Speaking purely in terms of mathematical relationships, a change in power ratio by a factor of 10 is a 10 dB change. A change in power ratio by a factor of two is approximately a 3 dB change.

However, the perception of sound by people isn't linear or logarithmic, or constant across frequencies. It varies from person to person, and upon frequency. "volume" isn't a scientific measure. If you're really, really deaf, it'll be a lot more than 10dB.

http://en.wikipedia.org/wiki/Fletcher–Munson_curves

However, 6dB is the accepted norm of perceptual volume doubling used for the sake of calculations, based upon white noise. Measurements of frequency corrected for these variances are called A-weighting. 6dB is a rule of thumb.

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The problem with maths and simulation is that the real-world phenomena are very complex and fine grained.

The rule of thumb 10x the amplifier power to get a perceptual doubling in volume is based upon all sorts of factors such as losses to heat, increased cone inertia etc etc etc. It holds out pretty well in the real world but it's a rule of thumb.

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For cars, I think these coaxials are pretty applicable: http://profesional.beyma.com/ingles/pdf/8CX300Nd.pdf

There are also 21 inch subwoofers: http://profesional.beyma.com/ingles/pdf/21SW1600Nd.pdf