I'm not sure if integrating pressure is the right thing to do.You want to start with DV/DT = Constant x Pressure.
But you've neglected the sun's gravity entirely which is the biggest weakness of the scheme.
Ah yes, 9 days instead of 9 hours.I was integrating pressure because I figured it would just add up over the journey.Note that, if you make the lower limit on the integral 0.01 AU instead of 0.1 AU, you end up with a final velocity of 0.03c. But that's of course assuming the sail doesn't rip apart being that close to the sun.
Mass of sail turns out to be almost negligible if itís only 1 nm thick:
Thus we could accelerate 100 metric tons to 0.01c just by using a big and thin enough solar sail.
Thanks for the responses. Doesn't hurt to toss some calculations out there!
If we scale up the sail to a side of 1 km, keeping the same thickness
OK so hereís some more calculations:The Ikaros sail, currently deployed, has a thickness of 0.0075 mm, or 7.5x10^-6 m.(http://www.jaxa.jp/projects/sat/ikaros/index_e.html) I couldnít find the density of the sail, so I just went with Beryllium (1.85 kg/m^3). (On the Ikaros web page they say that they used polyimide, which has a density of 1.43 x 10^3 kg/m^3, but I was pretty sure they coated it with some metal)The area of the Ikaros sail is just under 200 m^2, being 14 m on one side.If we scale up the sail to a side of 1 km, keeping the same thickness, the area is then 10^6 m^2, so the volume of the sail would be:10^6 m^2 * 7.5x10^-6 m = 7.5 m^3And the mass would be:7.5 m^3 * 1.85x10^3 kg = 1.39 x 10^4 kgAssuming the payload is 8.61x10^4 kg, for a total mass of 10^5 kg, we have (based on Jim Davisí formula for final velocity):Vfinal = sqrt(2 * S * k0 * R0 / m *9.9) = sqrt (2 * 10^6 m^2 * 4.6x10^-6 Pa * 1.5x10^11 m)/10^5 kg * 9.9) = 1.17 x 10^4 m/s, which is nowhere near the speed of light, but it is 2.46 AU/year.