Calculating Centre Of Gravity

Hi everyone. In one of my earlier posts, I talked about calculating flight speed and how a larger diameter of propeller offers more thrust and more pitch will increase the pitch speed because the propeller is taking a larger bite of air. One thing I want to add is that at the point where the pitch speed of the propeller is equal to the speed that the plane is moving through the air, there is no thrust.

CENTRE OF GRAVITY 

My Dad and I are trying to design an RC plane right now that will have a flight speed of about 90 km/h and a thrust to weight ratio of at least 1.2 for vertical climbs. We decided that since we know what our possibilities are for motors and batteries etc. we decided to estimate the centre of gravity to see if our design was any good in terms of balance. Here is a drawing I made of a design we made on the computer:

Of course, the vertical stabilizer is too small and the plane will be much more streamlined, but this is the best drawing that I could do. The big line going through the airfoil is where we want the centre of gravity to be. We estimated the c of g on a spreadsheet but I will show you as best as I can what we did. The arm is the distance of these different main parts from the centre of gravity and the motion comes from multiplying the weight by the arm. So, if the motion is roughly the same for behind the centre of gravity and in front of it, we will know that the plane is fairly well balanced. 

                          Front Of Plane                                    Back Of Plane 

              Weight     Arm  Motion                          Motion     Weight      Arm 

      Battery: 65 grams 7 cm  455                          1350 Motor: 54 grams 25cm

      Gear:     80 grams 20cm  1600                       315  ESC:   35 grams 9cm 

                                                                             354   Gear:  118 grams 3cm 

         Total Front Of Plane Motion:               Total For Back Of Plane:

                         2055                                                         2019

I should probably say that I don't remember exactly what the different arms where from the actual spreadsheet for this plane, but I think that most of the weights of the different parts are accurate, and these motions were very close to the ones that we got from the spreadsheet. On the actual spreadsheet, the difference between the front C of G and back C of G was only around100 which as far as I know is not very significant considering that the motions were around 2500. 

Estimating Stall Speed For A Trainer

I have been very interested in finding the calculation for stall speed. I have found it, but it is way to complicated for me to understand. So, I tried to make my own simplified version. I thought: Okay, what effects stall speed.

• Air density
• Maximum lift coefficient of the airfoil
• Wing loading

When I tried to go on this without much success, I decided to focus just on the relationship between wing loading and stall speed for a given lift coefficient and air density. Since the weather is not very good here in the wintertime, I went on the simulator and got the E-flite Apprentice with SAFE technology. Here is a graph I made with the relationship between wing loading and stall speed. 

The wing loading is the vertical (y) and the stall speed is the horizontal (x). What is basically happening is that the up until 61.8 grams/sq. decimetre of wing loading, for every 10 grams/sq dm. of wing loading I added, the stall speed or (more useful) landing speed increased by five kilometres per hour each time. After 61.8 grams per square decimetre, the landing speed was increasing by 3 - 4 kilometres per hour instead. I may repeat this test again just to be sure of these results. 

All of this means that my estimate for stall speed, with the airfoil of the Apprentice (which I'm guessing has a lift coefficient of 0.9 on landing) is: wing loading / 1.35 = stall speed. As far as I know, this would become less accurate after 60 grams/sq dm. or so because the relationship changes. 

Many people say that knowing the stall speed for an RC plane isn't useful because all you have is your eye which can't tell you exactly what speed the RC plane is flying at. This is true. 

But my suggestion is to set out some cones that your plane will have to fly over before it lands. By finding how far apart your cones are, and estimating your landing speed, you can say that if the RC plane went over those cones in x number of seconds, it's going at the right speed. 

Designing An RC Plane - Design Process

Now that we know some of the basics of RC plane design (different wing shapes, aspect ratio, wing loading, power systems and estimating maximum speed of a model), I thought it would be a good time to talk about a process that you could use to design your own RC plane. Airfield Models is a great sight to visit that really simplifies RC plane design and some of what I write is inspired by that website.

Step 1: Define The Purpose Of Your RC Plane

Here are some examples of things to consider when deciding on a purpose

- Maneuverability (aerobatics it should be capable of, maybe nothing) 

- Airspeed envelope (minimum and maximum flight speeds)

- Type of Plane (trainer, cargo RC plane, swept-wing jet etc.)
- Thrust To Weight Ratio

An airplane made by the youtube channel Aplane.  Has a low aspect ratio, rectangular wing, built for carrying lots of weight.

Step 2: Be More Specific! Decide On Some Specifications 


Things such as:

-Wingspan
-Chord or average chord (the width or distance across a wing. You can find average chord by adding up the chord at the part of the wing closest to the fuselage and the chord at the tip, then dividing by 2.)
-Weight (includes the weight of the servos, the receiver, battery, ESC, motor and airframe weight)
-Motor and prop combination (think about speed and thrust)
- Airspeed envelope (the minimum and maximum airspeeds that your plane should be able to fly at)




Step 3: Decide On A Target Wing Loading


Now that you know the weight of your electronics and have an estimate for airframe weight, add those two weights together. Then, you can decide on the target wing loading and play around with different wing areas until you find the wing loading that you are aiming for. Because of all things, wing loading should not be the surprise result after you have built the RC plane.

Highly loaded wing of an E-flite Habu 32

Step 4: Create A Plan

It doesn't matter whether its on a computer or on paper. Be specific with the dimensions of all the parts. 

Step 5: Build The Plane!

If you decide to change your specifications while building, remember to go back a step and see how this will affect the performance of your RC plane. Also, if the thing just won't fly or does not fly well, don't despair because this is almost exactly what happened with the TundraTrike from the previous post.

1. What was the problem

2. Why did it happen

3. How can you change the design and start flying again

Also, don't decide to stop any design because you feel that you don't know enough to make it fly properly. Just use your imagination and build what you have in your head. And again, if it doesn't fly, just analyze what went wrong, why it went wrong and redesign the plane. By doing it this way, you can get closer and closer to the RC plane that you really want, learn lots and make a great-flying airplane.