# Easy Aircraft Design

| March 23, 2014 | (26) Posted in How To

Hey Guys,

My friends at Darter Design, LLC and I wanted to give you all open ended step-by-step instructions on how to design a basic airplane with a large degree of artistic freedom and easy mathematics! You will need to watch the units you use! No crazy engineering needed here. I'll be using an example of a conventional airplane with the main wing in front of the stabilizers (Stab).  I'll also be using simple tapered wings to keep complexity low.

To start out analyzing your design you'll need a 3 view drawing of your plane on a piece of paper. I suggest a scale drawing on a piece of graph paper.  Here is a great example;

In aircraft design there are some critical measures that will determine if your plane will fly.  Those measures are the Static Margin (SM), Center of Gravity (CG), Horizontal Stabilizer Volume (VH), Vertical Stabilizer Volume (VV), and Cubic Wing Loading (CWL). When power is concerned the additional measures of Power-to-Weight Ratio (P/W) and Thrust-to-Weight Ratio (T/W) are very important.

In order to find these key measures we must first find a few other measures before hand.  These measures would be the dimensions and areas of the main wing, horizontal and vertical stabilizers, the aerodynamic centers (AC), Neutral Point (NP), and the distance between the two centers.  Don't worry about the AC and NP yet, I'll show you how to find them!

When finding the area and dimensions, the critical ones are the labeled dimensions A (Root Chord), B (Semi-Span), & C (Tip Chord) in the picture below;

With those dimensions and areas recorded we now move onto finding the Aerodynamic Center.  The AC is where all the aerodynamic forces act of the wing.  It is like a CG but for air. Below is a graphical representation of how to find AC of a wing panel by using the Mean Aerodynamic Chord (MAC) or Geometric Mean Chord (GMC). This method will work for most wings, tapered or not. Take the lengths you found before and add the tip chord measure (C) in front of and behind the Root Chord (A).  Next add the Root Chord (A) in front of and behind the Tip Chord (C).  Draw a diagonal line from each end of the newly created lines and find where the two intersect.  Now measure the distance of the GMC as seen in the picture below.  Write this length down as it is important!  With the GMC found, take 25% (1/4) of that distance from the leading edge and trace over to the root of the wing panel.  This point is the Aerodynamic Center of the wing panel. Find this point for the main wing and stabilizers before continuing.

Next Stop, Neutral Point! (NP)

With the AC of all your wing panels found, we can find the NP of your airplane.  The NP is like the AC of your entire airplane. With your drawing ready, measure LAC (The distance between the AC of the Main Wing and Horizontal Stab.) and use that in addition to the areas of both to find the length D.  The equation is listed in the middle of the three in the picture below.  We can now use D to find the location of NP by subtracting it from LAC. Great! Now we can find the location of the Center of Gravity (CG).  This is found by determining the Static Margin.  The Static Margin is a measure of stability of your plane.  Typically the SM is a distance based on the length of the GMC or MAC.  Most planes have a SM of 5% to 15% of the MAC which means the CG is 5% MAC to 15% MAC in front of the NP. 5% is limited stability and 15% is great stability. Never put the CG behind the NP!!!!! Just don't do it! You've been warned.

Awesome! We have NP, ACs, and CG found. What is next? the Tail Volumes! What are they? They are a measure of the effectiveness of the stabilizers.  We'll start with the horizontal stabilizer.  Using the Areas, Lengths, and MAC use the equation at the top of the picture above to find the Horizontal Stabilizer Volume (VH).  Typical values for this are between .35 and .8.  .35 is less effective and .8 is SUPER effective.  Now we can move onto finding the Vertical Stabilizer Volume (VV). Below is a photo of how to find VV.

Using the areas and distances once again, use the equation listed above and find VV.  Typical values for VV are between .02 and .05.  Once again .02 is a less effective tail and .05 is a SUPER effective tail.

Wow, so we actually are almost done.  Congrats on making it this far! Last but not least is a little secret called the Cubic Wing Loading (CWL).  CWL is the responsible big brother of regular 2D wing loading.  What do I mean? This value doesn't change with scale which means a full scale plane and model version of the same plane should have the same CWL if they want have the same flight characteristics.  To find this, it gets a bit tricky. Use the equation below to help. WCL equals the weight of your plane divided by the wing area multiplied by the square root of the wing area,

Similar aircraft have a range of WCL which dictates their flight abilities. Here is a short list of those values;

0-4 oz/ft^3 = Gliders
4-7 oz/ft^3 = Trainers
7-13 oz/ft^3 = Sport/Aerobatic
13+ oz/ft^3 = Racing

Depending on what type of plane you are designing, pick a value to use it to find the weight of your plane in oz.  This will give you a goal for what your plane should weigh before you take off!  By this I mean the All Up Weight (AUW) with batteries or fuel installed. It is a great point to work backwards from the find the suggested weight of your airframe once you have your electronics selected.

Speaking of electronics, one last tidbit of information to help make sure your aircraft will fly.  Power is an important factor for model aircraft. Here are two great ratios to consider in the design of your airplane. These are the mentioned ratio of Power-to-Weight (PW) and Static Thrust-to-Weight (STW).  There is a general range of PW that dictates performance. It is listed below;

25 W/lb = Minimum for level flight
50 W/lb = Trainer or Casual flight
75 W/lb = Sport/Aerobatic flight
100 W/lb = Aggressive Aerobatic flight
150 W/lb = 3D Aerobatic flight
200 W/lb = Unlimited high-speed vertical flight

Use the specifications of your motor to find the Wattage (Power) of your system and use that to determine the PW. For example a certain motor I use has a rated power of 150W when running on 3S Lipos.  I take that 150W and divide that by the airplane's weight (AUW).

Now we come to the final measure.  Whew, so much work but only a little left until you get to go building! Or redesigning if your design fell short. But once you get all other measures confirmed, to help choose a prop or power system, the Static Trust-to-Weight ratio is suggested to be around .5.  This will help ensure you have enough pull to power around the sky and not fall like a brick. Use data from the motor manufacturer, flying buddies, or electronic calculators to determine the Static Thrust (ST) of your motor/prop combo. Take this value and divde it by your airplane's AUW. Then you have your STW which I would recomend to be around .5 if possible.

Other than that that's all there is the aircraft design for the weekend warrior. That's all folks!

I hope you gain some great info from this article.  It summarizes my understanding of aircraft design and hopefully aids other as well.  Feel free to comment, PM, or email me with further questions or requests.

Thanks to my friends over at Dual Design R/C for confirming my thoughts and aiding me in writing this article.

- See more at: http://flitetest.com/articles/easy-aircraft-design?preview=1#sthash.3f9S0kqF.dpuf

apnewton on March 27, 2014
Superior article. I learned new stuff. Many thanks.
FLyBoy38L on April 4, 2014
Thanks for all the great comments guys! Is there more about aircraft design that you would like to see?
flyer353 on January 10, 2018
HI mate, I tried design a simple glider on wing area = (7.5*68) , horz tail = (14*10) all in cm.
L (dist of ac of wing and tail ) = 24.6 cm

it gives the D to be 5.3 which is very far to the rear is that suppose to be from leading edge?
Because it seems very tail heavy after I got my CG.
Just checking mate, you can compare with the setup by this : http://chrusion.com/BJ7/SuperCalc7.html

it gives the NP of 3.225cm from wing leading edge when comparing to your formulation, I obtained 7.175 which I think it is really off and caused my prototype to crash.
Flymann on March 27, 2014
This is a big help. Thanks!
galaxy engineer on March 27, 2014
Awesome article dude!! Well written and just the right amount of info given without being overdone! Very nice......congrats!
alibopo on March 29, 2014
Great article! Good to see where the numbers come from and how they change with the design. If anyone finds the math a bit daunting, there's loads of websites that condense the process down to a plug-and-play format. The page I use to find my CG has a calculator called the... "Aircraft Super Calculator 7.0" ...and can be found here;
http://chrusion.com/BJ7/SuperCalc7.html
Just plug in your numbers, press a button and the page does all the calcs for you, plus it allows you to play with the 'static margin' to give mushier or sharper response from the elevator. (the difference between nice and manageable and... !!!Oh my God - where's it going now!!!)
Another useful page with a Wing Load Calculator for RC planes can be found here;
It has two columns for each calculation which allows you to enter the raw data in either Imperial units (US) or metric units (most of the rest of the world, though lots of folks in the UK are metric/imperial 'bilingual'.)
Another useful page can be found here;
Units are a bit mixed (though taken individually they're probably the most common in use) - most interesting for me was a calculator that works out your likely peak speed, and the stall speed of a model.
Using these pages has helped me make some useful design decisions, though I think after a while, if you build enough planes, you start to get an inbuilt sense of how your plane is likely to fly. Still, it's easy enough to 'run-the-numbers' just to be sure. I've been quite surprised by some of the CG results, as they fall outside of the 'magic' 25%-30% range, dropping down to 22% in one instance. Had I just made a mid range first estimate for CG (around the 27% mark) I would have ended up with a very squirrelly and difficult to handle first flight for that plane.

Outstanding article. Well done.
Pukin_Dog on March 31, 2014
Nicely done!
Oldmiamicrasher on March 28, 2014
Thanks a lot, I was searching everywhere for articles like this one.
Great job.!!!!!!!!!!!!!!
dmlong on April 19, 2014
Great article. One part I part I didn't understand.

For the power or prop system, the static thrust to weight ratio is suggested to be around .5. What does this mean? Could you give an example?
FLyBoy38L on April 20, 2014
dmlong,

Here's an example using the FT Spitfire. A fair warning though, determining the trust of a certain motor/prop combo can be difficult to do if you don't have a few pieces of measuring equipment. You'll most likely need to rely on the following types of calculators to figure out the thrust. http://adamone.rchomepage.com/calc_motor.htm

The FT Spitfire will weigh about 600g when it is ready to fly. This 600g is the All Up Weight (AUW) of the aircraft. (Battery installed with all electronics in the air frame). Static Thrust-to-Weight is calculated by dividing the Static Thrust (ST) produced by the motor by the AUW of the FT Spitfire. ST/AUW = Static Thrust-to-Weight Ratio. If we want a Static Thrust-to-Weight Ratio of .5, that means the static thrust of the motor, the thrust of the motor when it is being held still and not moving through the air, will need to be 300g.
300g ST / 600g AUW = .5. Now remember this is a rule of thumb and is only a suggested starting point. Certain planes will fly with less or more static thrust.

Did this clear up your confusion?
TEAJR66 on July 9, 2014
Is this correct? "Typical values for this are between .35 and .8. .35 is less effective and .8 is SUPER effective.". It seems backwards. I was concerned when I ran the numbers on one of my new designs and I got .40. So I increased the HStab area and this number got larger also. Only makes sense that It would be higher since the number is a product of the HStab area and everything else. You increase stab effectiveness by increasing its size or lengthening the tail moment. Either way the VH value increases.
FLyBoy38L on July 9, 2014
TEAJR66, I'm confused about what you are trying to say. A smaller VV or VH value does indeed mean less control effectiveness. VH is calculated with the HStab area. VV is calculated with the VStab area. You are correct in your thinking that you either move the tail back or increase the area to increase the effectiveness. Please help me understand where you are confused. I'd like to help clear up the confusion.
TEAJR66 on July 12, 2014
My confusion is that of an old man not paying attention. Duh... .8 is bigger than .35. See what happens when you do the things as a kid that the adults told you not to do. Sorry for the ignorant post. I really did enjoy the article. You articulated the learning objectives concisely. Now, I am going to go do some math refresher. hehehe. Thanks again for the great article.
js on August 21, 2016
Great information I really appreciate this.

I have a comment though, and this is probably because I'm totally new to doing the math when trying to build a plane and have no experience of doing the math. Yet at least I need to sit down with this article and play with the math to grasp it better.
Am I just misunderstanding what goes into designing a plane or am I over engineering it, the later would not be unusual for me?

My current build is aiming for a small acrobatic motirised glider, and I'm not sure of what my next step should be.
FLyBoy38L on August 21, 2016
JS,

If you have the dimensions of the wing, that will dictate the size of the stabilizers. Also, you're desired performance will dictate the WCL, PW, and STW. You'll need the WCL of a glider and the PW & STW of an aerobatic plane.

As for the tail volumes, it is an iterative process to arrive at your final dimensions. For your application, you want a less stable plane as you'd like to do aerobatics. I'd shot for lower values of VH and VV. Start with what you think looks right and test it with the math. If not, you'll know what you need to change to go in the direction you need it to. If it is too stable, shorten/decrease the stabilizer or if not stable enough, do the opposite.

Does this help?
js on September 22, 2016
Hi, thanks for your reply, I had to put my plans on ice for a while only now did I check for a reply.
And yes I think i have some understanding of this now when I've had time to let it sink in.

Hopefylly I will have it built before the snow comes. Anyway thanks for all your help and efforts to make this understandable.
minimo on July 5, 2016