# Why are larger propellers generally more efficient than smaller ones?

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?

• 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. May 11, 2020 at 2:36
• @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
May 11, 2020 at 2:48
• 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. ;) May 11, 2020 at 2:55

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.

An explanation for why this is can be found in this Aviation.SE answer: Why aren't large, low-speed propellers widely used?, 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.

• 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. May 4, 2020 at 9:41
– ifconfig
May 4, 2020 at 16:55
• 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. May 4, 2020 at 21:37

Comment number 7 at this link 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.

• I'm not sure the correlation between efficiency and voltage sag is valid. Could you explain your reasoning?
– ifconfig
May 4, 2020 at 0:21
• @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. May 4, 2020 at 0:25
• Okay... but battery longevity isn't the same thing as power efficiency, which is what the OP asks about.
– ifconfig
May 4, 2020 at 0:27
• @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. May 4, 2020 at 0:28

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.