## Wednesday, December 4, 2013

### Calculating Brush-less motor and prop size for RC Airplanes.

If you have ever tried to figured out the size of the electric motor needed on a homemade or other type of RC airplane and delved into the world of kv and watts and ESC amps then you probably have a few less hairs on your head because of it. I stumbled a cross a few different calculators online and some trains of though from some really smart folks and decided to condense them into this one article to ease your pain. Online calculators come and go, but once you have the formulas you will always be able to calculate the right sizes.

This is just a rough guide to get you started. You will need to tweak your numbers once your flying to make the plane perform perfectly. But these formulas should get you in the air pretty easily. Note that these calculations are for single fixed wing aircraft. I cannot attest if these numbers will work on a Delta wing or Bi- & Tri-planes or anything unusual for that matter. If you use them and they do or don't work let me know so I can pass it on to everyone else.

Start with Square inches of Wing.
To do this properly you need some information from your plane. The first is the length and width of the wing in inches. We will multiply these numbers times each other to get the Square Inches (Wsi) of our wings surface. For our example we will be using a wing that is 47" (Wl) long and 7.5" (Ww)wide or deep depending on your view.

Wl x Ww = Wsi
47" x 7.5" = 352.5 sq. in.

Determine Prop Diameter
To determine our prop starting diameter we will take the result of the previous formulas Wsi and divide it by 65.

Wsi x 65 = PD
352.5 / 65 = 5.4231

So for our purposes it recommends a starting prop of 5 1/2" inches which they do make but a 6 inch is much easier to find. So I tend to round UP to the nearest whole number when I am calculating. So we are going to use the 6" prop as our basis.

Figure the Prop Pitch
Next we figure out the pitch of the prop (Pp) by multiplying our Prop Diameter (PD) x 0.7 and rounding up to the nearest number. You can go either way when rounding and probably be OK. In our case we went up to round the prop size so I will go down when selecting pitch size.

PD x 0.7 = Pp
6 x 0.7 = 4.2

So our resulting prop to start out is a 6 x 4 and it should get us into the air pretty good with this size wing.

Determine the size of Motor we need to get for our plane.
the hard part with motors is there are so many selections to choose from out runners, in runners and sizes and shapes of all kinds etc. I can't tell you what exact motor to get but I can help you make an informed purchase on t the power of motor you need.

Weigh your plane - You need to know how much weight your going to be throwing around in the sky to get an accurate sized motor. You need your weight in grams (W) but if you don't have a metric scale, weigh it in pounds and go here to convert it. Our Example planes weighs 680 grams, which is roughly 1.5 pounds by the way.  Divide this by 4 and this will give you the power in watts (P) your motor will require.

W / 4 = P
680 /4 = 170 watts

Determine your pitch speed - You can set any pitch speed (Ps) you like but I have been told that 50-70 MPH is a good starting point. I will be using 50 MPH for my Pitch Speed (Ps)on my trainer as I want a slower flying trainer. This will help us determine the KV rating of our motor. This formula is a little more complicated that the others, just make sure you do the calculations inside the parenthesis first. For battery voltage use what the battery your using is putting out . In my case I am using a 3s Lipo that is 11.1v, For prop pitch use your Pp result from earlier in this article.

KV = (Pitch Speed MPH  * 1056) / (V x Pp)
KV = (50 * 1056) / (11.1 x 4)
KV = 52,800 / 44.4
KV = 1189.1892

I would recommend rounding UP for this formula. So we are shown that we basically need a 1200KV motor for our plane.

Figure out ESC size -  To determine the size of our Electronic Speed Control (ESC) is as simple as divinding our motor power in Watts (P) by our battery voltage (V) then selecting the next size larger ESC for our plane. This is basic Ohms law by the way Amperage = Power in watts / Voltage (A= P/V)

ESC = P / V
ESC = 170 / 11.1
ESC = 15.31A

Again we round UP to the next size which is a 20A ESC that should handle everything this bird throws at it.

These are again very rough numbers but should get you close and flying so that you can adjust from there.