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Design: Trimming a paper model aeroplane

You would usually trim a paper model aeroplane by trial and error, but if you do it by calculation you'll also develop your engineers' eyes.
We started this week with a demonstration. It showed why you need to get the centre of gravity of an aeroplane in the right place. It matters for full size planes. It matters for model planes. We’re going to calculate the right place for the CG of a model glider and work out how and where to add weight to put it there. Here’s your task. You can download the PDF of the design drawings for making a model glider out of paper and a drinking straw. As it stands, it won’t fly. Its centre of gravity is too far aft– that is, to the back.
Conventional theory for a wing is that the centre of lift is one quarter of the cord back from the leading edge. The cord is the width of the wing from front to back. Your job is to specify the mass that we should add to the nose to align the centre of gravity with the centre of lift. There are things you need to know about the drawing. Make the following assumptions– the paper is 80 grams per square metre, the straw is 213 millimetres long and has a mass of half a gram. Notice that in the drawing, the dotted outline shows where the straw goes. It is not part of the paper component.
The wings and tail plane are made of a double thickness of paper. This is done by folding back the front half shown on the diagram, and gluing it on top of the back half. You can account for this in your calculation by doubling the grams per square metre. For a plane to fly, the wing must have an angle of attack, like this. This is why the drawing has the wings angled back. When the paper is wrapped around the straw, it takes up the required angle of attack, and at the same time, swings forward into a square position.
The small rectangular pieces of paper are glued on top of the join of the wings after you have wrapped the wings around the straw to hold them together. Two are needed for the wings to stiffen the wing root, but only one is needed for the tail plane. The tail plane wraps around, too, but this has a zero angle of attack. The two parts of the vertical fin are glued together at the same time as the tail plane is wrapped around. Finding the mass of each component. Because all the paper parts of the plane start off as rectangles, you can ignore the little triangle made by angling the wings. You can easily find their mass.
And because all the parts of the plane end up either as rectangles or tubes, you can easily specify the centre of gravity in the longitudinal direction. Once you have located the lengthwise coordinate of the centre of lift, that’s a quarter of the cord back from the front of the wing, you have one unknown– the mass required at the nose. You can find it out using a table like the one presented earlier. A spreadsheet can be convenient. You could pause the video and copy the table or download the PDF. Because the mass appears in two places in the calculations, you’ll have to do some algebraic manipulation, but it shouldn’t be too hard. Why not pause the video and try it.
We won’t give the answers this time. Post your results on the discussion, or make the glider and see if it flies when you add your calculated weight. You can weigh your mass using the balance from week 3, and you can use pieces of paper of known area as weights. If you do make the model glider, you’ll find that the wings work better with a little camber bent into them, so the wing is curved along its length. Also, in humid conditions, the wings will flop and need straightening. They’re flopped in this picture. Before flying it, we bend dihedral into them so that they are a shallow v shape. It’s a stability thing.
Try to make the plane as symmetrical as you can. You can fine tune the vertical fin by bending if the plane doesn’t fly straight. But it should fly.

You would usually trim a paper model aeroplane by trial and error, but if you do it by calculation you’ll also develop your engineers’ eyes.

This video explains the problem and shows you how to find the ballast weight the paper glider needs on its nose if it is to fly well. In the end you will specify the required mass.

To get a clearer idea of the task:

  1. Download and print out the design specification with the plans of the model plane.
  2. Download the table (this will help you with the calculations).
  3. Download and read the Paper Aeroplane Story.
  4. Make the aeroplane!

If you just watch the video it will take about 6 minutes. If you do the calculations it will take longer; how much longer depends on many factors, but allow a total of 30 minutes. It will take longer still if you make the paper glider, but what price fun?

If you are stuck (or even if you aren’t) you might like to look at the worked solution that is available from the Downloads section.

Talking points

  • Note from RF. I had hoped that my paper glider would perform better than the classic folded paper aeroplane. It didn’t seem to work out that way. But I’m still trying. Do you have any comments on this?
  • We’d like you know whether you built the paper glider, and if so, did you find the right ballast weight by trial and error, or by calculation? What was your experience?’
  • It’s been suggested that you could weigh the ballast weight, drinking straw and paper components using the cardboard balance from Week 3. You could cut out pieces of paper as your weights (an A4 sheet of 80 grams per square metre (gsm) weighs approximately 5 grams). What do you think of this suggestion?

If you attempt the design task, take a photo and upload it to our Through Engineers’ Eyes Padlet wall. You can include a link to your photo in the comments for this step (click on your post on the Padlet wall and then copy the web address).

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Through Engineers' Eyes: Engineering Mechanics by Experiment, Analysis and Design

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