<p>Thrust is proportional to the change in momentum of the air passing through the prop - i.e. how much the prop speeds it up. </p>

<p>The power required to do this is proportional to the kinetic energy of the air, which is proportional to speed squared. That 'squared' is the problem.</p>

<p>A smaller prop acts on less air, so it has to speed it up more to generate the same thrust. Half as much air moving twice as fast generates the same thrust, but takes twice as much power.</p>

<p>This explains why helicopters can hover relatively economically, propeller planes only if they're powerful aerobatic models, jets only if they're extremely powerful and carrying a minimum of weight, and no one uses rockets unless they have to.</p>

CC BY-SA 4.0
2022-12-31T12:52:29.487Z
"Helicopters can hover relatively economically"... that is a good joke . But in this context, true.
Lukáš Řádek
CC BY-SA 4.0
2023-01-01T15:15:44.057Z
@LukášŘádek - fair point! Maybe I should have said *model* helicopters can hover relatively economically.
Robin Bennett
CC BY-SA 4.0
2020-05-04T08:23:37.753Z
2020-05-04T08:30:35.683Z
2020-05-04T08:30:35.683Z
Robin Bennett
<p>An explanation for why this is can be found in this Aviation.SE answer: <a href="https://aviation.stackexchange.com/a/71243/2817">Why aren't large, low-speed propellers widely used?</a>, which I'll paraphrase here.</p>
<p>The thrust a propeller generates is a function of its velocity and geometry. It makes sense that a propeller spinning faster will also generate more thrust. For a smaller propeller to generate the same thrust as a larger one, it needs to spin considerably faster because of its smaller geometry.</p>
<p>The kinetic energy of a rotating object is equal to <span class="math-container">$\frac{Iω^2}{2}$</span> where:</p>
<ul>
<li><code>I</code> is the moment of inertia (<em>a measure of how hard it is to change the rotational velocity</em>)</li>
<li><code>ω</code> (<em>omega</em>) is a measure of the rotational velocity</li>
</ul>
<p>This means that kinetic energy of the propeller is proportional to the <em>square</em> of rotational velocity.</p>
<p>The same argument holds true for the air that the propellers accelerate, this time by the rule for kinetic energy <span class="math-container">$\frac{mv^2}{2}$</span> where</p>
<ul>
<li><code>m</code> is the mass of air being accelerated</li>
<li><code>v</code> is the velocity it's being accelerated to</li>
</ul>
<p>Likewise, the kinetic energy of the air is proportional to the <em>square</em> of linear velocity.</p>
<p>Because of these two facts, (<em>acceleration of the air ends up being far more important than propeller</em>) the energy the motor needs to put into spinning a smaller propeller to produce the same amount of thrust as a larger one is significantly greater, and thus smaller propellers are less efficient than larger ones.</p>

CC BY-SA 4.0
2020-05-04T09:41:23.620Z
I think you misunderstood that aviation answer, that's about it being more efficient to accelerate more _air_ but slower. This is exactly what larger propellers do, making them more efficient. It's not about accelerating the propellers themselves, that's only a small start-up energy cost.
KarelPeeters
CC BY-SA 4.0
2020-05-04T16:55:24.910Z
@ToddSewell I didn't think about that before, and I agree. Does the edit to my answer accurately describe your comments?
ifconfig
CC BY-SA 4.0
2020-05-04T21:37:01.787Z
It's getting there, but the kinetic energy of the propeller is actually a (tiny tiny) _negative_ effect. I would remove everything about kinetic energy of a rotating object to avoid confusion.
KarelPeeters
CC BY-SA 4.0
2020-05-03T23:51:22.960Z
2020-09-25T22:22:01.387Z
2020-09-25T22:22:01.387Z
ifconfig
<p>Comment number 7 at <a href="https://forum.flitetest.com/index.php?threads/how-does-a-bigger-propeller-affect-flight.13914/#post-149466" rel="noreferrer">this link</a> is an excellent source (and fairly trustworthy as it was written by Joshua Bardwell).</p>

<p>The main reason specified for the efficiency is that for a given amount of thrust, a larger propeller (on a motor with an appropriate KV) will draw less current than a smaller propeller on a higher KV motor, so there is less sag.</p>

<p>Another thing to think about that isn’t mentioned in the comment is the number of blades used. If you think of most long range quads, or camera quads like a Phantom, Marvic or even a Matrice, you will notice that they have two blades per propeller. This can increase efficiency as it will have one fewer wing-tip per propeller, meaning fewer wingtip vortices and less drag. Multiply this by the number of propellers and the effects add up.</p>

CC BY-SA 4.0
2020-05-04T00:21:30.517Z
I'm not sure the correlation between efficiency and voltage sag is valid. Could you explain your reasoning?
ifconfig
CC BY-SA 4.0
2020-05-04T00:25:31.297Z
@ifconfig sure - if voltage sag increases, the motors will have to draw more current to compensate, up to a point where the voltage is so low that it is no longer able to support the flight of the aircraft. Additionally, if one is conscientious about preserving the life of the battery, it is often recommended not to let it sag too low. Following this logic, if you have to land earlier to avoid battery sag, you won’t get as much flight time.
Drones and Whatnot
CC BY-SA 4.0
2020-05-04T00:27:44.310Z
Okay... but battery longevity isn't the same thing as power efficiency, which is what the OP asks about.
ifconfig
CC BY-SA 4.0
2020-05-04T00:28:55.517Z
@ifconfig in the context of this question, I took it to mean how come a quad with larger props can give you longer flight times. In this case, not needing to land earlier would give the longer flight times so I felt it is applicable.
Drones and Whatnot
CC BY-SA 4.0
2020-05-03T23:44:28.457Z
2020-05-03T23:44:28.457Z
Drones and Whatnot
<p>The easiest way to think about this is to remember that drag increases with the velocity squared. A smaller propeller will have to spin faster to achieve the same thrust as a larger propeller, and spinning faster creates more more drag.</p>

CC BY-SA 4.0
2020-05-13T17:34:20.470Z
2020-05-15T23:27:35.820Z
2020-05-15T23:27:35.820Z
Fraser Steen
<p>In almost every case, long-range drones use larger propellers than other drones that don't need to travel very far or don't need to fly for very long. I have heard that a major reason for this is because a drone with larger props can be much more efficient than a drone with smaller props. If this is the case, what is the reason that larger props are generally more efficient to use?</p>

CC BY-SA 4.0
2020-05-11T02:36:34.500Z
Jacob B, your question does not make sense when it insists on specifically 6 or 7 inch props. It's all relative, and in my domain a 6-inch prop would be ludicrously small and inefficient. However, larger propellers are more efficient than smaller ones in pretty much all domains. What is "long-range" is arbitrary, but the relationship between what's desirable for "long" and "short" is not.
Kenn Sebesta
CC BY-SA 4.0
2020-05-11T02:48:33.017Z
@KennSebesta I was just saying 6 or 7 inch because they are very frequently used in long range builds but I suppose you're right and so I have changed it.
Jacob B
CC BY-SA 4.0
2020-05-11T02:55:14.160Z
I mean, for a certain scale you're not wrong. But when you get away from hand-held things and toward BIG drones, suddenly the motor bell housing alone is 6" in diameter. ;)
Kenn Sebesta
<multirotor><propellers><efficiency><long-range-drone>
Why are larger propellers generally more efficient than smaller ones?
Jacob B
# Why are larger propellers generally more efficient than smaller ones?

(Asked by: username_0 on 2020-05-03)

In almost every case, long-range drones use larger propellers than other drones that don't need to travel very far or don't need to fly for very long. I have heard that a major reason for this is because a drone with larger props can be much more efficient than a drone with smaller props. If this is the case, what is the reason that larger props are generally more efficient to use?

**Tags:** multirotor, propellers, efficiency, long-range-drone

> **Comments:**
> **username_1**: username_0, your question does not make sense when it insists on specifically 6 or 7 inch props. It's all relative, and in my domain a 6-inch prop would be ludicrously small and inefficient. However, larger propellers are more efficient than smaller ones in pretty much all domains. What is "long-range" is arbitrary, but the relationship between what's desirable for "long" and "short" is not.  
> **username_0**: @KennSebesta I was just saying 6 or 7 inch because they are very frequently used in long range builds but I suppose you're right and so I have changed it.  
> **username_1**: I mean, for a certain scale you're not wrong. But when you get away from hand-held things and toward BIG drones, suddenly the motor bell housing alone is 6" in diameter. ;)  

---

## 4 answers

### Answer by username_2 on 2020-05-04. Score: 20

Thrust is proportional to the change in momentum of the air passing through the prop - i.e. how much the prop speeds it up.

The power required to do this is proportional to the kinetic energy of the air, which is proportional to speed squared. That 'squared' is the problem.

A smaller prop acts on less air, so it has to speed it up more to generate the same thrust. Half as much air moving twice as fast generates the same thrust, but takes twice as much power.

This explains why helicopters can hover relatively economically, propeller planes only if they're powerful aerobatic models, jets only if they're extremely powerful and carrying a minimum of weight, and no one uses rockets unless they have to.

> **Comments:**
> **username_3**: "Helicopters can hover relatively economically"... that is a good joke . But in this context, true.  
> **username_2**: @LukášŘádek - fair point! Maybe I should have said *model* helicopters can hover relatively economically.  

---

### Answer by username_4 on 2020-05-03. Score: 17

An explanation for why this is can be found in this Aviation.SE answer: [Why aren't large, low-speed propellers widely used?](https://aviation.stackexchange.com/a/71243/2817), which I'll paraphrase here.

The thrust a propeller generates is a function of its velocity and geometry. It makes sense that a propeller spinning faster will also generate more thrust. For a smaller propeller to generate the same thrust as a larger one, it needs to spin considerably faster because of its smaller geometry.

The kinetic energy of a rotating object is equal to $\frac{Iω^2}{2}$ where:

* `I` is the moment of inertia (*a measure of how hard it is to change the rotational velocity*)
* `ω` (*omega*) is a measure of the rotational velocity

This means that kinetic energy of the propeller is proportional to the *square* of rotational velocity.

The same argument holds true for the air that the propellers accelerate, this time by the rule for kinetic energy $\frac{mv^2}{2}$ where

* `m` is the mass of air being accelerated
* `v` is the velocity it's being accelerated to

Likewise, the kinetic energy of the air is proportional to the *square* of linear velocity.

Because of these two facts, (*acceleration of the air ends up being far more important than propeller*) the energy the motor needs to put into spinning a smaller propeller to produce the same amount of thrust as a larger one is significantly greater, and thus smaller propellers are less efficient than larger ones.

> **Comments:**
> **username_5**: I think you misunderstood that aviation answer, that's about it being more efficient to accelerate more _air_ but slower. This is exactly what larger propellers do, making them more efficient. It's not about accelerating the propellers themselves, that's only a small start-up energy cost.  
> **username_4**: @ToddSewell I didn't think about that before, and I agree. Does the edit to my answer accurately describe your comments?  
> **username_5**: It's getting there, but the kinetic energy of the propeller is actually a (tiny tiny) _negative_ effect. I would remove everything about kinetic energy of a rotating object to avoid confusion.  

---

### Answer by username_6 on 2020-05-03. Score: 6

Comment number 7 at [this link](https://forum.flitetest.com/index.php?threads/how-does-a-bigger-propeller-affect-flight.13914/#post-149466) is an excellent source (and fairly trustworthy as it was written by Joshua Bardwell).

The main reason specified for the efficiency is that for a given amount of thrust, a larger propeller (on a motor with an appropriate KV) will draw less current than a smaller propeller on a higher KV motor, so there is less sag.

Another thing to think about that isn’t mentioned in the comment is the number of blades used. If you think of most long range quads, or camera quads like a Phantom, Marvic or even a Matrice, you will notice that they have two blades per propeller. This can increase efficiency as it will have one fewer wing-tip per propeller, meaning fewer wingtip vortices and less drag. Multiply this by the number of propellers and the effects add up.

> **Comments:**
> **username_4**: I'm not sure the correlation between efficiency and voltage sag is valid. Could you explain your reasoning?  
> **username_6**: @username_4 sure - if voltage sag increases, the motors will have to draw more current to compensate, up to a point where the voltage is so low that it is no longer able to support the flight of the aircraft. Additionally, if one is conscientious about preserving the life of the battery, it is often recommended not to let it sag too low. Following this logic, if you have to land earlier to avoid battery sag, you won’t get as much flight time.  
> **username_4**: Okay... but battery longevity isn't the same thing as power efficiency, which is what the OP asks about.  
> **username_6**: @username_4 in the context of this question, I took it to mean how come a quad with larger props can give you longer flight times. In this case, not needing to land earlier would give the longer flight times so I felt it is applicable.  

---

### Answer by username_7 on 2020-05-13. Score: 3

The easiest way to think about this is to remember that drag increases with the velocity squared. A smaller propeller will have to spin faster to achieve the same thrust as a larger propeller, and spinning faster creates more more drag.


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