Verification of my sums...

[lisaj]

My nephew has a die-cast model of a 747, and we were discussing how realistic the weight was in scale to reality, and if not realistic, how much should the model weigh... Taking some ballpark figures for a 747-400, that has a wingspan of 64.67m and a takeoff weight of some 850,000lbs, and comparing it to the model that has a wingspan of 26cm and weighs 660g, I took a ratio of the wingspan cubed (since we're effectively after density), and devided by the weight. It was way too heavy, and my sums suggest the realistic weight for the model would be around 25g. This however, is the weight of a large cherry tomato!! Are my sums correct?

[sddsddean]

I'm not really sure you need to worry about cubes of measurement. If you are trying to compare scale values, you should just need to do to a straight ratio. Is the model a scale model (eg accurate), stand off scale (eg looks OK but is not accurate) or just a representation of a 747? Assuming it is a scale model the scale is 1:(64.67/.26) which is 1:248, say 1:250. This would give a scale weight of 850000/250 = 3400 which is 1.5tons! Now I have found a model 747 which is 1:300, with a 215mm wingspan, which gives a 'real' wingspan of 64.5m and using ratios of scales, would give your model a 258mm wingspan. So, it would appear that the 'size' is correct for yours to be a scale model, but a real 747 is obviously a lot, lot denser!

[lisaj]

This is why you cube the linear measurement of wingspan. If you don't, you do end up with the result that the model plane should weigh 1.5tons, which is, of course, ridiculous! I cubed because, as far as I can remember, weight is related to density rather than linear measurement.

[sddsddean]

Oh you have got me thinking now Lisa. I see where you are coming from using the density argument, but surely if something is a scale model, you should just use a linear scaling factor. Hmmm, I'll have to have another think, ' cos I just tried imagining scale areas in my head and I don't think that works either (the areas, not my head[Contrary to popular belief!]). I'll get back to you.

[BenDToy]

Re the "cube" argument. Try thinking about it as just that ie a big cube and a small cube. A small one may be one third the linear size of the large one, but is actuallly one twenty seventh of the volume (or weight). Like a Rubiks cube. Therefore the cube of the wingspan is one way of trying to take that into account. However remember that both structures contain a large volume of air - but I am not sure what the significance of that is!! I suggest that the 25g is probably not too bad. Remember that the material the model is made from will not be 1/250th the gauge or weight of the real stuff. If it was then the chances are that the model would be paper thin.

[sddsddean]

Yes, I think you are right Lisa. If you imagine a 10m x10m square, at a scale of 1:10, it is going to be 1m x 1m, but 100th the area. So following on from that the weight of your scale aircraft should be 850,000/250^3, which is 0.0544 lb = .87 oz = 24.6 g (your figure of 25g). I'm not convinced either of us is doing this correctly, but at least I agree with your sums!

[lisaj]

Well, I got an A at my Maths A-Level all those years ago...