# Homework Help: Wing surface

1. Feb 4, 2009

### Ayr4

1. The problem statement, all variables and given/known data
Lets say we have a normal fly/mosquito. Then we increase its size by 10x (10 times bigger). Before we increased its size it could fly just like a normal fly would.

The question is, would the fly be able to fly now, when its size have been increased by 10x?
The only thing we are considering is whenever it would have enough liftpower to manage to fly. (not in muscle and power terms, but by the mass of the fly compared to the size/span of the wings)

We were not informed of the weight or the wingspan of the fly.

2. Relevant equations

3. The attempt at a solution
My first thoughs was that because the fly have now increased in size by 10x, and the surface of the wings are sqare (m2) then the surface of the wings would be 10x10, or 100 times bigger, but the volume(m3) of the fly would be increased by 10x10x10, or 1000, and therefor there wouldnt be enough surface with lift on the wings, and therefor the fly wouldnt be able to fly...

But is this idea correct? Or would the fly still be able to fly?

Sorry for my bad formulations, language and my lack of math skills.

Thanks

2. Feb 4, 2009

### LowlyPion

Welcome to PF.

That would seem to be correct. The fly might still be able to fly if it's lift capacity was initially 10 times its weight, but ... I think we can expect that nature and evolution have not built that kind of over capicity into the current blueprint for a fly.

3. Feb 5, 2009

### Ayr4

Ok, so unless the fly had to begin with a lift capacity of 10 times its body weight it would be unable to fly now?

4. Feb 5, 2009

And thats why flies who have eaten too many Christmas puddings crash to the ground.

5. Feb 5, 2009

### Ayr4

What would be the best way to explain this to someone who thinks that the fly would still be able to fly, and who thinks that the wing surface after its size have been increased is enough to lift the entire fly?

6. Feb 5, 2009

### LowlyPion

While lift may be increased by a factor of 100 over the surface of the fly's wing, the load has been increased by a factor or 1000 due to the increased volume of its mass.

This would be comparable to an un-enlarged fly trying to lift off with 10 times its weight.

7. Feb 5, 2009

### Ayr4

That was what i told him, but he told me that even if the fly got 10 times heavier it would also get 10 times more liftpower...

Btw, if we also consider muscle power, would the muscles of the fly be able to lift it?

8. Feb 5, 2009

### LowlyPion

Make a necklace of 9 dead flies and tie it on to a live fly and see how far it goes.

When looking at muscle power, I'd say the strength comes from the cross sectional area not the volume. It will be a factor of 100 area-wise, hence 100 stronger, but it will need it for the 100 area wise increase in surface area of the wing. This will produce 100 times the lift of a regular fly, but alas it needs 1000 fold increase. Because of the 1000 times weight it will of course put it at some disadvantage with respect to gravity. (This completely overlooks the structural requirements that will need to be met to prevent the exoskeleton from collapsing under the increase in forces - which of course is wholly unproductive weight power wise.)

Last edited: Feb 5, 2009
9. Feb 5, 2009

### Ayr4

Hehe, okay

Thanks alot for the help!