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Just need some help with the math.

I am trying to design my first aircraft, and I am having problems with using the wing loading.
I have decided that the plane will be 1600 grams and have a wing area of 300 dm^2. The wings will have 225 dm^2 with an aspect ratio of ten.
|_______________________________| x
10 x

10x^2 = 225 dm^2
x= 4.75 dm
This means that the chord will be 47.5 centimeters.
I just find this hard to believe after comparing this to other trainers of similar design.
Am I doing something wrong? Something does not add up here.
Thank you for your time!


Cardboard Boy
Math? What in hell is that? I usually just eyeball my planes and hope it works ;)

The problem here is your weight, for a first trainer you should aim for a fairly light aircraft, not more than 800g but that's just me and I usually build my planes rather heavy too.
You can find plenty of calcs on the internet to help you as well


Elite member
I think your math is correct - but I am unsure about a couple of statements in your introduction and your assumptions around the plane you are trying to design.

First you say the wing area will be 300 dm^2, then you say the wings will have 225 dm^2 (another area) with an aspect ratio of 10.

Your calcs are correct for a wing area of 225 dm^2 but this is a really, really big wing, a 10x aspect ratio on a 225 dm^2 wing will be ~47cm chord and a 474 cm span (that's 15 feet!)

Either way, 225 dm^2 is huge and is a tiny wing load for 1600 grams.

Lets work back the other way. A good trainer wing loading is 15 ounces per square foot (per the interweb and ignoring the cubic loading approach to this)

You think your build will be ~1600 grams which is ~56 oz . So at 15 ounces per square foot you need ~ 3.75 square feet (56/15) which is which is ~35 dm^2 (okay - now you should see that the 300dm^2 assumption was a problem

Now you can runs your original calcs on the 10x aspect ratio and you will get a chord of ~19 cm (~7.5 inches) and a wingspan of 190 cm (~75 inches). This is still a pretty big plane, but as Fluburtur said, 1600 grams (~3.5 lbs) is a pretty heavy starting point for a trainer.

Let me know if this makes sense to you. I think the main issue was where you came up with the 300 and 225 dm^2 wing areas.



Posted a thousand or more times
Your math is correct
The wingspan will be 475 cm ! Will be a huge thing. I suggest that you define the cord you want and calculate from this as base.
Why you want a 225 dm area? That will be a wing load of 7g/dm^2. The load should be fine between 65 to 90 g/ dm^s. Are you sure the area you selected is not to big?


Old and Bold RC PILOT
Wing area and loading are just part of the story! Efficiency, Profile, and cord/thickness ratio all have great effect upon the lifting performance and maximum speed to expect from a design.

Whilst it might seem simple to get something flying, (and it is), if you really want the most from your design and want to use the maths to get it right then use all of the maths not just a single equation or 2 and hope it all works. Some of the factors you have not mentioned are critical in obtaining reasonable performance.

Give us the design brief and I am sure forum members experienced in design will point you in the correct direction without the grief and wasted effort.

Help is available if you want it!

Have fun!
Thanks a lot. I now see my problem and I have just recalculated the weight. Looks like my math is completely wrong. I am going to see if I can make a trainer that is 900 grams instead.


Posted a thousand or more times
900 gramm will be no problem. The FT simple cub weight about 600 gramm with lipo.
The wing load range i suggested is based on a ClarkY Airfoil, what's the typical wing foil for trainers and what you mostly get out of foam without problems. So take a look at existing designs like the Simple Cub as orientation. Search for data for the clarky profile and you will get the needed data to calculate the profile. You should also consider the geometry, the wing tips and the dihedral. As Ha-Lee wrote, there is more to consider.
I have been doing some research and am sticking to a twin boom design. I do not want to break my propeller, and it looks really cool.
Here is a proportions list I found off of the internet.
I will keep it simple and use a clark Y.
I like the RQ-7's design, so I will model it after that.
I found some great resources on arduino radio controlled planes, so I will use that to create a inverted V tail mixer.
Here is the video I found explaining motor mechanics.
I am still designing, I will update.


Old and Bold RC PILOT
Whilst the proportions mentioned will work quite well they are missing a lot of information or items of consideration for better tailored designs.

For instance the speed envelope has great effect upon the control surface area and its moment of action from the point of balance, (CG). The further a control surface is from the point of balance the smaller it can be or the smaller the control surface deflection required.

Also to consider is the planes required CG point range. The greater the range required the greater the moment required to allow for re-balance over the range of balance required. There are some very good planes or designs around that fly horribly if the CG is not almost exactly in the place required.

Roll rates and control effectiveness again look at moment. cord, deflection, and drag effect components. Other things to consider are the mass of the wing, Mass distribution, Variation in thickness ratio, and any dihedral or sweep all of which have great effect on roll and roll stability.

Final bunch list of things to consider include High lift devices, (Flaps Etc), wing/tail incidence angles, any pendulum stability components, Thrust line Vs Centre of Mass, propeller airflow effects on control surfaces and wing induced turbulence/airflow directions on control surfaces.

Not all of the above need to be resolved using maths but should be at least considered in checking your design and what you expect from it. Remember a tail is not required really it just provides for a more efficient platform and easier control.

When you are building you will find that a long tail boom will need to be heavier and stronger or the tail surfaces will wobble around and upset the handling and with a twin boom setup there is the torsion or twisting effect of the tail if the booms are not rigid enough.

Not trying to put you off but rather giving a small list of things to consider as you design and build so that your first flight experience will be that much sweeter rather than a month long session of seeking ideas from strangers who are guessing at the problems and a number of different prototypes all trying to get it to fly properly.

Looking forward to the design and build!

Have fun!