Just some simple formulas that dont take into account much by way of real world phenomenon like losses, but they can be useful for small changes:

Thrust:

1) Thrust from increased RPM, changes ∝ n^2
1) Thrust from Increased average speed due to diameter, changes ∝ D^2
2) Thrust from Increased length due to diameter, changes ∝ D
3) Thrust from Increased Chord, (not sure the symbol but calling it C) changes ∝ C. We assume this is proportional to diameter, therefore changes ∝ D.
4) Thrust from decreased average AOA, changes ∝ D^-1
5) Thrust from increased pitch, changes ∝ P.

So in total we get this:

Thrust ∝ N^2*D^2*D*D*D^-1*P = N^2*D^3*P

Current

Current is linear with torque, torque linear with thrust, so by the same token:

Current ∝ N^2*D^3*P

For 0 resistance or inductance,

N ∝ V
and also,
N ∝ Kv

Therefore,

N ∝ V*Kv

Short answer, the motor tries to run at Kv*V, but it never can get there, due to losses. A perfect motor would actually run at Kv*V.

Long (more interesting!) answer follows. I warn you, I am going to be super verbose with this:

First, some quick core concepts:

1) Whenever the motor is turning, it generates a voltage (called back EMF, BEMF) of RPM divided by Kv.

2) The torque generated by the motor is proportional to the current running through it, and inversely proportional to the Kv.

Now, step by step, what is happening to a motor (The motor is lets say 1000 Kv with 10 volts across it) at zero load (obviously doesn't happen in reality) with a voltage across it, and then what happens when you add a load:

Basically, we enter this example some time after the zero-load motor has been started and it has spun up to speed and reached equilibrium (it would generally take only a fraction of a second to spin our motors up to like 99.99% speed by the way). It is therefore running at 10k RPM (10v*1000Kv). Why doesn't it go faster? Well, at 10K Rpm, we know from concept 1 it is generating that voltage (back EMF) of 10000/1000Kv = 10V. This voltage opposes the battery voltage of 10V, and therefore the total voltage across the windings is zero. Current does not flow when voltage is zero. And concept 2 says torque generated by the motor is proportional to current. No current flow, no torque. So the motor has no torque to accelerate further.

So what happens when a wizard appears and...Continue Reading

I have a habit of going into too much detail when answering questions - which can be bad - but I think not sharing information at all can be worse. So I have come up with the solution! Turning those long, winding posts into blogs where they are not in the way of people who don't want to read them, but are available to those who do. I will start by copy and pasting a few large posts over to this blog. So, without further ado:

Designing and optimising a motor and prop system for your plane

I Haven't really done it enough times to have a set in stone procedure, in reality I suggest a more organic approach (loop around to previous steps, look for missed opportunities, etc) but if I had to make a step by step procedure for picking a motor and prop system, it would be as follows. Note that this is from the perspective of someone who considers 20 minute flight time a bit too short, 30 minutes average, and an hour good, so your mileage may vary.

Step by step:

1) Start by finding the largest diameter prop you can on there, which may be limited by flight dynamics with truly silly diameter, or a prop crash with the ground or fuse in a lot of cases, or even aesthetics or prop weight. We will play with pitch and Kv to suit this diameter, and modify it later if we must.

2)Generally use the cell count you already use on all your other stuff, it's more convenient to be able to share batteries amongst planes

3)Pick a Kv that will get you enough thrust [1] on a prop of the...Continue Reading

Hello,

I'm new to this hobby but am enjoying it a lot. It works well with my skillset and my own disposition to approaching problems.

I'm the kind of person that likes to overthink things a lot. I like to apply basic theory, maths, and physics to just about any situation until I actually understand it both mathematically and intuitively. I will spend far more time thinking about doing something than actually doing it, and I'll probably enjoy that time spent thinking a hell of a lot too.

So, you'll probably see me asking a lot of questions on the forums, taking peoples answers and my own deductions and trying to mold it all into useable conclusions, and then attempting to answer my own question or restate the answer someone else gave me in my own words, so they can correct me if I misunderstood.

Please always feel free to correct me, there's nothing worse than being satisfied that you understand something, and actually being completely wrong! I don't bite - I love a good discussion and especially one where it turns out I'm wrong, because that means I get to refine my thoughts on a subject!

Thanks for reading!