### Improving motor and propeller performance: theory and application (part1)

As promised, here is part 1 of our series on motor and propeller theory. Part 1 covers the coil magnet model, Kirchhoff's law for a motor, Back EMF, Kv, Kt, and motor efficiency.

By the end of the first video, you should really understand why is a motor is inefficient and the relation between electrical power, heat and mechanical power. The motor model is constructed part by part. I tried making this series different by giving a lot of examples while being backed by a solid theoretical background. We have more tutorials on our website. If you have any question or comment, my colleague and I will answer questions!

• I consulted with my copy of "Tailless Aircraft in Theory and Practice". The reason why the ground effect is stronger for flying wings is that the wing is usually much closer to the ground compared to conventional aircraft. If the wings are 1/10th of the wingspan from the ground the induced drag is reduced by half.

Model aircraft very rarely experience any significant ground effect.

Getting back to the subject of motor efficiency - one problem I have encountered is that for hand launch you want a large diameter low pitch prop and for cruise a lower diameter higher pitch prop. Essentially a square prop - 10x10 for example.

• @Damian,

1. He's speaking in layman terms in that video, but it's still not correct. I don't think the audience are aero engineers.

There are two issues with flying wings:

You can't have very large trailing edge flaps because it's not possible to compensate the extra negative pitching moment they create. Flaps increase the lift coefficient (CL) of the wing and increase drag. The higher the lift coefficient the slower a plane can fly. Using the term lift does not make much sense here because the lift is lower than the airplanes weight when landing. So how can it have too much lift?

Another issue is the ground effect, which almost eliminates induced drag. During landing this means that all of a sudden you have excess energy that you need to get rid of before you can land. A flying wing can not just put its tail down and start breaking like regular aircraft. Tailed aircraft also experience the ground effect, but can set their tail wheels down and start braking a lot sooner than flying wings.

In conclusion: when landing an aircraft needs to get rid off the excess energy by increasing drag(1), and decrease minimum flying speed (increase the lift coefficient)(2) by using high-lift devices such as slats and flaps. 1 is no problem for a flying wing, 2 is where it's outperformed by a conventional aircraft.

2. Sure, a flying wing airliner would also be more efficient than a regular tube with wings type airplane.

I'm no expert in aerodynamics so I might be wrong in some points.

• BTW in combat the B2 Spirit uses differential engine thrust for yaw; the Y drag ailerons are used for yaw only in public/non combat regimes to artificially increase radar cross section ...

I am just now designing a flat plank flying wing with twine engine differential thrust; I will keep you posted :)

• @Martin - Thanks for the great subject matter expert feedback!

1/ For the B2 Spirit case - my understanding is that they have relatively high landing AoA; because of their tricycle landing gear with the small wheel in the front; and their landing speed can not be very low as the control surfaces would have less authority than required for their margin of safety; so with some required minimal landing speed  (140mph) and higher AoA; they still have too much lift; so they use the anti lift devices (top part of their Y aileron) to get rid of the lift; they have to be carefull with the additional drag as they have to maintain their minimal landing speed

Meaning the lift and the wing are bigger than necessary for flying; they also mention that they have so much lift they do not need leading and trailing edge lift devices for landing/take off; meaning again the wing is unnecessary big for the cruise speed; E.g. Boeing 737 wing is well optimised for both cruise (thin) and landing/ takeoff (flaps)

2/ Agreed that tailless aircraft does not outperform flying wing in practice; however I have limited my use case above for the straightforward flight only; in this case I believe that tailless design would be more efficient with less drag and the tail does not provide any benefits with straight forward flight (UAV cruise); however for 3D aerobatics tailless design is inferior

• @Damian,

It's no entirely correct to say that a wing has so much lift it has difficulties landing. The glide ratio is too high, so more drag needs to be created. Drag is the only way for an aircraft to get rid of the excess energy. Manipulating the lift will only make the airplane speed up or gain altitude.

Also, tailless aircraft do not outperform conventional aircraft in practice. Though there are some other good reasons for going with a tailless design.

I agree with everything else you wrote.

• @Martin,

the idea for the fixed wing straight forward flight is that you define your target cruise speed; and then you match the airframe to the speed; meaning it should be as light as possible and the lift for the wing minimal drag angle of attack should match the weight. Based on your chosen or maximum allowed aspect ratio you add wings; but again just to create enough lift for your target weight; as an unnecessary bigger wing increases wet area surface drag.

so from the fixed wing straight flight power efficiency point of view you want to minimise prop thrust, wing lift, drag of the airframe and maximise aspect ratio; match the pitch prop speed with your target cruise speed; just enough to let it fly straight with your target cruise speed in mind; perhaps get rid of the tail; and run your motor and ESC in the best efficiency range (30% of the motor power)

the most efficient design for the straight flight would be a thin flying wing with high aspect ratio (very long wing) just with enough lift to keep it flying

E.g. B2 Spirit has so much lift it has difficulties to land; just because the wing is so big; so they could reduce the wing and drag; however they need some space for nuclear bombs and other design constraints so it is what it is

However the stuff above is for straight flight only; if you want to have slow landings/take off or 3D aerobatics or dynamic soaring you will have other requirements. So for example you can add flaps for slow landing/takeoff ...

• @Damian,

What do you mean by "match the lift for the weight of the airframe"? Lift is equal to the mass of the aircraft in horizontal flight or hover.

• I would love to design and build a multirotor motor that uses carbon nanotubes instead of copper wire:

I wonder what exactly are the hurdles to putting something like this into production? Seems like a revolutionary concept not just for multi-rotors, but anything that uses an electric motor (electric cars?).

• Great tutorial guys, look forward to more of them.

• to maximise the flight time:

- run the motor atabout 30% of its max power

- match the prop for just right amount of thrust and pitch speed for about 90% of the flight speed

- minimise weight

-minimise drag

- match the lift for the weight of the airframe