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I still don't understand how to match Kv to a certain prop

#1
I've poured over the classical DC motor model over and over. I can't quite get it to show me what kv is best for a certain prop. I've been going at it trying to maximize g/W. What's most curious is that the current at which the motor hits maximum efficiency is given by,

i @ max eff = sqrt(io*V/R)
where
io = idle current
V = input voltage
R = motor resistance

kv doesn't come into play yet. I can choose a kv if I pick a prop, then decide on a required thrust. This works because once i have a prop and a required thrust, I know how much power the motor must output. And for best system, I want this power to be converted from electrical to mechanical at the highest efficiency. This will maximize g/W. So using the above equation, I can pick kv. However, the kv that comes out of this process is dependent mostly on those motor internal losses, io and R. That is, the math doesn't yield a certain kv for a certain prop. Generally, it shows that bigger prop requires lower kv. But it depends on how much thrust you want, and again those motor values. How is it that we all decided 10x4.7 requires ~700-900 kv, etc.? My math is telling me that for a 10x4.7, at 500 g thrust, I need 450 kv if io=0.5 and R=0.2.

If I choose R=0.1 and io=0.5 then the optimal kv = 575
If I choose R=0.1 and io=1.0 then the optimal kv = 700
If I choose R=1.0 and io=1.0 then the optimal kv = 300

So it's quite dependent on those constants; confusing me.
 

bicyclemonkey

Flying Derp
Mentor
#2
This probably isn't going to be much help for your dilemma here but I take comfort in the fact that manufacturers give suggested prop sizes for each motor they sell. This saves time and keeps me from looking too dumb since I'm no good at math lol.

How is it that we all decided 10x4.7 requires ~700-900 kv, etc.? My math is telling me that for a 10x4.7, at 500 g thrust, I need 450 kv if io=0.5 and R=0.2.
A 450kv motor needs to be spinning a 14" thru 16" prop appox. The lower the kv the slower the motor spins. It wouldn't be able to spin a dinky 10" prop fast enough to generate enough thrust.

This is why you see huge 4-blade props on P-47's with 2500HP and little 2-blade wood props on 130HP TigerMoths
 
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#3
So i must know then, how do they come up with their recommendations? Maybe we're all doing it wrong, and could get better flight times with a little more math fidelity.
 
#4
i use a tool called drivecalc for these purposes. it has a database with tech-data of many popular brushless motors and also escs and props. you can start with anything you want like for instance, you have motor XYZ and want to know what prop to use on X cell lipo to get best performance, highest pitchspeed, thrust, g/W, whatever. then you would open the tool, pick the appropriate motor, choose your lipo and cellcount, and then select different props until you find the one that suits your needs best.


you can get the tool for free over here: http://www.drivecalc.de/
note: although the domain is german the website is in english and features an english version of the tool as well. there also is a manual which explains every feature of the program.
 

Klonas

Senior Member
#5
A 450kv motor needs to be spinning a 14" thru 16" prop appox. The lower the kv the slower the motor spins. It wouldn't be able to spin a dinky 10" prop fast enough to generate enough thrust.
It also depends on the voltage you're giving to the plane. Kv is essiancially rpm/V And if you have a 4S a 1000kv motor will spin at 14800rpm though a 3S with the same motor will spin at 11100 thus making less thrust off the same prop. Usually the lower kv the more cells you need...
 
#6
I understand that there are already calculators that do this. But using these is resorting to nothing more than trial and error. There must be some type of math behind these calculators. I want to know what that math is so that I can use it to optimize a power system, without randomly trying different motors. For example, the math can tell me that static thrust efficiency is maximized with largest possible prop. That's a good thing to know. If i didn't know that I'd try a bunch of different size props and not really be sure I'm going in the right direction. What I want to know is WHY a certain kv is proper for a certain prop.
 
#7
the tools rely on measured values as well and interpolate in between them. so the way the data for these tools is gathered is somewhat trial and error too. same motor is bench tested with different props and specific values like voltage, amps, watts, thrust etc are measured and thats what the tools work with.
 

Ak Flyer

Fly the wings off
Mentor
#9
Any motor will turn a variety of props at it's rated speed and amperage. There's a number of differences in the props you can use based on the type of flying you plan on doing and the plane you want to use. A sport/scale plane will generally use a faster prop than a heavy plane or a plane that you want to do 3D with. For instance, a motor might pull a 9 x 6 prop just fine and cruise pretty fast, or it might pull a 10 x 4 prop for more torque at a lower airspeed. There's a million other things to consider though. Torque roll can be affected by the size of prop. A larger diameter prop will have more torque roll effect than a smaller one with a steeper pitch.

There's also input voltage. A motor at 7.4 volts will spin slower than at 11.1 volts. It will require a larger prop to achieve the same thrust at 7.4 volts than it will at 11.1 volts.

I would start by looking at the turnigy easy match motors. They are sized accordingly with e-flite and electrifly but they have better information about how to match them up. You will find the kv, amperage, dimensions, recommended esc, prop, batteries etc. Then you can start to cross these over to some of the others that are a bit harder to understand.

http://www.hobbyking.com/hobbyking/store/__413__59__Brushless_Motors-TURNIGY_EasyMatch.html
 
#10
so what is it that tells you a prop is good for a certain motor? Is it g/W, or efficiency, or something else perhaps?
this will always be a question of what you want to achieve or what is the purpose of your plane.

you would certainly have different criteria in a scale warbird as compared to a pylon racer. there are so many parameters that can be taken into account and you cannot maximize all of them, so you have to focus on the parameters that are most important for you (for example when i want to look for a motor/prop combo for a speed model, then my main criteria will be RPM, pitch speed and amp draw on WOT).

the "everything at once" solution you seem to be looking for does not exist imho.
 
#11
I understand I can't have all parameters optimzied at once so one needs an objective function. In the case of multirotors, which this post is in the objective function is this:

Maximize static thrust efficiency (g/W)
Minimize mass of the propulsion system
Minimize current required, such that ESC and wire mass can be minimized

To do this I understand that the largest diameter prop should be used. So beyond experiment, how does everyone know that for a 14" prop you should use 600 kv, or such.
 

colorex

Rotor Riot!
Mentor
#12
how does everyone know that for a 14" prop you should use 600 kv, or such.
They've probably tried a lot of props and motors on a watt meter (power meter) and thrust meter, and find the best combination. If anyone had a working formula for that, we'd know it, or we'd have a calculator for it.
 

bicyclemonkey

Flying Derp
Mentor
#14
I have derived said formulas, and they suggest much lower Kv than that suggested by general guidelines. I wonder if perhaps we've all been using the wrong ones.
Try it out and see...then use a bigger prop, or one recommended by the motor manufacturer and see. Let us know the results. Do you have a watt meter you can plug into your ESC?