I never thought I'd be having a discussion abouth the density of airplanes... Most discussions I have about density are with my wife about my brain.

Density = mass / volume. The shape of the volume has no effect at all on buoyancy (unless you get into surface tension but we're not). However, you can take materials with the same amount of surface area and change the volume (take a box and flatten it, the volume went to nearly zero but the surface area stayed the same). The shape does matter if you care about stability (like keeping a boat right side up) but the objective here is just simple flotation for recovery purposes.

If you suspend an object of a given density in a liquid (or gas) of greater density, it will float. If they are the same density, the object will be neutrally bouyant, neither floating/rising nor sinking. If the density of the object is greater than the density of the liquid or gas then it will sink. It's that simple. That goes back exactly to what you said about the desnity of balsa being less than that of water; therefore it floats. I think we agree there.

Where it get's complicated is figuring the volume of complex objects, like an airplane. For starters, it's a combination of complex shapes. To make it more fun, those shapes aren't generally watertight so the volume of a fuselage effectively looks like the volume of the sides, formers, stringers, etc. and not the entire outer volume. If you can seal the fuselage or fill the non-watertight spaces with watertight volumes (like plastic, air-filled bags) then you can keep the volume larger.

Even so, calculating the volume is tricky so one method is to just measure it. Take an object and completely immerse it in a container that is full to the top with liquid. Measure the volume of the liquid that overflows (is displaced) and you have the volume of the object you immersed. If it's a plane then you have the volume of everything, engine, radio, servos and all. Archimedes figured that out in bathtub while trying to measure the volume of a king's crown. He got so excited he went running around naked yelling eureka!

Back to the story. Now, weigh the water. If the weight of the object is less than that of the water, it floats. Why?

Density of object = mass of object / volume of object
Density of water = mass of water / volume of water

We just said that in this simple case the volume of water and volume of the object are the same because we measured displaced volume.
So, Density of object / Density of Water = mass of object / mass of water. If the volumes are the same, then the densities are directly proportional to the weight.

Like kluivertfan2 said though, when you put a floatable object in a liquid it will only displace enough water to support the weight of the object. For recovery purposes, just floating seems like a good starting point.

So, are you going to dunk your plane to figure out it's volume? Let me know how that goes. Instead, I'd figure the weight of the plane and then determine what volume of water that corresponds to. Like 2slow2matter said, the density of water is 1g/ml (a gram is actually defined as the weight of 1ml of water at 4C) so if you know the weight in grams, the minimum volume needed is the same number in milliliters. Then I'd figure out a way to stuff enough sealed volume (bags again) inside the plane to make up that amount of volume. If you can seal enough volume inside the plane it will float (assuming it doesn't come apart on "landing").

Disclaimer: A physics purist will point out that mass and weight are not the same thing. Weight is the force subjected on an object of a given mass by an acceleration (like gravity). All experiments noted will take place in constant gravity on the surface of the earth so we'll say that mass and weight are directly proportional and treat them equally for now.

In a desperate effort to have this note apply to flight , I'll point out that it is the same exact principle that makes a blimp float. The density of a blimp has to be less than the density of air in order for it to float. That's why light gases like Hydrogen or Helium are used, they are much less dense than air.

I will never float as I am more dense than any object on the planet. Just ask my wife.


Mark