring in all these points, the given endurance might be plausible.</p>

CC BY-SA 4.0
2022-09-20T18:36:24.573Z
2022-09-21T08:02:03.697Z
sophit
<p>According to the <a href="https://www.droneassemble.com/product/quadcopter-drone-90-minutes-endurance/" rel="nofollow noreferrer">specifications, this quad-copter</a> offers a 90-minute flight time on a 14S-14000mah Li-ion battery.</p>
<p>The propellers being used have a 22-inch diameter and have 8-inch blades and the Maximum Take-off Mass is 8.</p>
<p>Is it possible for such a quadrotor to have a such a high endurance?
If so, could you please explain how?</p>

CC BY-SA 4.0
2022-09-14T05:15:48.953Z
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
<quadcopters>
Is this quadcopter specification realistic in terms of endurance?
falcon
# Is this quadcopter specification realistic in terms of endurance?

(Asked by: username_0 on 2022-09-14)

According to the [specifications, this quad-copter](https://www.droneassemble.com/product/quadcopter-drone-90-minutes-endurance/) 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?

**Tags:** quadcopters

> **Comments:**
> **username_1**: 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?  

---

## 1 answers

### Answer by username_2 on 2022-09-20. Score: 5

As usual, the simple [momentum theory](https://en.m.wikipedia.org/wiki/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.


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