A flying fish leaps out of the water and glides for up to 30 seconds. Does anyone know the equation for this. i.e. the surface area to volume ratio to stay in the air for a while.

Well according to Wikipedia terminal velocity is calculated as such:

 

[math]V_t= \sqrt{\frac{2mg}{\rho A C_d }}[/math]

where

 

[math]V_t[/math] = terminal velocity,

[math]m[/math] = mass of the falling object,

[math]g[/math] = gravitational acceleration,

[math]C_d[/math] = drag coefficient,

[math]\rho[/math] = density of the fluid through which the object is falling(air), and

[math]A[/math] = projected area of the object.

 

 

Terminal velocity is when the gravitational force is equalized by the drag thus the maximum speed at which the object will fall.

A flying fish leaps out of the water and glides for up to 30 seconds. Does anyone know the equation for this. i.e. the surface area to volume ratio to stay in the air for a while.

 

Sorry, but it is much more complicated than that. Aerodynamics depends on shape, speed, viscosity, density, etc. I'd say just put the flying fish in a wind tunnel and measure, rather than trying to calculate.

As Klaynos pointed out in the IRC channel earlier, the concept should be divided to 2 "sub" concepts: Gliding and "falling slower". Both are very different and require different mathematical concepts and equations.

 

In the IRC channel you seemed to have been interested in the second subject, langy666, is that still the case, or are you interested in gliding? or maybe specifically knowing how this *specific* fish is gliding?

 

If you're interested in knowing what makes this SPECIFIC fish glide, is "flying fish" its name? do you know what its actual name is? We could help out with finding research but we will need some details about it.

Morphology of flying fish with comments on gliding performance

 

More on flying fish (abstract only)

 

Wikipedia knows all

It seems these fish really fly (without losing altitude). This means they have lift.

 

The force balance (2 equations) you need therefore is: lift and gravity.

 

The lift is the complicated one... but in principle it works the same as for an airplane.

 

Finally, here's a (bad quality) youtube video of a flying fish.

Actually, they technically cannot fly, even though they generate lift, because they cannot also generate thrust while airborne. What they do is technically a form of gliding.