Usually the efficiency of motor+propeller is determined as a ratio thrust/(electrical power) in g/W units and is plotted vs rpm. These values allow to get rough estimation of flight time and compare different motors and propellers but give no information on how good is setup in general.

Here I will consider more general picture and consider efficiency as a merit (FOM) of how some specific device or setup is compared to ideal (based on calculated and experimental values typical for *tiny whoop* quad-copters).

Below I will use word “efficiency” in the meaning of Figure Of Merit (FOM), unit-less value in the range from 0 to 1.

Thrust of any air propulsion engine is determined on how much air and how fast we can accelerate it with given power. The thrust is equal to:

(1)

where *P* is power, *D* is a propeller diameter, а *r* is air density

In real life we need more power because both motor and propeller are not 100% efficient, thus are motor and propeller efficiencies (FOMs).

Using Eq. 1, can get hovering time in dependence on battery capacitance, propeller diameter and weight of the copter.

(2)

Where w is energy density (W*h/ kg)* and M _{craft }is mass of copter and a load, excluding battery.*

These equations are general and they are good for any copters, including electric, gasoline or man-powered. Here are some examples. For heavier copters total efficiency is about 0.3 – 0.5.

To check efficiencies of *tiny whoop* setups I tested the following motors and propellers: 0615 brushed motors: 16400 kV (redpawz r010), 17500 kV (redpawz r011) and 19000 kV (Crazypony “insane”) and also 0716 motors, 16500 kV (BoldClash Bwhoop B-03 pro-08). All the motors were tested with 30 mm 4-blade, 3 blade and 2-blade (cut of 4 blade).

In the first test, the voltage from power supply was varied from 2 to 4.3 V with the step of 0.1V and the current and thrust were measured for each of the voltage settings. The plots are the thrust versus V*I.

Solid lines are calculated with eq.1 (30 mm props) for indicated values of efficiencies.

- Efficiency does not depend on the the number of blades.
- Increasing the number of blades shifts curve toward higher power and simultaneously makes it wider (power range gets wider).
- Thrust vs power curves obey eq. 1, it does mean the efficiency does not change much at the given range of power.

Below is a summary plot (combination of the above for 4 blade props):

So, we got estimation of the total efficiency of the motor and propeller together. Now we will try to derive efficiencies of the motor and propeller separately.

The motor efficiency itself can be estimated easily assuming that input electrical power is being spent to useful mechanical power and useless heat. Heat is a Joule heat at the coil (I^{2}R) and a friction (which is small). In any case the efficiency is a product of “useful” voltage to “useful” current to the total electric power VI:

Where *R* is a resistance of the coil and *I _{0}* is current without load (without propeller). Here are the results:

Efficiency of 0615 (16400) and 0716 (16500) are about the same and is 0.65.

Efficiency of 0615 (17500) is about 0.6

Efficiency of so called “insane” motor 0615 (19000) is significantly lower and is about 0.47

Now we can get efficiency of the propeller by dividing total efficiency by efficiency of the motor. It gives value of about 0.36 (0.242/0.65=0.37; 0.216/0.6=0.36; 0.164/0.47=0.35)

- Efficiency does not change much in the given voltage range (2-4.3В)
- Efficiency drops for faster motors
- “Insane” 19000 kV motor has low efficiency of <50%. It produces strong overheat at high power, indeed the reported cases of motor damages due to sudden stops is mostly related to “insane” motors.
- The efficiency of the propeller is about 0.36.

Next, let us estimate flight time. We will consider hovering time when thrust is equal to the copter’s weight. Using eq. 2 and total efficiencies discussed above we get:

upd: new graphing tool can be used to see hovering time vs battery capacity and basic drone parameters;

The plots are calculated assuming tiny whop weight of 18g (without battery), propeller diameter 30 mm, and power density of 133 Wh/kg. In the case of 0716 we used 22g in our calculations because 0716 motors are heavier. These curves do not take into account discharge rates of batteries and limitation of maximal power of the motors, so don’t be surprised that tiny whoop cannot fly with say 1000 mAh battery. But to 400 mAh the plots show more or less real numbers for good batteries.

- If tiny whoop would have ideal motors and propellers it would fly 25-30 minutes with 250 mAh battery (black curve).
- If tiny whoop would have efficiency similar to DJI Mavic Pro it would fly 10 minutes with 250 мАч battery (1/3 of black).
- 0615, 16400 motor has the best hovering time (blue). Unfortunately this motor is not power enough to have some extra power for real flight, or even not power enough to hover if we will take into account voltage drop because of battery imperfection.
- Flight time for 0615 (17500) (blue) is about the same to heavier 0716 (16500) motors (magenta), it happens because of higher efficiency of 0716 motors.
- “Insane” 0615 (19000) (green) are not efficient, flight time is significantly lower, although they can provide more peak power than 0615 (17500)
- 4, 3, 2 blade propellers have similar flight times (if not limited by battery characteristics)

I’ve got experimental flight time (BoldClash B-03 frame, camera, canopy) close to calculated values For 0615 (17500) hovering time is 5 min 15 sec, for 0716 (16500) time is about 5 min My choice is 0716, they have wider range of power.

My tiny whoop

- BoldClash B-03 frame
- BoldClash 0716 16500 motors
- 3- blade props (crazypony)
- FC Beecore F3_EVO_Brushed ACRO
- 25 mWt camera (redpawz r011)