How to 3D Print an Aeroplane - Day 14 - Wing Loading, WCL & Why Elephants Can't Fly
The first iteration of the model is compete and it's time to start printing... Unfortunately my printer is has broken under the strain of producing PPE Hospital Visors in PETG. It has trashed the print bed and the Bowden tube clasp at the extruder stepper has failed. Whilst I wait for the new parts to arrive I thought it might be a good idea to talk about wing loading.
Wing loading is defined as the mass of the aircraft divided by the total area of the upper surface of the wing. For models, it is usually expressed in grammes per mm squared (or imperial equivalent).
Essentially it tells you how much lift each unit of area on the wing has to lift.
It is probably the most important measurement to know for a model plane as it tells you something about how it will fly. An aircraft with a high will loading will need to fly fast to get airborne, whilst an aircraft with low wing loading can fly slower. If your planning to build a hand launched aircraft then you'll need a low wing loading.
For model aircraft there is a further tweak to the wing loading figure we can use called wing cubic loading or WCL. Without going in to the maths it aims to give you a number that scales properly. In other words you could find the WCL for a real full scale Cessna Skymaster and if your model had the same number it would fly in a scale manner. That is not the same for wing loading since mass and area scale differently. A 747 has a maximum wing loading of 7300g/dm2. A normal RC model has wing loading between 20-50g/dm2. If you built an RC 747 with the same wing loading as a full size 747 , its not going to fly... The wing cubic loading however would scale down properly.
So, if it is so important for designing aircraft why didn't you say anything earlier Jon? Remember when we sketched the wings? I made the wing about 15% bigger, this was due to wing loading. I didn't want to turn everyone off at an early stage with loads of maths, and more importantly, you need to know a few things about your model before you can calculate the wing loading.
You need to know the mass and the wing area. The beauty of 3D printing means, at this stage we can get a really good estimate of the weight because Cura will calculate how much filament it is going to use for each print. Since we are not going to use supports this calculated weight will be pretty close to the weight of the aircraft.
It is a little bit chicken and egg here because you need to know what print settings you are going to use, as the mass could vary wildly between wall thicknesses and infill percentage. Needless to say, with experience you will be able to get a good idea of what will work and what won't.
After slicing all the parts and adding up the estimated mass, plus the weight of the radio gear, motor's and props, I have an estimated flying weight. I then used this online calculator tool to calculate the WCL:
So we have wing cube loading of 9.8, which is ok for a 3d printed plane. This is obviously only an estimate, but if the WCL at this stage is 20+ you might want to think about a re-design, either cutting some weight or making making the wing bigger.
To answer the question posed in the title, at around 3500kg, assuming an elephant would need the same wing loading as a bat of 5cm2 per gram, then the elephant would need a wing area of 1750m2, or approximately 6 tennis courts.
The point I am trying to make is that calculating the wing loading is a rough tool that you can use when designing an aeroplane - it is not the be all and end all, you can build an aeroplane with a good wing loading that won't fly very well. However, knowing your estimated wing loading may stop you from going too far down a dead end road, like trying to make an elephant fly.